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Applied Mathematics

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Undergraduate Program

The Applied Mathematics concentration consists of a broad undergraduate education in the mathematical sciences, especially in those subjects that have proved vital to an understanding of problems arising in other disciplines, and in some specific area where mathematical methods have been substantively applied. For concentrators, a core learning objective is building and demonstrating foundational knowledge in computation, probability, discrete, and continuous mathematics through the successful completion of the foundation and breadth courses. Students are also eligible to apply for an A.B./S.M. degree program.

Harvard School of Engineering offers a Doctor of Philosophy (Ph.D.) degree in Applied Mathematics. Doctoral students may earn the masters degree en route to the Ph.D. Students are drawn to Applied Mathematics by the flexibility it offers in learning about how to apply mathematical ideas to problems drawn from different fields, while remaining anchored to empirical data that drive these questions. Research and educational activities have particularly close links to Harvard’s efforts in Mathematics, Economics, Computer Science, and Statistics. Graduates go on to a range of careers in industry, academics, to professional schools in business, law, medicine, among others. All Ph.D.s are awarded through the Harvard Graduate School of Arts and Sciences.

Applied Mathematics

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Applied Mathematics is an area of study within the Harvard John A. Paulson School of Engineering and Applied Sciences. Prospective students apply through Harvard Griffin GSAS; in the online application, select  “Engineering and Applied Sciences” as your program choice and select “PhD Applied Math” in the Area of Study menu.

Applied Mathematics at the Harvard John A. Paulson School of Engineering is an interdisciplinary field that focuses on the creation and imaginative use of mathematical concepts to pose and solve problems over the entire gamut of the physical and biomedical sciences and engineering, and increasingly, the social sciences and humanities

Working individually and as part of teams collaborating across the University and beyond, you will partner with faculty to quantitatively describe, predict, design and control phenomena in a range of fields. Projects current and past students have worked on include collaborations with mechanical engineers to uncover some of the fundamental properties of artificial muscle fibers for soft robotics and developing new ways to simulate tens of thousands of bubbles in foamy flows for industrial applications such as food and drug production.

Graduates of the program have gone on to a range of careers in industry in organizations like the Kingdom of Morocco, Meta, and Bloomberg. Others have secured faculty positions at Dartmouth, Imperial College in London, and UCLA.

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GRE General:  Not accepted

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Lauren K. Williams

Dwight Parker Robinson Professor of Mathematics at Harvard and Sally Starling Seaver Professor at the Radcliffe Institute Science Center Room 510, Cambridge MA 02138 e-mail: williams @ math . harvard.edu pronouns: she/her/hers

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Mathematics for Teaching Master’s Degree Program

From Harvard-trained faculty, you'll learn new strategies that will dramatically improve your ability to teach.

Online Courses

11 out of 12 total courses

On-Campus Experience

One 3-week summer course

$3,220 per course

Program Overview

Through the master’s degree field in mathematics for teaching you:

  • Build deeper knowledge of mathematics content, with a particular focus on middle and high school math classrooms.
  • Learn tactics that can improve student motivation through interactive problem-solving activities.
  • Develop an enhanced understanding of what it means to learn math and where mathematical misconceptions and student confusion can occur.

Program Benefits

Customizable course curriculum and stackable certificates

A faculty of math instructors, many of who have earned PhDs in math from Harvard University and have taught at Harvard

Personalized academic & career advising

A capstone project or thesis option

Paid research opportunities

Harvard Alumni Association membership upon graduation

Customizable Course Curriculum

Our curriculum is flexible in pace and customizable by design. You can study part time, choosing courses that fit your schedule and align with your career goals.

As you work through the 12-course program, you’ll focus on topics such as discrete mathematics, mathematical modeling, graph theory, and calculus. To further personalize your experience, you choose between a thesis or capstone track. Along the way, you can earn a graduate certificate in learning design and technology or math leadership .

11 Online Courses

  • Asynchronous and synchronous formats
  • Fall, spring, January, and summer options

Immersive 3-week summer course: Appraising and Reimagining Middle and High School Mathematics Education

Capstone or Thesis Track

  • Thesis: features a 9-month independent research project with a faculty advisor
  • Capstone: includes exploring contemporary research in math education and creating a state-of-the-art lesson plan

The path to your degree begins before you apply to the program.

First, you’ll register for and complete 2 required courses, earning at least a B in each. These foundational courses are investments in your studies and count toward your degree, helping ensure success in the program.

Getting Started

We invite you to explore degree requirements, confirm your initial eligibility, and learn more about our unique “earn your way in” admissions process.

A Faculty of Mathematics Experts

You’ll learn from Harvard faculty and industry leaders who will help you gain real-world perspectives. Our instructors are renowned experts in mathematics — and how to teach the subject. They bring a genuine passion for teaching, with students giving our faculty an average rating of 4.6 out of 5.

Andrew Engelward

Assistant Dean of Academic Programs at Harvard Extension School

Our Community at a Glance

Most of our graduates are full-time middle school and high school math teachers. A number of graduates work as math tutors, either running their own private tutoring companies, or employed by such programs as the Russian School of Mathematics.

In this program, you'll join a community of fellow educators, grow as a teacher, and,ultimately earn your Harvard University degree — a Master of Liberal Arts (ALM) in Extension Studies, Field: Mathematics for Teaching.

Download: Mathematics for Teaching Master's Degree Fact Sheet

Average Age

Average Courses Taken Each Semester

Work Full Time

Would Recommend the Program

Professional Experience in the Field

Pursued to Deepen Expertise

My coursework at Harvard Extension supported and helped me to develop the concept behind Educational Justice... My professors at Harvard have not only been huge fans of our efforts, they’ve helped me to grow and support the venture in a number of key areas from research to networking.

Tuition & Financial Aid

Affordability is core to our mission. When compared to our continuing education peers, it’s a fraction of the cost.

After admission, you may qualify for financial aid . Typically, eligible students receive grant funds to cover a portion of tuition costs each term, in addition to federal financial aid options.

Learning & Connection

Deep learning springs from human connection. That’s why we work so hard to bring people together — whether in a live virtual classroom or an in-person seminar on campus.

Our approach to online learning fosters interaction without sacrificing flexibility. Each week, you’ll engage with your instructor, participate in peer discussions, and receive one-on-one support from teaching staff—all from your home or office.

Stackable Certificates

  • Learning Design and Technology Graduate Certificate
  • Math Leadership Graduate Certificate

Harvard Division of Continuing Education

The Division of Continuing Education (DCE) at Harvard University is dedicated to bringing rigorous academics and innovative teaching capabilities to those seeking to improve their lives through education. We make Harvard education accessible to lifelong learners from high school to retirement.

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Course Listing

For a snapshot of courses being offered by Harvard School of Engineering over the next four years, visit our multi-year course planning  tool.

