**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.

**lecture**

*Class Format:***regular problem sets, as well as a final project**

*Requirements/Evaluation:*

*Additional Info:*

*Additional Info2:***MATH 250, MATH 350, MATH 355**

*Prerequisites:***students who have previously taken number theory**

*Enrollment Preference:*

*Department Notes:*

*Material and Lab Fees:*

*Distribution Notes:***Division III,Quantitative and Formal Reasoning,Writing Intensive**

*Divisional Attributes:*

*Other Attributes:***19**

*Enrollment Limit:***8**

*Expected Enrollment:***3973**

*Class Number:*CLASSES | ATTR | INSTRUCTORS | TIMES | CLASS NUMBER |
---|---|---|---|---|

MATH 479 - 01 (S) LEC Additive Combinatorics (Q) (W) | Leo Goldmakher |
MWF 09:00 AM-09:50 AM | 3973 |