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All The Math Books You’ll Ever Need (Updated 2023)

Countless math books are published each year, however, only a tiny percentage of these titles are destined to become the kind of classics that are loved the world over by students and mathematicians.

Within this page, you’ll find an extensive list of math books that have sincerely earned the reputation that precedes them.

For many of the most important branches of mathematics, we’ve provided what we consider to be the best math books for the subject at hand. We aimed for a list of titles that were either introductory in nature or that fall into the category of “must-have” math reference books.

Naturally, a universal consensus doesn’t exist but the books below are as close as it gets to a wish list for any aspiring mathematician or person who’s interested in mathematics. We highly recommend each and every one of these titles and hope that you’ll enjoy them, too.

Please note, this list will constantly be updated so as to keep it current.

Math Books Menu

Abstract algebra books, contemporary abstract algebra.

by Joseph Gallian

Abstract Algebra

by David S. Dummit and Richard M. Foote

Algorithms Books

Introduction to algorithms, third edition.

by Thomas H. Cormen, Charles E. Leiserson and Ronald L. Rivest

The Art of Computer Programming, Volumes 1-3 Boxed Set

by Donald E. Knuth

Calculus Helpers Books

The calculus lifesaver: all the tools you need to excel at calculus.

by Adrian Banner

Calculus Made Easy

by Silvanus P. Thompson

Calculus I Books

Calculus, vol. 1.

by Tom M. Apostol

by Michael Spivak

Calculus II/III Books

Calculus, vol. 2, calculus on manifolds, coffee table math books, mathematicians: an outer view of the inner world.

by Mariana Cook

Sacred Mathematics: Japanese Temple Geometry

by Fukagawa Hidetoshi and Tony Rothman

Combinatorics Books

Principles and techniques in combinatorics.

by Chen Chuan-Chong and Koh Khee-Meng

Combinatorics and Graph Theory (2nd edition)

by John Harris, Jeffry L. Hirst, and Michael Mossinghoff

Differential Equations Books

Differential equations and their applications.

by Martin Braun

Encyclopedias of Mathematics Books

The princeton companion to mathematics.

by Timothy Gowers, June Barrow-Green and Imre Leader (Editors)

Encyclopedia of Mathematics

by James Stuart Tanton

Foundations of Mathematics Books

A mathematical introduction to logic, second edition.

by Herbert Enderton

Classic Set Theory for Guided Independent Study

by Derek C. Goldrei

Categories for the Working Mathematician

by Saunders Mac Lane

History of Mathematics Books

Mathematics: from the birth of numbers.

by Jan Gullberg

What Is Mathematics? An Elementary Approach to Ideas and Methods

by Richard Courant and Herbert Robbins

Mathematics and its History

by John Stillwell

Information Theory Books

Computational science and engineering.

by Gilbert Strang

Information Science

by David G. Luenberger

Introduction to Coding and Information Theory

by Steve Roman

Linear Algebra and Geometry Books

Linear algebra done right.

by Sheldon Axler

The Four Pillars of Geometry

Mathematical methods books, mathematical methods: for students of physics and related fields.

by Sadri Hassani

Mathematical Methods in the Physical Sciences

by Mary L. Boas

Number Theory Books

Elementary number theory.

by Gareth A. Jones and Josephine M. Jones

An Invitation to Modern Number Theory

by Steven J. Miller and Ramin Takloo-Bighash

An Introduction to the Theory of Numbers

by G. H. Hardy, Edward M. Wright and Andrew Wiles

Numerical Analysis Books

Numerical analysis with cd-rom.

by Timothy Sauer

Numerical Recipes 3rd Edition: The Art of Scientific Computing

by William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery

Precalculus Books

Precalculus mathematics in a nutshell: geometry, algebra, trigonometry.

by George F. Simmons

Basic Mathematics

by Serge Lang

Probability Books

Introduction to probability models, tenth edition.

by Sheldon M. Ross

An Introduction to Probability Theory and Its Applications

by William Feller

Probability Theory: The Logic of Science

by E.T Jaynes

Fifty Challenging Problems in Probability with Solutions

by Frederick Monsteller

Real and Complex Analysis Books

Principles of mathematical analysis, third edition.

by Walter Rudin

Real Analysis

by N.L Carothers

Real and Complex Analysis

A first course in complex analysis with applications.

by Dennis Zill and Patrick Shanahan

Visual Complex Analysis

by Tristan Needham

Statistics Books

Statistics in plain english, third edition.

by Timothy C. Urdan

Review : Just as the title implies, the author has submitted an unequivocal and palpable exposition on statistics. Statistics in Plain English is regarded by many as the most appropriate statistics primer for undergraduates. Urdan has managed to compress everything one needs to know about statistics into a compact 250 page book that doesn’t feel hurried or unfulfilling. The text is general enough to be used in a variety of mathematical areas yet retains its comprehensiveness and accuracy. Urdan masterfully moves through essential concepts without losing the reader the way many professors would. Students harboring apprehension towards statistics will tremendously enjoy this book. More info .

Introductory Statistics

by Neil A. Weiss

Statistics, 4th Edition

by David Freedman, Robert Pisani and Roger Purves

Topology Books

Introduction to topology and modern analysis, introduction to topology: third edition.

by Bert Mendelson

Feel free to get in touch if you think the list is really missing out by not listing a specific book. If you are a publisher and feel that we’re missing a great book of yours, drop us a line. Please understand that we recommend only what we consider to be the best books on the market today. No exceptions.

Disclaimer: Here at Math-Blog.com we believe in full disclosure. The links to Amazon.com, have our referral id which earns us a tiny commission every time you buy from these links. Think of it as a tip that won’t cost you a cent, to reward us for our time investment. We appreciate your support.

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Calculus online textbook.

First published in 1991 by Wellesley-Cambridge Press , this updated 3rd edition of the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor’s Manual and a student Study Guide .

The complete textbook (PDF) is also available as a single file.

Textbook Components

Table of Contents (PDF)

Chapter 0: Highlights of Calculus (PDF)

0.1 Distance and Speed // Height and Slope 0.2 The Changing Slope of $y=x^2$ and $y=x^n$ 0.3 The Exponential $y=e^x$ 0.4 Video Summaries and Practice Problems 0.5 Graphs and Graphing Calculators

Chapter 1: Introduction to Calculus (PDF)

1.1 Velocity and Distance 1.2 Calculus Without Limits 1.3 The Velocity at an Instant 1.4 Circular Motion 1.5 A Review of Trigonometry 1.6 A Thousand Points of Light

Chapter 2: Derivatives (PDF)

2.1 The Derivative of a Function 2.2 Powers and Polynomials 2.3 The Slope and the Tangent Line 2.4 Derivative of the Sine and Cosine 2.5 The Product and Quotient and Power Rules 2.6 Limits 2.7 Continuous Functions

Chapter 3: Applications of the Derivative (PDF)

3.1 Linear Approximation 3.2 Maximum and Minimum Problems 3.3 Second Derivatives: Bending and Acceleration 3.4 Graphs 3.5 Parabolas, Ellipses, and Hyperbolas 3.6 Iterations $x_{n+1}=F(x_n)$ 3.7 Newton’s Method (and Chaos) 3.8 The Mean Value Theorem and 1’Hôpital’s Rule

Chapter 4: Derivatives by the Chain Rule (PDF)

4.1 The Chain Rule 4.2 Implicit Differentiation and Related Rates 4.3 Inverse Functions and Their Derivatives 4.4 Inverses of Trigonometric Functions

Chapter 5: Integrals (PDF)

5.1 The Idea of an Integral 5.2 Antiderivatives 5.3 Summation versus Integration 5.4 Indefinite Integrals and Substitutions 5.5 The Definite Integral 5.6 Properties of the Integral and Average Value 5.7 The Fundamental Theorem and Its Applications 5.8 Numerical Integration

Chapter 6: Exponentials and Logarithms (PDF)

6.1 An Overview 6.2 The Exponential $e^x$ 6.3 Growth and Decay in Science and Economics 6.4 Logarithms 6.5 Separable Equations Including the Logistic Equation 6.6 Powers Instead of Exponentials 6.7 Hyperbolic Functions

Chapter 7: Techniques of Integration (PDF)

7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonometric Substitutions 7.4 Partial Fractions 7.5 Improper Integrals

Chapter 8: Applications of the Integral (PDF)

8.1 Areas and Volumes by Slices 8.2 Length of a Plane Curve 8.3 Area of a Surface of Revolution 8.4 Probability and Calculus 8.5 Masses and Moments 8.6 Force, Work, and Energy

Chapter 9: Polar Coordinates and Complex Numbers (PDF)

9.1 Polar Coordinates 9.2 Polar Equations and Graphs 9.3 Slope, Length, and Area for Polar Curves 9.4 Complex Numbers

Chapter 10: Infinite Series (PDF)

10.1 The Geometric Series 10.2 Convergence Tests: Positive Series 10.3 Convergence Tests: All Series 10.4 The Taylor Series for $e^x$, $\sin{x}$, and $\cos{x}$ 10.5 Power Series

Chapter 11: Vectors and Matrices (PDF)

11.1 Vectors and Dot Products 11.2 Planes and Projections 11.3 Cross Products and Determinants 11.4 Matrices and Linear Equations 11.5 Linear Algebra

Chapter 12: Motion Along a Curve (PDF)

12.1 The Position Vector 12.2 Plane Motion: Projectiles and Cycloids 12.3 Curvature and Normal Vector 12.4 Polar Coordinates and Planetary Motion

Chapter 13: Partial Derivatives (PDF)

13.1 Surface and Level Curves 13.2 Partial Derivatives 13.3 Tangent Planes and Linear Approximations 13.4 Directional Derivatives and Gradients 13.5 The Chain Rule 13.6 Maxima, Minima, and Saddle Points 13.7 Constraints and Lagrange Multipliers

Chapter 14: Multiple Integrals (PDF)

14.1 Double Integrals 14.2 Changing to Better Coordinates 14.3 Triple Integrals 14.4 Cylindrical and Spherical Coordinates

Chapter 15: Vector Calculus (PDF)

15.1 Vector Fields 15.2 Line Integrals 15.3 Green’s Theorem 15.4 Surface Integrals 15.5 The Divergence Theorem 15.6 Stokes’ Theorem and the Curl of F

Chapter 16: Mathematics after Calculus (PDF)

Index (PDF)

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10 Best Mathematics Books to Read in 2023

Introduction:.

Mathematics, often hailed as the universal language, is the foundation of countless scientific discoveries and technological advancements. It allows us to understand the fundamental principles that govern our world. If you possess a passion for exploring the beauty and power of mathematical concepts, consider Oxford Summer Courses. Embark on a transformative journey through our Mathematics summer school, where you will delve deep into the world of numbers, equations, and mathematical reasoning.

Disclaimer:

Please note that the following list of resources is recommended reading to broaden your knowledge and deepen your appreciation of Mathematics. While some of these resources may be included in the Oxford Summer Courses curriculum, the specific content of the summer school can vary. If you wish to study Mathematics with us, you can apply to our summer school.

Subscribe to our newsletter to receive helpful tips, tutorials, and thought-provoking articles that can inform and inspire your mathematical development. Sign up here.

1. "Principia Mathematica" by Isaac Newton

"In mathematics, there are more numbers than nouns."
Published in 1687, "Principia Mathematica" by Isaac Newton has long been considered a foundational work in the field of mathematics. This masterpiece laid the groundwork for classical mechanics, calculus, and our understanding of the physical universe.
Discussion: How do Newton's mathematical principles continue to shape our understanding of the natural world?

2. "Elements" by Euclid

"There is no royal road to geometry."
Set in ancient Greece, Euclid's "Elements" is a fundamental treatise on mathematics. This work, composed around 300 BCE, covers geometry and number theory, serving as a cornerstone for mathematical education for centuries.
Discussion: How does Euclid's approach to geometry in "Elements" still influence modern mathematics and education?

3. "The Joy of X: A Guided Tour of Math, from One to Infinity" by Steven Strogatz

"Mathematics, more than any other art form, reveals the structure of things."
"The Joy of X" is a contemporary masterpiece by Steven Strogatz that explores mathematics in an engaging and accessible manner. It delves into various mathematical concepts, from basic arithmetic to advanced calculus, making it suitable for readers of all mathematical backgrounds.
Discussion: How does "The Joy of X" make complex mathematical concepts relatable to a broader audience?

4. "The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography" by Simon Singh

"Cryptography is the science of protecting information by transforming it into an unreadable format."
Simon Singh's "The Code Book" takes readers on a historical journey through the world of cryptography. From ancient ciphers to quantum cryptography, this book uncovers the secrets behind codes and code-breaking.
Discussion: How has the evolution of cryptography, as explored in "The Code Book," influenced modern technology and security?

5. "Flatland: A Romance of Many Dimensions" by Edwin A. Abbott

"Do not all charms fly at the mere touch of cold philosophy?"
"Flatland" is a unique mathematical novella written by Edwin A. Abbott in 1884. It explores the concept of higher dimensions through the perspective of a two-dimensional world inhabited by geometric shapes.
Discussion: How does "Flatland" challenge our perception of reality and dimensions, and what relevance does it hold in modern mathematics?

