35 courses with the subject MATH, each shown exactly as we captured it from the college's catalog, with every element we hold. Where the wording looks broken, that is our reading of the catalog, not the college's text.
MATH 003Introduction to Mathematical Thinking1
Students will explore ideas and fundamental results from mathematics while we emphasize the thinking and problem-solving skills these ideas stimulate. Class meetings will involve presentation of new material; group work on problems and puzzles; and lively, maybe even passionate discussions about mathematics. This course is intended for students with little background in mathematics or those who may have struggled with math in the past. It is not open to students who already have received credit on their Swarthmore transcripts for mathematics (including Advanced Placement credit), who concurrently are taking another mathematics course, or who have placed out of any Swarthmore mathematics course. (See “ Placement Procedure ” earlier.) Students planning to go on to calculus should consult with the instructor. This course does not count toward a major in mathematics.
Placement into this course through Swarthmore’s Math/Stat Readiness Examination. Natural sciences and engineering. Writing course. 1 credit. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 015Single-Variable Calculus I1
A first-semester calculus course with emphasis on an intuitive understanding of the concepts, methods, and applications. Graphical and symbolic methods will be used. The course will mostly cover differential calculus, with an introduction to integral calculus at the end, including the fundamental theorem of calculus.
Placement through Swarthmore’s Math/Stat Readiness Examination. Students with prior calculus experience must also take Swarthmore’s Calculus Placement Examination (see “ Placement Procedure ” section earlier). Natural sciences and engineering. 1 credit. Fall 2026. Miller. Gomez. Johnson. Fall 2027 Staff. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 015XPrecalculus Workshop0.5
Math 015.X is an attachment to Math 015 for students who place into it based on the Math Readiness Test or who wish to strengthen their foundation in algebra and trigonometry. Topics will include logarithms, exponents, behaviors of functions and their corresponding graphs, solving equations and inequalities, and trigonometric functions and their inverses. Classtime in Math 015.X will primarily be spent solving problems in a collaborative environment. Each week, the problems will be aligned with the precalculus skills needed for that week’s Math 015 content. Graded: CR/NC
Students must be concurrently enrolled in MATH 015 to enroll in Math 015.X Natural Sciences and Engineering 0.5 credit. Fall 2026. Dandridge. Fall 2027 Dandridge. Access the class schedule to search for sections.
MATH 020Mathematics and Social Justice1
This course examines the roles that mathematics and mathematicians play in society, particularly through the lenses of equity and social justice. Students will explore what it means to practice mathematics ethically and we will discuss mathematical influence in areas such as policing, politics, healthcare, and the military-industrial complex. Eligible for PEAC
The continuation of MATH 015 , this course covers techniques and applications of integration, convergence properties of infinite sequences and series, the approximation of functions by Taylor polynomials, and an introduction to differential equations.
A grade of C+ or better in (or placement out of) MATH 015 . Natural sciences and engineering. 1 credit. Fall 2026. Reinhart. Russell. Spring 2027. Staff. Fall 2027 Staff. Spring 2028 Staff. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 027Linear Algebra1
This course covers systems of linear equations, matrices, vector spaces, linear transformations, determinants, and eigenvalues. Applications to other disciplines are presented. This course is a step up from calculus: it includes more abstract reasoning, proofs, and structures. Students may take only one of MATH 027 and MATH 028 for credit.
Either (1) a grade of C- or better in (or placement out of) MATH 025 ; or (2) a grade of C- or better in MATH 039 . Natural sciences and engineering. 1 credit. Fall 2026. Barranca. Delfin. Spring 2027. Staff. Fall 2027 Staff. Spring 2028 Staff. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 028Linear Algebra with Theory1
This course includes the topics in MATH 027 but covered with more depth and with a more theoretical, abstract, and rigorous approach. MATH 028 is intended for students with exceptionally strong mathematical skills, especially if they are thinking of a mathematics major. Students may take only one of MATH 027 and MATH 028 for credit.
