Introduction to differential and integral calculus for functions of one variable. The heart of calculus is the study of rates of change. Differential calculus concerns the process of finding the rate at which a quantity is changing (the derivative). Integral calculus reverses this process. Information is given about the derivative, and the process of integration finds the "integral," which measures accumulated change. This course aims to develop a thorough understanding of the concepts of differentiation and integration, and covers techniques and applications of differentiation and integration of algebraic, trigonometric, logarithmic, and exponential functions. MATH 115 is an introductory course designed for students who have not seen calculus before.

Units: 1

Max Enrollment: 24

Prerequisites: Not open to students who have completed MATH 116, MATH 120, MATH 205 or the equivalent. Not open to students whose placement is MATH 205 or MATH 206.

Instructor: Staff

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Summer; Spring; Fall

Semesters Offered this Academic Year: Fall; Spring

Notes:

Introduction to differential and integral calculus for functions of one variable. The heart of calculus is the study of rates of change. Differential calculus concerns the process of finding the rate at which a quantity is changing (the derivative). Integral calculus reverses this process. Information is given about the derivative, and the process of integration finds the "integral," which measures accumulated change. This course aims to develop a thorough understanding of the concepts of differentiation and integration, and covers techniques and applications of differentiation and integration of algebraic, trigonometric, logarithmic, and exponential functions. In addition to the material from Math 115, this course spends additional time strengthening students' precalculus skills, covering topics such as proportions and percents, linear and exponential growth, and logarithms. MATH 115P is an introductory course designed for students who have not seen calculus before and who would benefit from extra academic support on precalculus topics.

Units: 1.25

Max Enrollment: 30

Prerequisites: Permission of the instructor.

Instructor: Diesl

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Fall

Semesters Offered this Academic Year: Fall

Notes:

This class will offer a treatment of first-semester calculus aimed at students interested in the biological and social sciences. The course material is motivated by real-life problems in laboratory and data-driven studies. Students will be expected to work in groups both in and out of class, give presentations at the chalkboard, and submit work in both problem set and project formats. Topics include: functions, limits, continuity, differentiation and an introduction to integration.

Units: 1

Max Enrollment: 24

Prerequisites: Not open to students who have completed MATH 116, MATH 120, MATH 205 or the equivalent. Not open to students whose placement is MATH 205 or MATH 206.

Instructor: Diesl

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Semesters Offered this Academic Year: Not Offered

Notes:

The course begins with applications and techniques of integration. It probes notions of limit and convergence and adds techniques for finding limits. Half of the course covers infinite sequences and series, where the basic question is, What meaning can we attach to a sum with infinitely many terms and why might we care? The course can help students improve their ability to reason abstractly and also teaches important computational techniques. Topics include integration techniques, l'Hôpital's rule, improper integrals, geometric and other applications of integration, infinite series, power series, and Taylor series. MATH 116 is the appropriate first course for many students who have had AB calculus in high school.

Units: 1

Max Enrollment: 24

Prerequisites: MATH 115 or Math 115Z, or the equivalent. Not open to students who have completed MATH 120 or MATH 205. Not open to students whose math placement is MATH 206.

Instructor: Staff

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Summer; Spring; Fall

Semesters Offered this Academic Year: Spring; Fall

Notes:

This course is a variant of MATH 116 for students who have a thorough knowledge of the techniques of differentiation and integration, and familiarity with inverse trigonometric functions and the logarithmic and exponential functions. It includes a rigorous and careful treatment of limits, sequences and series, Taylor's theorem, approximations and numerical methods, Riemann sums, improper integrals, l'Hôpital's rule, and applications of integration.

Units: 1

Max Enrollment: 24

Prerequisites: Open by permission of the department to students who have completed a year of high school calculus. Students who have studied Taylor series should elect MATH 205. Not open to students who have completed MATH 116, MATH 205 or the equivalent.

Instructor: Yacoubou Djima

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Fall

Semesters Offered this Academic Year: Fall

Notes:

How can a candidate in a political race win the majority of votes yet lose the election? How can two competing candidates interpret the same statistic as being in their favor? How can the geometry of the voting district disenfranchise entire groups of voters? Can we quantify the power the President of the United States has? In this course, we will look at the mathematics behind these and related questions that arise in politics. We will study topics such as fairness, voting paradoxes, social choice, game theory, apportionment, gerrymandering, and data interpretation. The goal of the class will be to illustrate the importance of rigorous reasoning in various social and political processes while providing an introduction to some fascinating mathematics.

