Softcover ISBN:  9781470440398 
Product Code:  STML/86 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470448479 
Product Code:  STML/86.E 
List Price:  $49.00 
Individual Price:  $39.20 
Softcover ISBN:  9781470440398 
eBook: ISBN:  9781470448479 
Product Code:  STML/86.B 
List Price:  $108.00 $83.50 
Softcover ISBN:  9781470440398 
Product Code:  STML/86 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470448479 
Product Code:  STML/86.E 
List Price:  $49.00 
Individual Price:  $39.20 
Softcover ISBN:  9781470440398 
eBook ISBN:  9781470448479 
Product Code:  STML/86.B 
List Price:  $108.00 $83.50 

Book DetailsStudent Mathematical LibraryVolume: 86; 2018; 232 ppMSC: Primary 05
One of the great appeals of Extremal Set Theory as a subject is that the statements are easily accessible without a lot of mathematical background, yet the proofs and ideas have applications in a wide range of fields including combinatorics, number theory, and probability theory. Written by two of the leading researchers in the subject, this book is aimed at mathematically mature undergraduates, and highlights the elegance and power of this field of study.
The first half of the book provides classic results with some new proofs including a complete proof of the Ahlswede–Khachatrian theorem as well as some recent progress on the Erdős matching conjecture. The second half presents some combinatorial structural results and linear algebra methods including the Deza–Erdős–Frankl theorem, application of Rödl's packing theorem, application of semidefinite programming, and very recent progress (obtained in 2016) on the Erdős–Szemerédi sunflower conjecture and capset problem. The book concludes with a collection of challenging open problems.
ReadershipUndergraduate students interested in discrete mathematics and combinatorics.

Table of Contents

Chapters

Introduction

Operations on sets and set systems

Theorems on traces

The ErdősKoRado theorem via shifting

Katona’s circle

The KurskalKatona theorem

Kleitman theorem for no $s$ pairwise disjoint sets

The HiltonMilner theorem

The Erdős matching conjecture

The AhswedeKhachatrian theorem

Pushingpulling method

Uniform measure versus product measure

Kleitman’s correlation inequality

$r$cross union families

Random walk method

$L$systems

Exponent of $(10,\{0,1,3,6\})$system

The DezaErdősFrankl theorem

Füredi’s structure theorem

Rödl’s packing theorem

Upper bounds using multilinear polynomials

Application to discrete geometry

Upper bounds using inclusion matrices

Some algebraic constructions for $L$systems

Oddtown and eventown problems

Tensor product method

The ratio bound

Measures of cross independent sets

Application of semidefinite programming

A cross intersection problem with measures

Capsets and sunflowers

Challenging open problems


Additional Material

Reviews

No existing book has similar coverage.
D. V. Feldman, CHOICE 
[This book] makes cuttingedge results reasonably accessible to undergraduates...I am not aware of any other source for this material that allows wellprepared undergraduates to get up to speed in this area of mathematics.
Mark Hunacek, MAA Reviews


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One of the great appeals of Extremal Set Theory as a subject is that the statements are easily accessible without a lot of mathematical background, yet the proofs and ideas have applications in a wide range of fields including combinatorics, number theory, and probability theory. Written by two of the leading researchers in the subject, this book is aimed at mathematically mature undergraduates, and highlights the elegance and power of this field of study.
The first half of the book provides classic results with some new proofs including a complete proof of the Ahlswede–Khachatrian theorem as well as some recent progress on the Erdős matching conjecture. The second half presents some combinatorial structural results and linear algebra methods including the Deza–Erdős–Frankl theorem, application of Rödl's packing theorem, application of semidefinite programming, and very recent progress (obtained in 2016) on the Erdős–Szemerédi sunflower conjecture and capset problem. The book concludes with a collection of challenging open problems.
Undergraduate students interested in discrete mathematics and combinatorics.

Chapters

Introduction

Operations on sets and set systems

Theorems on traces

The ErdősKoRado theorem via shifting

Katona’s circle

The KurskalKatona theorem

Kleitman theorem for no $s$ pairwise disjoint sets

The HiltonMilner theorem

The Erdős matching conjecture

The AhswedeKhachatrian theorem

Pushingpulling method

Uniform measure versus product measure

Kleitman’s correlation inequality

$r$cross union families

Random walk method

$L$systems

Exponent of $(10,\{0,1,3,6\})$system

The DezaErdősFrankl theorem

Füredi’s structure theorem

Rödl’s packing theorem

Upper bounds using multilinear polynomials

Application to discrete geometry

Upper bounds using inclusion matrices

Some algebraic constructions for $L$systems

Oddtown and eventown problems

Tensor product method

The ratio bound

Measures of cross independent sets

Application of semidefinite programming

A cross intersection problem with measures

Capsets and sunflowers

Challenging open problems

No existing book has similar coverage.
D. V. Feldman, CHOICE 
[This book] makes cuttingedge results reasonably accessible to undergraduates...I am not aware of any other source for this material that allows wellprepared undergraduates to get up to speed in this area of mathematics.
Mark Hunacek, MAA Reviews