Computing with Python for Scientists and Engineers

APMTH 10 2024 Fall

Efthimios Kaxiras, Logan McCarty, Georgios Neofotistos Tuesday, Thursday 9:45am to 11:00am

This course is a systematic introduction to computing (with python and jupyter notebooks) for science and engineering applications. Applications are drawn from a broad range of disciplines, including physical, financial, and biological-epidemiological problems. The course consists of two parts: 1. Basics: essential elements of computing, including types of variables, lists, arrays, iteration and control flow (for, while loops, if statement), definition of functions, recursion, file handling and simple plots, plotting and visualization tools in higher dimensions. 2. Applications: development of computational skills for problem solving, including numerical and machine learning methods, and their use in deterministic and stochastic approaches; examples include numerical differentiation and integration, fitting of curves and error analysis, solution of simple differential equations, random numbers and stochastic sampling, and advanced methods like neural networks and simulated annealing for optimization in complex systems. Course work consists of attending lectures and labs, weekly homework assignments, a mid-term project and a final project; while work is developed collaboratively, coding assignments are submitted individually.

Solving and Optimizing

APMTH 22A 2024 Fall

Margo Levine Monday, Wednesday, Friday 9:00am to 10:15am

This course covers a combination of linear algebra and multivariate calculus with an eye towards solving systems of equations and optimization problems. Students will learn how to prove some key results, and will also implement these ideas with code.Linear algebra: matrices, vector spaces, bases and dimension, inner products, least squares problems, eigenvalues, eigenvectors, singular values, singular vectors.Multivariate calculus: partial differentiation, gradient and Hessian, critical points, Lagrange Multipliers.

Introduction to Applied Mathematics

APMTH 50 2024 Spring

Cengiz Pehlevan Monday, Wednesday, Friday 9:00am to 10:15am

This course provides an introduction to the problems and issues of applied mathematics, focusing on areas where mathematical ideas have had a major impact on diverse fields of human inquiry. The course is organized around two-week topics drawn from a variety of fields, and involves reading classic mathematical papers in each topic. The course also provides an introduction to mathematical modeling and programming.

APMTH 50 2025 Spring

Supervised Reading and Research

APMTH 91R 2024 Fall

Margo Levine

Supervised reading or research on topics not covered by regular courses. It cannot be taken as a fifth course. For AM concentrators, work may be supervised by faculty in other departments. For non-concentrators, work must be supervised by an AM faculty member. To be eligible to enroll in the course, students must receive the approval of the course instructors, including approved registration forms, prior to the start of the semester.

APMTH 91R 2024 Spring

Margo Levine, Sarah Iams

Supervised reading or research on topics not covered by regular courses.  For AM concentrators, work may be supervised by faculty in other departments.  For non-concentrators, work must be supervised by an AM faculty member.  Students must receive the approval of an (Associate) Director of Undergraduate Studies and obtain their signature before submitting AM91r forms.

APMTH 91R 2025 Spring

Thesis Research

APMTH 99R 2024 Fall

Provides an opportunity for students to engage in preparatory research and the writing of a senior thesis. Graded on a SAT/UNS basis as recommended by the thesis supervisor. The thesis is evaluated by the supervisor and by one additional reader.

APMTH 99R 2024 Spring

APMTH 99R 2025 Spring

Statistical Inference for Scientists and Engineers

APMTH 101 2024 Spring

Robert D. Howe Tuesday, Thursday 11:15am to 12:30pm

Introductory statistical methods for students in the applied sciences and engineering. Random variables and probability distributions; the concept of random sampling, including random samples, statistics, and sampling distributions; the Central Limit Theorem; parameter estimation; confidence intervals; hypothesis testing; simple linear regression; and multiple linear regression. Introduction to more advanced techniques as time permits.

APMTH 101 2025 Spring

Monday, Wednesday 3:45pm to 5:00pm

Complex and Fourier Analysis with Applications to Art, Science and Engineering

APMTH 104 2024 Fall

L Mahadevan Monday, Wednesday 10:30am to 11:45am

Complex analysis: complex numbers, functions, mappings, Laurent series, differentiation, integration, contour integration and residue theory, conformal mappings. Applications to visualization, art (especially M.C. Escher). Anamorphic images. Fourier Analysis: orthogonality, Fourier Series, Fourier transforms. Signal processing: sampling theorems (Nyquist, Shannon), fast Fourier transforms. Applications to image, audio analysis: filtering and deblurring.

Ordinary and Partial Differential Equations

APMTH 105 2024 Spring

Ordinary differential equations: power series solutions; special functions; eigenfunction expansions. Elementary partial differential equations: separation of variables and series solutions; diffusion, wave and Laplace equations. Brief introduction to nonlinear dynamical systems and to numerical methods.

APMTH 105 2025 Spring

Algebra for Models and Data

APMTH 106 2025 Spring

Anna Seigal Monday, Wednesday 3:00pm to 4:15pm

Introduction to abstract algebra and its applications. Rings, polynomials, and ideals. Factorization of matrices and polynomials. Applications to data analysis, statistical models, and optimization.

Graph Theory and Combinatorics

APMTH 107 2024 Spring

Adam Hesterberg Monday, Wednesday 11:15am to 12:30pm

Topics in combinatorial mathematics that find frequent application in computer science, engineering, and general applied mathematics. Course focuses on graph theory on one hand, and enumeration on the other. Specific topics include graph matching and graph coloring, generating functions and recurrence relations, combinatorial algorithms, and discrete probability. Emphasis on problem solving and proofs.

APMTH 107 2025 Spring

Leslie Valiant Tuesday, Thursday 9:45am to 11:00am

Nonlinear Dynamical Systems

APMTH 108 2024 Spring

Sarah Iams Monday, Wednesday, Friday 1:30pm to 2:45pm

An introduction to nonlinear dynamical phenomena, focused on identifying the long term behavior of systems described by ordinary differential equations. The emphasis is on stability and parameter dependence (bifurcations).  Other topics include: chaos; routes to chaos and universality; maps; strange attractors; fractals. Techniques for analyzing nonlinear systems are introduced with applications to physical, chemical, and biological systems such as forced oscillators, chaotic reactions, and population dynamics.

APMTH 108 2025 Spring

Introduction to PDEs and their Applications

APMTH 109 2024 Spring

Nick Trefethen Tuesday, Thursday 12:00pm to 1:15pm

This course serves as an introduction to partial differential equations (PDE) and their applications across the sciences. The course will familiarize students with the process of starting with a model, deriving the appropriate PDE, and solving it. Examples include wave equations, diffusion equations, the Laplace equation, and several nonlinear equations such as the Burgers and KdV equations. To build intuition for the analytical solutions, simple numerical simulations will be utilized.

APMTH 109 2025 Spring

Mathematical Modeling

APMTH 115 2024 Fall

Michael P. Brenner Tuesday, Thursday 10:30am to 11:45am

Abstracting the essential components and mechanisms from a natural system to produce a mathematical model, which can be analyzed with a variety of formal mathematical methods, is perhaps the most important, but least understood, task in applied mathematics. This course approaches a number of problems without the prejudice of trying to apply a particular method of solution. Topics drawn from biology, economics, engineering, physical and social sciences.

APMTH 115 2024 Spring

APMTH 115 2025 Spring

Zhiming Kuang Tuesday, Thursday 10:30am to 11:45am

Applied Linear Algebra and Big Data

APMTH 120 2024 Spring

Eli Tziperman Tuesday, Thursday 1:30pm to 2:45pm

Topics in linear algebra that frequently arise in applications, especially in the analysis of large data sets: linear equations, eigenvalue problems, linear differential equations, principal component analysis, singular value decomposition; data mining and machine learning methods: clustering (unsupervised learning) and classification (supervised) using neural networks and random forests. Examples from physical sciences, biology, climate, commerce, the internet, image processing, and more will be given. The approach is application-motivated, focusing on an intuitive understanding of the algorithms behind these methods obtained by analyzing small data sets. Programming assignments can be done using Python or Matlab.

