printer friendly pageMATH 137: Mathematical Methods of Classical Mechanics
Newtonian mechanics. Lagrangian formalism. E. Noether's theorem. Oscillations. Rigid bodies. Introduction to symplectic geometry. Hamiltonian formalism. Legendre transform. Variational principles. Geometric optics. Introduction to the theory of integrable systems. Prerequisites: 51, 52, 53, or 51H, 52H, 53H.
| UG Reqs: GER:DB-Math
MATH 138: Celestial Mechanics
Mathematically rigorous introduction to the classical N-body problem: the motion of N particles evolving according to Newton's law. Topics include: the Kepler problem and its symmetries; other central force problems; conservation theorems; variational methods; Hamilton-Jacobi theory; the role of equilibrium points and stability; and symplectic methods. Prerequisites: 53, and 115 or 171.
| UG Reqs: GER:DB-Math
MATH 162: Philosophy of Mathematics (PHIL 162, PHIL 262)
(Graduate students register for
PHIL 262.) 20th-century approaches to the foundations and philosophy of mathematics. The background in mathematics, set theory, and logic. Schools and programs of logicism, predicativism, platonism, formalism, and constructivism. Readings from leading thinkers. Prerequisite: PHIL151 or consent of instructor.
| UG Reqs: GER:DB-Math
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. Self-financing replicating portfolio. Black-Scholes pricing of European options. Dividends. Implied volatility. Optimal stopping and American options. Prerequisite: 53. Corequisites: 131, 151 or
STATS 116.
| UG Reqs: GER:DB-Math
OSPMADRD 53: Of Dice and Men: Chance, Evidence and Data in an uncertain world
Introduction to statistical ideas and thinking through examples. Heuristics and biases that can lead to inaccurate conclusions. Examples (drawn from Kahneman¿s Thinking Fast and Slow): the law of small numbers, availability biases, representativeness, base rates and Bayes¿ rule, regression to the mean. Also, a not-too-technical treatment of some important statistical ideas in medicine, public health and social statistics such as: trials of life (randomization), Simpson¿s paradox and hidden confounders. Some examples taken from the Spanish media as appropriate.
Terms: Win
| Units: 3-4
| UG Reqs: GER:DB-Math
Instructors:
Johnstone, I. (PI)
PHIL 50: Introductory Logic
Propositional and predicate logic; emphasis is on translating English sentences into logical symbols and constructing derivations of valid arguments.
Terms: Aut, Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Di Bello, M. (PI)
;
Duarte, S. (PI)
;
Di Bello, M. (TA)
...
more instructors for PHIL 50 »
Instructors:
Di Bello, M. (PI)
;
Duarte, S. (PI)
;
Di Bello, M. (TA)
;
Lee, P. (TA)
;
Mao, B. (TA)
;
Simon, A. (TA)
PHIL 150: Basic Concepts in Mathematical Logic (PHIL 250)
The concepts and techniques used in mathematical logic, primarily through the study of the language of first order logic. Topics: formalization, proof, propositional logic, quantifiers, sets, mathematical induction, modal logics and the logic of diagrams.
Terms: Aut
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
PHIL 150E: Logic in Action: A New Introduction to Logic
A new introduction to logic, covering propositional, modal, and first-order logic, with special attention to major applications in describing information and information-driven 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: Spr
| Units: 4
| UG Reqs: WAY-FR, GER:DB-Math
Instructors:
van Benthem, J. (PI)
;
Hawke, P. (TA)
PHIL 151: First-Order Logic (PHIL 251)
(Formerly 160A.) The syntax and semantics of sentential and first-order logic. Concepts of model theory. Gödel's completeness theorem and its consequences: the Löwenheim-Skolem theorem and the compactness theorem. Prerequisite: 150 or consent of instructor.
Terms: Win
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Sommer, R. (PI)
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.
Last offered: Winter 2013
| UG Reqs: GER:DB-Math, WAY-FR
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