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Course Criteria
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3.00 Credits
NA/QU R.Manning A survey of major algorithms in modern scientific computing, with a focus on continuous problems. Topics include root-finding, optimization, Monte Carlo methods, and discretization of differential equations, with applications in the natural and social sciences. Prerequisite: MATH 114 and 115, or advanced placement, or instructor consent. Typically offered in alternate years.
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3.00 Credits
NA (Cross-listed in Computer Science) S.Lindell Prerequisite: Math 215 ( may be taken concurrently). Offered occasionally.
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3.00 Credits
NA/QU W.Miao 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. Prerequisite: One of the following: MATH 203, PSYC 200, or ECON 203 or 204. MATH 215 is recommended. Typically offered in alternate years.
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3.00 Credits
NA D.Lippel An introduction to deductive reasoning, mathematical proof, and fundamental ideas of higher mathematics. Emphasis will be placed on developing strategies for understanding and constructing proofs. Topics include basic logic, set theory, and relations. This is a quarter-long course; it is taught in the first half of the fall semester. Prerequisite: MATH 121 and MATH 215. Concurrent registration in MATH 317 or MATH 333. Does not count toward the major.
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3.00 Credits
NA J.Sabloff A rigorous development of topics in calculus, including detailed treatment of the axioms of the real number line, cardinality, topology of normed spaces, compactness, and various notions of convergence. This course also serves as a thorough introduction to clear, correct writing of mathematical proofs. Prerequisite: MATH 215 and either MATH 121 or 216, or instructor consent. Corequisite of MATH 299 for students who have not had MATH 216 or math at the 300 level. Typically offered every Fall.
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3.00 Credits
NA J.Sabloff A continuation of MATH 317, focusing particularly on sequences and series of functions with applications (e.g., Fourier series, existence and uniqueness of solutions to differential equations). Other advanced topics (such as the Lebesgue integral, calculus of variations, Fourier transforms, special functions, approximation theorems or fixed point theorems) are included according to instructor and student interest. Prerequisite: MATH 317. Typically offered every Spring.
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3.00 Credits
NA Y.Tai A rigorous treatment of fundamental algebraic structures. Topics include: axioms for integers, modular arithmetic, polynomials, rings, fields, and introduction to groups. Prerequisite: Math 215 and either Math 121 or 216, or instructor consent. Corequisite of Math 299 for students who have not had Math 216 or math at the 300 level. Typically offered every Fall.
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3.00 Credits
NA D.Lippel A continuation of Math 333a. Topics include: Sylow's theorems for groups, finite abelian groups, finite fields, Galois theory, modules, and advanced linear algebra. Prerequisite: MATH 333 or instructor consent. Typically offered every Spring.
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3.00 Credits
NA J.Sabloff 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: MATH 317 and 333, or instructor consent. Typically offered yearly in alternation with Bryn Mawr.
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3.00 Credits
NA J.Sabloff Algebraic topology and its applications to low-dimensional topology. The course investigates surfaces, knots, and 3-manifolds using the fundamental group, basic simplicial homology, and the mapping class group. Prerequisite: MATH 335. Typically offered yearly in alternation with Bryn Mawr.
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