Bryn Mawr College Math Department: Courses

Courses

Bryn Mawr College offers a wide variety of mathematics courses at both the undergraduate and graduate level.

Additional courses are available at Haverford and Swarthmore colleges:

Bryn Mawr Courses

001. Fundamentals of Mathematics
Basic techniques of algebra, analytic geometry, graphing and trigonometry for students who need to improve these skills before entering other courses that use them, both inside and outside mathematics. Placement in this course is by advice of the department and permission of the instructor. (staff)

101, 102. Calculus with Analytic Geometry
Differentiation and integration of algebraic and elementary transcendental functions, with the necessary elements of analytic geometry and trigonometry; the fundamental theorem, its role in theory and applications, methods of integration, applications of the definite integral, infinite series. May include a computer lab component. Prerequisite: math readiness or permission of the instructor. (staff, Division II or Quantitative Skills)

104. Elements of Probability and Statistics
Basic concepts and applications of probability theory and statistics, including finite sample spaces, permutations and combinations, random variables, expected value, variance, conditional probability, hypothesis testing, linear regression and correlation. The computer is used; prior knowledge of a computer language is not required. This course may not be taken after any other statistics course. Prerequisite: math readiness or permission of instructor. (staff, Quantitative Skills)

201. Multivariable Calculus
Vectors and geometry in two and three dimensions, partial derivatives, extremal problems, double and triple integrals, line and surface integrals, Green’s and Stokes’ Theorems. May include a computer lab component. Prerequisite: Mathematics 102 or permission of instructor. (staff, Division II or Quantita-tive Skills)

203. Linear Algebra
Matrices and systems of linear equations, vector spaces and linear transformations, determinants, eigenvalues and eigenvectors, inner product spaces and quadratic forms. May include a computer lab component. Prerequisite: Mathematics 102 or permission of instructor. (staff, Division II or Quantitative Skills)

205. Theory of Probability with Applications
Random variables, probability distributions on Rn, limit theorems, random pro-cesses. Prerequisite: Mathematics 201. (Cheng, Division II or Quantitative Skills)

206. Transition to Higher Mathematics
An introduction to higher mathematics with a focus on proof writing. Topics include active reading of mathematics, constructing appropriate examples, problem solving, logical reasoning and communication of mathematics through proofs. Students will develop skills while exploring key concepts from algebra, analysis, topology and other advanced fields. Corequisite: Mathematics 203; not open to students who have had a 300-level math course. (Hughes, Division II or Quantitative Skills)

210. Differential Equations with Applications
Ordinary differential equations, including general first-order equations, linear equations of higher order and systems of equations, via numerical, geometrical and analytic methods. Applications to physics, biology and economics. Coreq-uisite: Math 201 or Math 203. (Donnay, Division II or Quantitative Skills)

221. Introduction to Topology and Geometry
An introduction to the ideas of topology and geometry through the study of knots and surfaces in 3-dimensional space. The course content may vary from year to year, but will generally include some historical perspectives and some discussion of connections with the natural and life sciences. Corequisite: Mathematics 201 or 203. (Melvin, Division II or Quanti-tative Skills)

225. Introduction to Financial Mathematics
Topics to be covered include market conventions and instruments, Black-Scholes option-pricing model, and practical aspects of trading and hedging. All necessary definitions from probability theory (random variables, normal and lognormal distribution, etc.) will be explained. Prerequisite: Mathematics 102. Eco-nomics 105 is recommended. (staff, Division II) Not offered in 2003-04.

231. Discrete Mathematics
An introduction to discrete mathematics with strong applications to computer science. Topics include set theory, functions and relations, propositional logic, proof techniques, recursion, counting techniques, difference equations, graphs and trees. (Weaver, Division II or Quantita- tive Skills; cross-listed as Computer Science 231 and Philosophy 230)

251. Introduction to Chaotic Dynamical Systems
Topics to be covered may include iteration, orbits, graphical and computer analysis, bifurcations, symbolic dynamics, fractals, complex dynamics and applications. Prerequisite: Mathematics 102. (staff, Division II or Quantitative Skills) Not offered in 2003-04.

290. Elementary Number Theory
Properties of the integers, divisibility, primality and factorization, congruences, Chinese remainder theorem, multiplicative functions, quadratic residues and quadratic reciprocity, continued fractions, and applications to computer science and cryptography. Prerequisite: Mathematics 102. (staff, Division II or Quantitative Skills)
Not offered in 2003-04.

295. Selected Topics in Mathematics
This course will cover topics that are not part of the standard departmental offerings and will vary from semester to semester. Students may take this course more than once. Prerequisites vary, depending on the topic. (staff, Division II)
Not offered in 2003-04.