Units: 1

Max Enrollment: 24

Crosslisted Courses: PEAC 123,MATH 123

Prerequisites: None.

Instructor: Volic

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Fall

Semesters Offered this Academic Year: Fall

Notes:

This course is a first-year seminar for students in the Wellesley Plus program. It will introduce students to important basic mathematical concepts as set theory, proof techniques, propositional and predicate calculus, graph theory, combinatorics, probability, and recursion.

Units: 1

Max Enrollment: 20

Prerequisites: None. Open to First-Years only.

Instructor: S. Chang

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Other Categories: FYS - First Year Seminar

Typical Periods Offered: Fall

Semesters Offered this Academic Year: Fall

Notes: Mandatory Credit/Non Credit.

This seminar surveys the work of Leonhard Euler (1707-1783), one of the most influential and prolific mathematicians of all time. It is geared toward students who would like a broad overview of what advanced mathematics (beyond calculus) is about, and how it got that way. Topics are drawn from a wide range of areas in pure and applied mathematics, such as algebra, number theory, analysis, and geometry. Highlights include the Basel problem, complex exponentials, the calculus of variations, the Euler line, and the bridges of Königsberg. The seminar is discussion-based: students retrace Euler's steps by making definitions, proposing conjectures, generating examples, and crafting and critiquing proofs, ever attentive to the balance between intuitive ingenuity and rigorous argument.

Units: 1

Max Enrollment: 15

Prerequisites: None. Open to First-Years only.

Instructor: Staff

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Other Categories: FYS - First Year Seminar

Typical Periods Offered: Fall

Semesters Offered this Academic Year: Spring

Notes:

This course is intended for students who are interested in mathematics and its applications in economics and finance. The following topics will be covered: mathematical models in economics, market equilibrium, first and second order recurrences, the cobweb model, profit maximization, derivatives in economics, elements of finance, constrained optimization, Lagrangians and the consumer, microeconomic applications, business cycles, European and American options, call and put options, Black-Scholes analysis.

Units: 1

Max Enrollment: 24

Prerequisites: MATH 116 or the equivalent.

Instructor: Bu

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Semesters Offered this Academic Year: Not Offered

Notes:

Most real-world systems that one may want to model, whether in the natural or in the social sciences, have many interdependent parameters. To apply calculus to these systems, we need to extend the ideas and techniques of single-variable Calculus to functions of more than one variable. Topics include vectors, matrices, determinants, polar, cylindrical, and spherical coordinates, curves, partial derivatives, gradients and directional derivatives, Lagrange multipliers, multiple integrals, vector calculus: line integrals, surface integrals, divergence, curl, Green's Theorem, Divergence Theorem, and Stokes’ Theorem.

Units: 1

Max Enrollment: 24

Prerequisites: MATH 116 or MATH 120, or the equivalent.

Instructor: Diesl, Kerr, Hirschhorn (Fall); Kerr, Schultz (Spring)

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Spring; Fall

Semesters Offered this Academic Year: Fall; Spring

Notes:

Linear algebra is one of the most beautiful subjects in the undergraduate mathematics curriculum. It is also one of the most important with many possible applications. In this course, students learn computational techniques that have widespread applications in the natural and social sciences as well as in industry, finance, and management. There is also a focus on learning how to understand and write mathematical proofs and an emphasis on improving mathematical style and sophistication. Topics include vector spaces, subspaces, linear independence, bases, dimension, inner products, linear transformations, matrix representations, range and null spaces, inverses, and eigenvalues.

Units: 1

Max Enrollment: 24

Prerequisites: MATH 205 or MATH 215; or, with permission of the instructor, MATH 116, MATH 120, or the equivalent.