A grade of B or better in a Math course numbered 025 or higher, or placement by examination, including both placement out of calculus and placement into this course via Part IV of Swarthmore’s Calculus Placement Exam (see “ Placement Procedure ” section). Natural sciences and engineering. 1 credit. Fall 2026. Grood. Fall 2027 Staff. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 033Basic Several-Variable Calculus1
This course considers differentiation and integration of functions of several variables with special emphasis on two and three dimensions. Topics include partial differentiation, extreme value problems, Lagrange multipliers, multiple integrals, line and surface integrals, Green’s, Stokes’, and Gauss’ theorems. The department strongly recommends that students take MATH 034 instead, which is offered every semester and provides a richer understanding of this material by requiring linear algebra ( MATH 027 or MATH 028 ) as a prerequisite and applying linear algebra concepts in the course. Students may take only one of MATH 033, MATH 034 , and MATH 035 for credit.
A grade of C- or better in, or placement out of, MATH 025 (see “ Advanced Placement and Credit Policy ” section). Students who have taken linear algebra at Swarthmore or elsewhere may not take MATH 033 without departmental approval. Natural sciences and engineering. 1 credit. Fall 2026. Devlin. Fall 2027 Staff. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 034Several-Variable Calculus1
Same topics as MATH 033 except in more depth using the concepts of linear algebra. The department strongly recommends that students take linear algebra first so that they are eligible for this course. Students may take only one of MATH 033 , MATH 034, and MATH 035 for credit.
Both (1) a grade of C- or better in, or placement out of, MATH 025 ; and (2) a grade of C- or better in, or placement out of a MATH 027 or MATH 028 .
Corequisite
` Natural sciences and engineering. 1 credit. Eligible for COGS Fall 2026. Fisher. Spring 2027. Staff. Spring 2028 Staff. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 035Several-Variable Calculus with Theory1
This course includes the topics found in MATH 034 but covered in a more theoretical, abstract, and rigorous manner. It is intended for students with exceptionally strong mathematical skills. Students may take only one of MATH 033 , MATH 034 , or MATH 035 for credit.
Both (1) A grade of C- or better in, or placement out of, MATH 025 and (2) one of the following: a grade of C- or better in MATH 028 , a grade of B or better in MATH 027 or placement out of MATH 027 together with successful completion of Part IV of the Calculus Placement Exam . Natural sciences and engineering. 1 credit. Spring 2027. Staff. Spring 2028 Staff. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 039Discrete Mathematics with an Introduction to Proof1
An introduction to noncontinuous mathematics. Topics will include mathematical induction and other methods of proof, basic set theory, bijections, counting, and graph theory. Additional topics may include algorithms, recurrence relations, probability, voting methods, and other topics at the discretion of the instructor. While it does not use any calculus, MATH 039 is a more sophisticated course than MATH 015 or MATH 025 ; thus success in a calculus course demonstrates the mathematical maturity needed for MATH 039. This course is an introduction to proof; thus, students who have taken two or more upper-level proof-based courses need the permission of the instructor to enroll in Math 039. Previously called Math 029.
Either (1) a grade of B or better in, or placement out of MATH 015 ; or (2) credit for MATH 025 . Natural sciences and engineering. 1 credit. Eligible for COGS Fall 2026. Devlin. Spring 2027. Staff. Fall 2027 Staff. Spring 2028 Staff. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 043Basic Differential Equations1
This course emphasizes the standard techniques used to solve differential equations, covering the basic theory of the field with an eye toward practical applications. Topics may include first-order equations, linear differential equations, series solutions, first-order systems of equations, Laplace transforms, approximation methods, and some partial differential equations. Compare with MATH 044 . Students may not take both MATH 043 and MATH 044 for credit. The department prefers majors to take MATH 044 .