6. "Gödel, Escher, Bach: An Eternal Golden Braid" by Douglas Hofstadter

"The 'strange loop' phenomenon occurs whenever, by moving upwards (or downwards) through the levels of some hierarchical system, we unexpectedly find ourselves right back where we started."
Douglas Hofstadter's Pulitzer Prize-winning book, "Gödel, Escher, Bach," intertwines mathematics, art, and music in an exploration of self-reference and the nature of intelligence.
Discussion: How does "Gödel, Escher, Bach" encourage interdisciplinary thinking and its impact on creativity and problem-solving?

7. "A Mathematician's Apology" by G. H. Hardy

"A mathematician, like a painter or a poet, is a maker of patterns."
G. H. Hardy's "A Mathematician's Apology" is a reflection on the aesthetics of mathematics and the role of pure mathematics in the scientific world.
Discussion: How does Hardy's perspective on the beauty of mathematics in "A Mathematician's Apology" influence our appreciation of abstract mathematical concepts?

8. "The Man Who Knew Infinity: A Life of the Genius Ramanujan" by Robert Kanigel

"An equation means nothing to me unless it expresses a thought of God."
"The Man Who Knew Infinity" tells the inspiring story of the self-taught Indian mathematician Srinivasa Ramanujan and his groundbreaking contributions to number theory.
Discussion: How does Ramanujan's life and work, as depicted in "The Man Who Knew Infinity," inspire future generations of mathematicians?

9. "How Not to Be Wrong: The Power of Mathematical Thinking" by Jordan Ellenberg

"The difference between a good mathematician and a bad one is the ability to see analogies between theorems."
In "How Not to Be Wrong," Jordan Ellenberg explores the practical applications of mathematics in everyday life, demonstrating how mathematical thinking can lead to better decision-making.
Discussion: How does "How Not to Be Wrong" illustrate the real-world relevance of mathematical concepts and problem-solving?

10. "Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem" by Simon Singh

"Anything that is in the world when you're born is normal and ordinary and is just a natural part of the way the world works. Anything that's invented between when you're fifteen and thirty-five is new and exciting and revolutionary and you can probably get a career in it."
"Fermat's Enigma" explores the history and eventual proof of Fermat's Last Theorem, a mathematical problem that remained unsolved for centuries.
Discussion: How does the journey to solve Fermat's Last Theorem, as detailed in "Fermat's Enigma," exemplify the perseverance and collaborative nature of mathematics?

Oxford Summer Courses invites you to immerse yourself in the enchanting world of mathematics. In this blog post, we present a meticulously curated list of 10 classic and contemporary books that will ignite your mathematical imagination and deepen your understanding of this captivating field. From the foundational works of Newton and Euclid to modern explorations of cryptography and mathematical thinking, these books will transport you to different realms of mathematics. Through our Mathematics programme, you will have the opportunity to explore and discuss these influential texts, gaining valuable insights into the power of mathematical thought. Join us on this mathematical odyssey and embark on a transformative journey that will shape your appreciation for the world of numbers, patterns, and problem-solving.

Apply now to study Mathematics at Oxford Summer Courses and elevate your mathematical education to new heights. Join a community of motivated learners from around the world and embark on a transformative mathematical experience. Apply here.

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Ignite your passion for mathematics at Oxford Summer Courses. Immerse yourself in a carefully selected list of books that delve into mathematical concepts, theories, and their real-world applications. Gain valuable insights from experts in the field and embark on a transformative journey to enhance your knowledge of mathematics.

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Book reviews, elementary number theory in nine chapters, an introduction to mathematical finance.

by Sheldon M. Ross

reviewed by Elie Bassouls (DAMTP, Cambridge University)

This refreshing little (184 pages) book was given an exactly appropriate title. No great mathematical, statistical, or financial expertise is needed to make sense of the material. Beginning with the mathematical aspects, the reader is taken to the central Black Scholes option pricing model through a sensible series of steps, such that it becomes a financially logical conclusion rather than some magical formula relying on abtruse mathematical ideas. Portofolio theory and more advanced asset pricing algorithms follow on, much in the same grain, which I found the great virtue of this text.

The first few chapters summarise basic probability concepts, the Normal distribution and Brownian motion, an understanding of which is essential when attempting to model investments. Interest rates, net present value analysis and the theory of arbitrage are then explained.

After this, the author comes to a position where he can derive a simplified version of the famous Black Scholes option pricing formula, the central theme of this book, as well as one of the foundation stones of mathematical finance. The formula relies on several assumptions. The market in the security and options on it must be liquid. This is alluded to by the statement that one should be able to trade continuously in the security. A clear mention would have helped. Problems inherent in estimating the security's volatility (sigma) are investigated, although the model's requirement that it be constant over the option's life can only be guessed from careful reading. An entry level text, should have made the fact clearer. After all, even pretendedly reputed institutions have lost large sums after forgetting about this.

The concept of utility, and its use in valuing investments begin the next chapter (No. 8), which then presents the capital asset pricing model (CAPM), without naming its authors (Modigliani and Miller). The chapter then touches on portofolio selection. Chapter nine takes a look at Asian and lookback or exotic option pricing, with monte carlo simulation and binomial models. The last two chapters consider cases where prices do not follow a geometric Brownian motion and propose other ways to represent them.

Altogether, a lot of ground gets covered in a small volume. So, one should regret not so much that fully rigorous mathematical demonstrations are not always given, but that their omission is not noted. For example, rigorous formulation of the Black Scholes model invokes stochastic integrals and Ito's lemma. At least a footnote to this effect could have helped. The reader does not need great preliminary expertise to follow the text, but those indeed lacking it could falsely believe the subject to be a lot simpler than it actually to be. Thus, I would recommend the book as an ideal appetiser in the subject, or to provide surface level understanding of it, but warn of its limitations. Despite this, I found the reading undemanding, yet interesting. I liked the way in which the author managed to write a story, which makes sense, for both mathematicians and financiers.

by John Allen Paulos reviewed by Mike Pearson (Plus editorial)

To be innumerate, my dictionary says, is to be "ignorant of or unskilled in mathematics and science". Lots of us don't like maths, and even take a perverse pride in our inability to manipulate numbers - "Well, don't ask me, I'm useless at maths!" This book, by a Professor of Mathematics, is about how innumeracy affects our lives - mainly in the form of mathematical misconceptions and inconsistencies.

The first couple of chapters deal with big numbers, and the problem we have visualising anything with a lot of noughts on the end of it. With big numbers go probabilities (such as being a road traffic accident statistic or winning a lottery) and the multiplication principle (how many different dinners can you concoct out of four appetisers, seven main courses and three deserts?). But the bit I liked best in this section is the observation that the size of a virus to a person is as the person to the earth, and an atom to a person is as a person to the earth's orbit round the sun.

In chapter two there's more about probability and coincidence, and in chapter three Professor Paulos tackles the topic of Pseudoscience. "Any bit of nonsense can be computerised - astrology, biorhythms, the I Ching - but that doesn't make the nonsense any more valid." He also considers the phenomenon of predictive dreams, and comes to the conclusion that about 3.6% of people are likely to have accurate predictive dreams in any one year (see pp 51 et seq.)

Professor Paulos ascribes the innumeracy that is so widespread in society to early mathematical education being poor. He believes that the basic algorithms are taught - but not their application. The student learns how to add, subtract, multiply, divide, and handle fractions, decimals and percentages, but not when it's appropriate to do so. He would like to see estimation and inductive reasoning on the school syllabus, and a greater use made of puzzles, games and riddles with a mathematical bent. The problem with innumeracy is not only the resulting inability to handle numbers in everyday life, but the likelihood of being taken in both by pseudoscience backed up by pseudomathematics, and by pseudostatistics peddled by politicians, salespersons or anyone else.

This book contains a great deal of interest to those who teach mathematics and to the reasonably numerate. I would disagree with Stefan Kanfer, who is quoted on the back cover as saying, "Those who break into a sweat at the mention of calculus or plane geometry can relax. This elegant little survival manual is brief, witty, and full of practical applications." Yes, possibly, but not in a form that the truly innumerate would be able to understand.

There are two other drawbacks to this book - firstly, the large number of American references within examples ( usually concerning strange American games like baseball, which may or may not be comprehensible to us Brits), and secondly a problem for the much younger generation who are now practically unable to cope with feet and inches - all the American units are Imperial.

But still an interesting book for the educator.

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13 Best Mathematics Books for Every Level

If you’re looking to delve deeper into the world of mathematics, there’s no better place to start than by reading a good book. With so many titles out there, it can be challenging to find the right one for your skill level and interest. That’s why we’ve compiled a list of the best mathematics books for every level of learner. Whether you’re a beginner or an expert, this list has something for everyone.

Introduction to the World of Mathematics Books

The world of mathematics is a fascinating and complex one, filled with endless possibilities and discoveries waiting to be made. Whether you’re a student just starting out on your mathematical journey, or a seasoned professional looking to expand your knowledge, there’s no shortage of resources available to you.

One of the best places to start is with textbooks. These comprehensive guides provide a thorough introduction to the core principles and concepts of mathematics, from algebra and geometry to calculus and beyond. Some of the most popular textbooks include “ Calculus: Early Transcendentals ” by James Stewart, “ Linear Algebra and Its Applications ” by Gilbert Strang, and “ Introduction to Probability ” by Sheldon Ross.

But textbooks aren’t the only way to explore the world of mathematics. Memoirs and biographies of famous mathematicians offer a unique glimpse into the lives and work of some of the most brilliant minds in history. For example, “ A Beautiful Mind ” by Sylvia Nasar tells the story of John Nash, a Nobel Prize-winning mathematician who struggled with mental illness throughout his career. “ The Man Who Knew Infinity ” by Robert Kanigel chronicles the life of Srinivasa Ramanujan, an Indian mathematician who made groundbreaking contributions to number theory.

For those who prefer a more accessible approach, popular science books can provide a fun and engaging introduction to mathematical concepts. “ The Joy of x ” by Steven Strogatz explores the beauty and wonder of mathematics through a series of entertaining and informative essays, while “ How to Bake Pi ” by Eugenia Cheng uses baking as a metaphor for understanding complex mathematical concepts.

Whatever your interests and preferences, there’s sure to be a book out there that will spark your curiosity and inspire you to delve deeper into the world of mathematics. So why not start exploring today?

Beginner Level Mathematics Books

Building a strong foundation in math.

For beginners, it’s essential to lay a strong foundation of mathematical skills and concepts. One of the best books for doing this is “ Basic Mathematics ” by Serge Lang. The book covers everything from arithmetic to algebra, geometry, and trigonometry, making it an excellent choice for those just starting.

If you’re struggling with math, this book is a great place to start. It’s written in a clear and concise manner, making it easy to understand even the most complicated concepts. The book is also filled with numerous examples and exercises that will help you practice and reinforce what you’ve learned.

By the time you finish “Basic Mathematics,” you’ll have a solid foundation in math that will serve you well in any future studies or endeavors.

Engaging Books for Young Learners

For young learners, the key to building an interest in mathematics is finding engaging books that are both fun and challenging. “ Math for Smarty Pants ” by Marilyn Burns is an excellent option. The book is full of puzzles, games, and riddles that will help kids develop critical thinking skills while having fun.

The book is written in a way that is easy for kids to understand, and the colorful illustrations and fun activities will keep them engaged and interested. “Math for Smarty Pants” is a great way to introduce kids to the world of mathematics and help them build a strong foundation for future learning.

Developing Essential Math Skills

“ The Math Book ” by Clifford A. Pickover is perfect for those looking to brush up on essential math skills. The book covers a wide variety of topics, from geometry to calculus, and is written in an engaging style that makes it easy to understand.

The book is filled with fascinating facts and stories about the history of mathematics, making it a great read for anyone interested in the subject. It also includes numerous exercises and problems to help you practice and reinforce what you’ve learned.

Whether you’re a student looking to improve your math skills or just someone interested in learning more about the subject, “The Math Book” is an excellent choice. It’s a comprehensive guide to mathematics that will help you develop a deeper understanding of the subject and its many applications.

Intermediate Level Mathematics Books

If you’re looking to take your math skills to the next level, there are several intermediate level mathematics books that can help you strengthen your problem-solving abilities, explore different branches of mathematics, and prepare for advanced math courses.

Strengthening Problem-Solving Abilities

One classic book on problem-solving is “ How to Solve It ” by George Polya. This book is perfect for those who want to improve their problem-solving abilities across all areas of math. The book is full of strategies and techniques that can help you approach problems in a more systematic and effective way.

Another great resource for strengthening your problem-solving abilities is “ Problem-Solving Strategies ” by Arthur Engel. This book covers a wide range of topics, including algebra, geometry, number theory, and combinatorics. It provides a wealth of examples and exercises that can help you develop your problem-solving skills.

