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
Instructors:
Kerckhoff, S. (PI)
;
Zhu, X. (PI)
;
Arana Herrera, F. (TA)
...
more instructors for MATH 171 »
Instructors:
Kerckhoff, S. (PI)
;
Zhu, X. (PI)
;
Arana Herrera, F. (TA)
;
Kraushar, N. (TA)
;
Ottolini, A. (TA)
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)
;
Zou, J. (TA)
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
Instructors:
Luk, J. (PI)
;
Wigderson, Y. (TA)
MATH 180: Introduction to Financial Mathematics
Financial derivatives: contracts and options. Hedging and risk management. Arbitrage, interest rate, and discounted value. Geometric random walk and Brownian motion as models of risky assets. Initial boundary value problems for the heat and related partial differential equations. Selffinancing replicating portfolio. BlackScholes pricing of European options. Dividends. Implied volatility. Optimal stopping and American options. Prerequisite: 53. Corequisites: 131, 151 or
STATS 116.
Terms: alternate years, given next year

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: not given this year

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
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 problem sets and shortanswer questions designed to solidify competence with the mathematical tools and to test conceptual understanding. This course replaces
PHIL 50.
Terms: Aut, Win

Units: 4

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Wang, J. (PI)
;
Kim, R. (TA)
PHIL 150: Mathematical Logic (PHIL 250)
An introduction to the concepts and techniques used in mathematical logic, focusing on propositional, modal, and predicate logic. Highlights connections with philosophy, mathematics, computer science, linguistics, and neighboring fields.
Terms: Aut

Units: 4

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
PHIL 150E: Logic in Action: A New Introduction to Logic
A new introduction to logic, covering propositional, modal, and firstorder logic, with special attention to major applications in describing information and informationdriven action. Highlights connections with philosophy, mathematics, computer science, linguistics, and neighboring fields. Based on the open source course 'Logic in Action,' available online at
http://www.logicinaction.org/.nFulfills the undergraduate philosophy logic requirement.
Terms: not given this year

Units: 4

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
PHIL 151: Metalogic (PHIL 251)
(Formerly 160A.) The syntax and semantics of sentential and firstorder logic. Concepts of model theory. Gödel's completeness theorem and its consequences: the LöwenheimSkolem theorem and the compactness theorem. Prerequisite: 150 or consent of instructor.
Terms: Win

Units: 4

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
PHIL 151A: Recursion Theory (PHIL 251A)
Computable functions, Turing degrees, generalized computability and definability. "What does it mean for a function from the natural numbers to themselves to be computable?" and "How can noncomputable functions be classified into a hierarchy based on their level of noncomputability?". Theory of relative computability, reducibility notions and degree structures. Prerequisite is
PHIL 150, or
PHIL 151 or
CS 103.
Terms: not given this year

Units: 4

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
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