APMTH 120 2025 Spring

Introduction to Optimization: Models and Methods

APMTH 121 2024 Fall

Melanie Weber Monday, Wednesday, Friday 12:00pm to 1:15pm

This course provides an introduction to basic mathematical ideas and computational methods for optimization. Topics include linear programming, integer programming, branch-and-bound, branch-and-cut, as well as first-order gradient-based methods with an emphasis on modeling and data science applications.

Physical Mathematics I

APMTH 201 2025 Spring

Michael P. Brenner Monday, Wednesday, Friday 10:30am to 11:45am

Introduction to methods for developing accurate approximate solutions for problems in the sciences that cannot be solved exactly, and integration with numerical methods and solutions. Topics include: dimensional analysis, algebraic equations, complex analysis, perturbation theory, matched asymptotic expansions, approximate solution of integrals.

Advanced Scientific Computing: Numerical Methods

APMTH 205 2024 Fall

Nick Trefethen Monday, Wednesday 3:00pm to 4:15pm

Mathematical theory and implementation aspects of well-established numerical algorithms applied in various scientific and engineering disciplines. The course will cover data fitting, numerical linear algebra, numerical differentiation and integration, optimization, and numerical solvers for differential equations. There will be a significant programming component. Students will be expected to implement a range of numerical methods as part of individual and group-based projects. The material is sufficiently diverse to match each student's background and programming skills.

Advanced Scientific Computing: Stochastic Methods for Data Analysis, Inference and Optimization

APMTH 207 2024 Fall

Petros Koumoutsakos Tuesday, Thursday 12:00pm to 1:15pm

The class aims to highlight the process of scientific discovery under uncertainty in the age of data. The class content stresses a unifying approach to data driven modeling and inference through stochastic  simulations, optimization and Bayesian uncertainty quantification. The class projects require transferring an idea to software in multi- and many-core computer architectures.

Geometric Methods for Machine Learning

APMTH 220 2024 Spring

Melanie Weber Monday, Wednesday 3:00pm to 4:15pm

Recently, there has been a surge of interest in exploiting geometric structure in data and models in machine learning. This course will give an overview of this emerging research area and its mathematical foundation, with a focus on recent literature and open problems. We will cover a range of topics at the intersection of geometry and machine learning including basic differential geometry, graph representation learning, manifold learning, graph neural networks, machine learning on manifolds, and geometric deep learning. Lectures will be complemented by student-led discussions of relevant papers.

APMTH 220 2025 Spring

Theory of Neural Computation

APMTH 226 2024 Fall

Cengiz Pehlevan Monday, Wednesday 9:00am to 10:15am

This course is an introduction to the theory of computation with artificial and biological neural networks. We will cover selected topics from theoretical neuroscience and deep learning theory with an emphasis on topics at the research frontier. These topics include expressivity and generalization in deep learning models; infinite-width limit of neural networks and kernel machines; deep learning dynamics; biologically-plausible learning and models of synaptic plasticity; reinforcement learning in the brain; neural population codes; normative theories of sensory representations; attractor network models of memory and spatial maps; sequential processing with recurrent neural networks and transformers; generative modeling.

Active Matter

APMTH 230 2025 Spring

L Mahadevan Friday 3:00pm to 5:45pm

Active matter describes out of equilibrium systems that consume energy to do work and become functional. Understanding their behavior and function has implications for biology and complex systems across scales, from cells to ecosystems, e.g., morphogenesis, collective behavior of flocks and herds, neurodynamics of locomotion, etc. The tools and concepts needed include non-equilibrium statistical mechanics, kinetic theory, soft matter, and hydrodynamics; methods for the analysis of the models include scaling, coarse-graining (homogenization, renormalization) and computational algorithms (for stochastic and deterministic DE). This course will provide an introduction to the questions, techniques and successes of this exploding field that cuts across the physical and biological sciences.

Decision Theory

APMTH 231 2024 Spring

Demba Ba Tuesday, Thursday 11:15am to 12:30pm

ES 201/AM 231 is a course in statistical inference and estimation from a signal processing perspective. The course will emphasize the entire pipeline from writing a model, estimating its parameters and performing inference utilizing real data. The first part of the course will focus on linear and nonlinear probabilistic generative/regression models (e.g. linear, logistic, Poisson regression), and algorithms for optimization (ML/MAP estimation) and Bayesian inference in these models. We will play particular attention to sparsity-induced regression models, because of their relation to artificial neural networks, the topic of the second part of the course. The second part of the course will introduce students to the nascent and exciting research area of model-based deep learning. At present, we lack a principled way to design artificial neural networks, the workhorses of modern AI systems. Moreover, modern AI systems lack the ability to explain how they reach their decisions. In other words, we cannot yet call AI explainable or interpretable which, as a society, poses important questions as to the responsible use of such technology. Model-based deep learning provides a framework to develop and constrain neural-network architectures in a principled fashion. We will see, for instance, how neural-networks with ReLU nonlinearites arise from sparse probabilistic generative models introduced in the first part of the course. This will form the basis for a rigorous recipe we will teach you to build interpretable deep neural networks, from the ground up. We will invite an exciting line up of speakers. Time permitting, we will provide a model-based pespective of the building blocks of modern language and image generative models.

Learning, Estimation, and Control of Dynamical Systems

APMTH 232 2024 Spring

Na Li Monday, Wednesday 9:45am to 11:00am

This graduate level course studies dynamic systems in time domain with inputs and outputs. Students will learn how to design estimator and controller for a system to ensure desirable properties (e.g., stability, performance, robustness) of the dynamical system. In particular, the course will focus on systems that can be modeled by linear ordinary differential equations (ODEs) and that satisfy time-invariance conditions. The course will introduces the fundamental mathematics of linear spaces, linear operator theory, and then proceeds with the analysis of the response of linear time-variant systems. Advanced topics such as robust control, model predictive control, linear quadratic games and distributed control will be presented based on allowable time and interest from the class. The material learned in this course will form a valuable foundation for further work in systems, control, estimation, identification, detection, signal processing, and communications.

Mathematics of High-Dimensional Information Processing and Learning

APMTH 254 2024 Fall

Yue Lu Tuesday, Thursday 12:45pm to 2:00pm

This course introduces students to fundamental results and recently developed techniques in high-dimensional probability theory and statistical physics that have been successfully applied to the analysis of information processing and machine learning problems. Discussions will be focused on studying such problems in the high-dimensional limit, on analyzing the emergence of phase transitions, and on understanding the scaling limits of efficient algorithms. This course seeks to start from basics, assuming just a solid understanding of undergraduate probability theory. Students will take an active role by exploring and applying what they learn from the course to their own research problems.

Special Topics in Applied Mathematics

APMTH 299R 2024 Fall

Madhu Sudan

Supervision of experimental or theoretical research on acceptable problems in applied mathematics and supervision of reading on topics not covered by regular courses of instruction.