Instructor: S. Chang, Lauer (Fall); Trenk, Yacoubou Djima (Spring)

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Spring; Fall

Semesters Offered this Academic Year: Fall; Spring

Notes:

What can we know about the shape of the universe? When is a molecule left- or right-handed and what does that mean? How can an inhabitant of a one- or two- or three-dimensional universe figure out the shape (geometry and topology) of their universe? This course provides an elementary introduction to mathematical topology (sometimes described as rubber-sheet geometry), and the tools to address questions such as these. In this context, the notions of knot invariants and geodesics (shortest paths) arise, and students learn how to use these tools to classify knots, and to classify all closed surfaces. Applications of topology and geometry to chemistry and molecular biology will be discussed.

Students will learn about fundamental topological and geometric ideas and develop their visual intuition, which can provide a valuable framework for MATH 302 and MATH 307.

Units: 1

Max Enrollment: 15

Prerequisites: MATH 116 or the equivalent. Open to First-Years only.

Instructor: Kerr

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Other Categories: FYS - First Year Seminar

Typical Periods Offered: Fall

Semesters Offered this Academic Year: Not Offered

Notes:

This course is designed to examine the degree to which a function can be determined by an algebraic relationship it has with its derivative(s) --- a so-called ordinary differential equation (ODE). For instance, can one completely catalog all functions which equal their own derivative? In service of developing techniques for solving certain classes of differential equations, some fundamental notions from linear algebra and complex numbers are presented. Differential equation topics include modeling with and solving first- and second-order ODEs, separable ODEs, and a discussion of higher order and non-linear ODEs; linear algebra topics include solving systems via elementary row operations, bases, dimension, determinants, column space, and eigenvalues/vectors.

Units: 1

Max Enrollment: 24

Prerequisites: MATH 116 or MATH 120, or the equivalent.

Instructor: H. Wang (Fall); Fernandez, Yacoubou Djima (Spring)

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Spring; Fall

Semesters Offered this Academic Year: Fall; Spring

Notes:

Probability is the mathematics of uncertainty. We begin by developing the basic tools of probability theory, including counting techniques, conditional probability, and Bayes's Theorem. We then survey several of the most common discrete and continuous probability distributions (binomial, Poisson, uniform, normal, and exponential, among others) and discuss mathematical modeling using these distributions. Often we cannot calculate probabilities exactly, and we need to approximate them. A powerful tool here is the Central Limit Theorem, which provides the link between probability and statistics. Another strategy when exact results are unavailable is simulation. We examine Markov chain Monte Carlo methods, which offer a means of simulating from complicated distributions.

Units: 1

Max Enrollment: 24

Crosslisted Courses: STAT 220

Prerequisites: MATH 205

Instructor: Tannenhauser

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Semesters Offered this Academic Year: Fall

Notes:

Number theory is the study of the most basic mathematical objects: the natural numbers (1, 2, 3, etc.). It begins by investigating simple patterns: for instance, which numbers can be written as sums of two squares? Do the primes go on forever? How can we be sure? The patterns and structures that emerge from studying the properties of numbers are so elegant, complex, and important that number theory has been called "the Queen of Mathematics." Once studied only for its intrinsic beauty, number theory has practical applications in cryptography and computer science. Topics include the Euclidean algorithm, modular arithmetic, Fermat's and Euler's Theorems, public-key cryptography, quadratic reciprocity. MATH 223 has a focus on learning to understand and write mathematical proofs; it can serve as valuable preparation for MATH 305.

Units: 1

Max Enrollment: 24

Prerequisites: One of the following - MATH 116, MATH 120, or CS 230 with permission of the instructor.

Instructor: Trenk

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Spring

Semesters Offered this Academic Year: Spring

Notes:

Number theory is the study of the most basic mathematical objects: the natural numbers (1, 2, 3, etc.). It begins by investigating simple patterns: for instance, which numbers can be written as sums of two squares? Do the primes go on forever? How can we be sure? The patterns and structures that emerge from studying the properties of numbers are so elegant, complex, and important that number theory has been called "the Queen of Mathematics." Once studied only for its intrinsic beauty, number theory has practical applications in cryptography and computer science. Topics include the Euclidean algorithm, modular arithmetic, Fermat's and Euler's Theorems, public-key cryptography, quadratic reciprocity. MATH 223 has a focus on learning to understand and write mathematical proofs; it can serve as valuable preparation for MATH 305.

Units: 1

Max Enrollment: 15

Prerequisites: Open to First-Years only.

