Department of Mathematics and Statistics
Courses
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About the Course Listings
Four views and tools each provide different ways of exploring the curriculum.
- Current Year Courses for this Department or Program lists only currently-offered classes, and includes scheduling and instructor information.
- The Three-Year Planner for this Department or Program lists all courses (in numerical order) offered during the current year and the last two years. Use it to understand the full course offerings from the department and how frequently courses are offered. This list does not include any scheduling information; instructor information is only historical and is likely to change in future years.
- The Tri-Co Course Search Engine lists the current offerings for all departments and programs at Haverford, Bryn Mawr, and Swarthmore Colleges, and includes scheduling and instructor information.
- The HC Academic Catalog Course Search Engine includes faceted searching (by division, domain, department, major, minor, and other fields) for all courses offered in the current year and the last two years. It does not contain scheduling information, but like the Three-Year Planner, can help you discover related interests and understand the typical pattern of offerings from year to year. This tool does not include all Bryn Mawr offerings.
Courses
MATH H103 INTRODUCTION TO PROBABILITY AND STATISTICS (1.0 Credit)
Division: Natural Science; Quantitative
Domain(s): C: Physical and Natural Processes
Basic concepts and methods of elementary probability and quantitative reasoning, with practical applications. Topics include: sample average and standard deviation, normal curves, regression, expected value and standard error, confidence intervals and hypothesis tests. Crosslisted: Mathematics, Statistics Prerequisite(s): Not open to students who have (a) placed into 121 or higher, (b) taken 118 or higher, (c) taken any other introductory statistics class at Haverford or Bryn Mawr, (d) received a score of 4 or 5 on the AP Statistics exam
MATH H105 APPLIED MODELING WITH CALCULUS (1.0 Credit)
Samuel Pérez-Ayala
Division: Natural Science; Quantitative
Domain(s): C: Physical and Natural Processes
An introduction to aspects of calculus useful in applied work in the natural and social sciences, with a strong emphasis on developing mathematical modeling skills. Topics include differential and integral calculus of functions of one variable, multivariable optimization, and modeling with differential equations. Applications to biology, economics, and physics. This course is taught at the level of a beginning calculus course, and no prior calculus experience is assumed. Prerequisite(s): Not open to students placing into MATH 118 or higher or Math 105 cannot be taken by students who have AP credit for calculus or with previous calculus credit, except with instructor consent
(Offered: Fall 2024)
MATH H118 CALCULUS: DYNAMICS AND INTEGRATION (1.0 Credit)
Rebecca Everett
Division: Natural Science; Quantitative
Domain(s): C: Physical and Natural Processes
A study of the evolution of systems defined by difference and differential equations. Methods of analysis come from calculus: the limit, the derivative, and the integral from numerical, graphical, and symbolic perspectives. Not open to students placing into Math 121 or higher, except with instructor permission. Prerequisite(s): MATH 105 or placement. Not open to students with credit for MATH B102 (Calculus II) or equivalent, except with instructor consent
(Offered: Fall 2024, Spring 2025)
MATH H121 MULTIVARIABLE CALCULUS (1.0 Credit)
Anthony Kling, Lawrence Seminario-Romero
Division: Natural Science; Quantitative
Domain(s): C: Physical and Natural Processes
An introduction to functions of several variables, vector geometry, partial derivatives, optimization, Taylor’s Theorem, multiple integrals, line integrals, and Green’s and Stokes’ Theorems. Prerequisite(s): MATH 118 or equivalent placement, or instructor consent. Not open to students who have previously taken multivariable calculus at the college level, either at Haverford or elsewhere, except with instructor consent
(Offered: Fall 2024)
MATH H146 ETHICS AND THE USE OF MATHEMATICS, WITH A FOCUS ON ANTI-RACISM (0.5 Credit)
Tarik Aougab
This half-credit seminar will explore what it means to “do math ethically”, to emphasize the ways in which mathematics is inherently political, and to think about anti-racism in mathematical disciplines. This course is graded P/F. Crosslisted: Independent College Programs, Mathematics
(Offered: Spring 2025)
MATH H203 STATISTICAL METHODS AND THEIR APPLICATIONS (1.0 Credit)
Lynne Butler
Division: Natural Science; Quantitative
Domain(s): C: Physical and Natural Processes