APMTH 299R 2024 Spring

APMTH 299R 2025 Spring

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Massachusetts General Hospital, Medical Analytics Group

Math and data science internship.

  • Share This: Share Math and Data Science Internship on Facebook Share Math and Data Science Internship on LinkedIn Share Math and Data Science Internship on X

We are looking for a graduate-level student with good background in math to work on applied data science projects.

We are particularly interested in studying the stability of machine learning models. This will require good knowledge of math, numerical methods, linear and/or Boolean algebra.

The Medical Analytics Group works within the Imaging Department at MGH and delivers data-driven process improvement solutions to increase hospital efficiency and improve patients’ experiences. Our projects combine big data analysis with application development.

Work in the Medical Analytics Group is diverse and fast paced. Our recent projects have included designing nonlinear/AI models for predicting and optimizing clinical workflow, finding risk factors for various patient conditions,  performing complex clinical data analyses, developing new pattern-recognition algorithms.

Read more at http://mag.mgh.harvard.edu

phd math harvard

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phd math harvard

The ‘Necessary Evil’ of Computer Science 124

Why might Kligfeld hope to make the course better? Take a look at the Spring 2023 QReports: “Do not take this class for pride”; “No social life. You will be maiden-less.”

Most students, however, aren’t taking Computer Science 124: Data Structures and Algorithms for pride. They’re taking it to fulfill the computer science concentration’s Algorithms requirement. Hence the course’s description as “a necessary evil” in the Q Guide.

Last year, the average number of hours students reported spending on coursework outside of class per week was 16.70, with the plurality of students reporting it took up 18-20 hours a week. But this isn’t the only reason the course draws complaints: while many computer science students are hoping to use their degree to go into industry, CS 124 is a theoretical course, focusing more on proofs than programming. This is consistent with Harvard’s CS department at large. Many students step foot on campus hearing about how theoretical Harvard’s CS department is.

Adam C. Hesterberg, the current assistant director of undergraduate studies for CS, says that the theoretical focus of courses like CS 124 is an attempt to circumvent the rapidly changing industry trends.

“We try to teach skills that will be useful to computer scientists even when the hottest language in industry moves onto the next thing, probably in a few years,” he says.

He views the department as equipping students with “timeless skills, not the currently useful languages in the industry.”

Boaz Barak, a CS professor and co-director of undergraduate studies, also hopes undergraduates will find a broad range of applicability from their CS studies.

“Our goal is to prepare Harvard CS concentrators to many possible career options,” Barak says. “Courses that focus too much on practical knowledge may become outdated before students even graduate.”

Hesterberg notes that he frequently hears back from former students of CS 124 who state that “what they learned in 124 was really useful to them.” Similarly, Barak says that it is “no accident that the material of CS 124 is the one that is often used by tech companies in their interviews.”

Computer science concentrator Amulya Garimella ’25 agrees, saying she really enjoyed the theoretical aspects of Harvard’s computer science classes.

“Understanding deep down why things work is helpful. I think that it also helps you understand how to think about problems like a machine would, which I think is really helpful,” says Garimella, a former Crimson magazine editor.

Garimella says that anyone could easily learn a language by searching up the syntax, but the ability to understand the “super base layer” of computer science had allowed her to code better in her research positions and even in a biotech startup.

“Most languages are pretty similar, deep down. They have some very important differences in how they’re implemented,” she says. “Certainly GPT-5 will be able to code very well, but deep down, it’s the math and the theory that even made those advances possible.”

Charlie Chen ’27, who plans to concentrate in Computer Science, says that he’s not concerned about finding a job despite Harvard’s CS being largely theoretical.

“I’m not too worried. I feel like with SWE interviews nowadays, a lot of the prep work comes from outside of classes where you have to write code. And Harvard also does have a lot of clubs that provide great relevant experience, like T4SG,” he says, referring to Tech For Social Good.

Still, there’s the course’s rigor: the 16.7 hours of week that caused one QReports writer to say, “Do not take this class if you wish to have work-life balance.”

In response to complaints and questions from students about the course’s rigor, Barak clarifies, “The instructors of CS 124 have worked at reducing difficulty in recent years, and in particular making it less dense by eliminating material that appears in other courses. We certainly shouldn’t make [the] course hard for the sake of being hard.”

The growing number of CS concentrators — which roughly doubled in the last decade, according to Hesterberg — has also presented a challenge in sourcing enough teaching staff to support students. Barak says this staff shortage likely contributes to the negative experiences students have reported in more challenging classes.

Though the rigorous theoretical and mathematical components have dissuaded many students from pursuing a computer science concentration, others remain undeterred.

“I feel like the material we learn is all really interesting, because it’s just very problem solve-y,” Chen says.

Typically, those with stronger math backgrounds coming into college have found the theoretical CS classes relatively easier, making the barriers of entry higher for those from under-resourced schools and backgrounds.

“Usually the people who are super exposed to math find it really easy to just pick up coding,” says Garimella, who took a linear algebra class in high school. “To keep up, it’s definitely a challenge.”

In a similar vein, many QReport comments recommend that students have a solid math foundation before taking the course, with one even suggesting that you should take the class “if you excel in Math 55 .”

Chen, however, says that he feels math background “isn’t that big.”

“A lot of the hard part of the course comes from being able to absorb a lot of hard information quickly,” he says. “It’s a lot more a question of how much time you can put into going to class, going to lectures, going to section and office hours.”

Garimella says that students might perceive the theoretical CS classes to be harder because they came into college having done well in their studies.

“You come to Harvard, and you might have a math lecture where you just understand none of that. I think that’s really disheartening,” she says.

“I think people should just stop being scared about these courses especially if you don’t want to go to grad school and your grades don’t matter as much,” she adds. “I think that people should be more comfortable with going to lecture not understanding anything.”

At the end of the day, CS 124 might not be all that different from the courses at other schools.

“Two of my apartment-mates are software engineers at Google who went to MIT, and were complaining pretty similarly about thinking that MIT’s CS classes were not really relevant to their jobs,” says Hesterberg, laughing. “My MIT alum apartment-mates were impressed at the practical applicability of our CS classes. So it seems like there is some amount of a ‘grass is always greener on the other side’ aspect.”

—Magazine writer Chelsie Lim can be reached at [email protected] .

—Staff writer Xinni (Sunshine) Chen can be reached at [email protected] . Follow her on X @sunshine_cxn .

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Alvin Bragg, Manhattan's district attorney, draws friends close and critics closer

Headshot of Walter Ray Watson

Walter Ray Watson

phd math harvard

Manhattan District Attorney Alvin Bragg speaks during a press conference following the arraignment of former U.S. President Donald Trump in New York City on April 4, 2023. Jennah Moon/The Washington Post/Getty Images hide caption

Manhattan District Attorney Alvin Bragg speaks during a press conference following the arraignment of former U.S. President Donald Trump in New York City on April 4, 2023.

Observers, friends and former colleagues view Alvin Bragg Jr., the Manhattan district attorney, as a smart, deliberate lawyer and a selfless public servant. And people who claim him as their friend say he's a thoughtful one.

Those who spoke to NPR, who know Bragg well or watch him closely, say he is neither moved nor driven by politics. Bragg declined to speak for this story.

Attorney Anurima Bhargava has been friends with Bragg since they were undergrads at Harvard University, where Bragg also earned his law degree.

