| Note: Text highlighted
in red indicates that a change
has been made to the course listing. The red text indicates the current, updated information. |
MATHEMATICS |
110.106 (Q) |
CALCULUS I (4) Ha Wilkin
For Biological and Social Sciences Majors Limit 28 25 per section Differential and integral calculus. Includes analytic geometry, functions, limits, integrals and derivatives, introduction to differential equations, functions of several variables, linear systems, and applications for systems of linear differential equations, probability distributions. |
Lec.
Sec. 01
02
03 |
MTW 10
F 9
F 12
Th 10:30-11:30 |
110.107 (Q) |
CALCULUS II (4) Spinu For Biological and Social Sciences Majors Limit 30 28 per section Prereq: Calculus I Differential and integral calculus. Includes analytic geometry, functions, limits, integrals and derivatives, introduction to differential equations, functions of several variables, linear systems, applications for systems of linear differential equations, probability distributions.
Sec. 06 added 12/20/06 |
Lec.
Sec. 01
02
03
04
05
06
|
MTW 10
F 9
F 12
F 12
Th 10:30-11:30
Th 10:30-11:30
F 12 |
110.109 (Q) |
CALCULUS II (4) Zucker
For Physical Sciences and Engineering MajorsLimit 28 per section Prereq: Calculus I Differential and integral calculus. Includes analytic geometry, functions, limits, integrals and derivatives, polar coordinates, parametric equations, Taylor's theorem and applications, infinite sequences and series.
Sec. 05 canceled 02/02/07 |
Lec.
Sec. 01
02
03
04
05
|
MTW 10
F 9
F 12
F 12
Th 10:30-11:30
F 9
|
110.201 (Q) |
LINEAR ALGEBRA (4)PaupertLimit 25 per section Prereq: Calculus I Vector spaces, matrices, and linear transformations. Solutions of systems oflinear equations. Eigenvalues, eigenvectors, and diagonalization ofmatrices. Applications to differential equations. |
Lec. I
Sec. 01
02
03
04
05
06 |
MTW 10
F 9
Th 10:30-11:30
F 12
F 12
F 9
Th 10:30-11:30 |
110.202 (Q) |
CALCULUS III (4) Wilkin Ha / Ching
Limit 28 25 per section Prereq: 110.107, 110.109 or 110.112. Calculus of functions of more than one variable: partial derivatives, and applications; multiple integrals, line and surface integrals; Green's Theorem, Stokes' Theorem, and Gauss' Divergence Theorem. |
Lec. I
Sec. 01
02
03
Lec. II
04
05
06
07 |
MTW 10
Th 9
Th 12
F 12
MTW 10
Th 9
Th 12
F 9
F 12 |
110.204 (Q) |
ELEMENTARY NUMBER THEORY (4) Zhang Limit 30 Prereq: a good high school background including a year of Calculus. Primes and prime factorization, congruences, Euler's function, quadratic reciprocity, primitive roots, solutions to polynomial congruences (Chevalley's theorem), Diophantine equations including the Pythagorean and Pell equations, Gaussian integers, Dirichlet's theorem on primes. |
Lec.
Sec. 01 |
MTW 11
F 12 |
110.211 (Q) |
HONORS MULTIVARIABLE CALCULUS (4) Wilkin Limit 35 Prereq: B+ or better in Calculus II or 5 in the BC AP exam This course includes the material in Calculus III (202) with some additional applications and theory. Recommended for mathematically able students majoring in physical science, engineering, or especially mathematics. 110.211-212 used to be an integrated yearlong course, but now the two are independent courses and can be taken in either order. |
Lec.
Sec. 01 |
MTW 12
F 12 |
110.212 (Q) |
HONORS LINEAR ALGEBRA (4) Ha Limit 45 Prereq: Calculus II or III or equivalent, preferably honors. This course includes the material in Linear Algebra (201) with some additional applications and theory. Recommended for mathematically able students majoring in physical science, engineering, or mathematics. |
Lec.