301, 302. Introduction to Real Analysis
The real number system, elements of set theory and topology, continuous functions, uniform convergence, the Riemann integral, power series, Fourier series and other limit processes. Prerequisite: Math- ematics 201. (Donnay, Traynor, Divi-
sion II)

303, 304. Abstract Algebra
Groups, rings, fields and their morphisms. Prerequisite: Mathematics 203. (Cheng, Melvin, Division II)
308. Applied Mathematics
In fall 2003, this course will explore techniques of operations research. Topics will range from linear optimization techniques, such as the simplex method, to nonlinear optimization methods and metaheuristics, such as genetic algorithms, simulated annealing and ant algorithms. Prerequisites: Mathematics 201 and 203 (or equivalent) or permission of instructor. (Geer, Division II or Quan-titative Skills)

310. Introduction to the Mathematics of Financial Derivatives
Topics to be covered may include Arbitrage Theorem, pricing derivatives, Wiener and Poisson processes, martingales and martingale representations, Ito’s Lemma, Black-Scholes partial differentiation equation, Girsanov Theorem and Feynman-Kac Formula. Prerequi-sites: Mathematics 201 and 205, Eco-nomics 105, or permission of instructor. Mathematics 311 is recommended. (staff, Division II) Not offered in 2003-04.

311. Partial Differential Equations
Heat and wave equations on bounded and unbounded domains, Laplace’s equation, Fourier series and the Fourier transform, qualitative behavior of solutions, computational methods. Applications to the physical and life sciences. Prerequisite: Mathematics 301 or permission of instructor. (staff, Division II)
Not offered in 2003-04.

312, 313. Topology
General topology (topological spaces, continuity, compactness, connectedness, quotient spaces), the fundamental group and covering spaces. Introduction to geometric topology (classification of surfaces, manifolds) and algebraic topology (homotopy theory, homology and cohomology theory, duality on manifolds). Prerequisites: Mathematics 201 and 203, or permission of instructor. (staff, Division II) Not offered in 2003-04.

315. Geometry
An introduction to geometry with an emphasis that varies from year to year. For fall 2003, the topic will be differential geometry, where local and global properties of parameterized curves and surfaces will be studied. Prerequisites: Mathematics 201 and 203 (or equivalent) or permission of instructor. (Traynor, Division II)

322, 323. Functions of Complex Variables
Analytic functions, Cauchy’s theorem, Laurent series, calculus of residues, conformal mappings, Moebius transformations, infinite products, entire functions, Riemann mapping theorem, Picard’s theorem. Prerequisite: Mathematics 301 or permission of instructor. (staff, Division II) Not offered in 2003-04.

351. Chaotic Dynamical Systems
Topics chosen from among Cantor set, periodic points of a map, chaotic maps on the interval, period doubling, symbolic dynamics, maps on a circle and torus, Mandelbrot set, fractals and Julia sets, and applied examples of dynamical systems. Prerequisites: Mathematics 201, 203 and 301 or permission of instructor. (Donnay, Division II)
Not offered in 2003-04.

361. Introduction to Harmonic Analysis and Wavelets
A first introduction to harmonic analysis and wavelets. Topics to be covered include Fourier series on the circle, Fourier transforms on the line and space, Discrete Wavelet Transform, Fast Wavelet Transform and filter-bank representation of wavelets. Prerequisite: Mathematics 203 or permission of instructor. (Cheng, Division II)

390. Number Theory
Algebraic number fields and rings of in- tegers, quadratic and cyclotomic fields, norm and trace, ideal theory, factorization and prime decomposition, lattices and the geometry of algebraic integers, class numbers and ideal class groups, computational methods, Dirichlet’s unit theorem. Prerequisite: Mathematics 303 or permission of instructor. (staff, Division II) Not offered in 2003-04.

395, 396. Research Seminar
A research seminar for students involved in individual or small group research under the supervision of the instructor. With permission, the course may be repeated for credit. Prerequisite: Mathe-matics 203 or permission of instructor. (staff, Division II)

398, 399. Senior Conference
A seminar for seniors majoring in mathematics. Topics vary from year to year. (Cunningham, Division II)

403. Supervised Work (staff)

501, 502. Real Analysis I and II

503, 504. Algebra I and II

505, 506. Topology I and II

511, 512. Complex Analysis I and II

515, 516. Geometry I and II

521, 522. Dynamical Systems I and II

523,524. Number Theory I and II

563, 564. Lie Algebras I and II

601, 602. Topics in Analysis

603, 604. Topics in Algebra