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
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
PHIL 150: Basic Concepts in Mathematical Logic (PHIL 250)
(Formerly 159.) 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, and enumerability.
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. Highlights connections with philosophy, mathematics, computer science, linguistics, and neighboring fields. Based on the open source logic course 'Logic in Action,' available online at
http://www.logicinaction.org/.nnFulfills the undergraduate philosophy logic requirement.
Terms: Spr
| Units: 4
| UG Reqs: WAY-FR, GER:DB-Math
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
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: Win
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Scott, D. (PI)
PHIL 152: Computability and Logic (PHIL 252)
Approaches to effective computation: recursive functions, register machines, and programming styles. 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:
Ten Cate, B. (PI)
;
Steinert-Threlkeld, S. (TA)
PHIL 154: Modal Logic (PHIL 254)
(Graduate students register for 254.) Syntax and semantics of modal logic, and technical results like completeness and correspondence theory. Applications to philosophy and computer science. Prerequisite: 150 or preferably 151.
Terms: Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
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.
Terms: Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR, WAY-AQR
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