Exploring Different Branches of Mathematics

If you’re interested in exploring different branches of mathematics, “ Mathematics: Its Content, Methods, and Meaning ” by A.N. Kolmogorov is an excellent book to start with. This book covers a wide range of topics, from algebra and topology to probability theory and even philosophical aspects of mathematics. It provides a comprehensive overview of the field and can help you develop a deeper understanding of the subject.

Another great book for exploring different branches of mathematics is “ Concrete Mathematics ” by Ronald Graham, Donald Knuth, and Oren Patashnik. This book covers topics such as combinatorics, number theory, and graph theory, and provides a wealth of examples and exercises to help you understand the material.

Preparing for Advanced Math Courses

For those preparing to take advanced math courses, “ Advanced Calculus ” by Louis Brand is an excellent resource. This book covers topics such as functions, differentiation, integration, and more, providing a solid foundation for future studies. It also includes a wealth of examples and exercises to help you master the material.

Another great book for preparing for advanced math courses is “ Linear Algebra ” by Gilbert Strang. This book covers the fundamentals of linear algebra, including matrices, vectors, and systems of linear equations. It also includes applications to fields such as engineering, physics, and computer science.

Whether you’re looking to strengthen your problem-solving abilities, explore different branches of mathematics, or prepare for advanced math courses, there are several intermediate-level mathematics books that can help you achieve your goals. These books provide a wealth of information, examples, and exercises, and can help you develop a deeper understanding and appreciation of the subject.

Advanced Level Mathematics Books

Mathematics is a subject that has intrigued many individuals over the years. From basic arithmetic to advanced calculus, the study of mathematics has helped us understand the world around us. If you’re someone who is looking to take their mathematical knowledge to the next level, then you’re in luck. In this article, we’ll be discussing some of the best advanced level mathematics books that you can use to enhance your understanding of complex mathematical concepts.

Diving into Complex Mathematical Concepts

“ Principles of Mathematical Analysis ” by Walter Rudin is an excellent book for those looking to dive deep into complex mathematical concepts. The book covers advanced topics in analysis, such as topology, measure theory, and functional analysis, making it a must-read for aspiring mathematicians. The book is written in a clear and concise manner, making it easy to follow along, even for those who are new to the subject.

If you’re interested in topology, then “ Topology ” by James R. Munkres is a great book to check out. The book covers a wide range of topics, including set theory, metric spaces, and continuity. The author uses a variety of examples and exercises to help readers understand the concepts covered in the book.

Books for Aspiring Mathematicians

“ The Road to Reality” by Roger Penrose is a massive book that covers topics from basic math to advanced physics and cosmology. While not strictly a math book, it’s an excellent resource for those looking to gain a deeper understanding of mathematics and its applications. The book is written in a conversational tone, making it easy to read and understand.

If you’re interested in number theory, then “ An Introduction to the Theory of Numbers ” by G. H. Hardy and E. M. Wright is a great book to check out. The book covers a wide range of topics, including prime numbers, diophantine equations, and continued fractions. The authors use a variety of examples and exercises to help readers understand the concepts covered in the book.

Mastering the Art of Mathematical Thinking

“ How to Prove It: A Structured Approach ” by Daniel J. Velleman is an excellent book on logic and proofs, making it a must-have for anyone looking to master the art of mathematical thinking. The book covers topics such as propositional logic, predicate logic, and proofs by induction. The author uses a step-by-step approach to help readers understand the concepts covered in the book.

If you’re interested in learning more about mathematical logic, then “ Mathematical Logic: A First Course ” by Joel W. Robbin and W. T. Robbin is a great book to check out. The book covers a wide range of topics, including propositional logic, predicate logic, and the incompleteness theorems. The authors use a variety of examples and exercises to help readers understand the concepts covered in the book.

Whether you’re a student, a teacher, or just someone who is interested in mathematics, these books are sure to provide you with the knowledge and skills you need to take your understanding of complex mathematical concepts to the next level.

Specialized Mathematics Books

Books on the history of mathematics.

“ A History of Mathematics ” by Carl B. Boyer is an excellent book on the history of mathematics. The book covers everything from ancient mathematics to modern-day developments, providing an in-depth look at how mathematics has evolved over time.

Biographies of Famous Mathematicians

“ Genius at Play: The Curious Mind of John Horton Conway ” by Siobhan Roberts is a biography of the celebrated mathematician John Conway. The book provides an insight into his life and work and is a must-read for anyone interested in the history of mathematics.

Mathematics in Art, Nature, and Everyday Life

“ Mathematics and Art: A Cultural History ” by Lynn Gamwell explores the relationship between mathematics and art, providing an insight into how math has influenced art throughout history. The book covers topics such as perspective, symmetry, and tessellations, making it a fascinating read for anyone interested in the intersection of math and the arts.

As you can see, there’s no shortage of excellent mathematics books out there for every skill level and interest. Whether you’re looking to build a strong foundation, take your skills to the next level, or explore the history of math, there’s a book on this list for you. We hope this article has inspired you to pick up a book and dive into the fascinating world of mathematics.

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Metamathematics: Foundations & Physicalization

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ISBN-10 1579550762
ISBN-13 978-1579550769
Publisher Wolfram Media, Inc.
Publication date December 16, 2022
Language English
Dimensions 7.5 x 1.25 x 9.5 inches
Print length 456 pages
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Publisher ‏ : ‎ Wolfram Media, Inc. (December 16, 2022)
Language ‏ : ‎ English
Hardcover ‏ : ‎ 456 pages
ISBN-10 ‏ : ‎ 1579550762
ISBN-13 ‏ : ‎ 978-1579550769
Item Weight ‏ : ‎ 2.26 pounds
Dimensions ‏ : ‎ 7.5 x 1.25 x 9.5 inches
#135 in Mathematical Logic
#208 in Mathematics History
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Stephen wolfram.

Stephen Wolfram has had a unique trajectory in science, technology and business. Widely known for his discoveries in basic science and his groundbreaking 2002 book "A New Kind of Science," he has spent more than three decades building what is now Wolfram Language: the knowledge-based computer language that powers Mathematica and Wolfram|Alpha and has contributed to countless inventions and discoveries, as well as to the education of several generations of students.

Wolfram was born in London and educated at Eton, Oxford and Caltech, earning his PhD in physics in 1979 at the age of 20. After a brief but distinguished academic career, he founded Wolfram Research in 1987 and as CEO has built it into one of the world’s most respected and innovative software companies, whose products are relied on by millions of people around the world.

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Radiant by Brad Gooch review – art with heart

The life and untimely death of Keith Haring, whose work burst with vitality and warmth

M adonna is on the road with her Celebration tour. The show-stopping moment is her song Live to Tell, in which she pays tribute to friends – and the multitudes she didn’t know – who died from Aids. Keith Haring’s bespectacled and adorably geeky face is one of those displayed on a huge screen. He was only 31 when he died in 1990, Madonna having called him on his deathbed. One of the most harrowing sections in Radiant, a compelling biography of the artist by Brad Gooch, describes Haring’s friend Bruno Schmidt encouraging him to take off his T-shirt on the beach on one of the artist’s final holidays, then being appalled by what was revealed: a back completely blackened by Kaposi’s sarcoma, the skin cancer Aids patients often developed.

Haring’s cruel fate still seems outrageous. How can a man whose work bursts with such warmth and vitality have died so young? Gooch’s meticulous retelling of his story underlines the loss. Born in Reading, Pennsylvania, and brought up in nearby Kutztown, Haring went though several teen identities – evangelical Christian, Grateful Dead fan – until he found himself in New York in 1978. Galvanised by emerging hip-hop culture, of which graffiti was a pillar, Haring realised that his drawings should not be confined to gallery walls. One day, he noticed that the matt black paper exposed when advertising hoardings on the subway were left vacant was ideal for making quick artworks in chalk.

Soon, Haring’s drawings covered the subway – dogs, TVs, dancing figures and, above all, his signature tag, the crawling radiant baby, from which this book takes its name. At the same time, he was becoming an integral part of the downtown art scene, showing his work at Club 57 and the Mudd Club, and then the new galleries that sprang up on the Lower East Side. Haring was able to straddle these two worlds throughout his short life – he had credibility with Harlem’s graffiti writers, but was also feted by New York’s art world, if not always by its critics. His peers and friends included Jean-Michel Basquiat ; Andy Warhol and Yoko Ono both took him under their wings. After Haring’s funeral, Ono kept a handful of his ashes, which she scattered in Paris, the city in which, as a schoolboy, he had dreamed of making it as an artist.

Pictures poured out of Haring. He conjured entire shows right at the last minute, and he never did any preparatory studies: his unmistakable figures went straight from his brain on to the wall or canvas.

Alongside his shows in official gallery spaces, he made a point of painting huge public murals that anyone could enjoy – including on the Berlin Wall – that often made sociopolitical statements. His Crack Is Wack mural, which still exists in a repainted version, took the message to the Harlem community affected by the drug; the orgy scene he painted in the toilets of New York’s Lesbian, Gay, Bisexual & Transgender Community Center (again, it’s still there), is wistfully called Once Upon a Time, a lament for the days of carefree gay sex.

It’s to Haring’s credit that, once he had settled on his sexuality (he had a girlfriend as a teenager), he was unapologetically and publicly gay – penises are another recurring motif in his work. He was also aware of his privilege as a white man engaging in hip-hop culture. Haring usually got off with a slap on the wrist if caught painting graffiti by the New York cops: “They just sort of call him a fairy and let him go,” Warhol noted in his diary. Meanwhile, the 25-year-old Black artist Michael Stewart was allegedly beaten into a coma in police custody after being arrested for scrawling on a subway wall – he died 13 days later. Basquiat, Haring and Warhol each memorialised this outrage in a piece of art; Haring felt particularly guilty as he had turned Stewart away from a party at his house earlier that evening.

Gooch vividly evokes New York in the early 1980s, surely one of the most culturally exciting eras of all time, and Haring was right in the thick of it. A good dancer, he was a regular at Paradise Garage, the groundbreaking nightclub presided over by DJ Larry Levan, and on Spotify you can listen to the mixtapes he played while working, mainly the soul, pop and house music of the day, though there is a detour into Bach and Stravinsky. The stars of the time pop in and out of this book: Grace Jones and dancer Bill T Jones , whose skin he painted, the former for a Robert Mapplethorpe portrait; he even struck up an unlikely friendship with Brooke Shields, years after depicting her with a penis in an early artwork.

Gooch is frank about the fact that Haring had his head turned by celebrity during this period – even Michael Jackson wanted to meet him – and that the work lost some of its purpose as a result. Yet in the years after his Aids diagnosis, Haring redoubled his efforts, both as an artist and activist. With great bravery, he divulged his condition and participated in actions by the pressure group Act Up. His 1989 works Ignorance = Fear and Silence = Death are calls to arms against the disease, that have all the immediate accessibility of his best work.

Like many great artists, Haring seems at once a product of his time and far ahead of it. He was great with children and yearned for some of his own. In 1986, he opened the Pop Shop to turn his work into merchandise in a way that is ubiquitous now but was controversial then, and it stood in SoHo until 2005. A second branch, in Tokyo, failed during his lifetime. It was in Japan that Haring spotted the lesion that confirmed his worst fears. At the funeral of his ex-boyfriend Juan Dubose, he stared into the coffin and said: “Well, soon it will be me there.”

The suffering that gay men endured in the Aids crisis is still shocking, and Haring was luckier than most. Though they didn’t talk about his sexuality, his family never rejected him; his final hours were spent with his parents, who held him as he died. As his faculties failed, his ability to draw was the last thing to go. Along with numerous great pictures of Haring’s work, and Polaroids of him and his friends, the book includes his final drawing – his ultimate symbol of life, the radiant baby.

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Mathematics for Elementary Teachers

(18 reviews)

Michelle Manes, Honolulu, HI

Publisher: University of Hawaii Manoa

Language: English

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Reviewed by Kevin Voogt, Assistant Professor, Grace College on 4/20/23

There seem to be subjects missing that are typical of the common core mathematics for elementary teachers texts (e.g., Ratios/Proportions, clear Partitive/Measurement division ideas, percentages, certain ideas in Geometry, Measurement). read more

Comprehensiveness rating: 4 see less

Content Accuracy rating: 5

I did not find mathematical errors in the text during my review.

Relevance/Longevity rating: 3

I think there is need for quite a few updates to the text in regards to what is covered in elementary mathematics through the common core. The topics listed in my review of the Comprehensiveness above are just a start. I also see a need to add more activities to each section where prospective elementary teachers could do more exploration of the mathematics rather than what seems to be a more traditional approach of having the text explain it followed by problem sets alone.

Clarity rating: 5

The wording was quite clear and had nice explanations throughout.

Consistency rating: 5

It seems consistent throughout - with recurrent use of the same technical terms as needed.

Modularity rating: 4

There were a few issues with being able to assign the texts at different points within the course, as is the case for many math texts, in that many of the sections rely heavily on prior knowledge. If reorganization were to occur, there would be some need to re-structure how certain sections are taught.

