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: not given this year

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
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:
Diaconis, P. (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: alternate years, given next year

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
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: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: not given this year

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
MATH 162: Philosophy of Mathematics (PHIL 162)
General survey of the philosophy of mathematics, focusing on epistemological issues. Includes survey of some basic concepts (proof, axiom, definition, number, set); mindbending theorems about the limits of our current mathematical knowledge, such as Gödel's Incompleteness Theorems, and the independence of the continuum hypothesis from the current axioms of set theory; major philosophical accounts of mathematics: Logicism, Intuitionism, Hilbert's program, Quine's empiricism, Field's program, Structuralism; concluding with a discussion of Eugene Wigner's `The Unreasonable Effectiveness of Mathematics in the Natural Sciences'. Students won't be expected to prove theorems or complete mathematical exercises. However, includes some material of a technical nature. Prerequisite: PHIL150 or consent of instructor.
Terms: Win

Units: 4

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
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:
Gu, Y. (PI)
;
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: Aut

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
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
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