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Polynomial methods and incidence theory

Sheffer, Adam.

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Polynomial methods and incidence theory

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Polynomial methods and incidence theory/ Adam Sheffer.
作者:	Sheffer, Adam.
出版者:	Cambridge :Cambridge University Press, : 2022.,
面頁冊數:	xvi, 245 p. :ill., digital ;23 cm.
附註:	Title from publisher's bibliographic system (viewed on 18 Mar 2022).
標題:	Combinatorial geometry. -
電子資源:	https://doi.org/10.1017/9781108959988
ISBN:	9781108959988

Polynomial methods and incidence theory
Sheffer, Adam.

Polynomial methods and incidence theory[electronic resource] /Adam Sheffer. - Cambridge :Cambridge University Press,2022. - xvi, 245 p. :ill., digital ;23 cm. - Cambridge studies in advanced mathematics ;197. - Cambridge studies in advanced mathematics ;197..

Title from publisher's bibliographic system (viewed on 18 Mar 2022).

The past decade has seen numerous major mathematical breakthroughs for topics such as the finite field Kakeya conjecture, the cap set conjecture, Erdős's distinct distances problem, the joints problem, as well as others, thanks to the introduction of new polynomial methods. There has also been significant progress on a variety of problems from additive combinatorics, discrete geometry, and more. This book gives a detailed yet accessible introduction to these new polynomial methods and their applications, with a focus on incidence theory. Based on the author's own teaching experience, the text requires a minimal background, allowing graduate and advanced undergraduate students to get to grips with an active and exciting research front. The techniques are presented gradually and in detail, with many examples, warm-up proofs, and exercises included. An appendix provides a quick reminder of basic results and ideas.

ISBN: 9781108959988Subjects--Topical Terms:

612600
Combinatorial geometry.

LC Class. No.: QA167 / .S357 2022

Dewey Class. No.: 511.66

Polynomial methods and incidence theory
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300 $a xvi, 245 p. : $b ill., digital ; $c 23 cm.
490 1 $a Cambridge studies in advanced mathematics ; $v 197
500 $a Title from publisher's bibliographic system (viewed on 18 Mar 2022).
520 $a The past decade has seen numerous major mathematical breakthroughs for topics such as the finite field Kakeya conjecture, the cap set conjecture, Erdős's distinct distances problem, the joints problem, as well as others, thanks to the introduction of new polynomial methods. There has also been significant progress on a variety of problems from additive combinatorics, discrete geometry, and more. This book gives a detailed yet accessible introduction to these new polynomial methods and their applications, with a focus on incidence theory. Based on the author's own teaching experience, the text requires a minimal background, allowing graduate and advanced undergraduate students to get to grips with an active and exciting research front. The techniques are presented gradually and in detail, with many examples, warm-up proofs, and exercises included. An appendix provides a quick reminder of basic results and ideas.
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650 0 $a Geometry, Algebraic. $3 532048
650 0 $a Discrete geometry. $3 728299
650 0 $a Finite fields (Algebra) $3 579167
650 0 $a Partitions (Mathematics) $3 709302
650 0 $a Incidence algebras. $3 699794
650 0 $a Polynomials. $3 604754
830 0 $a Cambridge studies in advanced mathematics ; $v 197. $3 3645683
856 4 0 $u https://doi.org/10.1017/9781108959988