Organization/Structure/Flow rating: 4

The text lacks much of the wonderful mathematical connections that could be made between ideas. While some connections are made, they seem a little outdated at times. I also think it would make more sense to have the properties of operations within their corresponding sections on operations rather than after all 4 operations are introduced.

Interface rating: 5

I did not see any issues with the interface. It was pretty user-friendly.

Grammatical Errors rating: 5

I did not notice any errors during my review.

Cultural Relevance rating: 5

I did not see anything insensitive or offensive in the text.

The text is just a small sampling of the many methods that could be used in teaching these mathematical ideas. I would have liked to see more activities for elementary teachers built into the lessons in each chapter as a means for learning and exploring ideas to facilitate more discussion as this text is used. There also are so many more connections that could be made between mathematical ideas that were lost a bit, especially with the general organization. On the whole, it is a nice resource and I could see it as useful for students studying for their certification exams to get some perspectives on the mathematical ideas they might encounter.

Reviewed by Sandra Zirkes, Teaching Professor, Bowling Green State University on 4/14/23

The text covers whole numbers, fractions, decimals, and operations well, and it provides some topics in geometry and algebraic thinking. However, the topics of ratio, proportion, and percent, as well as a more thorough coverage of geometry and... read more

All information in the text is mathematically accurate and the writing and diagrams are error-free.

Relevance/Longevity rating: 4

While all of the information in the text is accurate and thought-provoking, some specific approaches are outdated with respect to the current standards and pedagogy. Approaching the concept of place value through the "Dots and Boxes" method, without reference to base ten blocks that are overwhelmingly used in the elementary math classroom, limits the coverage of this important topic. Similarly, approaching fractions using the "pies and kids" scenario is not consistent with the standards which emphasize the understanding of all fractions as iterations of unit fractions.

The text is written using clear and understandable prose that is both mathematically accurate and accessible to college level pre-service teachers.

The text has a clear organization and focus and uses consistent approaches and terminology throughout.

Much of the text is easily divisible into smaller subsections for student use. With respect to reorganization and realignment for a particular course, while some topics are revisited at appropriate points in the text, if those original topics were not covered in the course, revisiting the topic may not provide enough basis for the new topic. For example, the understanding of decimals is highly reliant on a student's understanding of the Dots and Boxes approach to place value earlier in the text.

Organization/Structure/Flow rating: 5

The topics in the text are organized in a logical way that is consistent with the structure of a typical mathematics education course.

Interface rating: 4

Navigating the text itself was seamless and intuitive. However, the videos that I viewed had poor visual quality and there was no audio.

The text is well written with no grammatical errors.

There is no apparent cultural insensitivity in the text.

This text has a problem solving focus and emphasizes deep thinking and reasoning about mathematics. Its approaches are clear and understandable. While its approaches are mathematically correct and thought-provoking, it is missing some key topics such as ratio, proportion, percent, and a more thorough coverage of geometry and measurement, as well as some standards-based approaches such as base ten blocks and understanding fractions as iterations of unit fractions.

Reviewed by Fred Coon, Assistant Professor, Anderson University on 2/16/23

The text covers all major points to help develop future teachers. read more

Comprehensiveness rating: 5 see less

The text covers all major points to help develop future teachers.

Text appears to be accurate.

The content is consist with concepts that elementary teachers should know. The methods are small in diversity.

Topics where well explained.

Text appears to use understandable and consistent terms.

Modularity rating: 5

Units appear to be mostly independent and can be used as stand alone units.

The topics are presented in a manner that build on each other but can be rearrange if desired.

Interface was useful and aided in navigating text.

I found no errors.

The text has no culturally insensitive or offensive items that I noticed.

I would like to have seen more diversity in methods discussed.

Reviewed by Perpetual Opoku Agyemang, Professor of Mathematics, Holyoke Community College on 6/17/21

The content in this text is built to help its readers, especially, pre-service elementary education majors learn to think like a mathematician in some very specific ways. The content addresses the subject framework in a complete yet concise manner. Although it does not provide an effective index/or glossary, LCD was not extensively tackled using factor tree, multiples or tables to express it, I still give props to the author since there are a lot of pictorial examples and a question bank for most of the various concepts. Furthermore, Dots and Boxes game on chapter 1 was very engaging and fun.

This text is very accurate and informative using a variety of felicitous examples to suit a diverse student population.

Conventional concepts are presented in a current and applied manner which allows for easier association with similar organized and retained information. This text could use some updated fraction problems and examples involving mixed numbers. Some of the YouTube videos have no sound at all.

Clarity rating: 4

Content material was presented in an easy to understand prose. Introduction of concepts and new terms were usually done by association or relevant previous knowledge. Some of the concepts like Multiplying Fractions, have YouTube videos embedded in the introductions.

Terminologies and framework are consistent throughout the text. The use of different notations were consistent throughout the various chapters and subunits.

This text has easily divisible content as stand alone subunits. However, numbering these chapters and subunits would have gone a long way to help its readers.

The topics in this text are organized from basic to complex concepts in a logical, clear fashion.

This text has an awesome interface (Online, PDF and XML). Moreover, it is untainted by distractions that may confuse its reader. Hyperlinks should have been included in the content.

I did not spot any grammatical errors in this text.

This content material contains no recognizable cultural insensitivity. It could use more examples involving modern affairs that are inclusive of diverse backgrounds.

I truly love the concise format of this text and how many different examples it uses to explain the concepts. The Geometry of Arts and Science and Tangrams were so informative with fun activities. It's easy to tell when one example ends and another begins, although index/or glossary and a system of links from the table of contents would be greatly appreciated. I did not see Points on a Coordinate Plane. Additionally, the number of exercises per section is too small. Of course this can be remedied by adding more. As with any textbook, the reader will need to supplement certain sections and clarify particular terms and concepts to best fit their situation. Pre-service elementary education majors could transition to this book fairly easily and successfully teach K-6 students in the United States in alignment with current Common Core Math Standards.

Reviewed by April Slack, Math Instructor, Aiken Technical College on 5/13/21

This text covers elementary mathematics strands including place value, numbers and operations, fractions, patterns, algebraic thinking, decimals, and geometry. Measurement and Data and Statistics strands are not included in this particular text. The last chapter supplies the audience with problem-based learning approaches that include some measurement, but not in the detail of previous chapters of the book. It does incorporate problem solving strategies and pedagogical techniques teachers may use in the classroom. Examples with solutions and clarifying notes are provided throughout the text. The text does address Common Core Standards as well as the eight mathematical process standards. The textbook also provide teachers with a conceptual understanding of elementary mathematics along with appropriate mathematical terminology. The text does not offer an index or glossary.

The mathematics content provided in this text is accurate and provides thorough examples of teaching elementary mathematics for pre-service teachers. I found the text to build conceptual understanding and procedural fluency rather than just focus on basic algorithms to solve math problems. This is especially important for pre-service teachers, as they need to truly understand the "why" behind the math tricks that are often taught in early grades. The embedded links throughout the text are all in working order, as well.

The problem-solving approach to mathematics is especially relevant for elementary pre-service teachers; the intended audience. The book does expand beyond elementary mathematics, however, this is deemed extremely useful for all levels of mathematics teachers. Knowing the mathematical concepts beyond elementary strands allows teachers to know where there students are going and the mathematical purpose of content standards at each grade level. Many of the pedagogical techniques presented in the text are aligned with current research and instructional strategies for the elementary classroom.

This text provides explanations and defines mathematical terminology and has accessible prose. Beginning with the problem solving chapter before the specific content strands allows teachers to apply and consider strategies throughout the text. Often times, textbooks save problem solving for the end, but this text addresses strategies upfront and spirals nicely throughout the text. Some of the examples and visual representations are intended for an audience with mathematical background knowledge and strengths. A pre-service teacher may need help with content review prior to understanding the selection of particular problems highlighted in the text.

The text is well-organized and consistent with terminology throughout. The text is also consistent with provided examples that are used by mathematics teachers in everyday classrooms. There are multiple examples throughout each of the content chapters for pre-service teachers to reference and use in their own experiences.

This book is an easy read and may be easily broken up for weekly reading assignments and reflections. It seems as if mathematics teachers had a hand in writing this book. Bulleted and numbered lists are used throughout the text. The text also presents examples in clear, colored blocks. Visual models are clear and concise.

The book is well-organized with headings, subheadings, and the use of italics and boldface make this book extremely student friendly. The topics and content presented in this text are clear and in a logical order. Bulleted and numbered lists are reader friendly and easily understood. I found having the problem solving chapter appear first in the text stresses the importance and relevance of helping students become natural problem solvers. Often times texts and even worksheets save problem solving until the end, which poses a problem with students in the classroom.

This book is very easily navigated. The contents tab and drop down menu allows for the reader to quickly navigate to particular chapters and specific content. The previous and next buttons located at the bottom of the text allows readers to toggle between chapters very quickly. All embedded links work as they should and visual models are clear and understandable. There are no distractors present when trying to navigate the text. There is no index / glossary offered with this text.

The text is free from grammatical errors.

Cultural Relevance rating: 4

This text is not culturally offensive in any way. The final chapter of the text is dedicated to problem based learning and is centered around Voyaging on Hōkūle`a. The text provides embedded links to culturally relevant videos and models that help illustrate the cultural practices of Polynesians.

This textbook has a solid foundation and is well-organized for it's intended audience, the elementary mathematics pre-service teacher. This text will help build conceptual understanding of mathematics that will lead to procedural fluency for teachers. The text also provides clear examples of instructional strategies to be used in today's classrooms. Methods courses for pre-service teachers will find this text extremely useful and easy to incorporate in elementary mathematics methods instruction.

Reviewed by Kane Jessen, Math Instructor, Community College of Aurora on 8/13/20

This textbook is intended to cover the mathematics topics necessary to prepare pre-service elementary education majors to successfully teach K-6 students in the United States in alignment with current Common Core Math Standards. The textbook is a mostly comprehensive collection of K-6 Common Core elementary math topics ranging from non-numerical problem solving through summative PBL assessments incorporating algebra, geometry and authentic problem solving. However, several topics related to K-6 CCSS Standards are not covered or minimally covered. CCSS topics with minimal coverage include set theory, logic, integers, probability, graphing and data analysis. At the beginning of the book, there is an effective and accessible table of contents with links included. However, sections and subsections are labeled only with names and page numbers. The text does not contain an index, glossary or appendices. Chapter summaries and links to previous concepts/problems are not included but would support student learning if included. More visuals and historical explorations would increase comprehensiveness.

Content was found to be accurate, error-free and unbiased.

Relevance/Longevity rating: 5

The language and examples of this text are written with a constructivist and meta-pedagogical voice that is both academic and accessible. The author immediately addresses the importance of CCSS and consistently utilizes the “Exploding Dots” curriculum. The “Exploding Dots” curriculum is a brave and differentiated approach to holistically teaching multi-base mathematics to K-12 students. “Exploding Dots” has been a core focus of K-12 Global Math Project and was pioneered by James Tanton . As future teachers, students can expect to teach “Exploding Dots” or similar CCSS curriculum sometime during their teaching career.

The language of the text is well-written, accessible and clear. Some sections and examples could be expanded for clarity/depth. Prior definitions/review concepts are not consistently linked.

The text is internally consistent in terms of its own terminology, framework and graphics. The “Exploding Dots” infusion helps maintain continuity throughout the text but is not present in all modules.

This text follows the common sequence that many “Mathematics for Elementary Teachers” textbooks commonly follow. The text is organized into eight modules. The text initially builds upon itself without being overly self-referential. The text’s sections, subsections, definitions, axioms and problem banks are all well delineated but lack sections/subsection numbers/identifiers and links to previous concepts/definitions

This textbook has a solid flow and follows a common sequence shared by most for profit “Mathematics for Elementary Teachers” texts. The text is well organized and builds upon itself.

Minimal issues involving interface were observed. Observed interface issues include, one broken video link and unnumbered sections. Definitions and review topics are not linked or referenced with page numbers/sections, however, this creates minimal usability issues. The text contains adequate procedural visuals and also cultural and historical visuals that enhance the student learning experience.

This text is largely free from grammatical errors. Grammatical errors that were observed were minor and non-persistent.

The text is not culturally insensitive or offensive in any way. It consistently uses examples that are inclusive of a variety of races, ethnicities, and backgrounds. Textbook examples often include references to Hawaiin culture. These references are easily understandable and could be readily adapted for students in other places. In an effort to increase relevance, further additions to the text could be made to provide a more equitable and historical focus on women, minorities and problem based learning cross-sectional explorations similar to the Hōkūleʻa section.

This textbook has a solid structure and great flow, I thoroughly enjoyed reviewing this textbook. I am genuinely excited to incorporate Michelle Manes ‘Mathematics for Elementary Teachers’ into my upcoming semester’s curriculum. With subsequent editions and revisions, this textbook will become a wonderful text for students majoring in primary education, especially those who are either lacking in basic math skills or math confidence.

