math 230 homework 6

• Basic probability
• Stochastic Calculus
• Characteristic functions (aka Fourier Transforms)
• Counting some Examples
• Generating Functions and Limit Theorems
• Collected HW for Math 230 from various years
• Style Guide
• Bibliography

Here are the homework assignments from two different years. I think I was most happy with Spring 2015. Notice there were less HW in 2013 as I fell behind in making assignments at some point that year.

• F13, S15, F22 : [Taking classes ], [ Arithmetic sum ]  [ Coin Flips: describe events ] [ Calculus: Differentiation] [ Calculus: Infinite Sums ] [ Calculus: Areas ] [ Calculus : Exponentials integrals ] [ Practice with inclusion, exclusion ] [ Random Letters ]
• F13, S15., F22 : [ Finding a good phone ] [ Balls in a Box: Counting [ Polya’s urn ] [ Conditional risk ] [ The chance of being English ] [ Chance of an Acciden t] [ Cards: Independence ]
• S15, F22: [ Independence of two hearts ? ] [ Picking a box then a ball ] [ Human error is the most common kind ] [ Airline Overbooking ] [ Drawing tickets ] [ Coin Flips: typical behavior ] [ Leukemia Test ] [ School admissions ]
• F13: [ Defective Machines ] [ Approximation: Rare vs Typical ]  [ Airline Overbooking ] [ Coin Flips: typical behavior ] [ Leukemia Test ] [ School admissions ]
• S15: [ Defective Machines ] [ Cards again ] [ Approximation: Rare vs Typical ] [ Poker Hands: counting ] [ The matching problem ] [ Leukemia Test ]
• F13: [ Ordered Random Variables ]  [ Coin tosses: independence and sums ] [ Poker Hands: counting ] [ Dice rolls: Explicit calculation of max/min ] [ Blocks of Bernoulli Trials ] [ The matching problem ]
• F22: [Which deck is rigged ?]   [ Defective Machines ]  [ Cards again ] [ Approximation: Rare vs Typical ]  [ Poker Hands: counting ]  [ The matching problem ]
• S15: [ Indicator Functions and Expectations – II ] [ Coin tosses: independence and sums ] [ Expected Value and Mean Error ] [ Putting expectations together ] [ Expection and dice rolls ] [ Dice rolls: Explicit calculation of max/min ] [ Blocks of Bernoulli Trials ]
• F13: [ Overloading an Elevator ] [ Indicator Functions and Expectations – II ]  [ Random Digit ] [ A simple mean calculation ] [ Expected Value and Mean Error ]  [ Stuffing Envelopes ] [ Putting expectations together ] [ Expection and dice rolls ]
• [Overloading an Elevator] [Indicator Functions and Expectations – II]
• S15: [ Overloading an Elevator ] [ Random Digit ] [ Games with Black and White Balls ] [ Expectation of geometric distribution ] [ Basic Random Walk ] [ Stuffing Envelopes ]
• F13: [ Approximating sums of uniform random variables [ geometric probability: marginal densities ]  [ probability density example ] [ Raindrops are falling ] [ Mixing Poisson Random Variables 1 ] [ Random Errors in a Book ] [ Games with Black and White Balls ] [ Expectation of geometric distribution ]
• S15: [ Handing back tests ] [Up by two] [ Population ] [ Raindrops are falling ] [ Mixing Poisson Random Variables 1 ] [ Random Errors in a Book ]
• F13: [ Calls arriving ] [ Tail-sum formula for continuous random variable ] [ Min, Max, and Exponential ]  [Change of Variable: Gaussian ] [ Change of variable: Weibull distribution ] [ Change of Variable: Uniform ]
• S15: [ Benford’s Law ] [ Conditioning a Poisson Arrival Process ] [ Calls arriving ] [ Approximating sums of uniform random variables ] [ geometric probability: marginal densities ] [ probability density example ]
• F13: [ Difference between max and min ] [ A Joint density example II ] [ Closest Point ][ A joint density example I ][ Point of increase ][ An example of min and change of variable ] [ Box-Muller I ]
• S15: [ Closest Point ] [ An example of min and change of variable ] [ Min, Max, and Exponential ] [ Order statistics I ] [ Change of Variable: Gaussian ] [ Change of variable: Weibull distribution ] [ Change of Variable: Uniform ]
• F13: [ conditional densities ] [ Expected max/min given min/max ] [ Beta-binomial ] [ Conditioning and Polya’s urn ] [ Expectation of hierachical model ] [ Expectation of mixture distribution]
• S15: [ Joint, Marginal and Conditionin g] [ A joint density example I ] [ conditional densities ] [ Difference between max and min ] [ Joint Density of Arrival Times ] [ Conditioning and Polya’s urn ] [ Expectation of hierachical model ]
• F13: [ Selling the Farm ] [ Computers on the Blink ] [ Basic Markov Chains ]
• F15: [ Selling the Farm ] [ Computers on the Blink ] [ Point of increase ] [ Expectation of mixture distribution]

