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41 - 50 of 66 results for: all courses

MATH 143: Differential Geometry

Geometry of curves and surfaces in three-space. Parallel transport, curvature, and geodesics. Surfaces with constant curvature. Minimal surfaces. Prerequisite: Math 52.
Terms: Aut | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR

MATH 145: Algebraic Geometry

An introduction to the methods and concepts of algebraic geometry. The point of view and content will vary over time, but include: affine varieties, Hilbert basis theorem and Nullstellensatz, projective varieties, algebraic curves. Required: 120. Strongly recommended: additional mathematical maturity via further basic background with fields, point-set topology, or manifolds.
Terms: Spr | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR
Instructors: Zhang, Z. (PI)

MATH 147: Differential Topology

Introduction to smooth methods in topology including tranvsersality, intersection number, fixed point theorems, as well as differential forms and integration. Prerequisites: Math 144 or equivalent.
Terms: Spr | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR
Instructors: Chodosh, O. (PI)

MATH 148: Algebraic Topology

Fundamental group, covering spaces, Euler characteristic, homology, classification of surfaces, knots. Prerequisite: 109 or 120.
Terms: Win | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR

MATH 151: Introduction to Probability Theory

A proof-oriented development of basic 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. CS majors can petition to use Math 151 in place of CS 109, provided they expect to take either CS 228 or CS 229 as well. Prerequisite: Math 61CM, or Math 52 and either Math 56 or Math 115 (or equivalent).
Terms: Win | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR

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. Prerequisite: Math 51 and proof-writing experiences (e.g., Math 56).
Terms: Win | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR

MATH 154: Algebraic Number Theory

Properties of number fields and Dedekind domains, quadratic and cyclotomic fields, applications to some classical Diophantine equations. Prerequisites: 120 and 121, especially modules over principal ideal domains and Galois theory of finite fields.
Last offered: Spring 2023 | UG Reqs: GER:DB-Math, WAY-FR

MATH 155: Analytic Number Theory

Introduction to Dirichlet series and Dirichlet characters, Poisson summation, Gauss sums, analytic continuation for Dirichlet L-functions, applications to prime numbers (e.g., prime number theorem, Dirichlet's theorem). Prerequisites: Complex analysis ( Math 106 or 116), Math 152 (or comparable familiarity with the Euclidean algorithm, multiplicative group modulo n, and quadratic reciprocity), and experience with basic analysis arguments.
Terms: Aut | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR

MATH 161: Set Theory

Informal and axiomatic set theory: sets, relations, functions, and set-theoretical operations. The Zermelo-Fraenkel axiom system and the special role of the axiom of choice and its various equivalents. Well-orderings and ordinal numbers; transfinite induction and transfinite recursion. Equinumerosity and cardinal numbers; Cantor's Alephs and cardinal arithmetic. Open problems in set theory. Prerequisite: Math 56 or comfort with proof-writing.
Last offered: Autumn 2022 | UG Reqs: GER:DB-Math, WAY-FR

MATH 171: Fundamental Concepts of Analysis

Recommended for Mathematics majors and required of honors Mathematics majors. A more advanced and general version of Math 115, introducing and using metric spaces. Properties of Riemann integrals, continuous functions and convergence in metric spaces; compact metric spaces, basic point set topology. Prerequisite: Math 61CM, or 61DM, or Math 51 and Math 115. WIM
Terms: Aut, Spr | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR
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