An introduction to statistical methods used to analyze data in the natural and social sciences. It covers descriptive statistics, the binomial and normal distributions, expected value and variance, confidence intervals and hypothesis testing, comparison of two samples, regression, and analysis of variance. A required computer lab, using R, is taught alongside this course. Crosslisted: Mathematics, Statistics Prerequisite(s): MATH 118 or higher, placement into MATH 121 or higher, or instructor consent. Students who have taken another introductory statistics course at Haverford or Bryn Mawr may only enroll in STAT 203 with instructor consent
(Offered: Fall 2024)
MATH H204 DIFFERENTIAL EQUATIONS (1.0 Credit)
Robert Manning
Division: Natural Science; Quantitative
Domain(s): C: Physical and Natural Processes
An introduction to the theory of ordinary differential equations (ODEs) including algebraic techniques for solving a single ODE or a linear system of ODEs, numerical techniques for generating approximate solutions, geometric techniques for displaying solutions to understand their behavior, analyzing nonlinear systems, and some key theorems (such as existence and uniqueness of solutions). The focus of this course will be on applications of the methods and solving real systems. Prerequisite(s): MATH 121 or MATH 215 (or 216) or consent of instructor. Lottery Preferences: juniors, then sophomores, then seniors, and then first-year students
MATH H206 INTRODUCTION TO MATHEMATICAL CRYPTOGRAPHY (1.0 Credit)
Anthony Kling
Division: Natural Science
Domain(s): C: Physical and Natural Processes
This course introduces modern cryptography from a mathematical perspective, focusing on public key cryptosystems. We will emphasize the theory, analysis, and practical application of various cryptosystems. Topics will include Diffie-Hellman, RSA, and elliptic curve cryptography. We will also develop any necessary mathematical background, including modular arithmetic. Pre-requisite(s): MATH 121 or 215, or permission of the instructor Lottery Preference: Random
MATH H210 LINEAR OPTIMIZATION (1.0 Credit)
Robert Manning
Division: Natural Science
Domain(s): C: Physical and Natural Processes
An introduction to the optimization of a linear function subject to linear constraints, with applications that include game theory, transportation problems, and network flows. The course includes some theoretical material on the properties of these linear optimization problems, and also a strong emphasis on algorithms, especially the simplex method and some enhancements to it (which are especially relevant since many applications involve many variables and many constraints). Crosslisted: Mathematics, Computer Science, Economics Prerequisite(s): Co-requisite of Math 121 or 215, or equivalent placement, or instructor consent
(Offered: Fall 2024)
MATH H215 LINEAR ALGEBRA (1.0 Credit)
Jeffrey Tecosky-Feldman
Division: Natural Science; Quantitative
Domain(s): C: Physical and Natural Processes
An abstract introduction to linear algebra, focusing on proof techniques. Topics covered include: vector spaces, linear transformations and matrices, determinants, eigenvalue problems, quadratic forms, and the spectral theorem. Prerequisite(s): MATH 121 or equivalent placement, or 118 with instructor consent, or CMSC 231
(Offered: Fall 2024)
MATH H216 MULTIVARIABLE CALC USING LINEAR ALGEBRA (1.0 Credit)
Joshua Sabloff
Division: Natural Science; Quantitative
Domain(s): C: Physical and Natural Processes
Calculus in n-dimensional Euclidean space: continuous and differentiable functions, extreme value problems, multiple integration, line and surface integrals, parametrized surfaces, Green's, Gauss' and Stokes' Theorems. Tools from linear algebra are used to formulate general statements of definitions, theorems and proofs. Prerequisite(s): Not open to students who have previously taken multivariable calculus at the college level, either at Haverford or elsewhere, except with instructor permission. Requites a strong background in single-variable calculus and a course in linear algebra, or instructor consent
(Offered: Spring 2025)
MATH H218 PROBABILITY (1.0 Credit)
Lynne Butler
Division: Natural Science; Quantitative
Domain(s): C: Physical and Natural Processes
An introduction to probability theory. Topics include: sample spaces, combinatorics, conditional probability, independence, discrete and continuous random variables, functions of random variables, expected value and variance, the moment generating function, and some basic limit theorems. Prerequisite(s): MATH 216 or 121 or consent
(Offered: Fall 2024)
MATH H222 SCIENTIFIC COMPUTING: CONTINUOUS SYSTEMS (1.0 Credit)
Rebecca Everett
Division: Natural Science; Quantitative
Domain(s): C: Physical and Natural Processes