"One of the things that is so intensely remarkable," she says, "is that he's had friends, and colleagues, and people he grew up with, and he's stayed close to all of us."

Bhargava leads Anthem of Us, a consulting firm. She says Bragg finds ways to stay connected.

"This year, I had a movie premiere," she says. "He was working, but he showed up in the back, and made sure I knew that he was in the room. And that's the kind of stuff that, like, even if it's for 10 minutes, it means something."

phd math harvard

Attorney Anurima Bhargava has been a friend of Manhattan District Attorney Alvin Bragg since they attended Harvard University in the 1990's. She says his presence had always made her feel and supported. José A. Alvarado Jr. for NPR hide caption

Attorney Anurima Bhargava has been a friend of Manhattan District Attorney Alvin Bragg since they attended Harvard University in the 1990's. She says his presence had always made her feel and supported.

Bragg was featured in Harvard's student newspaper, The Crimson, in a 1995 article. He was described as "empathetic" and gregarious."

"Alvin is always the person to go and start a conversation," Bhargava says, and adds, he was at the center of difficult campus conversations, and someone who defied stereotypes as an actively listener, even with people he just met. Bhargava says whether at a committee meeting or a party, Bragg was a warm, welcoming presence.

"If Alvin was in the room, like, I always felt really safe and supported," Bhargava says. "I felt like there was someone in the room who would always have my back."

Alvin Bragg is now at the center of the first-ever criminal trial of a former American president.

The Manhattan district attorney now oversees a team of six prosecutors trying the case against Donald Trump. Trump is charged with 34 felony counts of falsifying business records in the first degree.

Last year, the former president was arraigned and pleaded not guilty to all charges. Bragg then held a news conference.

"Under New York State law, it is a felony to falsify business records with the intent to conceal another crime," Bragg said. "That is exactly what this case is about."

Jury selection is expected to be complete by the end of the week. Opening arguments could happen as early as Monday. Donald Trump faces a penalty of up to four years in prison.

The former president has claimed Bragg's prosecution to be politically motivated. Trump's defense attorneys have filed and failed to have the case delayed or dismissed. The presiding judge, Juan Merchan, has denied all those motions.

Some view the case as a distraction, compared to three other criminal cases pending against Trump, where prosecutors allege his actions present far more serious threats to democracy.

phd math harvard

Terri Gerstein worked with Alvin Bragg in the New York Attorney General's office. He is smart and a careful lawyer, she says. Gerstein is now a director at the Wagner Graduate School of Public Service at New York University. José A. Alvarado Jr. for NPR hide caption

Terri Gerstein recalls Alvin Bragg as thoughtful and detail-oriented. "He's one of the smartest people that I've known," she says. "I know how careful he is as a lawyer."

Bragg supervised Gerstein in the New York Attorney General's office, where she was labor bureau chief.

"He would carefully read all of the pleadings or briefs or memos that we were writing. And look up the cases himself and, like, really, really delve into them," she says.

Gerstein now is a director at the Wagner Graduate School of Public Service at NYU. She remembers working on a couple of wage theft cases where home care aides went unpaid, caring for older patients and people with disabilities.

"That case really touched a nerve with him," she says. "That people would be doing this kind of work, and that someone would take advantage of them in that way."

The employers pleaded guilty in both cases.

Before he was elected Manhattan district attorney, Bragg was steeped in prosecuting white collar crime and public corruption cases working for both the U.S. Attorney for the Southern District of New York (SDNY) and the New York Attorney General.

He grew up as a son of Harlem

Alvin Bragg Jr. attended Trinity, a private K-12 college prep school. He was nurtured in a storied section of Harlem called Strivers' Row. His mother, Sadie, taught high school math and later was vice president at Borough of Manhattan Community College. His father, Alvin Sr., headed the local Urban League for several years. He retired as the city's director of homeless shelters. Bragg's parents wanted their only child to be open and experience all kinds of people.

Bragg worshiped at Abyssinian Baptist Church in Harlem as a child, and still does now with his wife and children. He teaches Sunday school there. In 2021, the late pastor Calvin Butts III introduced candidate Bragg during a Sunday service as "a son of Harlem." Rev. Butts gave Bragg a few moments to make his pitch to potential voters.

"I had a gun pointed at me six times, three by the NYPD during lawless stops, and three by people who were not police officers," Bragg told the congregation.

"After the first gunpoint stop by the NYPD, I saw our pastor, Reverend Butts, and he guided me through how to file a civilian complaint. That was the beginning of my advocacy." He was a high school student at the time.

Bragg campaigned and won on his lived experience, and became the first black person elected Manhattan district attorney.

Jelani Cobb has covered Bragg as a staff writer for The New Yorker.

phd math harvard

Jelani Cobb, a staff writer for The New Yorker, observes progressive district attorneys like Bragg must balance their ability to make reform in the system with the public's perception of its safety. David Buchan/Penske Mediaa/Getty Images hide caption

Jelani Cobb, a staff writer for The New Yorker, observes progressive district attorneys like Bragg must balance their ability to make reform in the system with the public's perception of its safety.

"Alvin Bragg is somebody who grew up in Harlem at the time that 'stop and frisk' was just a part of life," Cobb says. "The Central Park Five are now kind of a stand-in for that whole era of policing."

"And so, it means a lot," says Cobb, who is also dean at Columbia University's Journalism School. "That there's somebody who has experienced both sides of the ledger, serving as a prosecutor, but also witnessing some of the areas in which the system has gone wrong."

Bragg seeks to strike a balance between public safety and reform

D.A. Bragg declared prosecuting violent crime his top priority. He has also advocated for alternatives to jail when appropriate, and dropped prosecutions for low-level offenses.

Tina Luongo says Bragg has put people in high places of his administration who "think outside the box" in terms of reform. Tina Luongo heads criminal defense practice for the Legal Aid Society, the city's primary source for public defenders. They were familiar with Bragg for many years and aware of his reform efforts when he worked in the New York Attorney General's office.

Bragg is different from his predecessors, Luongo says.

phd math harvard

Legal Aid Chief Attorney Tina Luongo says Alvin Bragg is an attentive listener. "He may or may not agree with my position, but he hears me out," she says. She is shown speaking at a rally to protest the 17th death on Rikers Island at City Hall in New York City in 2022. Michael M. Santiago/Getty Images hide caption

Legal Aid Chief Attorney Tina Luongo says Alvin Bragg is an attentive listener. "He may or may not agree with my position, but he hears me out," she says. She is shown speaking at a rally to protest the 17th death on Rikers Island at City Hall in New York City in 2022.

"I do believe that if I pick up a phone and I call Alvin and I complain about something, he's listening," Loungo says. "And he may or may not agree with my position, but he hears me out."

Some of Bragg's reforms, intended to reduce recidivism, draw criticism from conservative media who accuse Bragg of being "soft on crime."

Jelani Cobb says Bragg works in a dynamic space where challenging the status quo on law and order issues can be tricky.

"For progressive prosecutors in general, I would say him included, their ability to make reform in the system is always counterbalanced by the public's perception of its safety," says Cobb.

A call for new ideas invites critics

Former prosecutor Karen Friedman Agnifilo was second in command to Cy Vance, the last Manhattan district attorney. "It really is a time in our history for a person of color to be the district attorney," she says. Friedman says she decided not to run for the office after Vance declined a fourth bid.

