MATHEMATICS

110.106 (Q)

CALCULUS I (4) Khosravi
For Biological and Social Sciences Majors   Limit 28 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

MWF 10-10:50

T 4:30-5:20

Th 3-3:50

Th 4:30-5:20

110.107 (Q)

CALCULUS II (4) Ching
For Biological and Social Sciences MajorsLimit 30 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. 07 added 01/22/08

Lec.
Sec. 01
02
03
04
 05
06
07

MWF 10-10:50
T 1:30-2:20
T 3-3:50
T 4:30-5:20
Th 1:30-2:20
Th 3-3:50
Th 4:30-5:20
T 1:30-2:20

110.109 (Q)

CALCULUS II (4) Mese
For Physical Sciences and Engineering Majors   Limit 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.

Lec.
Sec. 01
02
03
04
05

MWF 10-10:50
T 3-3:50
T 4:30-5:20
Th 1:30-2:20
Th 3-3:50
Th 4:30-5:20

110.201 (Q)

LINEAR ALGEBRA (4)Ha Limit 25 per section   Prereq: Calculus I Vector spaces, matrices, and linear transformations. Solutions of systems of
linear equations. Eigenvalues, eigenvectors, and diagonalization of matrices. Applications to differential equations.

Lec. II and Secs. 07, 08, & 09 added 11/29/07

Lec. I
Sec. 01
02
03
04
05
06

Lec. II
Sec. 07
08
09

MWF 10-10:50
T 1:30-2:20
T 3-3:50
T 4:30-5:20
Th 1:30-2:20
Th 3-3:50
Th 4:30-5:20

MWF 11-11:50
T 1:30-2:20
T 3-3:50
Th 1:30-2:20

110.202 (Q)

CALCULUS III (4) Spinu Limit 28 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.

Sec. 08 added 01/22/08

Lec. I
Sec. 01
02
03
08

Lec. II
04
05
06
07

MWF 11-11:50
T 1:30-2:20
T 3-3:50
Th 4:30-5:20
T 1:30-2:20

MWF 12-12:50
Th 4:30-5:20
Th 1:30-2:20
Th 3-3:50
Th 4:30-5:20

110.211 (Q)

HONORS MULTIVARIABLE CALCULUS (4) Brown    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

MW 12-1:15

F 12-12:50

110.212 (Q)

HONORS LINEAR ALGEBRA (4) Wilkin 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

MW 1:30-2:45

F 1:30-2:20

110.302 (E,Q)

DIFFERENTIAL EQUATIONS WITH APPLICATIONS (4) Goldberg
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

MWF 12-12:50
T 1:30-2:20
T 3-3:50
     Th 3-3:50
  Th  4:30-5:20

MWF 1:30-2:20
T 4:30-5:20
Th 1:30-2:20
Th 3-3:50

110.304 (Q)

ELEMENTARY NUMBER THEORY (4) Shallika   Limit 25

Lec.

Sec. 01

MWF 12-12:50

Th 3-3:50

110.402 (Q)

ADVANCED ALGEBRA II (4.5) ChingLimit 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

MW 12-1:15

F 12-12:50

110.405 (Q)

ANALYSIS I (4.5) Khosravi     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

MW 1:30-2:45 2:20

F  1:30-2:20

110.406 (Q)

CALCULUS ON MANIFOLDS (4.5) Wilkin   Limit 35 Course canceled 12/3/07

Sec. 01

TTh 1:30-2:20

110.413 (Q)

INTRODUCTION TO TOPOLOGY (4.5) Morava Limit 25 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

TTh 10:30-11:45 11:20

110.416 (Q)

HONORS ANALYSIS II (4) Anton   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

MW 1:30-2:45 2:20

F 1:30-2:20

110.417 (E,Q)

PARTIAL DIFFERENTIAL EQUATIONS FOR APPLICATIONS (4.5) Zou   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

TTh 12-1:15

110.421 (Q)

DYNAMICAL SYSTEMS (4) Zhang 
Limit 35   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

TTh 1:30-2:45 2:20

110.586

INDEPENDENT STUDY Course added 01/30/08

TBA

110.602

ALGEBRA Kong   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

TTh 12-1:15

110.607

COMPLEX VARIABLES Mese  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

MW 1:30-2:20

110.608

RIEMANN SURFACES  Zucker
Limit 20 

Sec. 01

TTh 1:30-2:55

110.619

LIE ALGEBRAS AND LIE GROUPS Wentworth   Limit 20

Sec. 01

TTh 9-10:15

110.635

MICROLOCAL ANALYSIS Sogge  Limit 20 Prereq: An introductiory graduate course in Real Analysis, such as 110.605. This course can be thought of as a second semester of 110.605. It will present some of the tools from harmonic and microlocal analysis that are used to study partial differential equations. Much of the course will be based on my book, "Fourier integrals in classical analysis".

Sec. 01

MW 12-1:15

110.640

SPECTRAL THEORY Shallika Limit 25 Course canceled 01/29/08

Sec. 01

MW 1:30-2:45

110.641

COMPUTATIVE ALGEBRA 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

TTh 12-1:15

110.646

RIEMANNIAN GEOMETRY Minicozzi   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

MW 1:30-2:15

110.660

QUALIFYING EXAM PROBLEMS Staff  Limit 20

Sec. 01

TBA

110.726

TOPICS IN ANALYSIS Zelditch  Limit 20

Sec. 01

TTh 10:30-11:45

110.727

TOPICS IN ALGEBRAIC TOPOLOGY Wilson  Limit 20

Sec. 01

TTh 10:30-11:45

110.730

TOPICS IN COMPLEX GEOMETRY Staff   Limit 20

Sec. 01

W 3-5:30

110.734

TOPICS IN ALGEBRAIC NUMBER THEORY Ono  Limit 20

Sec. 01

MW 12-1:15

110.742

TOPICS IN PDE (MONGE-AMPERE EQUATIONS) Spruck  Limit 20

Sec. 01

TTh 1:30-2:45

110.762

JAMI SEMINAR Nakamura

Sec. 01

TBA

110.801 799

THESIS RESEARCH Staff

110.800

INDEPENDENT STUDY