printer friendly pagePHIL 151: Metalogic (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
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
PHIL 152: Computability and Logic (PHIL 252)
Approaches to effective computation: recursive functions, register machines, and Turing machines. Proof of their equivalence, discussion of Church's thesis. Elementary recursion theory. These techniques used to prove Gödel's incompleteness theorem for arithmetic, whose technical and philosophical repercussions are surveyed. Prerequisite: 151.
Terms: Spr
| Units: 4
| UG Reqs: GER:DB-Math
Instructors:
Sommer, R. (PI)
PHIL 154: Modal Logic (PHIL 254)
(Graduate students register for 254.) Syntax and semantics of modal logic, and technical topics like completeness and correspondence theory, including both classical and recent developments. Applications to topics in philosophy, computer science, and other fields. Prerequisite: 150 or preferably 151.
Terms: Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Wang, Y. (PI)
;
van Benthem, J. (PI)
PHIL 162: Philosophy of Mathematics (MATH 162, PHIL 262)
(Graduate students register for
PHIL 262.) General survey of the philosophy of mathematics, focusing on epistemological issues. Includes survey of some basic concepts (proof, axiom, definition, number, set); mind-bending 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:DB-Math
Instructors:
Donaldson, T. (PI)
PHIL 166: Probability: Ten Great Ideas About Chance (PHIL 266, STATS 167, STATS 267)
Foundational approaches to thinking about chance in matters such as gambling, the law, and everyday affairs. Topics include: chance and decisions; the mathematics of chance; frequencies, symmetry, and chance; Bayes great idea; chance and psychology; misuses of chance; and harnessing chance. Emphasis is on the philosophical underpinnings and problems. Prerequisite: exposure to probability or a first course in statistics at the level of
STATS 60 or 116.
Last offered: Spring 2013
| UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR
PSYCH 10: Introduction to Statistical Methods: Precalculus (STATS 60, STATS 160)
Techniques for organizing data, computing, and interpreting measures of central tendency, variability, and association. Estimation, confidence intervals, tests of hypotheses, t-tests, correlation, and regression. Possible topics: analysis of variance and chi-square tests, computer statistical packages.
Terms: Aut, Win, Spr, Sum
| Units: 5
| UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR
STATS 50: Mathematics of Sports (MCS 100)
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: Aut
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Pekelis, L. (PI)
STATS 60: Introduction to Statistical Methods: Precalculus (PSYCH 10, STATS 160)
Techniques for organizing data, computing, and interpreting measures of central tendency, variability, and association. Estimation, confidence intervals, tests of hypotheses, t-tests, correlation, and regression. Possible topics: analysis of variance and chi-square tests, computer statistical packages.
Terms: Aut, Win, Spr, Sum
| Units: 5
| UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR
Instructors:
Bacallado, S. (PI)
;
DiCiccio, C. (PI)
;
Mukherjee, R. (PI)
...
more instructors for STATS 60 »
Instructors:
Bacallado, S. (PI)
;
DiCiccio, C. (PI)
;
Mukherjee, R. (PI)
;
Sun, D. (PI)
;
Thomas, E. (PI)
;
Walther, G. (PI)
;
DiCiccio, C. (TA)
;
Janson, L. (TA)
;
Sun, D. (TA)
STATS 110: Statistical Methods in Engineering and the Physical Sciences
Introduction to statistics for engineers and physical scientists. Topics: descriptive statistics, probability, interval estimation, tests of hypotheses, nonparametric methods, linear regression, analysis of variance, elementary experimental design. Prerequisite: one year of calculus.
Terms: Aut, Sum
| Units: 4-5
| UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR
Instructors:
He, H. (PI)
;
Taylor, J. (PI)
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