She says "fresh, new ideas" are needed to solve recidivism, because "the old ways" or patterns of prosecution and incarceration are not working.

" I've never worked with him, but he's doing a really good job," she says.

phd math harvard

Karen Friedman Agnifilo was former Chief Assistant District Attorney for Manhattan District Attorney Cy Vance. Every new district attorney has missteps in the beginning, she says. José A. Alvarado Jr. for NPR hide caption

Karen Friedman Agnifilo was former Chief Assistant District Attorney for Manhattan District Attorney Cy Vance. Every new district attorney has missteps in the beginning, she says.

Bragg stumbled early on with the release of the Day One Memo, a document that outlined policy shifts for bail and sentencing, among other changes. It was sent office-wide via email, without any discussion.

"It didn't go well at all," says Catherine Christian, a veteran Assistant District Attorney who worked for three decades in the office before becoming a law partner in private practice.

phd math harvard

Catherine Christian, a former assistant district attorney in the Manhattan District Attorney's office and currently in private practice, believes Alvin Bragg is someone who learns from his mistakes. José A. Alvarado Jr. for NPR hide caption

Catherine Christian, a former assistant district attorney in the Manhattan District Attorney's office and currently in private practice, believes Alvin Bragg is someone who learns from his mistakes.

Christian, who left seven months into Bragg's term, says he recovered after a long period of chaos and found his footing after about a year. "I think he's someone who's willing to learn, and learns from mistakes. And listens," she says.

Only a few weeks in office, Bragg had another set of challenges.

Bragg reportedly questioned the lead prosecutors, Mark Pomerantz and Carey Dunne, in several meetings. He'd stopped their team from presenting evidence against Donald Trump to a grand jury in a criminal probe into Trump's involvement in fraud for overvaluing his assets. (New York Attorney General Letitia James later successfully pursued a civil lawsuit against the Trump Organization, largely along the same lines of evidence pursued by Mark Pomerantz, and it resulted in a $454 million penalty against Trump.)

Bragg had doubts about moving forward, and both Pomerantz and Dunne resigned in protest a month later. In March 2023, Bragg empaneled a new grand jury that voted to indict Trump.

"I know that there were a few missteps in the beginning, and growing pains," Karen Friedman Agnifilo says. "But I think he's maturing really nicely."

The Manhattan District Attorney's office is staffed by more than 1,500 people. The work ranges from prosecuting white collar crime to human trafficking to street crime to addressing needs of survivors, exonerating wrongful convictions police misconduct, and returning of stolen antiquities.

In January 2023, a New York state court ordered the Trump Organization to pay fines totaling 1.6 million in a tax fraud case. D.A. Bragg's office successfully won that prosecution.

Bragg may be seen as maturing in his job, but he continues to be tested by cases and critics. Earlier this year, several migrants allegedly attacked police officers in Times Square. At the hearing, prosecutors did not request bail, due to a lack of evidence at the time. The suspected attackers were set free, and Bragg took heat for his handling of the case from politicians and others.

"Why are these four individuals released on their own recognizance?" Patrick Hendry asked during a news conference. Hendry is president of the Police Benevolent Association (PBA), the city's largest police union. "Why aren't they in jail right now?"

Prosecutors did a thorough investigation. Bragg defended his office.

"We do not tolerate people assaulting police officers," Bragg told the press. "But in a court of law, our profound obligation is to make sure we have the right people charged with the right crimes."

Prosecutors filed charges after many days and several suspects were held for trial.

"You're not allowed to talk about details and facts," says Karen Friedman Agnifilo. Bragg, like all district attorneys, is confronted by cases where he can't share information with the public, or respond to critics the way politicians do.

"You're an officer of the court and the highest law enforcement official, first and foremost," Agnifilo Friedman says, "and you're a politician second."

The unprecedented trial of Donald Trump is a case that Alvin Bragg Jr. doubted, delayed and later revived. Now underway, it will put the Manhattan district attorney to the test.

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Helen Vendler, a towering presence in poetry criticism, has died

Harvard professor emerita was considered the nation’s ‘leading poetry critic’.

Professor Vendler, a university professor emerita at Harvard, wrote and edited some 30 books of poetry essays, criticism, and anthologies, becoming one of the influential figures in her field.

Struggling as a single mother in 1967 to raise a son on scant funds while teaching 10 college courses a year, Helen Vendler realized that “the only way I could make my life easier was to give up writing” — something she couldn’t face.

" ‘They can’t make me,’ I said to myself in panic and fear and rage. ‘They can’t make me do that,’ " she recalled in an essay decades later. “I suppose ‘They’ were the Fates, or the Stars, but I knew that to stop writing would be a form of self-murder.”

As she had done before and would do again, Professor Vendler found a path through that crisis. And soon she published the second of some 30 books of poetry criticism she wrote or edited while becoming one of the most influential and esteemed figures in her field.

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Professor Vendler, whose careful consideration of poems helped some of her era’s best poets better understand what they had accomplished and what more they needed to do, was 90 when she died Tuesday in her Laguna Niguel, Calif., home, her family said.

“I believe poetry is for everybody,” Professor Vendler, who was still writing and publishing essays , said in an interview for this obituary as her health was failing.

She was the Arthur Kingsley Porter university professor, emerita , at Harvard University, where she began teaching in 1980. A university professorship is the highest honor Harvard bestows on a faculty member, and poets she wrote about afforded her their own recognition.

“Helen understood that all poets needed what she did so they could take the next step,” said Jorie Graham , a Pulitzer Prize-winning poet who had barely heard of Professor Vendler when she reviewed Graham’s earliest work for The New York Times in the early 1980s.

“I encountered the most lucid account of what I was doing that I could ever hope for,” Graham, who became a friend and Harvard colleague , said of those first reviews. “She certainly taught me right away that there was more to a poem than I could fathom on my own.”

Seamus Heaney , the late Nobel Prize-winning poet whose work Professor Vendler championed early on, once said that “she is like a receiving station picking up on each poem, unscrambling things out of word-waves, making sense of it and making sure of it. She can second-guess the sixth sense of the poem.”

In a 2006 New York Times profile , Rachel Donadio called her “the leading poetry critic in America.”

Professor Vendler started teaching at Harvard University in 1980.

For Professor Vendler, no other vocation would do.

Early on, “it gave me a ratifying satisfaction to vow that whatever ‘the profession’ might think of me, I would always write only about poetry, without confining myself to a single century or a single country,” she wrote in her 2015 book “The Ocean, the Bird, and the Scholar: Essays on Poets and Poetry.”

In 2004, the National Endowment for the Humanities selected Professor Vendler as the Jefferson Lecturer , the federal government’s foremost honor in the humanities.

In addition to writing scores of essays and reviews, Professor Vendler published books about poets such as Keats, Yeats, Wallace Stevens, and George Herbert. One book examined Shakespeare’s sonnets, another focused on Emily Dickinson, including poems other critics had ignored.

“I liked exhuming some of her largely uncommented upon poems,” Professor Vendler said in this year’s interview. “And I am extremely happy that I took it upon myself to write on each of Shakespeare’s sonnets, which no one had ever done.”