Sec. 01 |
MTW 12
F 12 |
110.302 (E,Q) |
DIFFERENTIAL EQUATIONS WITH APPLICATIONS (4) DeSilva/ Brown Limit 35 per section Prereq: Calculus II III This is an applied course in ordinary differential equations, which is primarily for students in the biological, physical and social sciences, and engineering. The purpose of the course is to familiarize the student with the techniques of solving ordinary differential equations. |
Lec. I
Sec. 01
02
03
04
Lec. II
Sec. 05
06
07 |
MTW 12
F 9
Th 12
Th 12
F 12
MTW 1
Th 10:30-11:30
F 12
F 12 |
110.328 (Q) |
NON-EUCLIDEAN GEOMETRY (4) Paupert Limit 25 Prereq: Calculus III This is an applied course in ordinary differential equations, which is primarily for students in the biological, physical and social sciences, and engineering. The purpose of the course is to familiarize the student with the techniques of solving ordinary differential equations. |
Lec.
Sec. 01 |
MTW 1
F 12 |
110.402 (Q) |
ADVANCED ALGEBRA II (4.5) Kong Limit 30 Prereq: 110.401 Splitting field of a polynomial, algebraic closure of a field. Galois theory: correspondence between subgroups and subfields. Solvability of polynomial equations by radicals. |
Lec.
Sec. 01 |
MTW 11
Th 9 |
110.405 (Q) |
ANALYSIS I (4.5) DeSilva Limit 35 Prereq: Calculus III, Linear Algebra Real and complex number systems, topology of metric spaces, limits, continuity, infinite sequences and series, differentiation, Riemann-Stieltjes integration. |
Lec.
Sec. 01 |
MTW 1
F 9 |
110.406 (Q) |
ANALYSIS II (4.5) Nakamura Limit 35 Prereq: 110.405 Continuation of 110.405 notions of modern analysis. Sequences and series of functions, Fourier series, equicontinuity and the Arzela-Ascoli theorem, the Stone-Weierstrass theorem. Functions of several variables, the inverse and implicit function theorems, introduction to the Lebesgue integral. |
Lec.
Sec. 01 |
MTW 1
F9 |
110.413 (Q) |
INTRODUCTION TO TOPOLOGY (4.5) ChingLimit 15 Topological spaces, connectedness, compactness, quotient spaces, metric spaces, function spaces. An introduction to algebraic topology: covering spaces, the fundamental group, and other topics as time permits. |
Sec. 01 |
MTW 2 |
110.416 (Q) |
HONORS ANALYSIS II (4) Goldberg Limit 15 Prerequisite: 110.415, or 110.405 and permission of the instructor. Continuation of 110.415, introduction to real analysis. Lebesgue integration and differentiation. Elementary Hilbert and Banach space theory. Baire category theorem. |
Lec.
Sec. 01 |
MTW 1
F 10:30-11:30 |
110.417 (E,Q) |
PARTIAL DIFFERENTIAL EQUATIONS FOR APPLICATIONS (4.5) Blair Limit 35 Prereq: Calculus III, Linear Algebra Recommended: 110.405 Classification of second order equations, well-posed problems, separation of variables and expansions of solutions. The wave equation: Cauchy problem, Poisson's solution, energy inequalities, domains of influence and dependence. |
Sec. 01 |
MTW 12 |
110.421 (Q) |
DYNAMICAL SYSTEMS (4) Brown Limit 35 15 Prereqs: Calculus III, Linear Algebra, ODEs. This is a course in the modern theory of Dynamical Systems. Topic include existence and uniqueness of general ODEs, nonlinear analysis and stability, including bifurcation theory and stable and center manifolds, smooth flows, limit sets, Hamiltonian mechanics, perturbation theory and structural stability. |
Sec. 01 |
MTW 3 |
110.423 (Q)
|
LIE GROUPS FOR UNDERGRADUATES (4) Boardman Limit 25 Prereq: Calculus III , Prior knowledge of group theory would be helpful. This course is an introduction to Lie Groups and their representations at the upper undergraduate level. It will cover basic Lie Groups such as SU (2), U (n), the Euclidean Motion Group and Lorentz Group. This course is useful for students who want a working knowledge of group representations. We will also discuss some aspects of the role of symmetry groups in particle physics such as some of the formal aspects of the electroweak and the strong interactions. A good reference is the book Lie Algebras in Particle Physics by Howard Georgi. Course canceled 12/06/06
