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# 51 - 60 of 77 results for: all courses

## 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, last offered Winter 2015 | Units: 3 | UG Reqs: GER:DB-Math | 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:DB-Math | 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: alternate years, given next year | Units: 3 | UG Reqs: GER:DB-Math | 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:DB-Math | Grading: Letter or Credit/No Credit

## 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: students should be comfortable doing proofs.
Terms: not given this year | Units: 3 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit

## MATH 162:Philosophy of Mathematics (PHIL 162)

Mathematics is a very peculiar human activity. It delivers a type of knowledge that is particularly stable, often conceived as a priori and necessary. Moreover, this knowledge is about abstract entities, which seem to have no connection to us, spatio-temporal creatures, and yet it plays a crucial role in our scientific endeavors. Many philosophical questions emerge naturally: What is the nature of mathematical objects? How can we learn anything about them? Where does the stability of mathematics comes from? What is the significance of results showing the limits of such knowledge, such as Gödel's incompleteness theorem? The first part of the course will survey traditional approaches to philosophy of mathematics ("the big Isms") and consider the viability of their answers to some of the previous questions: logicism, intuitionism, Hilbert's program, empiricism, fictionalism, and structuralism. The second part will focus on philosophical issues emerging from the actual practice of mathemat more »
Mathematics is a very peculiar human activity. It delivers a type of knowledge that is particularly stable, often conceived as a priori and necessary. Moreover, this knowledge is about abstract entities, which seem to have no connection to us, spatio-temporal creatures, and yet it plays a crucial role in our scientific endeavors. Many philosophical questions emerge naturally: What is the nature of mathematical objects? How can we learn anything about them? Where does the stability of mathematics comes from? What is the significance of results showing the limits of such knowledge, such as Gödel's incompleteness theorem? The first part of the course will survey traditional approaches to philosophy of mathematics ("the big Isms") and consider the viability of their answers to some of the previous questions: logicism, intuitionism, Hilbert's program, empiricism, fictionalism, and structuralism. The second part will focus on philosophical issues emerging from the actual practice of mathematics. We will tackle questions such as: Why do mathematicians re-prove the same theorems? What is the role of visualization in mathematics? How can mathematical knowledge be effective in natural science? To conclude, we will explore the aesthetic dimension of mathematics, focusing on mathematical beauty. Prerequisite: PHIL150 or consent of instructor.
Terms: Win | Units: 4 | UG Reqs: GER:DB-Math | 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:DB-Math, WAY-FR | 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 Hardy-Littlewood maximal function and Lebesgue differentiation. Prerequisite: 171 or consent of instructor.
Terms: Spr | Units: 3 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit

## 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:DB-Math | 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:DB-Math | Grading: Letter or Credit/No Credit
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