Reviewed by Reina Ojiri, Assistant Professor, Leeward Community College on 7/27/20

Comprehensiveness rating: 2 see less

The book begins with a reference to the Common Core State Standards (CCSS) for Mathematics and the eight “Mathematical Practices". Though not all states have adopted and/or are currently using the Common Core Standards, with its incorporation at the beginning of the text I initially thought that the Common Core standards would be revisited consistently throughout the text.

Though the "Think Pair Share" sections are great additions for discussion to the book they do not include common misconceptions or tips for instructors to use to help guide these discussion prompts. The focus on just one type of discussion "Think Pair Share" also does not give future teachers a broader experience with different cooperative learning strategies in the classroom. There are many strategies in addition to “Think Pair Share” that are also great and seeing the same strategy over and over did not provide variation or keep me engaged as I read through the text.

There are a few key concepts that are not included in the text including Measurement & Data and Statistics & Probability.

The text also does not include an effective index and/or glossary. I have found that students do use the index and/or glossary that is typically in the back of the book to help them find information in the text quickly.

Content Accuracy rating: 3

The content is error-free however some of the images included on the PDF version are blurry and hard to read. There does not seem to be consistency between the different readable versions of the text.

There also seems to be a bias for the dots and boxes strategy throughout the text and the content lacks current practices of teaching concepts.

Just like any text, this textbook needs to be updated to match current best practices and research in math education. Since this text is Attribution-ShareAlike which allows “others to remix, adapt, and build upon your work even for commercial purposes, as long as they credit you and license their new creations under the identical terms” it does seem that updates and instructor/course-specific content will be relatively easy to implement as needed.

Clarity rating: 3

This text is written in a way unique way that makes it easier for students to read through and follow. It is very student friendly however might not be as useful as an instructor text since the instructor needs to fill-in-the-blanks on their own.

Consistency rating: 3

The text is written with consistent terminology however the framework for each chapter is not consistent. Some chapters include Explorations and additional sections while others end consistently with a problem bank.

Modularity rating: 3

The text is divided into smaller reading sections however the titles of each section are not easily recognized by students. Though I imagine the titles were meant to be creative for each section, having something more straight forward to make it easier for students to navigate is more important than creativity especially for future teachers who might be teaching these concepts for the first time.

Organization/Structure/Flow rating: 3

It would be good to organize the material consistently throughout the text (e.g.each section should end with a problem bank). The variation in the different sections can be confusing to both the instructor and student when trying to find something in the text.

I also noticed that the online version does not include page numbers while the PDF version does. This is not helpful when referring students to particular sections of the book. The PDF version also has many completely blank pages. I am not sure if this was meant to be on purpose (for printing purposes) but these pages can be very distracting to the reader.

Interface rating: 2

Navigation throughout the text is fine however, there are noticeable differences between the online and PDF versions of the text. The images in the PDF versions are noticeably blurry and lower quality than those in the online version. In some instances, it seems as though images were screenshot and copied and pasted which could account for the image quality.

Some images, in particular, should not have been included at all and are unreadable, for example, the Hokulea on page 441.

I did not notice grammatical errors.

The connection to the Hawaiian culture was a nice touch.

I would use this text as a reference but would not adopt this book as the main text for my class.

Reviewed by Thomas Starmack, Professor, Bloomsburg University of Pennsylvania on 3/26/20

The book is somewhat dated and does not include current research based best practices like concrete, representational, then abstract. Like most authors, they make assumptions that students have the ability to understand abstract and start the lesson there, which is contradictory to how the brain works and what current research says about effective math instruction and learning.

I agree the content is accurate, but in many areas the learner must have a very strong understanding of mathematical concepts, structures, and applications. There lacks current best practice and current NCTM recommendations to approaching the teaching of mathematical content.

Relevance/Longevity rating: 1

Although mathematical concepts at the elementary level remain the same, the approach to engaging students in learning and the methods of instruction have evolved greatly. The book lacks many of the newer approaches and is outdated. The arrangement of the concepts is okay. I would recommend that the big ideas of teaching math are in the beginning and providing an overview of what is mathematics and best approaches to teaching/learning mathematics. Then scaffold the specific concepts. Fractions is one of the most complex and abstract, and this book starts there as a first topic.

Once again, the book is okay in terms of math learning but dated on best practice approaches. The book does not use jargon per say, but does not provide the best approaches for students to learn how to effectively teach mathematics.

Consistency rating: 4

Yes the book is consistent throughout.

The text is divisible, just not relevant to today nor provides current approaches. The order of the content is not in line with a methods of teaching course I would follow.

Organization/Structure/Flow rating: 2

I think the topics are clear but dated and not in the order as described above.

The text provides a variety of interfaces, none of which are confusing for the student who has a very strong math background. The text does mislead students to think starting with abstract is how to instruct elementary students, which is contradictory to brain research and current best practices.

Grammatical Errors rating: 4

I did not notice any grammar errors.

Cultural Relevance rating: 3

I think the text is culturally appropriate. Not certain about the final chapter as it focuses on one population. Having a chapter or theme woven throughout the text that provides students with a stronger understanding that although mathematics is a universal language, there are cultural differences to teaching and learning as evidenced in the 1999 TIMSS report.

The text is outdated. The text is an okay resource but I would not be able to use as the main guide for learning in a college level methods of teaching elementary mathematics course.

Reviewed by Jamie Price, Assistant Professor, East Tennessee State University on 3/20/20

This book introduces the reader to the standards for mathematical practice (SMP) from the Common Core standards in the introduction. I appreciated this as these standards cover all grades and are a unifying theme of the Common Core standards, yet many times overlooked. In addition, many states, including mine, that are not following Common Core directly have adopted the SMPs. The book does not cover two of the mathematical strands, namely measurement and statistics/data. Among the strands that are covered, however, the author does a thorough job of explaining the content, using a unified theme throughout, such as dots and boxes introduced in place value that appear again in number operations. I particularly liked the final chapter of the book and its connection to Hawaiian culture. The author could easily incorporate ideas related to teaching and learning measurement into this chapter in order to make the book more comprehensive.

The content was very accurate. I did not come across any mathematical errors or biases. The author did a good job of incorporating "think, pair, share" elements throughout each chapter as a model for future teachers. To further guide future teachers, I would have liked to see the author include information in each chapter about common misconceptions students have when learning the related material and ideas on how to address those misconceptions. In my experience, I find that pre-service teachers are unaware of these misconceptions and it is helpful to make them aware of them so that they can anticipate them in their own classrooms.

The content presented in this book is up-to-date and will remain relevant for a long time. Due to the fact that this book focuses more on content rather than methods, I do not foresee a need for many updates moving forward.

The book is written in a very clear and concise way that is approachable to future and current elementary teachers. The author presents key words in bold throughout the book to draw attention to them. I liked the way that the author included videos as well as written explanations of ideas, such as in the Number and Operations chapter, section titled Addition: Dots and Boxes. The author explains, in words, how to use this method to add multi-digit numbers and follows the written example with a video explanation. This helps to reach a variety of learners and learning styles. The author also addresses common "jargon" associated with particular mathematical concepts, such as proper and improper fractions (section titled What is a Fraction?), and discusses how this jargon can be misleading for students.

Each chapter in the book includes an introduction, multiple opportunities for think-pair-share discussions, and several problem sets to practice. I appreciated the consistency in the Dots and Boxes method introduced in the Place Value chapter and then carried into the Number and Operations chapter.

The book uses a modular approach to present the material. Each module contains numerous sections that help to break up the content into smaller chunks so that the content does not seem overwhelming. The modules are set up in an order that makes sense for the mathematics, but a reader could begin reading at any module and still make sense of the content.

The organization of the topics makes sense according to the mathematics presented and is logical.

I did not find anything distracting or confusing in relation to the interface of the text. The book was easy to navigate, with a clearly defined table of contents. I was able to easily click through the various modules and sections within each module. The book uses figures well to provide engagement to the reader as well as to further clarify content. The use of videos embedded within the modules helps to strengthen understanding of the content. It did take me a minute to find the navigation link that allowed me to move to the next section in a module (right arrow at bottom right corner of the page), but once I found it I was able to navigate seamlessly to each subsequent section.

I did not find any grammatical errors in the text.

In my opinion, this was one of the biggest strengths of this text. The author did a nice job of incorporating Hawaiian culture into the text. For example, the author includes an image in the Place Value chapter (Number Systems section) that references the use of tally marks on a sign at Hanakapiai Beach. In addition, a full chapter was devoted to Voyaging on Hōkūle`a. I particularly liked how the author connected this idea to beginning teaching of elementary mathematics and encouraged future teachers to think about ways to see mathematics outside of traditional mathematical settings.

I am glad that I came across this resource. I primarily teach math methods courses for elementary pre-service teachers, but I found many aspects of this text that I can incorporate into my classes to help students think more deeply about the mathematics that they will teach. I appreciated the author's attempt to challenge students in their thinking about elementary mathematics. Initially, I was surprised to find that there was no "answer key" provided for the many problem sets that were included throughout the text. After reading the quote presented on the introductory page to the Problem Solving chapter, I realized that this may have been an intentional decision made by the author to encourage readers to go beyond "a trail someone else has laid." I find that many pre-service elementary teachers want to "just know the answer" when it comes to mathematics; a no answer key approach will encourage discussion and justification, two elements important to ensuring equity in the teaching and learning of mathematics.

Reviewed by Shay Kidd, Assistant Professor- Mathematics Education, University of Montana - Western on 12/30/19

The content that elementary teachers need to have that is not covered in this book is graphing, probability, statistics, exponents, visual displays of data. The coverage of operations is very specific in the examples and does not cover the wide... read more

Content Accuracy rating: 4

While the core topics presented are correct, the number of problems that are provided without any solutions is alarming. The majority of problems that are provided are meant for the reader to perform but do not provide any type of answer key for checking the work. In this way, the book seems to assume the reader to have a solid knowledge of the topics already and this book discusses a few different approaches to these topics.

The specific content presented is up-to-date and usable.

The book's prose seem to be more of a teaching guide than a textbook. This is nice for the conversational aspect that a reader may want in their learning, but should be explained more or possibly a change of title for the book. Something more like "Exploring the concepts of Elementary Mathematics" would provide a more reading friendly approach the book offers.

The author has a consistent voice of teaching and presenting the material.

Modularity rating: 2

The break-up of the text with boxes is difficult to follow the purpose of each box. While some of the box styles are clear, such as the think, pair, share or problem boxes, others seem to break up the line of discussion. A problem box may be discussed more directly immediately following the box and the presentation of the problem. Most of the problem boxes are not discussed again in the main text. This cased issues for wanting to read with a specific purpose. When the reader wants to understand a problem more, there is generally not more discussion, but unclear about when that would be provided or not. Other times boxes were used without any "box type" provided and these were just to break up the flow of the text.

Place value was a major topic to start the book and had good coverage, then operations and fractions were discussed, then a return to place value with decimals. It would seem that a connection of place value and decimals would work better to follow the other place value discussion.

Interface rating: 3

There are several pages that have large blank parts or are totally blank. This may be due to the PDF version that I chose. When I did use the internet-connected version, there seems to be a dependence on youtube to help do some of the teaching.

There are a few minor issues that would be resolved with a good proofread.

The book does seem to be written with the Hawaiian culture in mind. This may be difficult for other cultures to connect to or understand but does not present any insensitivities.

The book's title suggests a full discussion of the topics that elementary education pre-service teachers would need to know and teach, but this book is very lacking in the topics required for this. I selected this book to review because I teach classes that would use the textbook, but I would not use this textbook as is. There are a few topics that I plan to add to my own instruction, but the book as a whole needs additional help to be able to stand alone. This really appears to be a teaching guide based on the constant think-pair-share setup. This also is a specific teaching and method that seems to require the students to already have much of the content mastered. It does not teach all the content that is required to the level of the discussion had.

Reviewed by Ryan Nivens, Associate Professor, East Tennessee State University on 10/25/19

The book covers all the expected mathematical strands except for measurement and data/stats. There are some obvious connections to the strands of mathematical practice from the Common Core standards. While the abstract specifically lists MP1, MP2, and MP3, the introduction clearly lists all 8. The chapter "Voyaging on Hōkūle`a" contains activities that will require use of measurement and units, but there is no explanation on how measurement topics should be taught or approached. However, this chapter does provide a good project-based learning set of materials, and is an exceptional resource for navigation. The book also includes a chapter on Problem Solving, which is important for those students who must complete the EdTPA and address the 3rd subject specific emphasis area. All embedded links to Youtube videos or Vimeo videos are working and play within the textbook pages.

I find the mathematics to be entirely accurate. There are many teaching strategies, such as "think pair share" that are found throughout the chapters. This is particularly helpful for future teachers.

This book should last a very long time in terms of relevance.

This book is very clear, with mathematical words in bold and proper definitions provided. The text also addresses common math classroom jargon. For an excellent example of this, see the heading "What is a Fraction" in the chapter on Fractions. Toward the bottom is a sub-heading "Jargon: Improper Fractions" that has students consider the usefulness of proper and improper fractions.

This book is consistently laid out, with multiple examples, problems to try, and diagrams to support the transfer of information.