Math 230: Abstract and Discrete Mathematics

Homework 2 consists of the following exercises. A quiz selecting 2 or 3 of these exercises will be given on Tuesday September 13: 8.2, 8.4, 8.8, 8.10, 8.15. 9.2, 9.5, 9.7, 9.9, 9.11. 10.1, 10.4, 10.9, 10.12, 10.13. 11.1, 11.2, 11.4, 11.7. 12.1, 12.5, 12.9, 12.12, 12.21, 12.24, 12.30. Homework 2 Solutions . Solutions to 10.12 and 10.13 .

Homework 3 consists of the following exercises. A quiz selecting 2 or 3 of these exercises will be given on Monday October 3: Read Sections 17 and 22. 17.3, 17.4, 17.5, 17.8, 17.11, 17.16, 17.21, 17.37. 22.4, 22.5, 22.6, 22.7. Solutions .

Homework 4 consists of the following exercises. A quiz selecting 2 or 3 of these exercises will be given on Wednesday October 19: Read Sections 14, 15 and 16. 14.1, 14.3 (no need to prove here), 14.5, 14.6, 14.10, 14.17 (proofs required in 14.6 and 14.10). 15.1, 15.3 (no proof required here), 15.7, 15.8, 15.14, 15.15. 16.1, 16.10, 16.15. Solutions .

Homework 5 consists of the following exercises. A quiz selecting 2 or 3 of these exercises will be given on Wednesday October 26: 22.16, 22.17 20.4, 20.5, 20.9, 20.10, 20.13. 21.3, 21.7, 21.9. Solutions .

Homework 6 consists of the following exercises. A quiz selecting 2 or 3 of these exercises will be given on Friday November 11: 24.1, 24.2, 24.5, 24.6, 24.8, 24.14, 24.16, 24.17, 24.20. Solutions . (Note: Solutions to 24.6 have some errors. 24.6a should be "all the odd integers". 24.6f should be "[0,1]"

Homework 7 consists of the following exercises. A quiz selecting 2 or 3 of these exercises will be given on Friday November 18: 25.2, 25.6, 25.7, 25.9, 25.13, 26.7, 26.9, 26.10. Also do 26.1 to practice. Solutions .

Homework 8 consists of the following exercises. A quiz selecting 2 or 3 of these exercises will be given on Friday December 2: Homework 8 Homework 8 Solutions .

Homework 9 consists of the following exercises. A quiz selecting 2 or 3 of these exercises will be given on Wednesday December 7: 54.1, 54.2, 54.3, 54.4, 54.8. 55.1, 55.2, 55.5, 55.7. 56.1, 56.5. Suggested extra work : After 54.4, think about the width of the poset defined in 54.3 for any n (Hint: Consider n even and n odd separately). 54.9 is a very good exercise to get more practice with posets. 56.7 is "alphabetical" ordering in disguise (this ordering has the more technical name of "lexicographic ordering"). Solutions .

Please ensure that your password is at least 8 characters and contains each of the following:

• a special character: @$#!%*?&

Programming

Math 230 : fall 2023, course description.