|
Sec. 01
|
MTW 1
|
110.602 |
ALGEBRA Shokurov Limit 20 Prereq: 110.401-402 An introductory graduate course on fundamental topics in algebra to provide the student with the foundations for Number Theory, Algebraic Geometry, and other advanced courses. Topics include group theory, commutative algebra, Noetherian rings, local rings, modules, and rudiments of category theory, homological algebra, field theory, Galois theory, and non-commutative algebras. |
Sec. 01 |
MTW 1 |
110.607 |
COMPLEX VARIABLES Zelditch Limit 20 Prereq: 110.311, 110.405 Analytic functions of one complex variable. Topics include Mittag-Leffler Theorem, Weierstrass factorization theorem, elliptic functions, Riemann-Roch theorem, Picard theorem, and Nevanlinna theory. |
Sec. 01 |
MTW 2 |
110.616 |
ALGEBRAIC TOPOLOGY Boardman Limit 20 Prereq: 110.401, 110.413 Polyhedra, simplicial and singular homology theory, Lefschetz fixed-point theorem, cohomology and products, homological algebra, Künneth and universal coefficient theorems, Poincaré and Alexander duality theorems. |
Sec. 01 |
ThF 2-3:15 |
110.620 |
LIE GROUPS AND LIE ALGEBRAS Boardman Limit 25 Course added 12/06/06 |
Sec. 01 |
MTW 11 |
110.632 |
PARTIAL DIFFERENTIAL EQUATIONS Minicozzi Limit 20 Prereq: 110.605-606 An introductory graduate course in partial differential equations. Classical topics include first order equations and characteristics, the
Cauchy-Kowalevski theorem, Laplace's equation, heat equation, wave equation,
fundamental solutions, weak solutions, Sobolev spaces, maximum principles.
The second term focuses on special topics such as second order elliptic theory. |
Sec. 01 |
MW 9:30-11 |
110.640 |
SPECTRAL THEORY Goldberg Limit 20 |
Sec. 01 |
MTW 3 |
110.644 |
ALGEBRAIC GEOMETRY ShokurovLimit 20 Affine varieties and commutative algebra. Hilbert's theorems about polynomials in several variables with their connections to geometry. General varieties and projective geometry. Dimension theory and smooth varieties. Sheaf theory and cohomology. Applications of sheaves to geometry; e.g., the Riemann-Roch Theorem. Other topics may include Jacobian varieties, resolution of singularities, geometry on surfaces, schemes, connections with complex analytic geometry and topology. |
Sec. 01 |
MTW 2 |
110.646 |
RIEMANNIAN GEOMETRY Mese Limit 20 Prereq: 110.405, 110.413Differential manifolds, vector fields, Frobenius’ theorem. Differential forms, deRham’s theorem, vector bundles, connections, curvature, Chern classes, Cartan structure equations. Riemannian manifolds, Bianchi identities, geodesics, exponential maps. Geometry of submanifolds, hypersurfaces in Euclidean space. Other topics as time permits, e.g. harmonic forms and Hodge’s theorem, Jacobi equation, variation of arc length and area, Chern-Gauss-Bonnet theorems. |
Sec. 01 |
MTW 12-1:15 |
110.660 |
QUALIFYING EXAM PROBLEMS Staff Limit 20 |
Sec. 01 |
TBA |
110.725 110.726 |
TOPICS IN ANALYSIS (NONLINEAR DISPERSIVE EQUATIONS WAVE EQUATIONS) SoggeLimit 20 |
Sec. 01 |
MTW 11 |
110.730 |
TOPICS IN COMPLEX GEOMETRY Shiffman Limit 20 |
Sec. 01 |
MW 2-3:15 |
110.732 |
TOPICS IN MATHEMATICAL PHYSICS Zelditch Limit 20 |
Sec. 01 |
MTW 1 |
110.734 |
TOPICS IN ALGEBRAIC NUMBER THEORY Ono Limit 20 |
Sec. 01 |
MW 1:30-3 |
110.738 |
TOPICS IN ALGEBRAIC GEOMETRY (MOTIVES) Consani Limit 20 |
Sec. 01 |
MTW 11 3 |
110.742 |
TOPICS IN PDE (MONGE-AMPERE EQUATIONS) Spruck Limit 20 |
Sec. 01 |
TTh 2-3:15 |
110.762 |
JAMI SEMINAR Nakamura |
Sec. 01 |
TBA |
110.799 |
THESIS RESEARCH Staff |
|
|
110.800 |
INDEPENDENT STUDY |
|
|