Instructor: Lange

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Other Categories: FYS - First Year Seminar

Typical Periods Offered: Fall

Semesters Offered this Academic Year: Not Offered

Notes:

Combinatorics is the art of counting possibilities: for instance, how many different ways are there to distribute 20 apples to 10 kids? Graph theory is the study of connected networks of objects. Both have important applications to many areas of mathematics and computer science. The course will be taught emphasizing creative problem-solving as well as methods of proof, such as proof by contradiction and induction. Topics include: selections and arrangements, generating functions, recurrence relations, graph coloring, Hamiltonian and Eulerian circuits, and trees.

Units: 1

Max Enrollment: 24

Prerequisites: MATH 116 or MATH 120, or the equivalent; or CS 230 together with permission of the instructor.

Instructor: Schultz, Trenk (Fall ), C. Chan, Hirschhorn (Spring)

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Spring; Fall

Semesters Offered this Academic Year: Fall; Spring

Notes:

Units: 1

Max Enrollment: 25

Prerequisites:

Instructor:

Semesters Offered this Academic Year: Spring; Fall

Notes:

Units: 0.5

Max Enrollment: 25

Prerequisites:

Instructor:

Semesters Offered this Academic Year: Spring; Fall

Notes:

Real analysis is the study of the rigorous theory of the real numbers, Euclidean space, and calculus. The goal is to thoroughly understand the familiar concepts of continuity, limits, and sequences. Topics include compactness, completeness, and connectedness; continuous functions; differentiation and integration; limits and sequences; and interchange of limit operations as time permits.

Units: 1

Max Enrollment: 24

Prerequisites: MATH 205 and MATH 206.

Instructor: H. Wang (Fall), S. Chang (Spring)

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Spring; Fall

Semesters Offered this Academic Year: Fall; Spring

Notes:

**Topic for 2023-20****24: PDEs and Geometric Analysis**

This course is an introduction to Geometric Analysis through the study of partial differential equations (PDEs). The focus is on studying the properties of solutions. Topics covered include: the Laplace and Heat equation, maximum principles, gradient flows, and the role of non-smoothness in PDEs. In the second half of the course we study geometric PDEs such as the minimal surface equation and curve shortening flow in the plane.

Units: 1

Max Enrollment: 15

Prerequisites: MATH 302.

Instructor: S. Chang

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Spring

Semesters Offered this Academic Year: Spring

Notes: This is a topics course and can be taken more than once for credit as long as the topic is different each time.

In this course, students examine the structural similarities between familiar mathematical objects such as number systems, matrix sets, function spaces, general vector spaces, and mod n arithmetic. Topics include groups, rings, fields, homomorphisms, normal subgroups, quotient spaces, isomorphism theorems, divisibility, and factorization. Many concepts generalize number theoretic notions such as Fermat's little theorem and the Euclidean algorithm. Optional subjects include group actions and applications to combinatorics.

Units: 1

Max Enrollment: 24

Prerequisites: MATH 206

Instructor: Schultz (Fall), Lange (Spring)

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Spring; Fall

Semesters Offered this Academic Year: Fall; Spring

Notes:

**Topic for Spring 24: Galois Theory**

**Topic for Spring 24: Galois Theory**

This course offers a continued study of the algebraic structures introduced in MATH 305, culminating in the Fundamental Theorem of Galois Theory, a beautiful result that depicts the circle of ideas surrounding field extensions, polynomial rings, and automorphism groups. Applications of Galois theory include the unsolvability of the quintic by radicals and geometric impossibility proofs, such as the trisection of angles and duplication of cubes. Cyclotomic extensions and Sylow theory may be included in the syllabus.

Units: 1

Max Enrollment: 15

Prerequisites: MATH 305

Instructor: Diesl

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Semesters Offered this Academic Year: Spring

Notes: This is a topics course and can be taken more than once for credit as long as the topic is different each time.

This course covers some basic notions of point-set topology, such as topological spaces, metric spaces, connectedness and compactness, Heine-Borel Theorem, quotient spaces, topological groups, groups acting on spaces, homotopy equivalences, separation axioms, Euler characteristic, and classification of surfaces. Additional topics include the study of the fundamental group (time permitting).

Units: 1

Max Enrollment: 15

Prerequisites: MATH 302. Co-requisite - MATH 305.