A grade of C- or better in MATH 033 , MATH 034 , or MATH 035 ; or a grade of B or better in MATH 025 and concurrent enrollment in one of MATH 034 or MATH 035 . Natural sciences and engineering. 1 credit. Eligible for COGS Spring 2027. Staff. Spring 2028 Staff. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 044Differential Equations1
An introduction to differential equations that has a more theoretical and rigorous flavor than MATH 043 and is intended for students who enjoy delving into the mathematics behind the techniques. It introduces the key ideas of ordinary differential equations in a more conceptual, dynamical as well as computational framework. Topics include existence and non-existence, uniqueness and continuous dependence of solutions on data, qualitative behavior of solutions such as asymptotic behavior and stability, as well as boundary value problems and bifurcation. Numerical and computational methods will be used throughout as appropriate. Linear and nonlinear systems will be considered. Additional topics depend on the interests of the instructor and students. The department recommends that majors take MATH 044.
Either (1) credit for, or placement out of, MATH 027 or MATH 028 and a grade of C- or better in one of MATH 033 , MATH 034 , or MATH 035 ; or (2) a grade of B or better in, or placement out of MATH 027 or MATH 028 and concurrent enrollment in one of MATH 033 , MATH 034 , or MATH 035 . Natural sciences and engineering. 1 credit. Eligible for COGS Fall 2026. Kataboh. Spring 2027. Staff. Fall 2027 Staff. Spring 2028 Staff. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 046Theory of Computation1
(Cross-listed as CPSC 046 ) Natural sciences and engineering. 1 credit. Eligible for COGS
MATH 053Topics in Analysis: Analytic Number Theory1
The Ukrainian mathematician Maryna Viazovska won the 2022 Fields Medal, the most famous prize in mathematics, for her work in analysis and number theory. Specifically, Viazovska proved a seemingly intractable conjecture about the most efficient way to pack spheres in eight-dimensional space. Her work is a tour of some of the most powerful and interesting tools in contemporary mathematics, including lattices, Fourier analysis, and modular forms. This class will introduce some of the key ideas in her proof. Alternate years.
A grade of C- or better in, or placement out of, one of MATH 033 , MATH 034 , or MATH 035 ; or departmental approval. Some experience reading and writing mathematical proofs is strongly recommended. Natural sciences and engineering. 1 credit. Eligible for COGS Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 054Partial Differential Equations1
An introduction to linear partial differential equations. Topics include first-order linear equations and second-order equations of elliptic, parabolic, and hyperbolic type via the Laplace equation, the heat equation, and the wave equation. Solutions to these equations are studied from analytical, qualitative, and numerical viewpoints. Additional topics depend on the interests of the students and instructor. Alternate years.
Credit for, or placement out of, MATH 027 or MATH 028 , and a grade of C- or better in one of MATH 043 or MATH 044 . Natural sciences and engineering. 1 credit. Eligible for COGS Spring 2027. Staff. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 055Intermediate Topics in Geometry1
Knot Theory: Tie a knot in a string then glue the ends together. Can this knot be untangled without cutting it open? This question and many others relating to these “mathematical knots” have increasingly been studied by mathematicians, with many breakthroughs occurring in the past 20 years. In this course we will discuss methods of knot tabulation, invariants (properties) of knots such as the bridge-number, surfaces associated to knots, ties to Hyperbolic Geometry, Physics, Chemistry, Molecular Biology, and other sciences, as well as open problems in the field. While our proof-based approach will heavily feature drawing, artistic skill is not a prerequisite.
Credit for, or placement out of, one of MATH 027 or MATH 028 , and credit for, or placement out of, one of MATH 033 , MATH 034 , or MATH 035 , with a grade of C- or better in at least one of these courses; or departmental approval. Natural sciences and engineering. 1 credit. Catalog chapter: Mathematics and Statistics Department website: https://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 056Modeling1
(Cross-listed as ENVS 079 ) An introduction to the formulation and analysis of mathematical models. This course will present a general framework for the development of discrete and continuous models of diverse phenomena. Principles of modeling will be drawn from multiple areas, such as kinetics, population dynamics, disease spread, traffic flow, particle mechanics, and network science. Mathematical techniques and theory useful for understanding models will be emphasized, such as dimensional analysis, phase plane diagrams, stability analysis, bifurcation theory, conservation laws, random walks, constitutive relations, chaos theory, and computer simulation. A primary goal of this course is to give insights into the connections between mathematics and real-world problems, allowing students to apply the course concepts to applications that excite them.
