printer friendly pageMATH 138: Celestial Mechanics
Mathematically rigorous introduction to the classical N-body problem: the motion of N particles evolving according to Newton's law. Topics include: the Kepler problem and its symmetries; other central force problems; conservation theorems; variational methods; Hamilton-Jacobi theory; the role of equilibrium points and stability; and symplectic methods. Prerequisites: 53, and 115 or 171.
Last offered: Autumn 2014
| UG Reqs: GER:DB-Math
MATH 143: Differential Geometry
Geometry of curves and surfaces in three-space and higher dimensional manifolds. Parallel transport, curvature, and geodesics. Surfaces with constant curvature. Minimal surfaces.
Last offered: Spring 2015
| UG Reqs: GER:DB-Math
MATH 145: Algebraic Geometry
Hilbert's nullstellensatz, complex affine and projective curves, Bezout's theorem, the degree/genus formula, blow-up, Riemann-Roch theorem. Prerequisites: 120, and 121 or knowledge of fraction fields. Recommended: familiarity with surfaces equivalent to 143, 146, 147, or 148.
Last offered: Winter 2015
| UG Reqs: GER:DB-Math
MATH 146: Analysis on Manifolds
Differentiable manifolds, tangent space, submanifolds, implicit function theorem, differential forms, vector and tensor fields. Frobenius' theorem, DeRham theory. Prerequisite: 52 or 52H.
Last offered: Autumn 2014
| UG Reqs: GER:DB-Math
MATH 147: Differential Topology
Smooth manifolds, transversality, Sards' theorem, embeddings, degree of a map, Borsuk-Ulam theorem, Hopf degree theorem, Jordan curve theorem. Prerequisite: 115 or 171.
Terms: Spr
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Wieczorek, W. (PI)
;
Nguyen, D. (TA)
MATH 148: Algebraic Topology
Fundamental group, covering spaces, Euler characteristic, homology, classification of surfaces, knots. Prerequisite: 109 or 120.
Last offered: Spring 2015
| UG Reqs: GER:DB-Math
MATH 151: Introduction to Probability Theory
Counting; axioms of probability; conditioning and independence; expectation and variance; discrete and continuous random variables and distributions; joint distributions and dependence; central limit theorem and laws of large numbers. Prerequisite: 52 or consent of instructor.
Last offered: Winter 2015
| UG Reqs: GER:DB-Math
MATH 152: Elementary Theory of Numbers
Euclid's algorithm, fundamental theorems on divisibility; prime numbers; congruence of numbers; theorems of Fermat, Euler, Wilson; congruences of first and higher degrees; quadratic residues; introduction to the theory of binary quadratic forms; quadratic reciprocity; partitions.
Terms: Win
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Soundararajan, K. (PI)
;
Warner, E. (TA)
MATH 154: Algebraic Number Theory
Properties of number fields and Dedekind domains, quadratic and cyclotomic fields, applications to some classical Diophantine equations; introduction to elliptic curves. Prerequisites: 120 and 121, especially modules over principal ideal domains and Galois theory of finite fields.
Last offered: Spring 2015
| UG Reqs: GER:DB-Math
MATH 155: Analytic Number Theory
Topics in analytic number theory such as the distribution of prime numbers, the prime number theorem, twin primes and Goldbach's conjecture, the theory of quadratic forms, Dirichlet's class number formula, Dirichlet's theorem on primes in arithmetic progressions, and the fifteen theorem. Prerequisite: 152, or familiarity with the Euclidean algorithm, congruences, residue classes and reduced residue classes, primitive roots, and quadratic reciprocity.
Terms: Spr
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Soundararajan, K. (PI)
;
Florea, A. (TA)
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