printer friendly pageMATH 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.
Terms: Aut
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Lindblad Petersen, O. (PI)
;
Fauteux-Chapleau, F. (TA)
MATH 144: Introduction to Topology and Geometry
Point set topology, including connectedness, compactness, countability and separation axioms. The inverse and implicit function theorems. Smooth manifolds, immersions and submersions, embedding theorems. Prerequisites:
Math 61CM, or
Math 51 and familiarity with linear algebra and analysis arguments at the level of 113 and 115 respectively.
Terms: Win
| Units: 3
| UG Reqs: WAY-FR
Instructors:
Manolescu, C. (PI)
;
Nguyen, D. (TA)
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.
Last offered: Autumn 2018
| UG Reqs: GER:DB-Math, WAY-FR
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 62CM or
Math 144.
Terms: Spr
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Chodosh, O. (PI)
;
Pandit, N. (TA)
MATH 148: Algebraic Topology
Fundamental group, covering spaces, Euler characteristic, homology, classification of surfaces, knots. Prerequisite: 109 or 120.
Terms: Aut
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Kerckhoff, S. (PI)
;
Arana Herrera, F. (TA)
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. nPrerequisite: Either
Math 61CM or
Math 52, and
Math 115 or equivalent.
Terms: Win
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Kwan, M. (PI)
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, WAY-FR
Instructors:
Soundararajan, K. (PI)
;
Miagkov, K. (TA)
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.
Terms: Spr
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Conrad, B. (PI)
;
Cotner, S. (TA)
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.
Last offered: Spring 2020
| UG Reqs: GER:DB-Math, WAY-FR
MATH 158: Basic Probability and Stochastic Processes with Engineering Applications (CME 298)
Calculus of random variables and their distributions with applications. Review of limit theorems of probability and their application to statistical estimation and basic Monte Carlo methods. Introduction to Markov chains, random walks, Brownian motion and basic stochastic differential equations with emphasis on applications from economics, physics and engineering, such as filtering and control. Prerequisites: exposure to basic probability.
Terms: Spr
| Units: 3
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