Credit for, or placement out of, MATH 027 or MATH 028 , and a grade of C- or better in one of MATH 043 or MATH 044 . Natural sciences and engineering. 1 credit. Eligible for ENVS. COGS. Spring 2028 Staff. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 057Topics in Algebra1
Course content varies each year, depending on student and faculty interest. Recent offerings have included coding theory, groups and representations, finite reflection groups, and advanced matrix theory. See also MATH 077 .
A grade of C or better in MATH 027 or MATH 028 , and any proof-based math class, such as Math 28, 35, 39, etc., or permission of the instructor. Natural sciences and engineering. 1 credit. Eligible for COGS Spring 2028 Staff. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 058Number Theory1
This course covers the fundamentals of elementary number theory, including divisibility, congruences, and prime numbers. Topics may include Gaussian integers, sums of squares representations, and quadratic reciprocity. Alternate years. Alternate years.
A grade of C- or better in one of MATH 027 or MATH 028 . Natural sciences and engineering. 1 credit. Eligible for COGS Fall 2026. Hsu. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 063Introduction to Real Analysis1
This course concentrates on the careful study of the principles underlying the calculus of real valued functions of real variables. Topics include continuity, compactness, connectedness, uniform convergence, differentiation, and integration. There is a strong emphasis on good mathematical writing, especially on mathematical proofs. Each section of this course includes a required additional weekly problem session with the same professor.
Credit for, or placement out of, MATH 027 or MATH 028 , and a grade of C- or better in, or placement out of, one of MATH 033 , MATH 034 , or MATH 035 . Natural sciences and engineering. Writing course. 1 credit. Eligible for COGS Fall 2026. Talvacchia. Mavinga. Grood. Fall 2027 Staff. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 064Introduction to Topology1
An introduction to topological spaces focusing on point-set topology, with a sampling of more advanced topics in and applications of topology. Alternate years
Either a grade of C- or better in MATH 063 ; or a grade of C- or better in MATH 034 / MATH 035 and concurrent enrollment in MATH 063 . Natural sciences and engineering. 1 Credit. Fall 2027 Staff. Department website: Mathematics and Statistics Access the class schedule to search for sections.
MATH 065Introduction to Geometry1
The course content varies from year to year but is often either the differential geometry of curves and surfaces or the algebraic geometry of conics and cubics. Alternate years.
Credit for, or placement out of, MATH 027 or MATH 028 and one of MATH 033 , MATH 034 , or MATH 035 , with a grade of C- or better in at least one of these courses. Natural sciences and engineering. 1 credit. Eligible for COGS Fall 2026. Chen. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 066Stochastic and Numerical Methods1
In mathematical problems that arise from real-world applications, exact solutions often cannot be obtained due to complicating characteristics, such as nonlinearity, uncertainty, and randomness. This course will introduce theory and techniques to numerically approximate solutions to these types of mathematical problems. This course will also survey the mathematical theory of stochastic processes. Additional topics may be included, depending on the instructor.
Credit for, or placement out of, MATH 027 or MATH 028 , and a grade of C- or better in MATH 043 or MATH 044 . Natural sciences and engineering. 1 credit. Eligible for COGS Fall 2026. Goldwyn. Fall 2027 Staff. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 067Introduction to Modern Algebra1
This course is an introduction to abstract algebra and will survey basic algebraic systems-groups, rings, and fields. Although these concepts will be illustrated by concrete examples, the emphasis will be on abstract theorems, proofs, and rigorous mathematical reasoning. There is a strong emphasis on good mathematical writing, especially on mathematical proofs. This course includes a required additional weekly problem session.
