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.
Terms: Win

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
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:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Tsai, C. (PI)
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, alternate years, not given next year

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Tsai, C. (PI)
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: not given this year, last offered Spring 2018

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
MATH 161: Set Theory
Informal and axiomatic set theory: sets, relations, functions, and settheoretical operations. The ZermeloFraenkel axiom system and the special role of the axiom of choice and its various equivalents. Wellorderings and ordinal numbers; transfinite induction and transfinite recursion. Equinumerosity and cardinal numbers; Cantor's Alephs and cardinal arithmetic. Open problems in set theory. Prerequisite: students should be comfortable doing proofs.
Terms: Win

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Sommer, R. (PI)
MATH 171: Fundamental Concepts of Analysis
Recommended for Mathematics majors and required of honors Mathematics majors. Similar to 115 but altered content and more theoretical orientation. Properties of Riemann integrals, continuous functions and convergence in metric spaces; compact metric spaces, basic point set topology. Prerequisite: 61CM or 61DM or 115 or consent of the instructor. WIM
Terms: Aut, Spr

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 172: Lebesgue Integration and Fourier Analysis
Similar to 205A, but for undergraduate Math majors and graduate students in other disciplines. Topics include Lebesgue measure on Euclidean space, Lebesgue integration, L^p spaces, the Fourier transform, the HardyLittlewood maximal function and Lebesgue differentiation. Prerequisite: 171 or consent of instructor.
Terms: Spr

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Hershkovits, O. (PI)
MATH 175: Elementary Functional Analysis
Linear operators on Hilbert space. Spectral theory of compact operators; applications to integral equations. Elements of Banach space theory. Prerequisite: 115 or 171.
Terms: Win

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Wang, Y. (PI)
MCS 100: Mathematics of Sports (STATS 50)
The use of mathematics, statistics, and probability in the analysis of sports performance, sports records, and strategy. Topics include mathematical analysis of the physics of sports and the determinations of optimal strategies. New diagnostic statistics and strategies for each sport. Corequisite:
STATS 60, 110 or 116.
Terms: Spr

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Cauchois, M. (PI)
PHIL 49: Survey of Formal Methods
Survey of important formal methods used in philosophy. The course covers the basics of propositional and elementary predicate logic, probability and decision theory, game theory, and statistics, highlighting philosophical issues and applications. Specific topics include the languages of propositional and predicate logic and their interpretations, rationality arguments for the probability axioms, Nash equilibrium and dominance reasoning, and the meaning of statistical significance tests. Assessment is through a combination of problems designed to solidify competence with the mathematical tools and shortanswer questions designed to test conceptual understanding.
Terms: Spr

Units: 4

UG Reqs: GER:DBMath, WAYFR

Grading: Letter (ABCD/NP)
Instructors:
Chipman, J. (PI)
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