A survey of major algorithms in modern scientific computing, with a focus on continuous problems. Topics include numerical differentiation and integration, numerical linear algebra, root-finding, optimization, Monte Carlo methods, and discretization of differential equations. Basic ideas of error analysis are presented. Regular computer work in class introduces students to the software package Matlab, in which the algorithms are implemented and applied to various problems in the natural and social sciences. Crosslisted: Mathematics, Computer Science Prerequisite(s): Math 121
MATH H235 INFORMATION AND CODING THEORY (1.0 Credit)
Steven Lindell
Domain(s): C: Physical and Natural Processes
This course covers the mathematical theory of the transmission (sending or storing) of information. Included will be encoding and decoding techniques, both for the purposes of data compression and for the detection and correction of errors. Prerequisite(s): CMSC 231 or equivalent background in mathematics
MATH H295 TOPICS IN MATHEMATICS: COMPUTATIONAL NUMBER THEORY (1.0 Credit)
Anthony Kling
Division: Natural Science
Domain(s): C: Physical and Natural Processes
A 200-level course in a topic in mathematics. Fall 2024: An introduction to number theory with a heavy focus on computation and algorithms. We will explore properties of integers and their relationships through primarily computational techniques. Throughout, we will emphasize both theoretical understanding and practical application. Topics will include primality testing, arithmetic functions, complexity, Diophantine equations, and investigating conjectures. We will be using Python in this course, but prior programming experience is not needed. Prerequisite: MATH 121 or permission from instructor Lottery Preference: Math majors, then math/stat minors
(Offered: Fall 2024)
MATH H299 JUNIOR SEMINAR IN MATHEMATICS AND STATISTICS (1.0 Credit)
Robert Manning
Division: Natural Science
Domain(s): C: Physical and Natural Processes
A course to introduce all math majors to research and communication methods used by mathematicians and statisticians, and to discuss the structures and workings of mathematical communities, including the ethical implications of bringing mathematical skills to a workplace or community. Students produce a “junior paper” anchored in an application of linear algebra, helping prepare them to write a thesis as a senior, and plan a colloquium or panel discussion open to the entire Haverford community. Pre-requisite(s): Linear Algebra (MATH H215) or instructor consent Lottery Preference: Math Majors, by seniority within that group
(Offered: Fall 2024, Spring 2025)
MATH H317 ANALYSIS I (1.0 Credit)
Samuel Pérez-Ayala
Division: Natural Science; Quantitative
Domain(s): C: Physical and Natural Processes
A rigorous development of topics in calculus, including the axioms of the real number line, cardinality, convergence of sequences, point-set topology (open/closed sets, compactness, connectedness), continuity, differentiability, and the Riemann integral. The course also has a major focus on the writing of clear and correct mathematical proofs. Prerequisite(s): MATH 215 and either 121 or 216, or instructor consent
(Offered: Fall 2024, Spring 2025)
MATH H318 ANALYSIS II: COMPLEX ANALYSIS (1.0 Credit)
Joshua Sabloff
Division: Natural Science
Domain(s): C: Physical and Natural Processes
A continuation of Math 317. The topic for Spring 2023 is complex analysis, including the algebra and geometry of complex numbers, analytic functions, complex integration (including the Cauchy integral formula and the calculus of residues), and conformal mappings (including, hopefully, the Riemann Mapping Theorem). Prerequisite: Math 317 or permission of instructor
MATH H328 MATHEMATICAL STATISTICS (1.0 Credit)
Weiwen Miao
Division: Natural Science
Domain(s): C: Physical and Natural Processes
An introduction to mathematical theory of statistics. Topics include: Estimation, Hypothesis Testing, one-sample inference, two-sample inference, and regression. Additional topics may include: goodness-of-fit tests and analysis of variance. Crosslisted: Mathematics, Statistics Prerequisite(s): MATH 218
MATH H333 ALGEBRA I (1.0 Credit)
Tarik Aougab
Division: Natural Science; Quantitative
Domain(s): C: Physical and Natural Processes
A rigorous treatment of fundamental algebraic structures. Topics include: introduction to groups, modular arithmetic, polynomials, rings, fields, Galois theory, vector spaces, and modules. Prerequisite(s): MATH 215 and either 121 or 216, or instructor consent
(Offered: Fall 2024)
MATH H334 ALGEBRA II: ALGEBRAIC GEOMETRY (1.0 Credit)
Anthony Kling
Division: Natural Science
Domain(s): C: Physical and Natural Processes
We will build upon our algebraic tools to study geometric objects. In particular, we will study affine varieties, plane curves, projective varieties, and morphisms between these objects. We will also cover significant results, including Hilbert's Nullstellensatz and Bezout's Theorem. Prerequisite(s): MATH 333 or instructor consent
MATH H335 TOPOLOGY (1.0 Credit)
