Treatment of (mostly) differential calculus. Includes an introduction to integration as well. Compared to 103, which covers the same calculus topics, the slower pace of 101 allows more in-class review of fundamental precalculus material including basic trigonometry, the graphs and properties of standard functions (e.g. logarithms, exponentials), inverse functions, algebraic techniques for solving equations (e.g. factoring, completing the square), equations for ellipses, hyperbolas and parabolas.

# All courses in Fall 2011

First semester of the standard 3-semester calculus sequence 103/104/201. Every spring about half of the students from this course continue the sequence with 104. Others continue with 175.

Second semester of the 3-semester calculus sequence 103/104/201. Main topics are Integration and Series. Offered Fall and Spring.

Taken concurrently with EGR/MAT/PHY 192, this course offers an integrated presentation of the material from PHY 103 (General Physics: Mechanics and Thermodynamics) and MAT 201 (Multivariable Calculus) with an emphasis on applications to engineering. Physics topics include: mechanics with applications to fluid mechanics; wave phenomena; and thermodynamics. Open only to BSE freshmen and adminstered by the Keller Center.

Taken concurrently with EGR/MAT/PHY 191, this course offers an integrated presentation of the material from PHY 103 (General Physics: Mechanics and Thermodynamics) and MAT 201 (Multivariable Calculus) with an emphasis on applications to engineering.
Open only to BSE freshmen and administered by the Keller Center.

Last offered in Spring 2012. Replaced by MAT175, beginning Fall 2012.
One semester of multivariable mathematics for finance certificate or for math-track economics majors. Covers selected topics from linear algebra and multivariable calculus in order to give minimal preparation for upper division quantitative courses in economics. (Not sufficient preparation for 300-level math courses).

Linear Algebra, mostly in real n-space. Companion course to 201. Main topics are matrices, linear transformations, linear independence and dimension, bases and coordinates, determinants, orthogonal projection, least squares, eigenvalues, eigenvectors and their applications to quadratic forms and dynamical systems. Offered Fall and Spring.

Advanced multivariable calculus. More theoretical treatment of limits, continuity, differentiation and integration for functions of several variables than that found in MAT201, but less theoretical than MAT218. A course for those with a strong mathematical background and interest. Recommended for physics majors and students interested in applied math. Offered Fall only.

Rigorous, proof-based introduction to classical number theory, to prepare for higher-level courses in the department. Topics include Pythagorean triples and sums of squares, unique factorization, Chinese remainder theorem, arithmetic of Gaussian integers, finite fields and cryptography, arithmetic functions and quadratic reciprocity. There will be a topic, chosen by the instructor, from more advanced or more applied number theory: possibilities include p-adic numbers, cryptography, and Fermat's Last Theorem. Suitable both for students preparing to enter the Mathematics Department and for non-majors interested in exposure to higher mathematics. Fall Only.

Rigorous course in multivariable analysis. Continuation of MAT215/217 (or MAT203/204, with instructor's permission). Topics include metric spaces, completeness, compactness, total derivatives, partial derivatives, inverse function theorem, implicit function theorem, Riemann integrals in several variables, Fubini's theorem, change of variables theorem, and the theorems of Green, Gauss, and Stokes.

A treatment of the theory of differential equations. The objective is to provide the student with an ability to solve problems in this field. Administered and staffed by the Mechanical Engineering Department (MAE).

Introduction to the study of ordinary differential equations; explicit solutions, general properties of solutions, and applications. (Renumbered as MAT427 beginning AY 2012-13)

This course introduces students to Combinatorics, a fundamental mathematical discipline as well as an essential component of many mathematical areas. (Renumbered as MAT377 beginning in AY 2012-13)

An introduction to probability and its applications.

Introduction to real analysis, Lebesgue theory of measure and integration on the line and n-dimensional space, introduction to Fourier Series.

Calculus of functions of one complex variable, power series expansions, residues, and conformal mapping. (Renumbered as MAT330 beginning AY 2012-13)

Group theory, field extensions, splitting fields, the main theorem of Galois theory, cyclotomic extensions, Kummer extensions, solvability by radicals. (Replaced by MAT345 beginning AY 2012-13).

Singular homology, cellular complexes, Poincare duality, Lefschetz fixed point theorem. (Renumbered as MAT560 beginning AY 2012-13)

Riemannian geometry of surfaces. Surfaces in Euclidan space, second fundamental form, minimal surfaces, geodesics, Gauss curvature, Gauss-Bonnet Theorem, uniformization of surfaces. (Renumbered as MAT355 beginning AY 2012-13)

Study of functions of a complex variable, with emphasis on interrelations with other parts of mathematics. (Renumbered as MAT335 beginning AY 2012-13)

The study of local fields and its application ot Galois theory.

Introductory course in modern Analysis with applications to Partial Differential Equations,Distribution Theory, Maximal Functions, Littlewood/Paley decompositions and applications, Strichartz inequalities, Bilinear Estimates, Concentrated compactness and applications. (Renumbered as MAT520 beginning AY 2012-13)

An introduction to modern cryptography with an emphasis on the fundamental ideas.

The course will cover the essentials of the first eleven chapters of the textbook, "Analysis" by Lieb and Loss.

Algebraic number theory. (Renumbered as MAT419 beginning AY 2012-13)

Lie algebras and Lie groups are important in many areas of mathematics as well as theoretical physics. The course gives an introduction to the topic.

Junior Seminar on the mathematical theory of knots, with John Baldwin.