MATH 479 Spring 2015 Additive Combinatorics (Q) (W)

Lying at the interface of combinatorics, ergodic theory, harmonic analysis, number theory, and probability, Additive Combinatorics is an exciting field which has experienced tremendous growth in recent years. Very roughly, it is an attempt to classify subsets of a given field which are almost a subspace. We will discuss a variety of topics, including sum-product theorems, the structure of sets of small doubling (e.g. the Freiman-Ruzsa theorem), long arithmetic progressions (e.g. Roth's theorem), structured subsets of sumsets, and applications to computer science (e.g. to pseudorandomess). Depending on time and interest, we may also discuss higher-order Fourier analysis, the polynomial method, and the ergodic approach to Szemeredi's theorem.
Class Format: lecture
Requirements/Evaluation: regular problem sets, as well as a final project
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Prerequisites: MATH 250, MATH 350, MATH 355
Enrollment Preference: students who have previously taken number theory
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Divisional Attributes: Division III,Quantitative and Formal Reasoning,Writing Intensive
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Enrollment Limit: 19
Expected Enrollment: 8
Class Number: 3973
MATH 479 - 01 (S) LEC Additive Combinatorics (Q) (W) Division 3: Science and MathematicsWriting IntensiveQuantitative and Formal Reasoning Leo Goldmakher
MWF 09:00 AM-09:50 AM Physics 114 3973
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