Instructor: Hirschhorn

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Spring; Fall

Semesters Offered this Academic Year: Fall

Notes:

This course will introduce students to aspects of set theory and formal logic. The notion of set is one of the fundamental notions of modern mathematics. In fact, other mathematical notions, such as function, relation, number, etc., can be represented in terms of purely set theoretical notions, and their basic properties can be proved using purely set theoretic axioms. The course will include the Zermelo-Fraenkel axioms for set theory, the Axiom of Choice, transfinite arithmetic, ordinal numbers, and cardinal numbers.

Units: 1

Max Enrollment: 15

Prerequisites: MATH 302 or MATH 305.

Instructor: S. Chang

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Every other year

Semesters Offered this Academic Year: Not Offered

Notes:

Complex analysis is the study of the differential and integral calculus of functions of a complex variable. Complex functions have a rich and tightly constrained structure: for example, in contrast with real functions, a complex function that has one derivative has derivatives of all orders and even a convergent power series. This course develops the theory of complex functions, leading up to Cauchy's theorem and its consequences, including the theory of residues. While the primary viewpoint is calculus, many of the essential insights come from geometry and topology, and can be used to prove results such as the Fundamental Theorem of Algebra.

Units: 1

Max Enrollment: 15

Prerequisites: MATH 302

Instructor: Fernandez

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Semesters Offered this Academic Year: Fall

Notes:

Differential geometry has two aspects. Classical differential geometry, which shares origins with the beginnings of calculus, is the study of local properties of curves and surfaces. Local properties are those properties which depend only on the behavior of the curve or the surface in a neighborhood of a point. The other aspect is global differential geometry: here we see how these local properties influence the behavior of the entire curve or surface. The main idea is that of curvature. What is curvature? It can be intrinsic or extrinsic. What's the difference? What does it mean to have greater or smaller (or positive or negative) curvature? We will answer these questions for surfaces in three-space, as well as for abstract manifolds. Topics include curvature of curves and surfaces, first and second fundamental forms, equations of Gauss and Codazzi, the fundamental theorem of surfaces, geodesics, and surfaces of constant curvature.

Units: 1

Max Enrollment: 15

Prerequisites: MATH 302.

Instructor: Tannenhauser

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Every other year

Semesters Offered this Academic Year: Not Offered

Notes: Ann E. Maurer '51 Speaking Intensive Course.

Einstein's general theory of relativity conceives of gravity as a manifestation of the geometry of spacetime. In John Archibald Wheeler's summary: "Spacetime tells matter how to move; matter tells spacetime how to curve." Differential geometry supplies the mathematical language for describing curvature. We begin by defining and building up the relevant mathematical ideas: manifolds, tensors, covariant derivatives, geodesics, and the Riemann tensor. We then apply these ideas to the physics, developing the Einstein field equation and some of its consequences, including the Schwarzschild solution and black holes, cosmology, and gravitational waves.

Units: 1

Max Enrollment: 20

Crosslisted Courses: PHYS 313

Prerequisites: At least one 300-level course in mathematics or physics, or permission of the instructor. MATH 302 or MATH 305 is recommended. Students can receive major credit for both MATH 312 and MATH 313.

Instructor: Tannenhauser

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Semesters Offered this Academic Year: Not Offered

Notes:

This course examines the number 𝝅 from various points of view in pure and applied mathematics. Topics may include: (1) Geometry: Archimedes’ estimates; volume and surface area of spheres in arbitrary dimensions; Buffon’s needle (and noodle); Galperin’s colliding balls; the isoperimetric inequality; triangles in spherical and hyperbolic geometry; Descartes’s theorem on total angular defect (discrete Gauss-Bonnet). (2) Digit hunting: Viète’s infinite product; Wallis’s product and related ideas (the Gaussian integral and its multidimensional extension, saddle point approximation, Stirling’s approximation); the Leibniz-Gregory formula and Machin-type formulae; spigot algorithms and the Bailey-Borwein-Plouffe formula; elliptic integrals, the arithmetic-geometric mean, and the Brent-Salamin algorithm. (3) Analysis: complex exponentials; Fourier series; the Riemann zeta function, dilogarithms, Bernoulli numbers, and applications to number theory (means of arithmetic functions). (4) Algebra: the irrationality and transcendence of *e* and 𝝅.