This book is entirely modular. You can pick it up, and easily start in any chapter and not be lost. The heading, subheading, use of italics and boldface make it easy to locate information. As a mathematics education book, this is quite nice.

A mathematician wrote this, the layout is logical without question.

The book is extremely easy to navigate, with a logical structure to the table of contents that you can easily click through. A drop down menu in the upper left corner allows you to view the outline of the book while still viewing a page, and you can collapse/expand chapters within the menu.

The many figures that are present throughout the textbook are perfectly displayed and fit the reading material.

There is nothing I find distracting in the layout and interface.

I could not find any errors.

An entire chapter is dedicated to Voyaging on Hōkūle`a, with exceptional videos and diagrams to illustrate the cultural practices of the early Polynesians.

I was excited to find this book in the Open Educational Resources library. As a professor who frequently teaches methods courses in mathematics for elementary teachers, I feel that this book may be a terrific book to use to replace previous texts that I've adopted. I would like to see a chapter on Measurement to make the Voyaging on Hōkūle`a chapter more useful. It is obvious from the first page you open to that this book was well planned and thought out. I'm impressed.

Reviewed by Monica Rose Gilmore, Graduate Student, CU Boulder on 7/1/19

Comprehensiveness rating: 3 see less

This textbook goes into depth about different mathematical concepts that are important for elementary school teachers to understand in teaching mathematics. However, the text is missing a focus on statistics and probability, which are key areas of focus in elementary math classrooms. The text is also missing an index or glossary but does define new terms as they are introduced.

The content, mathematical diagrams and depictions are accurate and error-free. Each chapter also accurately shows various ways to understand mathematical concepts. However, the diagrams are geared towards an audience that already has some understanding of advanced mathematics.

The content is organized in a way that necessary updates would be straightforward to implement. More specifically, much of the content reflects current mathematical practices and activities endorsed by up-to-date research in mathematics education.

The text is written in accessible prose and provides context for jargon and technical terminology. Additionally, the text clearly separates different terms for different strategies and concepts. For example, in the Problem Solving Strategy section, the interface is divided into different strategies for the reader to explore. This is helpful in keeping new concepts and strategies organized for the reader.

The text is written with consistent terminology. More specifically, the text consistently gives examples of what concepts are called by mathematicians and teachers. This is helpful for pre-service teachers that might be teaching mathematical concepts and strategies for the first time.

The text is easily divided into smaller reading sections. These sections include not only explanations of mathematical concepts, but also theorems, activities and diagrams which can be referenced by the teacher at any point. Also, the text gives teachers ideas for activities and additional problems to try with students.

Though the topics in the texts are presented in a logical, clear fashion, it might be beneficial for pre-service or elementary teachers to see how to specifically scaffold the different concepts within those topics for elementary students at different grade levels. Additionally, the text could also demonstrate how students typically confuse topics so teachers and pre-service teachers are prepared to navigate new concepts for the class.

The interface is easy to navigate since the content clearly outlines chapters and the topics within them. Sections such as notation and vocabulary, think pair shares and theorems are clearly outlined, organized and conceptually scaffolded. However, it might be helpful to have an index so the reader does not have to click within each topic to find the concept they are exploring.

This text is free from grammatical errors.

This text is not culturally insensitive or offensive and includes examples from the Hawaiian culture. Though the text is mainly made up of mathematical explanations, there are a variety of people's names in different problems that could be attributed to a variety of cultures. Additionally, the text reflects Polya's advice (1945) to try adapt the problem until it makes sense. Though the text includes mainly mathematical explanations, it does call for adapting problems which could potentially be applied to a variety of students of different backgrounds.

Reviewed by Glenna Gustafson, Professor, Radford University on 5/22/19

This is book is fairly comprehensive and I feel could be used by most foundational courses in elementary mathematics. The structure and writing provide a good foundation for students learning the "why" behind the mathematics and becoming mathematical thinkers. There were some areas that could possibly use more development. In geometry for example there was no discussion of perimeter, area, and volume. Estimation, measurement of weight, time, and probability also appears to be missing. The text is well organized and written so that the chapters do not have to be completed in the order in which they are presented. While there is not index or glossary, the author uses colored text boxes to explain specific content or terms.

The content of the text is accurate and represented in a variety of formats to support learning, Not only does it provide solutions to problems, but also the mathematical thinking behind those solutions.

The text is very relevant for K-6 elementary pre-service teachers. It would be beneficial to know the specific grade levels that the author considers as "elementary" since this does vary by location. The content is "standard" for most elementary math courses and would not need to be updated often and the consistent layout and formation would make changes easy to make.

The text is written in a conversational tone. The simplicity and straight-forwardness of the text should appeal to those students that have sometimes been overwhelmed by writing in more traditional math texts.

The text is organized consistently from chapter to chapter. The table of contents and chunking of content in the chapters is logical and clear, Each chapter includes graphics as well as sections for: Think-Pair-Share; Definitions; Theorems (when appropriate); and, Problems. This consistent structure makes navigation easy.

The table of contents and chunking of content in the chapters is logical and clear. This also makes it easy to not necessary to move sequentially through the text, but to have the option of reviewing or using only needed topics. Subtitles and graphic captioning are appropriate for the content.

The text is easy to read and the organization within each chapters makes navigation easy.

This text is easy to navigate. The inclusion of graphics, charts, photos, and videos support learning. There are several pages where graphics in the Geometry chapter are skewed in the PDF version, but this does not seem to be a problem in the online version, Not all of the video links work within the PDF version.

There were no obvious grammatical errors. Several of the errors that were found were typos and/or word omissions.

The text is culturally inclusive. One thing that should be noted is that it seems male names are over-represented in the Problem sections. A reference to Hawaiian culture and life is evident. The Hōkūle`a voyage found in the last chapter is a good example of problem based learning and the integration of math with other subject areas.

This would be a wonderful text to use as a supplement or compliment to an elementary math methods course. It is not as overwhelming as other math texts, and would provide pre-service teachers with a good foundational review of math concepts, including vocabulary and some pedagogy.

Reviewed by Karise Mace, Mathematics Instructor, Kuztown University on 5/16/19, updated 11/9/20

This book is fairly comprehensive for a one-semester course, although it does not include much detail about several topics. The section on number systems barely touches on Roman numerals and only mentions Mayan and Babylonian counting systems. The sections on addition, subtraction, and division would be more robust if the author included other algorithms for these operations. The chapter on Geometry does not address perimeter, area, surface area and volume. The book does not include an index or glossary.

While the book is not error free, it is unbiased. Most of the errors seem to be typographical and/or related to web links or LaTeX. In the section on number systems, the author incorrectly explains how one million would be represented using Roman numerals and incorrectly claims that the Mayans did not use a symbol for zero. Further, the Mayan number system was not a true vigesimal system, as the text indicates.

This text uses a constructivist approach to help students build their understanding of the mathematics included in the book. It is well organized and written so that the chapters do not have to be completed in the order in which they are presented. Because of this, the text should be easy to update. When concepts that are presented earlier in the text are used in later chapters, the author includes a brief but thorough review that would allow students to understand the later chapter even if they had not read and completed the problems in the earlier chapter. The "dots and boxes" approach is timely, as it uses the idea of the "exploding dots" that are part of the Global Math Project (https://www.globalmathproject.org).

The textbook is clearly written and enjoyable to read...even for the math-phobic student. The tone is conversational and is even funny at times. The author defines important mathematical terminology in a way that is both mathematically accurate and accessible to students. The chapter on problem solving is fantastic and really gives students insight into how to think and problem solve like a mathematician. The pies per child model for fractions is not the most effective model for helping students understand fractions and this part of the text would be improved if the author replaced this type of modeling with pattern block modeling.

Overall, the text is consistent in its chapter structure and terminology use. However, there is inconsistent notation when using "dots and boxes."

The text is well-organized but can be reorganized in order to suit an instructor's preference. However, it would be best to complete the chapter on problem solving first, as it sets the stage for the rest of the book. Most of the chapters are structured more like an activity book with lots of great problems and thought provoking questions that will help students think deeply about the mathematical concepts being presented. With the exception of the chapter on problem solving, there is not a whole lot of text for students to read.

Although the topics presented could be reorganized to meet student needs, the order in which they are presented is logical and clear.

With only a few exceptions, the images it the text are clear. In the section titled "Careful Use of Language in Mathematics: =" some of the scale images need to be modified so that the items on the scale appear to actually sit on the pans. The same issue occurs in the section titled "Structural and Procedural Algebra." Some of the images in the sections titled "Platonic Solids" and "Symmetry" spill off of the page. The image that appears on page 89 and then again on page 144 would be more clear if a different font was used to label the line segments.

No grammatical errors were noted. However, there were a few typographical errors that could cause confusion for students as on page 219.

The text was culturally sensitive and nothing offensive was noted. As the focus of the text is purely mathematical, there are not many cultural references at all, unless they are references to historical cultures. The author does use names for hypothetical students that are diverse and represent a variety of ethnicities. The last chapter is an integrated unit that focuses on the Hawaiian culture. Unfortunately, the links and web addresses in this chapter do not work and/or are no longer active.

The book includes three sections at the end of the problem solving chapter in which the author articulately explains the language that mathematicians use to succinctly and precisely explain their problem solving and solutions. These sections will help students who may not think of themselves as mathematicians learn to think like mathematicians. So many mathematics textbooks are full of exercises but no true problems. On the other hand, this text is full of wonderful problem solving and critical thinking problems that are embedded in the sections as well as in the problem banks. The author also includes many "Think/Pair/Share" exercises and questions that will facilitate mathematical thinking and conversation among students. The constructivist approach used by the author will help students build deep understanding about the mathematics covered in the text. While there is some room for revision and improvement, this is a very good text to use with elementary education majors, and I definitely plan to use this book the next time I teach them.

Reviewed by Desley Plaisance, Associate Professor, Nicholls State University on 4/29/19

This textbook seems to be appropriate for the first course typically taught for elementary teachers which usually includes topics of problem solving, place value, number and operations. Most books are able to be used for a second course which... read more

Content seems to be accurate.

Topics are somewhat static for a course like this, so the textbook will not become obsolete within a short period of time.

Appears to be clear.

The flow from topic to topic is consistent in presentation.

Divided into clear sections.

Topics are presented logically and in a similar order to most books of this type.

Easy to navigate with clear images and other items such as tables.

Book is written in simple language and appears to be free of grammatical errors.

Appears to be culturally diverse.

This book could definitely be used for a first course of elementary math for teachers with the teacher providing resources. As with many open books, the print and layout is very simple without cluttering pages with unnecessary items.

Reviewed by Lisa Cooper, Assistant Professor, LSUS on 4/26/19

This text covers many concepts appropriately; however, a few concepts are missing, such as; data analysis and statistics. For more than ten years, data-driven instruction has been a major focus in education along with many other uses. This text... read more

The content is well organized and accurate. Multiple representations and diverse examples are provided throughout the text which supports an unbiased approach to those entering elementary education.

The text is quite relevant to the classroom today, incorporating such resources as YouTube, varied strategies to promote differentiated instruction, scaffolding between concepts, and problem-solving opportunities. Some states may find issues with Common Core standards being addressed; however, mathematical practices could be interchanged with the "standards."

The text is written free from educational jargon; it is straightforward and easy to understand.

The text is consistent in its structure; color is not distracting, problems, strategies, diagrams, charts, and definitions are provided throughout.

The text is appealing with the page layout; it's not too busy or distracting. Colors are attractive and text is broken down into appropriate amounts.

The text has a well-organized flow with the layout of each topic/chapter.

The text has charts, pictures, diagrams, real-world examples throughout; several different versions of the text are offered too.

No grammatical errors were observed in my review of the text.

The text provides a variety of backgrounds, races, and ethnicities while providing learning experiences and pedagogical approaches to support student engagement and learning.

Reviewed by Demetrice Smith-Mutegi, Instructor/Coordinator, Marian University on 3/6/19

This text covers place value, numbers and operations, fractions, patterns, algebraic thinking, decimals, and geometry. However, elementary teachers are expected to also know and understand statistics and probability. This text does not address... read more

The text makes non-traditional, yet, accurate representations of mathematical concepts. In some sections, different solutions are presented and explained. This eliminates bias and provides a diverse representation of ideas when solving math problems.

The text is representative of common core problem-solving standards, however, it does require mathematical knowledge beyond elementary school. The problem-solving nature of the text is very relevant to elementary pre-service and in-service teachers (the audience for the book).

The text language is clear and accessible. There is a section on terminology, which is very helpful. Additional diagrams would help to improve the clarity in some cases.

I was expecting to see videos embedded throughout, after seeing them in the first section. It would be great to have a consistent format throughout the text, however, I understand that it is not always feasible to do so. There were other obvious and clear patterns presented, color-coded sections (think/pair/share), problems, examples.

The chapters and subchapters can be easily accessed, breaking the material into smaller sections.