Tarik Aougab
Division: Natural Science
Domain(s): C: Physical and Natural Processes
Generalizes topological concepts from Euclidean spaces to arbitrary topological spaces, and introduces elements of algebraic topology. Concepts covered include continuity, connectedness, and compactness. The course culminates in an exploration of the fundamental group and covering spaces. Prerequisite(s): MATH 317 with MATH 333 as a co-requisite, or instructor consent
(Offered: Spring 2025)
MATH H340 ANALYSIS OF ALGORITHMS (1.0 Credit)
Steven Lindell
Division: Natural Science; Quantitative
Domain(s): C: Physical and Natural Processes
Qualitative and quantitative analysis of algorithms and their corresponding data structures from a precise mathematical point of view. Performance bounds, asymptotic and probabilistic analysis, worst case and average case behavior. Correctness and complexity. Particular classes of algorithms such as sorting searching will be studied in detail. Crosslisted: Computer Science, Mathematics Prerequisite(s): CMSC 106 or 107 or B206, and 231, or instructor consent
(Offered: Fall 2024)
MATH H345 THEORY OF COMPUTATION (1.0 Credit)
Division: Natural Science
Domain(s): C: Physical and Natural Processes
Introduction to the mathematical foundations of computer science: finite state automata, formal languages and grammars, Turing machines, computability, unsolvability, and computational complexity. Attendance at the weekly discussion section is required. Crosslisted: Computer Science, Mathematics Prerequisite(s): (CMSC 106, 107, 151, or 206) and CMSC 231, and junior or senior standing, or instructor consent
(Offered: Spring 2025)
MATH H360 MATHEMATICAL ECONOMICS (1.0 Credit)
Giri Parameswaran
Division: Quantitative; Social Science
Domain(s): C: Physical and Natural Processes
A study of advanced mathematical tools used in economic analysis. Topics include eigenvalues and quadratic forms, differential equations, convex programming and dynamic programming. Applications to consumer theory, generalized linear regression, stability of equilibrium, and models of growth and search. Fulfills Mathematic Economics (MTEC) concentration. Crosslisted: Economics, Mathematics Prerequisite(s): MATH 215; either MATH 121 or 216; ECON 203 or 204 or MATH 203 or SOCL 215 or PSYCH 200 or Bryn Mawr’s ECON B253 recommended
MATH H361 APPLIED MULTIVARIATE STATISTICAL ANALYSIS (1.0 Credit)
Weiwen Miao
Division: Natural Science; Quantitative
Domain(s): C: Physical and Natural Processes
An introduction to multivariate statistical analysis. The course includes methods for choosing, fitting, and evaluating multiple regression models and analysis of variance models. A required computer lab, using R, is taught alongside this course. Crosslisted: Mathematics, Statistics Prerequisite(s): MATH 215 and one of the following: ECON 204, MATH 203, PSYC 200, SOCL 215
(Offered: Fall 2024)
MATH H382 MATHEMATICAL MODELING AND DIFFERENTIAL EQUATIONS (1.0 Credit)
Rebecca Everett
Division: Natural Science
Domain(s): C: Physical and Natural Processes
An introduction to modeling in applied mathematics using differential equations, with examples from biology, chemistry, engineering, physics, and/or the social sciences. Through these examples, we build mathematical models that reflect real world scenarios and analyze them to gain an understanding of the problem. Techniques of analysis may include phase plane methods, stability analysis, bifurcation theory, and computer simulation. Pre-requisite(s): MATH H204 or equivalent, or permission of the instructor Lottery Preference: Math majors, then math minors, then by seniority
MATH H383 PARTIAL DIFFERENTIAL EQUATIONS (1.0 Credit)
Robert Manning
Division: Natural Science
Domain(s): C: Physical and Natural Processes
This course is an introduction to partial differential equations, involving a mix of (1) analysis (the use of various tools to ask questions of existence and uniqueness of solutions and, in special cases, find solutions), (2) computation (the development of numerical techniques to find approximate solutions on the computer), and (3) modeling (the connection of mathematics to real problems). The balance of these features will vary from instructor to instructor. Pre-requisite(s): MATH H204 or equivalent, or instructor permission Lottery Preference: Math majors, then math minors, then by seniority
(Offered: Fall 2024)
MATH H390 ADVANCED TOPICS IN ALGEBRA: ALGEBRAIC COMBINATORICS (1.0 Credit)
Division: Natural Science
Domain(s): C: Physical and Natural Processes
A 300-level course in algebra, building on the introductory abstract algebra course MATH 333, with the particular topic(s) varying each time it is offered. Fall 2023: An introduction to applications of algebra to combinatorics and vice versa. Topics include Polya's theory of counting, generating functions, the matrix-tree theorem, the Robinson-Schensted-Knuth correspondence, symmetric functions, and the basic theory of Coxeter groups. Prerequisite(s): MATH 333
