printer friendly pageMATH 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 Hardy-Littlewood maximal function and Lebesgue differentiation. Prerequisite: 171 or consent of instructor.
Terms: Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Sun, W. (PI)
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: Win
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Malinnikova, E. (PI)
;
Qin, Q. (TA)
OCEANS 174H: Experimental Design and Probability (OCEANS 274H)
Nature is inherently variable. Statistics gives us the tools to quantify the uncertainty of our measurements and draw conclusions from data. This course is an introduction to experimental design, probability, and data analysis. Topics include summary statistics, data visualization, probability distributions, statistical inference, and general linear models (e.g., t-tests, analysis of variance, regression). Students will use R to explore and analyze datasets relevant to the life and ocean sciences. No programming or statistical background is assumed. This course takes place in-person only at Hopkins Marine Station; for information on how to spend spring quarter in residence:
https://hopkinsmarinestation.stanford.edu/undergraduate-studies/spring-courses-23-24 (Individual course registration also permitted.) Depending on enrollment numbers, a weekly shuttle to Hopkins or mileage reimbursements for qualifying carpools will be provided; terms and conditions apply. Graduate students register for
OCEANS 274H.
Terms: Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-AQR, GER: DB-NatSci, WAY-FR
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 problems designed to solidify competence with the mathematical tools and short-answer questions designed to test conceptual understanding.
Terms: Spr
| Units: 4
| UG Reqs: WAY-FR, GER:DB-Math
Instructors:
Bassett, R. (PI)
;
Forster, M. (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:DB-Math, WAY-FR
Instructors:
Icard, T. (PI)
;
Apsel, L. (TA)
;
Bassett, R. (TA)
;
Thobani, I. (TA)
;
Tilton, S. (TA)
PHIL 151: Metalogic (PHIL 251)
In this course we will go through some of the seminal ideas, constructions, and results from modern logic, focusing especially on classical first-order ("predicate") logic. After introducing general ideas of induction and recursion, we will study a bit of elementary (axiomatic) set theory before then covering basic definability theory, viz. assessing the theoretical limits of what can and cannot be expressed in a first-order language. The centerpiece result of the class is the completeness - and closely related compactness - of first-order logic, a result with a number of momentous consequences, some useful, some philosophically puzzling. We will then study a connection with game theory, whereby a certain type of game characterizes precisely the expressive power of first-order logic. Further topics may include: the 0-1 law in finite model theory, second-order logic, and the algebraic approach to logic. Prerequisite: 150 or consent of instructor.
Terms: Win
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Icard, T. (PI)
;
Bassett, R. (TA)
;
Kemmann, B. (TA)
...
more instructors for PHIL 151 »
Instructors:
Icard, T. (PI)
;
Bassett, R. (TA)
;
Kemmann, B. (TA)
;
Schechtman, K. (TA)
;
Tilton, S. (TA)
PHIL 152: Computability and Logic (PHIL 252)
Kurt G¿del's ground-breaking Incompleteness Theorems demonstrate fundamental limits on formal mathematical reasoning. In particular, the First Incompleteness Theorem says, roughly, that for any reasonable theory of the natural numbers there are statements in the language that are neither provable nor refutable in that theory. In this course, we will explore the expressive power of different axiomatizations of number theory, on our path to proving the Incompleteness Theorems. This study entails an exploration of models of computation, and the power and limitations of what is computable, leading to an introduction to elementary recursion theory. At the conclusion of the course, we will discuss technical and philosophical repercussions of these results. Prerequisite: 151/251.
Terms: Spr
| Units: 4
| UG Reqs: GER:DB-Math
Instructors:
Sommer, R. (PI)
;
Tan, J. (TA)
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 classical and recent 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
Instructors:
van Benthem, J. (PI)
;
Kemmann, B. (TA)
PHIL 162: Philosophy of Mathematics (PHIL 262)
Prerequisite: PHIL150 or consent of instructor. This is a general overview of the philosophy of mathematics, focusing on the nature of mathematical truth and knowledge, the metaphysics of mathematical objects, and issues arising from mathematical practice. Topics to be discussed will include logicism, intuitionism, formalism, Goedel's incompleteness theorem, platonism, nominalism, fictionalism, structuralism, the nature of mathematical rigor, the role of diagrams in mathematics, and mathematical beauty.
Last offered: Winter 2023
| UG Reqs: GER:DB-Math
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
Instructors:
Chi, K. (PI)
;
Fan, J. (PI)
;
Kim, G. (PI)
;
Lim (Chun Hui), C. (PI)
;
Martinez, J. (PI)
;
Schwartz, S. (PI)
;
Walther, G. (PI)
;
Xiang, V. (PI)
;
Abdelrahim, S. (TA)
;
Gunawardana, D. (TA)
;
Jeong, Y. (TA)
;
Ji, W. (TA)
;
Kanekar, R. (TA)
;
Kazdan, J. (TA)
;
Smith, H. (TA)
;
Song, Z. (TA)
;
Tanoh, I. (TA)
;
Yan, R. (TA)
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