Last year, the American Academy of Arts and Letters awarded her its gold medal for belles lettres and criticism, calling her “our foremost critic of poetry.”

“I do understand, I think, what it feels like to be a poet, even though I’m not one,” Professor Vendler told the Harvard Gazette afterward. “I was born with a mind that likes condensed and unusual language, which is what you get from poetry.”

Born in Boston on April 30, 1933, Helen Hennessy was a daughter of George Hennessy, who taught Romance languages at English High and Roxbury Memorial High, and Helen Conway Hennessy, who taught in the Boston Public Schools before resigning upon marrying because of rules requiring female teachers to be single.

Professor Vendler wrote that her mother “was the fount of poetry in the house, quoting it frequently in conversation.”

Talking at 9 months, Professor Vendler had a vocabulary of 100 words when she turned 1 (her parents kept a list). Her father, who had taught in Puerto Rico, passed along fluency in Spanish, French, and Italian to his daughters, Elizabeth and Helen, while their younger brother, George, “fled the house after school.”

Young Helen also learned some Latin in Catholic schools and by singing settings of Psalms at Mass. Her ear for music later guided her to some voices she celebrated in lyric poetry.

By high school, she was quietly rebelling against her “exaggeratedly observant Catholic household.” She “pleaded” to attend Girls Latin School and Radcliffe College, but her parents insisted she go to Catholic schools, which she found limiting.

“Women intellectuals were not thick on the ground in the Catholic Church,” she recalled in the interview for this obit. “There was no place for me to be. There was no club for me to join.”

At Emmanuel College, from which she graduated summa cum laude, Professor Vendler decided against studying literature — taught there, she wrote, “as a branch of faith and morals.”

Majoring in chemistry, she found science crucial to her intellectual development.

“I think it’s the base of everything I do,” she said in a 2004 National Endowment for the Humanities interview . “You have to be exact in all your writing in science: your flow chart has to go from beginning to end with all the steps accounted for, and all the equations have to balance out. Evidence has to be presented for each step of your reason.”

Awarded a Fulbright Fellowship to study mathematics at the University of Louvain, in Belgium, Professor Vendler decided en route to Europe that she would switch to literature and set aside thoughts of medical school.

Returning home afterward, she took a dozen courses in literature at Boston University as a special student in order to enter Harvard’s doctoral program, from which she graduated in 1960. On her first day, Harvard’s English department chairman told her: “We don’t want you here, Miss Hennessy. We don’t want any women here.”

Thirty-four years later, she became the first woman to receive the “university professor” distinction at Harvard, its highest honor for a faculty member.

While studying for her Harvard doctorate, she met Zeno Vendler , who had trained as a Jesuit priest and was a philosophy graduate student. They married, divorced a few years later, and she raised their son, David, alone.

Dr. Vendler turned down a job offer at Harvard to accompany Zeno to Cornell University. She taught there, at Haverford, Swarthmore, Smith, and for many years at Boston University . Starting in 1980, she held joint appointments at BU and Harvard until moving to Harvard full time in 1985 .

Being a mother, meanwhile, “made me a whole person and turned me into someone who had to pay attention to somebody,” she said in this year’s interview.

“Someone once called me and asked, ‘How do you explain your mother’s meteoric rise and career,’ and the best thing I could say was I never noticed,” said David Vendler, who lives in Laguna Beach, Calif. “She was a great mother and had a rule that she never worked while I was awake. She lived by that. She was a mom first.”

In addition to David, Professor Vendler leaves her brother, George of Hyannis, and two grandchildren.

Ranging in her writings across centuries of poetry, Professor Vendler provided an education to readers and poets alike — not just to students and not just about literature.

“You came away from reading a review of Helen’s or a book of Helen’s learning more about poetry, but also more about life,” said her friend Peter Sacks , a painter, poet , and Harvard professor. “She had this gift of seeing what the continuity of life and art might be, and to see the poem as a living entity.”

To poets, however, her writings had special resonance.

“When Helen undertook to explicate your work, then you knew what you had done and knew what you might need to do next,” Graham said.

For writers shaken by tremors of doubt, Graham said, the experience was “like being on a tightrope and feeling an unseen hand that said, ‘Trust me, you’re not going to fall.’ "

At Harvard, Professor Vendler also taught a celebrated core course, “Poems, Poets, Poetry,” which was aimed at non-humanities majors.

“I thought — and still think — that all people would like poetry if they were only brought up with it and shown how easily it is entered into and what enormous solace it has to offer,” she wrote in a 1994 essay .

Poems offered vital comfort and support to her as well.

“Helen needed poetry to live by,” Graham said. “She fashioned and honed her moral sense not through the church, but through the church of poetry — the whole history of poetry. I can’t imagine a poem that she didn’t know.”

Mark Feeney of the Globe staff contributed to this obituary.

Bryan Marquard can be reached at [email protected] .

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Bringing an investigator’s eye to complex social challenges

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Anna Russo sits in a red armchair with her legs crossed, smiling at the camera

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Anna Russo likes puzzles. They require patience, organization, and a view of the big picture. She brings an investigator’s eye to big institutional and societal challenges whose solutions can have wide-ranging, long-term impacts.

Russo’s path to MIT began with questions. She didn’t have the whole picture yet. “I had no idea what I wanted to do with my life,” says Russo, who is completing her PhD in economics in 2024. “I was good at math and science and thought I wanted to be a doctor.”

While completing her undergraduate studies at Yale University, where she double majored in economics and applied math, Russo discovered a passion for problem-solving, where she could apply an analytical lens to answering the kinds of thorny questions whose solutions could improve policy. “Empirical research is fun and exciting,” Russo says.

After Yale, Russo considered what to do next. She worked as a full-time research assistant with MIT economist Amy Finkelstein . Russo’s work with Finkelstein led her toward identifying, studying, and developing answers to complex questions. 

“My research combines ideas from two fields of economic inquiry — public finance and industrial organization — and applies them to questions about the design of environmental and health care policy,” Russo says. “I like the way economists think analytically about social problems.”

Narrowing her focus

Studying with and being advised by renowned economists as both an undergraduate and a doctoral student helped Russo narrow her research focus, fitting more pieces into the puzzle. “What drew me to MIT was its investment in its graduate students,” Russo says.

Economic research meant digging into policy questions, identifying market failures, and proposing solutions. Doctoral study allowed Russo to assemble data to rigorously follow each line of inquiry.

“Doctoral study means you get to write about something you’re really interested in,” Russo notes. This led her to study policy responses to climate change adaptation and mitigation. 

“In my first year, I worked on a project exploring the notion that floodplain regulation design doesn’t do a good job of incentivizing the right level of development in flood-prone areas,” she says. “How can economists help governments convince people to act in society’s best interest?”

It’s important to understand institutional details, Russo adds, which can help investigators identify and implement solutions. 

“Feedback, advice, and support from faculty were crucial as I grew as a researcher at MIT,” she says. Beyond her two main MIT advisors, Finkelstein and economist Nikhil Agarwal — educators she describes as “phenomenal, dedicated advisors and mentors” — Russo interacted regularly with faculty across the department. 

Russo later discovered another challenge she hoped to solve: inefficiencies in conservation and carbon offset programs. She set her sights on the United States Department of Agriculture’s Conservation Reserve Program because she believes it and programs like it can be improved. 