Units: 1

Max Enrollment: 20

Prerequisites: MATH 302 or MATH 305; open to students with advanced background in physics, computer science, or related fields with permission of the instructor.

Instructor: Tannenhauser

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Fall

Semesters Offered this Academic Year: Not Offered

Notes:

Geometry is concerned with the properties of rigid shapes (either planar, or in higher dimensions). When confronted with a geometric question (e.g. computing a tangent line to a curve), one often thinks first of using the tools of calculus. However, this is not the only option. Many of the most common geometric objects (e.g. lines, circles, etc.) can be defined by polynomial equations, and can therefore be studied using algebra. In this course, we will explore this connection. Specifically, we will see how one can associate a certain ring to such a geometric object, and how questions about geometry can then be translated into questions about the algebra of this ring. This course will expand upon the material learned in Math 305, with a view toward such connections to geometry. Both computational and theoretical topics will be addressed.

Students can NOT satisfy the presentation requirement in this course.

Units: 1

Max Enrollment: 15

Prerequisites: MATH 305.

Instructor: Diesl

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Spring

Semesters Offered this Academic Year: Not Offered

Notes:

Linear algebra at this more advanced level is a basic tool in many areas of mathematics and other fields. The course begins by revisiting some linear algebra concepts from MATH 206 in a more sophisticated way, making use of the mathematical maturity picked up in MATH 305. Such topics include vector spaces, linear independence, bases, and dimensions, linear transformations, and inner product spaces. Then we will turn to new notions, including dual spaces, reflexivity, annihilators, direct sums and quotients, tensor products, multilinear forms, and modules. One of the main goals of the course is the derivation of canonical forms, including triangular form and Jordan canonical forms. These are methods of analyzing matrices that are more general and powerful than diagonalization (studied in MATH 206). We will also discuss the spectral theorem, the best example of successful diagonalization, and its applications.

Units: 1

Max Enrollment: 15

Prerequisites: MATH 305.

Instructor: S. Chang

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Every other year

Semesters Offered this Academic Year: Not Offered

Notes:

Graph Theory has origins both in recreational mathematics problems (i.e., puzzles and games) and as a tool to solve practical problems in many areas of society. Topics covered will include trees and distance, connectivity and paths, network flow, graph coloring, directed graphs, and tournaments. In addition, students will gain a sense of what it means to do research in graph theory.

Units: 1

Max Enrollment: 15

Prerequisites: MATH 225 and either MATH 305 or MATH 302; or permission of the instructor.

Instructor: Trenk

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Every other year

Semesters Offered this Academic Year: Not Offered

Notes: Majors can fulfill the major presentation requirement in this course in 2023-24.

This course covers questions of enumerations, existence, and construction in combinatorics, building on the fundamental ideas introduced in MATH 225. Topics include: famous number families, combinatorial and bijective proofs, counting under equivalence, combinatorics on graphs, combinatorial designs, error-correcting codes, and partially ordered sets.

Units: 1

Max Enrollment: 15

Prerequisites: MATH 225. Co-requisite - MATH 305.

Instructor: S. Chang

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Every other year

Semesters Offered this Academic Year: Spring

Notes: Majors can fulfill the major presentation requirement in this course in Spring 2024.

In this course, students will leverage their prior mathematical knowledge to communicate complex mathematical ideas to audiences ranging from the general public to other mathematicians. Each week, students will research a new topic and produce a piece of writing explaining this topic in a specific context. Assignments may include research abstracts, book reviews, interviews with mathematicians, newspaper articles, and technical documentation. Class time will be devoted to discussing the mathematical content behind each assignment as well as workshopping students' writing. This course will give students the opportunity to ground (and expand on) the mathematics they have learned and make connections across the discipline. Moreover, this course's unique format will help students develop their research and independent learning skills.

Units: 1

Max Enrollment: 12

Prerequisites: MATH 302 and MATH 305, or permission of the instructor.