The topics were presented in a logical, clear fashion, however, not all of the chapters would end with a problem bank. In some cases, there were additional sections after the problem bank. It would be great if each section included key objectives or goals of the section.

The text comes in pdf, XML, and an online web version. The search feature on the online version was a valuable addition.

I did not observe any obvious grammatical errors.

Cultural awareness was very obvious in this text. While it was more relevant to Hawaiian culture, it also included cultural awareness of other cultures and backgrounds.

Overall, this text assumes that the student has successfully completed mathematics through basic calculus. There should be more support in this area, as some elementary math students are not prepared to complete problems with this focus.

This a great "discussion" text.

Reviewed by Kandy Noles Stevens, Assistant Professor of Education, Southwest Minnesota State University on 12/28/18

This text covers the areas applicable to elementary mathematics extremely well (with the exception of omitting probability and data analysis) and provides graphically visual boxes within the text to define terms and instructional strategies. Additionally, the text provides thinking routines that support understanding more than just the concept, but also, the how's and why's of conceptual understanding.

The content is accurate and organized in a way to supports student learning for those training to become elementary teachers of mathematics.

The content of the book is relevant to today's elementary classroom in that it provides future elementary educators with the content knowledge, but also pedagogical approaches that would support student learning. Additionally, the text is organized in a way that is consistent and provides scaffolding support for those who might struggle with any one of the concepts. For Minnesota standards the only item of note is that there is not a section devoted to probability or data analysis, but the latter is touched upon in other chapters. There are three mentions of the Common Core standards in the text. Minnesota is not an adopter of the CC mathematics standards, but the references to the CCSS are in regards to the practices of mathematics and not on standards specifically.

While a great text for training future math teachers, this book does not read as a "typical" mathematics textbook. Students who have struggled in the past with mathematics might find the authors' writing style to be approachable and accessible for all levels of mathematics competence and confidence.

The text is consistent in its terminology and the structure of the framework is uniform throughout, relying on supporting student learning through exercises, think-pair-share activities, and continuous dialog and reflection.

A majority of the chapters begin with a section that introduces the strand of elementary mathematics covered. Not all chapters have this introduction which may pose challenging to interrupt the mathematical progression of some established courses.

The text is very well organized and has an easy-to-read format and flow.

The text is graphically rich with succinct advanced organizers, diagrams, and photos to support learning.

The text is written with professional level writing and is free of grammatical errors.

A variety of races, ethnicities, and backgrounds are present in the exercises used to support student learning throughout. The end of the text involves a Hōkūle`a voyage as a part of a problem-based learning (integrated curriculum) experience. This was something that really made this text stand out in that it gave future elementary teachers an example of using mathematical concepts in authentic (and exciting) learning experiences. This Polynesian voyage would provide many students with an introduction to life culturally different from their own.

I have been a STEM educator for more than two decades and I come from a long line of mathematics educators. While wrapping up my reading of this text, I happened to have my father (a 46 year veteran mathematics educator) here visiting. I shared the text with him and several times I heard him utter, "I like the way this problem is set up". We both found the book to be very knowledgeable for mathematical conceptual understandings, but even more so for introducing ideas for instructional strategies and classroom discourse to help future teachers become equipped with speaking the "language of mathematics" to guide their future students.

I. Problem Solving

Introduction
Problem or Exercise?
Problem Solving Strategies
Beware of Patterns!
Problem Bank
Careful Use of Language in Mathematics
Explaning Your Work
The Last Step

II. Place Value

Dots and Boxes
Other Rules
Binary Numbers
Other Bases
Number Systems
Even Numbers
Exploration

III. Number and Operations

Addition: Dots and Boxes
Subtration: Dots and Boxes
Multiplication: Dots and Boxes
Division: Dots and Boxes
Number Line Model
Area Model for Multiplication
Properties of Operations
Division Explorations

IV. Fractions

What is a Fraction?
The Key Fraction Rule
Adding and Subtracting Fractions
What is a Fraction? Revisited
Multiplying Fractions
Dividing Fractions: Meaning
Dividing Fractions: Invert and Multiply
Dividing Fractions: Problems
Fractions involving zero
Egyptian Fractions
Algebra Connections
What is a Fraction? Part 3

V. Patterns and Algebraic Thinking

Borders on a Square
Careful Use of Language in Mathematics: =
Growing Patterns
Matching Game
Structural and Procedural Algebra

VI. Place Value and Decimals

Review of Dots & Boxes Model
Division and Decimals
More x -mals
Terminating or Repeating?
Operations on Decimals
Orders of Magnitude

VII. Geometry

Triangles and Quadrilaterals
Platonic Solids
Painted Cubes
Geometry in Art and Science

VIII. Voyaging on Hokule?a

Worldwide Voyage

Ancillary Material

About the book.

This book will help you to understand elementary mathematics more deeply, gain facility with creating and using mathematical notation, develop a habit of looking for reasons and creating mathematical explanations, and become more comfortable exploring unfamiliar mathematical situations. The primary goal of this book is to help you learn to think like a mathematician in some very specific ways. You will: • Make sense of problems and persevere in solving them. You will develop and demonstrate this skill by working on difficult problems, making incremental progress, and revising solutions to problems as you learn more. • Reason abstractly and quantitatively. You will demonstrate this skill by learning to represent situations using mathematical notation (abstraction) as well as creating and testing examples (making situations more concrete). • Construct viable arguments and critique the reasoning of others. You will be expected to create both written and verbal explanations for your solutions to problems. The most important questions in this class are “Why?” and “How do you know you're right?” Practice asking these questions of yourself, of your professor, and of your fellow students. Throughout the book, you will learn how to learn mathematics on you own by reading, working on problems, and making sense of new ideas on your own and in collaboration with other students in the class.

About the Contributors

Michelle Manes, Associate Professor, Department of Mathematics, University of Hawaii

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In this photo-illustration, a child sits on a seesaw set in a field of emerald green grass. On the other side of the seesaw is a giant smartphone.

Coddling Plus Devices? Unequivocal Disaster for Our Kids.

In “The Anxious Generation,” Jonathan Haidt says we’re failing children — and takes a firm stand against tech.

Credit... Alex Merto

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By Tracy Dennis-Tiwary

Tracy A. Dennis-Tiwary is a professor of psychology and neuroscience, director of the Emotion Regulation Lab at Hunter College.

Published March 26, 2024 Updated March 27, 2024
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THE ANXIOUS GENERATION: How the Great Rewiring of Childhood Is Causing an Epidemic of Mental Illness , by Jonathan Haidt

Imagine that your 10-year-old daughter gets chosen to join the first human settlement on Mars. She’s ready to blast off but needs your permission.

You learn that the billionaire architect of the mission hasn’t considered the risks posed by the red planet’s toxic environment, including kids developing “deformities in their skeletons, hearts, eyes and brains.”

Would you let her go?

The cover of “The Anxious Generation,” by Jonathan Haidt, portrays a child in a pit of yellow balls, immersed in the screen of her phone. The text is white.

It’s with this “Black Mirror”-esque morality play that Jonathan Haidt sets the tone for everything that follows in his erudite, engaging, combative, crusading new book, “The Anxious Generation.” Mars is a stand-in for the noxious world of social media. If we’d say no to that perilous planet, we should of course say no to this other alien universe.

Instead, we hem and haw about the risks, failing to keep our kids safely grounded in nondigital reality. The result can no longer be ignored: deformities of the brain and heart — anxiety, depression, suicidality — plaguing our youth.

Haidt, a social psychologist, is a man on a mission to correct this collective failure. His first step is to convince us that youth are experiencing a “tidal wave” of suffering. In a single chapter and with a dozen carefully curated graphs, he depicts increases in mental illness and distress beginning around 2012. Young adolescent girls are hit hardest, but boys are in pain, too, as are older teens.

The timing of this is key because it coincides with the rise of what he terms phone-based childhood. From the late 2000s to the early 2010s, smartphones, bristling with social media apps and fueled by high-speed internet, became ubiquitous. Their siren call, addictive by design and perpetually distracting, quickly spirited kids to worlds beyond our control.

It wasn’t phones alone. A second phenomenon coincided with the rise of the machines: the decline of play-based childhood. This change started in the 1980s, with kidnapping fears and stranger danger driving parents toward fear-based overparenting. This decimated children’s unsupervised, self-directed playtime and restricted their freedom of movement.

With parents and children alike stuck in “Defend mode,” kids were in turn blocked from discovery mode, where they face challenges, take risks and explore — the building blocks of anti-fragility, or the ability to grow stronger through adversity. Compared to a generation ago, our children are spending more time on their phones and less on, well, sex, drugs and rock n’ roll. While fewer hospital visits and teen pregnancies are obvious wins, less risk-taking overall could stunt independence.

That’s why parents, he argues, should become more like gardeners (to use Alison Gopnik’s formulation) who cultivate conditions for children to independently grow and flourish, and less like carpenters, who work obsessively to control, design and shape their offspring. We’ve overprotected our kids in the real world while underprotecting them in the virtual one, leaving them too much to their own devices, literally and figuratively.

It’s this one-two punch of smartphones plus overprotective parenting, Haidt posits, that led to the great rewiring of childhood and the associated harms driving mental illness: social deprivation, sleep deprivation, attention fragmentation and addiction. He has a lot to say about each of these.

Here is where his ideas and interpretation of research become contentious. Few would disagree that unhealthy use of social media contributes to psychological problems, or that parenting plays a role. But mental illness is complex: a multidetermined synergy between risk and resilience. Clinical scientists don’t look for magic-bullet explanations. They seek to understand how, for whom and in what contexts psychological problems and resilience emerge.

Haidt does recognize that nuance complicates the issue. Online — but not in the book — he and colleagues report that adolescent girls from “wealthy, individualistic and secular nations” who are “less tightly bound into strong communities” are accounting for much of the crisis. So perhaps smartphones alone haven’t destroyed an entire generation. And maybe context matters. But this rarely comes through in the book.

The final sections offer advice for reducing harmful, predatory aspects of technology and helping parents, educators and communities become more gardener and less carpenter. Some tips will be familiar (ban phones from school; give kids more independence). Other advice might give readers pause (no smartphones before high school; no social media before 16). Yet, taken together, it’s a reasonable list.

Still, Haidt is a digital absolutist, skeptical that healthy relationships between youth and social media are possible. On this point, he even rebuffs the U.S. Surgeon General’s more measured position. We’re better off banning phones in schools altogether, he asserts. Because, as he quotes a middle school principal, schools without phone bans are like a “zombie apocalypse” with “all these kids in the hallways not talking to each other.”

Whether or not you agree with the zombie apocalypse diagnosis, it’s worth considering the failure of prior absolutist stances. Nancy Reagan’s Just Say No drug campaign? A public health case study in what not to do. During the AIDS crisis, fear mongering and abstinence demands didn’t prevent unsafe sex. Remember the pandemic? Telling Americans to wear masks at all times undermined public health officials’ ability to convince them to wear masks when it really mattered.

Digital absolutism also risks blinding us to other causes — and solutions. In 1960s Britain, annual suicide rates plummeted. Many believed the drop was due to improved antidepressant medications or life just getting better. They weren’t looking in the right place. The phaseout of coal-based gas for household stoves blocked the most common method of suicide: gas poisoning. Means restriction, because it gives the despairing one less opportunity for self-harm, has since become a key strategy for suicide prevention.

“I’ve been struggling to figure out,” Haidt writes, “what is happening to us? How is technology changing us?” His answer: “The phone-based life produces spiritual degradation, not just in adolescents, but in all of us.” In other words: Choose human purity and sanctity over the repugnant forces of technology. This dialectic is compelling, but the moral matrix of the problem — and the scientific foundations — are more complex.

Yes, digital absolutism might convince policymakers to change laws and increase regulation. It might be a wake-up call for some parents. But it also might backfire, plunging us into defense mode and blocking our path of discovery toward healthy and empowered digital citizenship.

THE ANXIOUS GENERATION : How the Great Rewiring of Childhood Is Causing an Epidemic of Mental Illness | By Jonathan Haidt | Penguin Press | 385 pp. | $30

Inside the World of Gen Z

The generation of people born between 1997 and 2012 is changing fashion, culture, politics, the workplace and more..

For many Gen-Zers without much disposable income, Facebook isn’t a place to socialize online — it’s where they can get deals on items they wouldn’t normally be able to afford.

Dating apps are struggling to live up to investors’ expectations . Blame the members of Generation Z, who are often not willing to shell out for paid subscriptions.

Young people tend to lean more liberal on issues pertaining to relationship norms. But when it comes to dating, the idea that men should pay in heterosexual courtships still prevails among Gen Z-ers .

We asked Gen Z-ers to tell us about their living situations and the challenges of keeping a roof over their heads. Here’s what they said .

What is it like to be part of the group that has been called the most diverse generation in U.S. history? Here is what 900 Gen Z-ers had to say .

Young people coming of age around the world are finding community in all sorts of places. Our “Where We Are” series takes you to some of them .

A visually arresting graphic novel reflects on the Holocaust’s long shadow

In ‘victory parade,’ leela corman captures the pain carried from one generation to the next.