MATH H391 ADVANCED TOPICS IN GEOMETRY AND TOPOLOGY (1.0 Credit)
Tarik Aougab
Division: Natural Science
Domain(s): C: Physical and Natural Processes
A 300-level course in geometry and/or topology, sometimes building on the introductory topology course MATH 335, with the particular topic(s) varying each time it is offered. Spring 2024: The goal of this course is to introduce you to a suite of topological invariants, which are properties of topological spaces that must be preserved under homeomorphism. When one is aware of many topological invariants, it becomes easier to tell spaces apart (for example, if space A disagrees with space B with respect to some given invariant, they can not possibly be homeomorphic!) It turns out that the most fruitful place for developing invariants comes from abstract algebra. We will learn about how one can start with a topological space, and produce various groups and rings, such that if two spaces are homeomorphic, the corresponding algebraic structures must be isomorphic. Prerequisite(s): MATH 335 and co-req of MATH 333
MATH H392 ADVANCED TOPICS IN ANALYSIS: FUNCTION SPACES AND DIFFERENTIAL EQUATIONS (1.0 Credit)
Joshua Sabloff
Division: Natural Science; Quantitative
Domain(s): C: Physical and Natural Processes
A 300-level course in analysis. Fall 2024: Introduction to analysis in spaces of functions with a focus on generalizing ideas from the reals. Foundational topics include uniform convergence, power series, Weierstrass approximation, and compactness. We will then build on those foundations by studying functionals and the calculus of variations, operators and ordinary differential equations, and Hilbert spaces and Laplace’s equation. Prerequisite: MATH 317.
(Offered: Fall 2024)
MATH H394 ADVANCED TOPICS IN THEORETICAL COMPUTER SCIENCE: MATH FOUNDATIONS OF MACHINE LEARNING (1.0 Credit)
Division: Natural Science
Domain(s): C: Physical and Natural Processes
A 300-level course on the mathematical foundations of computer science, with the particular topic(s) varying each time it is offered. Fall 2023: An introduction to the mathematical principles behind modern machine learning algorithms. Covers advanced topics in linear algebra, vector calculus, probability theory, and optimization, with a particular focus on their relevance to machine learning tasks. We will also discuss various practical applications. Crosslisted: Mathematics, Computer Science. Prerequisite(s): MATH 121 and 215, or instructor permission
MATH H396 ADVANCED TOPICS: PROBABILITY AND STATISTICS (1.0 Credit)
Weiwen Miao
Division: Natural Science; Quantitative
Domain(s): C: Physical and Natural Processes
A 300-level course in probability and/or statistics, with the particular topic(s) varying each time it is offered. Spring 2025: The main topics for this course are nonparametric methods and categorical data analysis. Students will learn nonparametric statistical tests in one-sample, two-sample and k-sample situations as well as basic categorical data analysis. Crosslisted: Mathematics, Statistics. Prerequisite(s): MATH 218 and one of the following: MATH 203, ECON 203/204, PSYC 200, SOCL 215 or instructor permission
(Offered: Spring 2025)
MATH H397 ADVANCED TOPICS IN APPLIED MATHEMATICS: MODELS FOR DYNAMIC PROCESSES (1.0 Credit)
Division: Natural Science
Domain(s): C: Physical and Natural Processes
will cover dynamical systems' models construction and analysis. First, we will see how physical, biological and sociological principles drive the models' construction. We will perform qualitative analysis of these models. Later, we will discuss data driven dynamical processes' modeling with R software and its practical applications (e.g., econometrics and finance). If time permits, we will investigate an idea of combining physical principles with a data driven approach. Prerequisites: Math 215 or instructor permission
(Offered: Spring 2025)
MATH H399F SENIOR SEMINAR (0.5 Credit)
David Lippel
Division: Natural Science
Domain(s): C: Physical and Natural Processes
Seminar for students writing senior papers, dealing with the oral and written exposition of advanced material.
(Offered: Fall 2024)
MATH H399I SENIOR SEMINAR (0.5 Credit)
Joshua Sabloff, Staff
Division: Natural Science
Seminar for students writing senior papers, dealing with the oral and written exposition of advanced material.
(Offered: Spring 2025)
MATH H400 SENIOR RESEARCH (0.5 Credit)
Joshua Sabloff, Robert Manning, Tarik Aougab, Weiwen Miao, Staff
Division: Natural Science; Quantitative
Domain(s): C: Physical and Natural Processes
Work on Senior Thesis with Advisor.
(Offered: Fall 2024)
MATH H460 TEACHING ASSISTANT (1.0 Credit)
Staff
(Offered: Spring 2025)
MATH H480 INDEPENDENT STUDY (1.0 Credit)
David Lippel
Independent Study
(Offered: Fall 2024)