This course serves as an introductory programming course for mathematics majors. Basic programming techniques for solving problems typically encountered by mathematicians will be developed. The course covers basic procedural techniques such as algorithms, variables, input/output, data types, selection, iteration, functions, and graphing. Good programming and commenting practices will be emphasized.

Cesar Aguilar , South Hall 325A

Office Hours

Tue 8:30-9:30, 10:45-11:45 Thu 10:45-11:45

Class Meetings

Tue & Thu, 9:30-10:45, South Hall 336

Tuesday, December 19, 3:30-6:00PM, South Hall 336

Textbook and Resources

• Automate the Boring Stuff with Python This is the main textbook
• Udemy Course
• Python Essentials Labs
• Whirlwind Tour of Python (good book)
• Python Data Science Handbook (good book)
• Official Python Tutorial

Student File Upload

The current week content will be displayed here during the semester. For now, see the Schedule tab.

• Introduction
• Data Types & Variables
• A Small Program
• Booleans, Comparison Operators, Boolean Operators
• if/elif/else
• while Loops
• Importing Modules (Ignore material on installing modules and the pyperclip module)
• Defining Functions
• Global and Local Scope
• Catching Errors
• Guess the Number Game
• More Function Basics with Mosth
• Looping Over Lists
• List Methods
• More List Basics with Mosh
• More List Methods with Mosh
• More Tuples with Mosh
• Slicing with Lists
• List Comprehensions
• Textbook - Chapter 5
• Dictionaries in Python - realpython.com
• Udemy Course - Section 7
• Textbook - Chapter 6
• Strings in Python - realpython.com
• Udemy Course - Section 8
• Textbook - Chapter 9
• Reading and Writing Files - realpython.com
• state_capitals.csv
• Udemy Course - Section 11
• student_gpas.csv
• student_names.csv
• leading_nba_scorers.csv
• Introduction to NumPy
• Matrices & Looping
• Universal Methods
• Python Essentials Lab 5
• np.linspace() - realpython.com
• Basic Plotting
• Saving & Subplots
• Review of Riemann Sums (watch first)
• Coding Examples

Learning Outcomes

Upon successful completion of MATH 230 - Programming, a student will be able to:

Grading Scheme

Below is the tentative course grading scheme. The grading scheme may change during the semester at the discretion of the instructor. Any changes to the grading scheme will be announced in class before the final exam. If homework assignments are done in groups, then a student must achieve a passing grade in all individual assessments (e.g., tests and final exam) to pass the course.

Tests and Exam

There will be 3-4 tests scheduled evenly throughout the semester. The final exam is scheduled for Tuesday, December 19, 3:30-6:00PM, South Hall 336. The final exam will be cumulative, that is, any topic covered in the course could be tested in the final exam. There will be no make-up for a missed test or final exam under any circumstances. If a student misses a test and can present evidence of an extenuating circumstance then the weight of the missed test will be redistributed to the final exam weight. Having the cold or flu is not an extenuating circumstance. Examples of extenuating circumstances include a medical emergency, a serious prolonged illness, or the death of a member of your immediate family.

There will be approximately 10-12 homework assignments throughout the semester. You will be given approximately 5 days to submit your solutions to the homework problems. Homework solutions should be written in Python using a .py file extension and your .py file should be uploaded using the file upload link. I encourage you to collaborate with your colleagues on your assignments/labs but your final submitted work should be your own (see Academic Dishonesty statement below).

There are two recommended textbooks for the course: Automate the Boring Stuff with Python and Think Python . Both textbooks are free. I will primarily reference the first book (Automate the Boring Stuff with Python) and you may want to enroll in the Udemy Course that accompanies the textbook. The first 15 videos of the course can be found on YouTube . To view the remaining videos you would need to enroll in the Udemy course.

We will be using the general purpose programming language Python for this course. Download and install Python here .

