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# 61 - 70 of 77 results for: all courses

## 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:DB-Math, WAY-FR | 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 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: not given this year, last offered Spring 2014 | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR | Grading: Letter or Credit/No Credit

## PHIL 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 | 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, last offered Winter 2013 | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR | Grading: Letter or Credit/No Credit

## 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 | Grading: Letter or Credit/No Credit
Instructors: Briggs, R. (PI)

## PHIL 154:Modal Logic (PHIL 254)

(Graduate students register for 254.) Syntax and semantics of modal logic and its basic theory: including expressive power, axiomatic completeness, correspondence, and complexity. Applications to topics in philosophy, computer science, mathematics, linguistics, and game theory. Prerequisite: 150 or preferably 151.
Terms: Spr | Units: 4 | UG Reqs: GER:DB-Math, WAY-FR | Grading: Letter or Credit/No Credit
Instructors: Ten Cate, B. (PI)

## PHIL 162:Philosophy of Mathematics

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: not given this year, last offered Winter 2018 | Units: 4 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit

## 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: not given this year, last offered Spring 2016 | Units: 4 | UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR | Grading: Letter or Credit/No Credit

## 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 | Grading: Letter or Credit/No Credit

## 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: Spr | Units: 3 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit
Instructors: Cauchois, M. (PI)
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