The CRP is a land conservation plan administered by USDA’s Farm Service Agency. In exchange for a yearly rental payment, farmers enrolled in the program agree to remove environmentally sensitive land from agricultural production and plant species that will improve environmental health and quality.

“I think we can tweak the program’s design to improve cost-effectiveness,” Russo says. “There’s a trove of data available.” The data include information like auction participants’ bids in response to well-specified auction rules, which Russo links to satellite data measuring land use outcomes. Understanding how landowners bid in CRP auctions can help identify and improve the program’s function. 

“We may be able to improve targeting and achieve more cost-effective conservation by adjusting the CRP’s scoring system,” Russo argues. Opportunities may exist to scale the incremental changes under study for other conservation programs and carbon offset markets more generally.  

Economics, Russo believes, can help us conceptualize problems and recommend effective alternative solutions.

The next puzzle

Russo wants to find her next challenge while continuing her research. She plans to continue her work as a junior fellow at the Harvard Society of Fellows, after which she’ll join the Harvard Department of Economics as an assistant professor. Russo also plans to continue helping other budding economists since she believes in the importance of supporting other students.   

Russo’s advisors are some of her biggest supporters. 

Finklestein emphasizes Russo’s curiosity, enthusiasm, and energy as key drivers in her success. “Her genuine curiosity and interest in getting to the bottom of a problem with the data — with an econometric analysis, with a modeling issue — is the best antidote for [the stress that can be associated with research],” Finklestein says. “It's a key ingredient in her ability to produce important and credible work.”

“She's also incredibly generous with her time and advice,” Finklestein continues, “whether it's helping an undergraduate research assistant with her senior thesis, or helping an advisor such as myself navigate a data access process she's previously been through.”

“Instead of an advisor-advisee relationship, working with her on a thesis felt more like a collaboration between equals,” Agarwal adds. “[She] has the maturity and smarts to produce pathbreaking research.

“Doctoral study is an opportunity for students to find their paths collaboratively,” Russo says. “If I can help someone else solve a small piece of their puzzle, that’s a huge positive. Research is a series of many, many small steps forward.” 

Identifying important causes for further investigation and study will always be important to Russo. “I also want to dig into some other market that’s not working well and figure out how to make it better,” she says. “Right now I’m really excited about understanding California wildfire mitigation.” 

Puzzles are made to be solved, after all.

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  1. Harvard Mathematics Department Graduate Information

    News. Welcome to the Math PhD program at Harvard University and the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences. Learn more about Harvard's Math community and our statement on diversity and inclusion.. The Harvard Griffin GSAS Office of Equity, Diversity, Inclusion & Belonging offers student affinity groups for graduate students and many other resources.

  2. Mathematics

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    The graduate Mathematics Program at Harvard is designed for students who hope to become research mathematicians and show definite promise in this direction. Once the student has demonstrated a command of basic mathematical concepts by passing the qualifying examination, the emphasis is on getting to the frontiers of some field by independent ...

  5. Harvard Mathematics Department : Information

    Department of Mathematics Harvard University One Oxford Street Cambridge MA 02138 USA To reach the department, please contact the main office Tel: (617) 495-2171, Fax: (617) 495-5132. Chair As of July 1, 2020, the Chair of the Mathematics Department is Michael Hopkins, Science Center, [email protected]. Director of Graduate Studies

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    Harvard School of Engineering offers a Doctor of Philosophy (Ph.D.) degree in Applied Mathematics. Doctoral students may earn the masters degree en route to the Ph.D. Students are drawn to Applied Mathematics by the flexibility it offers in learning about how to apply mathematical ideas to problems drawn from different fields, while remaining anchored to empirical data that drive these questions.

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    Perkins Professor of Mathematics Director of Graduate Studies ... math[dot]harvard[dot]edu: Guess which one is a chef? Research Interests Galois representations, p-adic Hodge theory, Shimura varieties. You can find some of my papers here. Editorial boards Inventiones (2007-) Cambridge Journal of Mathematics (2013-) Algebra and Number Theory ...

  12. How to Apply

    The application fee of $105.00. Should you want to request a fee waiver from Harvard Griffin Graduate School of Arts and Sciences, you may do so in the fee section of the application. Please list only SEAS ladder faculty on the application. "Affiliate faculty" cannot admit PhD students. There are many SEAS ladder faculty with formal joint ...

  13. Applied Mathematics

    Applied Mathematics at Harvard School of Engineering is an interdisciplinary field that focuses on the creation and imaginative use of mathematical concepts to pose and solve problems over the entire gamut of the physical and biomedical sciences and engineering, and increasingly, the social sciences and humanities. Working individually and as part of teams collaborating across the University ...

  14. Harvard Mathematics Department : Home page

    Department of Mathematics FAS Harvard University One Oxford Street Cambridge MA 02138 USA Tel: (617) 495-2171 Fax: (617) 495-5132.

  15. Lauren K. Williams

    e-mail: williams @ math. harvard.edu pronouns: she/her/hers Teaching, Mentoring, and Seminars ... , CUNY graduate center, August 14-25, 2023; Integrability and algebraic combinatorics, IPAM, April 15-19, 2024 Program on Mathematical aspects of scattering amplitudes, Harvard CMSA, April 15-May 24, 2024

  16. Mathematics for Teaching Master's Degree Program

    Through the master's degree field in mathematics for teaching you: Build deeper knowledge of mathematics content, with a particular focus on middle and high school math classrooms. Learn tactics that can improve student motivation through interactive problem-solving activities. Develop an enhanced understanding of what it means to learn math ...

  17. Courses

    9:45am to 11:00am. This course is a systematic introduction to computing (with python and jupyter notebooks) for science and engineering applications. Applications are drawn from a broad range of disciplines, including physical, financial, and biological-epidemiological problems. The course consists of two parts: 1.

  18. Math and Data Science Internship

    We are looking for a graduate-level student with good background in math to work on applied data science projects. We are particularly interested in studying the stability of machine learning models. This will require good knowledge of math, numerical methods, linear and/or Boolean algebra.

  19. Katya Ivshina

    721 likes, 4 comments - katya.ivshinaApril 19, 2024 on : "yes i like studying at harvard business school even tho i'm an applied math phd student #Mindgrasp".

  20. The 'Necessary Evil' of Computer Science 124

    Most students aren't taking Computer Science 124: Data Structures and Algorithms for pride. They're taking it to fulfill the computer science concentration's Algorithms requirement. Hence ...

  21. Alvin Bragg, Manhattan's district attorney, draws friends close and

    Bragg was featured in Harvard's student newspaper, The Crimson, in a 1995 article. He was described as "empathetic" and gregarious." "Alvin is always the person to go and start a conversation ...

  22. Helen Vendler, a towering presence in poetry criticism, has died

    Professor Vendler, a university professor emerita at Harvard, wrote and edited some 30 books of poetry essays, criticism, and anthologies, becoming one of the influential figures in her field.

  23. Bringing an investigator's eye to complex social challenges

    While completing her undergraduate studies at Yale University, where she double majored in economics and applied math, Russo discovered a passion for problem-solving, where she could apply an analytical lens to answering the kinds of thorny questions whose solutions could improve policy. "Empirical research is fun and exciting," Russo says.