Office Hours and Math Learning Center

I encourage you to come to my office (South Hall 325A) whenever you are having trouble with any part of the course material, seeking academic advice, or you just want to chat about mathematics in general. If you want to meet with me outside of my office hours, you will need to make an appointment, preferably via email. I also encourage you to visit the Math Learning Center located in South Hall 332 where you can receive free tutoring on a walk-in basis by highly qualified upper level students. Access to in-person office hours and to the MLC will depend on social distancing guidelines set by the College.

Email Communication

I will do my best to reply to student email regarding the logistics of the course within 24 hours during the working week (Mon-Fri). However, due to the potential large volume of emails, inquiries regarding homework problems and/or specific course content should be made during office hours or after class.

Academic Dishonesty and Plagiarism

Please read, and follow, Geneseo's Academic Dishonesty and Plagiarism policy . Below is the definition of plagiarism and its consequences as described in SUNY Geneseo's Academic Dishonesty and Plagiarism statement:

Plagiarism is the representation of someone else's words or ideas as one's own, or the arrangement of someone else's material(s) as one's own. Such misrepresentation may be sufficient grounds for a student's receiving a grade of E for the paper or presentation involved or may result in an E being assigned as the final grade for the course.

If there is sufficient evidence of academic dishonesty on a homework assignment, all students involved will receive a zero score on the homework assignment and I will provide the department chairperson, the dean of academic planning and advising, and the student(s) with a written report of the violation, the penalty imposed and the counseling provided to the students involved. A second instance of academic dishonesty on a homework assignment will result in a final grade of E for the course for all students involved. Academic dishonesty on a test/final exam will result in a final grade of E for the course.

Academic Accommodations

SUNY Geneseo is dedicated to providing an equitable and inclusive educational experience for all students. The Office of Accessibility (OAS) will coordinate reasonable accommodations for persons with disabilities to ensure equal access to academic programs, activities, and services at Geneseo.

Students with approved accommodations may submit a semester request to renew their academic accommodations. Please visit the OAS website for information on the process for requesting academic accommodations .

Questions? Contact the OAS by email, phone, or in-person:

Office of Accessibility Services Erwin Hall 22 585-245-5112 [email protected]

MATH 230 Fall 2021

CALCULUS II (4 semester hours)   Continuation of MATH 229.

PREREQUISITE:   MATH 229 with a grade of C or better.

COURSE OBJECTIVES:

• To understand and connect concepts of the calculus with real world problems and other scientific disciplines.
• To value mathematics and develop an ability to communicate mathematics, both in writing and orally.
• To develop mathematical reasoning, and an ability to solve problems.
• To attain computational facility in integral calculus, and sequences and series.

TEXT:   Calculus (eighth edition) by James Stewart, published by Cengage Learning.

Some additional references:

• Thomas and Finney,   Calculus and Analytic Geometry.
• Edwards and Penney,   Calculus and Analytic Geometry.
• Swokowski,   Calculus with Analytic Geometry.
• Leithold,   The Calculus with Analytic Geometry.

SYLLABUS:   Suggested lecture pace .

HOMEWORK:   Suggested homework exercises .

GRADING:   Grades will be assigned on the basis of 650 points, as follows:

• 3 hour exams worth 100 points each
• Quizzes and/or homework, 150 points total
• Final exam, 200 points

GRADING SCALE:   The grading scale for this class will at least guarantee the following:

• 85% for an A
• 75% for a B
• 60% for a C
• 50% for a D

EXAMS:   The first and third hour exams will be done on a section-by-section basis. See your instructor for details.

MIDTERM and FINAL EXAMS:   The second exam (midterm) is scheduled for   6:00-6:50 PM, Wednesday, October 13, 2021 .

This will be a departmental exam and all sections of the course will take the same second exam at the same time.

The Final Exam is scheduled for   12:00-1:50PM, Thursday, December 9, 2021   The final exam will be a comprehensive, departmental examination.

All sections of this course will take the same final exam at the same time. The final exam will be comprehensive.

Please note that these exams will likely NOT be in your regular classroom. Room assignments from the university are usually made one to two weeks before the exams.