A grade of C- or better in, or placement out of, MATH 027 or MATH 028 . Natural sciences and engineering. Writing course. 1 credit. Eligible for COGS Spring 2027. Staff. Spring 2028 Staff. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 069Combinatorics1
This course continues the study of material begun in MATH 039 . The primary topics are enumeration and graph theory. The first area includes, among other things, a study of generating functions and Polya counting. The second area is concerned with relations between certain graphical invariants. Additional topics may include one or more of the following: design theory, extremal graph theory, Ramsey theory, matroids, matchings, codes, and Latin squares.
A grade of C- or better in MATH 039 and at least one other Math course numbered 27 or higher; or departmental approval. Students who have taken two or more Math courses numbered 50 or higher may take this course without Math 39; please see the instructor. Natural sciences and engineering. 1 credit. Eligible for COGS Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 073Advanced Topics in Analysis1
An advanced version of MATH 053 , sometimes offered instead, and requiring the core course in analysis.
A grade of C- or better in MATH 063 . Natural sciences and engineering. 1 credit. Eligible for COGS Spring 2027. Staff. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 077Advanced Topics in Algebra1
An advanced version of MATH 057 , sometimes given instead, and requiring the core course in algebra.
A grade of C- or better in MATH 067 . Natural sciences and engineering. 1 credit. Eligible for COGS Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 083Complex Analysis1
A brief study of the geometry of complex numbers is followed by a detailed treatment of the Cauchy theory of analytic functions of a complex variable: integration and Cauchy’s theorem, power series, residue calculus, conformal mapping, and harmonic functions. Various applications are given, and other topics-such as elliptic functions, analytic continuation, and the theory of Weierstrass-may be discussed.
A grade of B or better in MATH 063 or departmental approval. Natural sciences and engineering. 1 credit. Fall 2027 Staff. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 093Directed Reading
Graded CR/NC. May be taken multiple times for credit. Natural sciences and engineering.
Course majors in math/stat are required to take this zero-credit course in both the fall and spring of their senior year. This comprehensive will have students engage with mathematicians and statisticians who present lectures on various topics and will have students participate in a range of departmental activities. Any student who will not be on campus during one of those semesters should instead arrange with their advisor to take this course during their last two semesters on campus. 0 credit. Fall 2026. Staff. Spring 2027. Staff. Fall 2027 Staff. Spring 2028 Staff.
This seminar is a continuation of Introduction to Real Analysis ( MATH 063 ). Topics include the inverse and implicit function theorems, differential forms, calculus on manifolds, measurability, and Lebesgue integration.
A grade of B or better in MATH 063 or departmental approval. Natural sciences and engineering. 1 credit. Eligible for COGS Spring 2027. Staff. Spring 2028 Staff. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 104Topology II1
A continuation of the topics from Math 64, including an in-depth exploration of the fundamental group and covering spaces. Additional topics will be drawn from algebraic, differential, and/or geometric topology. Previous to Spring 2026, this was a 2-credit seminar. Alternate years.
A grade of B or better in MATH 063 , MATH 064 , and MATH 067 ; or a grade of B or better in MATH 063 and MATH 064 and concurrent enrollment in MATH 067 . Natural sciences and engineering. 1 credits. Spring 2028 Staff. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 105Geometry II1
The course content varies from year to year among differential geometry, differential topology, and algebraic geometry. In 2021, the topic was algebraic geometry. Alternate years.
A grade of B or better in MATH 065 or departmental approval. Natural sciences and engineering. 1 credit. Spring 2027. Staff. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
MATH 107Modern Algebra II1
This seminar is a continuation of Introduction to Modern Algebra ( MATH 067 ). Topics covered include field theory, Galois theory (including the insolvability of the quintic), and the Sylow theorems. Other topics are usually chosen from the structure theorem for modules over principal ideal domains, a theoretical development of linear algebra, or an introduction to representation theory. Additional topics may be studied depending on the interests of students and instructor.
A grade of B or better in MATH 067 or departmental approval. Natural sciences and engineering. 1 credit. Fall 2026. Chen. Fall 2027 Staff. Catalog chapter: Mathematics and Statistics Department website: http://www.swarthmore.edu/mathematics-statistics Access the class schedule to search for sections.