It’s 1943 in Brooklyn. Women are working in the Brooklyn Navy Yard while the men are fighting the Nazis in Germany. In between raising her daughter, Eleanor, and her job as a welder, Rose Arensberg finds company in George Finlay, a disabled war veteran. Ruth, a Jewish refugee whom Rose took in as a child, is laid off from her job at the Yard after defending herself from sexual harassment and eventually finds her way into the world of women’s wrestling. Across the Atlantic, Allied soldiers liberate concentration camps, witnessing indescribable horrors. When they come back, they are never the same.

“ Victory Parade ” is a graphic novel about the intergenerational suffering and personal demons that rise out of the mass trauma of genocide. Love, longing, loneliness and ghosts animate the narrative as the characters slide between reality and dream while moving from Brooklyn to Buchenwald, and briefly to Berlin. Its author and artist, Leela Corman, is descended from a family of Holocaust survivors, and she creates a cast of characters who can go for months without hearing from their families in Europe, only to hear rumors about trains to Warsaw and then nothing. The women — Jewish, immigrants, refugees — often find themselves in marriages where they are abused or cheated on, and in illicit relationships where they find love. But in each other, they find camaraderie.

Corman’s story inhabits the comics medium so fully that its formal ingenuity may not be immediately apparent. “Victory Parade” is meant to unsettle, to convey a semblance of the brutish violence to which the characters are subjected. Visible sketch layers, unerased lines and deliberate unevenness contribute to the ambiance. Splotches of paint metamorphose into silhouettes of battle tanks that bleed, time periods coalesce, trauma spills over across continents, and narrative disintegration mimics the war-torn society. We move from person to person, dream to dream. Corman’s painterly style ebbs and flows, restrained at places and maximalist at others. Visibly textured watercolor with blooms, backruns and crackles made out of ink makes us linger on the physicality of her brushstrokes.

Corman is not concerned with easy legibility. Her symbolism is both obvious and obscure, but deeply evocative either way. Disembodiment becomes a recurring theme. Early in the story, a bath scene disintegrates into a nightmare made up of severed fingers and limbs, followed by a sequence of Rose drowning, being pulled into a nameless abyss.

Yet there is also tenderness, especially in Eleanor’s relationship with Ruth, her not-sister, not-cousin, who has been around for as long as she can remember. Or in the image of a window, lighted with a strikingly luminescent yellow and enveloped by jet-black darkness, which precedes a candid conversation between Rose and George about their feelings for each other, despite the doomed nature of their relationship.

“Victory Parade” is a moving map of war and genocide’s labyrinthine consequences for survivors across generations. In death, there is some measure of release from human cruelty, and even vengeance on those who perpetrated it. When American soldiers liberate Buchenwald, a ghost drives an SS officer (who had used the skull of the specter as a paperweight) from his hiding spot to the yard, where newly freed prisoners hang him in synchronized glee. The sequence is styled after Busby Berkeley’s musicals, with their dancers bursting inward and outward in kaleidoscopic Technicolor. There’s something choreographic about Corman’s use of space and time. Her characters — dead and alive — have tenuously connected stories, but there’s a method to the madness and synchronicity in the chaos. An unnamed German veteran (probably from WWI) on the sidewalks of a busy street in Berlin reminds us of George back home. Those who have been wounded, physically and otherwise, are left to fend for themselves everywhere. There is no closure in “Victory Parade,” no real triumph for the winners or the liberated.

Ruth survives a childhood in Nazi Germany, only to get profiled as a “Kraut” in Brooklyn. Unsure of her place in postwar Brooklyn, little Eleanor wonders what happened to her not-sister, not-cousin, why her parents — always fighting in their war-haunted home — never talk about Ruth. Her questions about Germany and the trains likewise go unanswered, though her father has witnessed the horrors perpetrated at the end of the tracks.

For all the trauma that the characters endure, they seldom talk to each other about it. They cope in isolation, and we witness them in their ruins. Corman conjures their tortured interior reality through references to Greek tragedies, homages to 20th-century painters and other intertextual visual allusions. We find out through an Otto Dix painting called “The Skat Players,” for example, that Ruth’s mother was forced into sex work. The original Dix image centers three German military officers with prominent scarring and prosthetics. In Corman’s iteration, there’s a woman, undressed, pouring alcohol for the men.

Elsewhere, Rose and George read Sophocles’ play “Philoctetes” in bed. Philoctetes, while traveling to the Trojan War, is bitten in the leg by a serpent sent by an angry deity. The cursed and unhealable wound leaves him in constant agony and releases an unbearable stench, which causes his fellow Greeks to abandon him on the island where the bite occurs. Eventually the Greeks discover that they need the bow of Heracles, which Philoctetes possesses, to win the war, and return to get it from him, first by trickery and then by pleading. Though originally reluctant, Philoctetes agrees when the now-divine Heracles returns to command him to do so, promising future healing. As is the case for Corman’s characters, though, true restoration is deferred, perhaps indefinitely.

“Victory Parade” is not an easy comic to digest, and perhaps even likely to throw off some readers. But it is one that thoroughly exploits the medium’s potential to visualize the unspeakable. The final scene, where Sam, Rose’s husband (although it could be anybody else), picks up a passenger in his yellow cab, reinforces the isolation of mass trauma. The passenger, a weary veteran from the Pacific theater, asks Sam whether he saw any “real action” during his time in Germany. Sam responds, “Nothing special.” But the exhaust fumes trailing behind the car silently carry the remains of the dead.

Kay Sohini is a writer and cartoonist based in New York. Her graphic novel “This Beautiful, Ridiculous City” is set to be published this year.

Victory Parade

By Leela Corman

Shocken. 173 pp. $29

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Mindbourne Mathematics Grade 10 Textbook and Workbook
Mathematics
Oxford University Press :: Oxford Successful Mathematics Grade 5
A Complete Mathematics Course for Secondary School Book 1
NEW Pearson Mathematics for the IB Middle Years Programme Year 1 ( Pri

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Topics in Applied Mathematics and Modeling: Concise Theory with Case Studies. Oscar Gonzalez. March 30, 2024. Mathematical Modeling, Textbooks, Perturbation Theory, Dynamical Systems, Calculus of Variations.
All The Math Books You'll Ever Need (Updated 2023)
Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry. by George F. Simmons. Review: George Simmons takes newbies and out of practice scholars alike, through a refreshing crash course in three basic mathematical practices (Geometry, Algebra and Trigonometry) in their simple but often hated form.
OpenStax
OpenStax offers free college textbooks for all types of students, making education accessible & affordable for everyone. ... About us Team Research K12 Books & Resources Institutional Partnerships Technology ... Menu. Subjects. All Business College Success Computer Science Humanities Math Nursing Science Social Sciences. View Spanish. View ...
(PDF) A review and content analysis of mathematics textbooks in
According to the findings of this study, the two text books evaluated elevate critical thinking features such as interpretation, analysis, evaluation, explanation, inference, and self-regulation ...
AMS :: Mathematical Reviews
Mathematical Reviews. ®. /MathSciNet. ®. Since 1940, Mathematical Reviews ® (MR) has served researchers and scholars in the mathematical sciences by providing timely information on peer-reviewed articles and books. MathSciNet®, the electronic version of MR, presents a fully searchable database with many tools designed to help navigate the ...
What Is Mathematics? An Elementary Approach to Ideas and Methods
The book is wonderful because it's not a typical "For Dummies" book. It has some real mathematics in it, and many of the theorems and proofs are mathematical masterpieces that every Ph.D. student should know. If you want to master the basics, I would use this book along with your text books. This book gives a really good overview of many ...
Discrete Mathematics: An Open Introduction
Discrete Mathematics: An Open Introduction is a free, open source textbook appropriate for a first or second year undergraduate course for math majors, especially those who will go on to teach. The textbook has been developed while teaching the Discrete Mathematics course at the University of Northern Colorado. Primitive versions were used as the primary textbook for that course since Spring ...
Fundamentals of Mathematics
About the Book. Fundamentals of Mathematics is a work text that covers the traditional study in a modern prealgebra course, as well as the topics of estimation, elementary analytic geometry, and introductory algebra. It is intended for students who: This text will help the student devlop the insight and intuition necessary to master arithmetic ...
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Mathematics books, ebooks, and academic textbooks
Cambridge Mathematical Textbooks is a program of undergraduate and beginning graduate level textbooks for core courses, new courses, and interdisciplinary courses in pure and applied mathematics. These texts provide motivation with plenty of exercises of varying difficulty, interesting examples, modern applications, and unique approaches to the ...
Calculus Online Textbook
Textbook. First published in 1991 by Wellesley-Cambridge Press, this updated 3rd edition of the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor's Manual and a student Study Guide.
Best Books About Mathematics (412 books)
Books about all areas of mathematics including the history of mathematics, recreational mathematics, and any other book exploring the wonders of math. flag All Votes Add Books To This List. 1: Gödel, Escher, Bach: An Eternal Golden Braid by. Douglas R. Hofstadter. 4.29 avg rating — 49,310 ratings. score: 16,313, ...
10 Best Mathematics Books to Read in 2023
3. "The Joy of X: A Guided Tour of Math, from One to Infinity" by Steven Strogatz "Mathematics, more than any other art form, reveals the structure of things." "The Joy of X" is a contemporary masterpiece by Steven Strogatz that explores mathematics in an engaging and accessible manner.
Book reviews
Book reviews Share this page. June 2000. ... The author has created a textbook based on real lectures given to American undergraduates that neatly straddles the divide between school and college mathematics. The chapters are self contained and full of extensive explanation, mathematical biographies, worked examples, and a huge number of ...
EdReports
Explore our latest reviews of K-12 math, English language arts, and science instructional materials. 2024. i-Ready Classroom Mathematics. Subject. Math. View Report. 2023 ... it's easy to think that receiving the textbooks you've chosen is the end of the process. But really it's only the beginning.
Cambridge Mathematical Textbooks
About Cambridge Mathematical Textbooks. Cambridge Mathematical Textbooks is a program of undergraduate and beginning graduate level textbooks for core courses, new courses, and interdisciplinary courses in pure and applied mathematics. These texts provide motivation with plenty of exercises of varying difficulty, interesting examples, modern ...
Mathematical Reasoning: Writing and Proof, Version 2.1
The textbook, like most undergraduate mathematics textbooks, is partitioned into chapters (organized by major topic, e.g., functions) and sections (smaller topics falling under the main topic's umbrella, e.g., bijections, composition, inverse functions). Each section is an appropriate length to be covered in one standard 75 minute class meeting.
OpenStax
With philanthropic support, this book is used in 739 classrooms, saving students 38,783,879 dollars this school year. Learn more about our impact and how you can help. Study algebra online free by downloading OpenStax's College Algebra 2e book and using our accompanying online resources including an algebra study guide.
13 Best Mathematics Books for Every Level
Some of the most popular textbooks include " Calculus: Early Transcendentals " by James Stewart, " Linear Algebra and Its Applications " by Gilbert Strang, and " Introduction to Probability " by Sheldon Ross. But textbooks aren't the only way to explore the world of mathematics. Memoirs and biographies of famous mathematicians ...
Metamathematics: Foundations & Physicalization
"What is mathematics?" is a question that has been debated since antiquity. This book presents a groundbreaking and surprising answer to the question—showing through the concept of the physicalization of metamathematics how both mathematics and physics as experienced by humans can be seen to emerge from the unique underlying computational structure of the recently formulated ruliad.
Laugh Riot
Fintan O'Toole is the Advising Editor at The New York Review and a columnist for The Irish Times. His most recent book, We Don't Know Ourselves: A Personal History of Modern Ireland , was published in the US last year.
'I Cheerfully Refuse' by Leif Enger book review
When I first read George Orwell's terrifying book in the 1970s, I worried we'd never make it to 1984, let alone to the 21st century. But now that Leif Enger has written an apocalyptic novel ...
Radiant by Brad Gooch review
The stars of the time pop in and out of this book: Grace Jones and dancer Bill T Jones, whose skin he painted, the former for a Robert Mapplethorpe portrait; he even struck up an unlikely ...
8 New Books We Recommend This Week
Suggested reading from critics and editors at The New York Times. Our fiction recommendations this week include a "gleeful romp" of a series mystery, along with three novels by some heavy ...
Mathematics for Elementary Teachers
About the Book. This book will help you to understand elementary mathematics more deeply, gain facility with creating and using mathematical notation, develop a habit of looking for reasons and creating mathematical explanations, and become more comfortable exploring unfamiliar mathematical situations. The primary goal of this book is to help ...
Book Review: New Horror Books
Our columnist reviews this month's haunting new releases. By Gabino Iglesias Gabino Iglesias is a writer, editor, literary critic and professor. He is the Bram Stoker and Shirley Jackson award ...
Book Review: 'The Anxious Generation' by Jonathan Haidt
But this rarely comes through in the book. The final sections offer advice for reducing harmful, predatory aspects of technology and helping parents, educators and communities become more gardener ...
Review: 'Victory Parade' by Leela Corman
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