PREVIOUS MID-TERM EXAMS: Note that the course changes and so do the exams. Our goal is to help you learn the material in Calculus 2, not specifically to prepare you for the midterm exam. Midterm Exam (Spring 2021) MidtermExam (Spring 2020) Midterm Exam (Spring 2019) Midterm Exam (Fall 2019)

PREVIOUS FINAL EXAMS:   Note that the course changes and so do the exams. Our goal is to help you learn the material in Calculus 2, not specifically to prepare you for the final exam. Final Exam (Spring 2021) Final Exam (Spring 2020) Final Exam (Spring 2019) Final Exam (Fall 2019)

CALCULATORS:   Students may consider having a graphing calculator with roughly the capabilities of the TI-83. You will find this useful for investigating the concepts of the class, so you can experiment with additional examples. You may also want to verify parts of your homework calculations.

On exams and quizzes, however,   no calculator with graphing capability will be allowed.   A scientific calcultor can be used, however.

RESOURCES ON THE WEB: Understanding Mathematics: a study guide , from the University of Utah. Calculus resource list from the   Math Archives , from the University of Tennessee at Knoxville. Symbolic calculators which will compute   derivatives   and   integrals .

ACADEMIC CONDUCT:   Good academic work must be based on honesty. The attempt of students to present as their own work that which they have not produced is regarded by the faculty and administration as a serious offense. Students are considered to have cheated if they copy the work of another during an examination or turn in a paper or an assignment written, in whole or in part, by someone else. Students are guilty of plagiarism, intentional or not, if they copy material from books, magazines, or other sources without identifying and acknowledging those sources or if they paraphrase ideas from such sources without acknowledging them. Students guilty of, or assisting others in, either cheating or plagiarism on an assignment, quiz, or examination may receive a grade of F for the course involved and may be suspended or dismissed from the university.

DRC STATEMENT:   Northern Illinois University is committed to providing an accessible educational environment in collaboration with the Disability Resource Center (DRC). Any student requiring an academic accommodation due to a disability should let his or her faculty member know as soon as possible. Students who need academic accommodations based on the impact of a disability will be encouraged to contact the DRC if they have not done so already. The DRC is located in Suite 180 of the Campus Life Building, and can be reached at 815-753-1303 or [email protected].

COVID:   If you have symptoms of COVID-19, stay home and contact NIU’s COVID helpline (815-753- 0444) to report your symptoms and get advice. Inform your instructor promptly to discuss accommodation options.

Read more about Protecting the Pack at   Protecting the Pack

EXTRA PRACTICE:   Note that many of the exercises below are unchanged from previous semesters, so they have "Spring 2012" in the title. Review of the Definite and Indefinite Integral Volumes by Slicing Solids of Revolution l'Hopital's Rule Review of the Definite and Indefinite Integral Areas Between Curves Approximate Integration Volumes, Part I Volumes, Part II Arc lengths and Surface Area The Natural Logarithm Inverse Functions The Exponential Function General Exponential and Logarithm Functions Inverse Trigonometric Functions Limits and L'Hopital's Rule Sequences Integration by Parts Trigonometric Integrals Trigonometric Substitutions Partial Fractions Integration Recap Improper Integrals Power Series Taylor Polynomials Taylor Series Infinite Series The Integral Test More Comparison Tests for Series Alternating Series and Absolute Convergence The Ratio and Root Tests Radius and Interval of Convergence

ADVICE:   Perhaps the single most important factor in your success in this course is your   study habits.   This is a fast paced course, with little room for catching up if you fall behind. Successful students have good time management skills. Set aside at least three nights a week to study the topics and work the homework problems. Do not wait until exam time to try to learn new material.

Learn mathematics like you would learn a language. Work on the concepts until they make sense. Don't just memorize facts and then forget them a few weeks later. You will need to know this stuff for Calculus III and other courses.

Master each homework problem---beyond just getting a correct answer. Be aware of your mistakes in algebra and trigonometry.

In summary, to succeed in this course:

• read the book and the lecture notes;
• work the homework;
• always come to class, and while you're there, think, listen, and ask questions.