Instructor: Lange

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Other Categories: CSPW - Calderwood Seminar in Public Writing

Typical Periods Offered: Spring

Semesters Offered this Academic Year: Not Offered

Notes:

**Topic for Fall 2023: Introduction to Applied Harmonic Analysis**

**Topic for Fall 2023: Introduction to Applied Harmonic Analysis**

This course aims to introduce students to harmonic analysis, in particular Fourier series and wavelets, which are the foundations of modern mathematical techniques used in various areas ranging from signal processing in engineering to medicine and finance. We will start from the philosophy of harmonic analysis: analyze a function by decomposing it into a linear combination of elementary, oscillatory building blocks such as sines and cosines. The first part of the course will be dedicated to Fourier analysis: Fourier series, the Discrete Fourier Transform, the Fast Fourier Transform, and continuous Fourier integrals (including convolution, Plancherel’s formula, sampling, and the uncertainty principle). Then, we will introduce other orthogonal sets of functions, particularly wavelets and Haar bases, and the powerful concept of a multiresolution analysis. Next, we will discuss the applications of these orthogonal sets in fields such as approximation theory, signal and image analysis, and differential equations. Finally, time permitting, we will consider machine learning applications in dimensionality reduction and manifold learning.

Two 75-min class sessions + 50 min class for the computational lab. We will use Matlab or Mathematica for biweekly labs.

**Topic for Spring 2024: Knot Theory**

Topology deals with the properties of an object that no amount of bending, twisting, stretching, or shrinking can change (unlike geometry, which deals with the rigid properties of objects, such as length and angles). Take a piece of string, tie a knot in it, and glue the ends together. The result is a knot. Knot theory is a branch of topology that deals with knots and links in three-dimensional space. Given a knot, how do you decide if it can be untangled? Given two knots, how do you decide if one can be made to look like the other, using only bending, twisting, stretching, or shrinking? The study of knots is over 100 years old, and some of the most exciting results have occurred in the last ten years. Knot theory has evolved from an area in "pure" mathematics to include applications in molecular biology, chemistry, fluid dynamics, and quantum mechanics. This course is an introduction to the theory of knots. Among other topics, we will cover methods of knot tabulation, surfaces applied to knots, polynomials associated to knots, and applications of knot theory.

Units: 1

Max Enrollment: 15

Prerequisites: MATH 302 or permission of the instructor.

Instructor: Yacoubou Djima

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Fall

Semesters Offered this Academic Year: Fall; Spring

Notes: This is a topics course and can be taken more than once for credit as long as the topic is different each time.

Units: 1

Max Enrollment: 25

Prerequisites: Permission of the instructor. Open to juniors and seniors.

Typical Periods Offered: Spring; Fall

Semesters Offered this Academic Year: Fall; Spring

The first course in a two-semester investigation of a significant research project, culminating in the preparation of a thesis and defense of that thesis before a committee of faculty from the Mathematics department. If sufficient progress is made, students may continue with thesis research (365) in the second semester. This route does not lead to departmental honors.

Units: 1

Max Enrollment: 15

Prerequisites: Permission of the Department. GPA in Mathematics Courses above 100-level must exceed 3.0.

Instructor: Staff

Typical Periods Offered: Fall and Spring

Semesters Offered this Academic Year: Fall; Spring

Notes:

Units: 1

Max Enrollment: 25

Prerequisites: Permission of the department.

Instructor:

Typical Periods Offered: Spring; Fall

Semesters Offered this Academic Year: Fall; Spring

Notes: Students enroll in Senior Thesis Research (360) in the first semester and carry out independent work under the supervision of a faculty member. If sufficient progress is made, students may continue with Senior Thesis (370) in the second semester.

The second course a two-semester investigation of a significant research project, culminating in the preparation of a thesis and defense of that thesis before a committee of faculty from the Mathematics department. This route does not lead to departmental honors.

Units: 1

Max Enrollment: 15

Prerequisites: MATH 355 and permission of the Department.

Instructor: Staff

Typical Periods Offered: Fall and Spring

Semesters Offered this Academic Year: Fall; Spring

Notes:

Units: 1

Max Enrollment: 25

Prerequisites: MATH 360 and permission of the department.

Typical Periods Offered: Spring; Fall

Semesters Offered this Academic Year: Spring; Fall

Notes: Students enroll in Senior Thesis Research (360) in the first semester and carry out independent work under the supervision of a faculty member. If sufficient progress is made, students may continue with Senior Thesis (370) in the second semester.