國立虎尾科技大學 |

Polynomial methods and incidence theory /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Polynomial methods and incidence theory // Adam Sheffer.
作者:	Sheffer, Adam
面頁冊數:	1 online resource (xvi, 245 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 18 Mar 2022).
標題:	Polynomials. -
電子資源:	https://doi.org/10.1017/9781108959988
ISBN:	9781108959988 (ebook)

Polynomial methods and incidence theory /
Sheffer, Adam(Professor of mathematics),

Polynomial methods and incidence theory /Adam Sheffer. - 1 online resource (xvi, 245 pages) :digital, PDF file(s). - Cambridge studies in advanced mathematics ;197. - Cambridge studies in advanced mathematics ;134..

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

Incidences and classical discrete geometry -- Basic real algebraic geometry in R p2 s -- Polynomial partitioning -- Basic real algebraic geometry in Rd -- The joints problem and degree reduction -- Polynomial methods in finite fields -- The Elekes-Sharir-Guth-Katz framework -- Constant-degree polynomial partitioning and incidences in C p2 s -- Lines in R p3 s -- Distinct distances variants -- Incidences in Rd -- Incidence applications in Rd -- Incidences in spaces over finite field -- Algebraic families, dimension counting, and ruled surfaces.

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: 9781108959988 (ebook)Subjects--Topical Terms:

528565
Polynomials.

LC Class. No.: QA167 / .S357 2022

Dewey Class. No.: 511/.66

Polynomial methods and incidence theory /
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490 1 $a Cambridge studies in advanced mathematics ; $v 197
500 $a Title from publisher's bibliographic system (viewed on 18 Mar 2022).
505 0 $a Incidences and classical discrete geometry -- Basic real algebraic geometry in R p2 s -- Polynomial partitioning -- Basic real algebraic geometry in Rd -- The joints problem and degree reduction -- Polynomial methods in finite fields -- The Elekes-Sharir-Guth-Katz framework -- Constant-degree polynomial partitioning and incidences in C p2 s -- Lines in R p3 s -- Distinct distances variants -- Incidences in Rd -- Incidence applications in Rd -- Incidences in spaces over finite field -- Algebraic families, dimension counting, and ruled surfaces.
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.
650 0 $a Polynomials. $3 528565
650 0 $a Incidence algebras. $3 848150
650 0 $a Partitions (Mathematics) $3 856957
650 0 $a Finite fields (Algebra) $3 883005
650 0 $a Discrete geometry. $3 672137
650 0 $a Geometry, Algebraic. $3 580393
650 0 $a Combinatorial geometry. $3 768943
776 0 8 $i Print version: $z 9781108832496
830 0 $a Cambridge studies in advanced mathematics ; $v 134. $3 1133579
856 4 0 $u https://doi.org/10.1017/9781108959988