
Book DetailsAnneli Lax New Mathematical LibraryVolume: 48; 2017; 275 ppWinner of a CHOICE Outstanding Academic Title Award for 2017!
Reprinted edition available: NML/50
What does style mean in mathematics? Style is both how one does something and how one communicates what was done. In this book, the author investigates the worlds of the wellknown numbers, the binomial coefficients. The author follows the example of Raymond Queneau's Exercises in Style. Offering the reader 99 stories in various styles. The book celebrates the joy of mathematics and the joy of writing mathematics by exploring the rich properties of this familiar collection of numbers. For any one interested in mathematics, from high school students on up.

Table of Contents

cover

Exercises in (Mathematical) Style

Preface

Contents

Notations

Combinatorial thinking

An algebraic relation

Combinatorial consequences

Downtown Carré

Proof without words

A geometric representation

(6 choose 3) tetrads

A footnote

Fancy evaluations

Careful choices

An explicit formula

Explicit counting

History

The diagonal club

The ChuVandermonde identity

Up and down

Mind the gaps

Recurrence

Rabbits

Repetition

Left out

Sets

The Ramsey game

The Principle of Inclusion and Exclusion

Inversion

Derangements

Seating the visiting dignitaries

Multinomials, passively

Don't choose, distribute

Tanka**

Ode to a little theorem**

Divisibility by a prime**

A far finer gambit**

Congruence modulo a prime**

Alchemy**

Close reading**

An algorithm to recognize primes**

Shifting entries**

DIY primes**

Polynomial relations

The generalized binomial theorem

Four false starts

Protasisapodosis**

Matrices**

Bourbaki

Generating repetitions

Dialogue concerning generating functions

Counting trees

qanalogues

A breakthrough**

Partitions of numbers

Take it to the limit

qbinomial theorem

The quantum plane***

Scrapsheet

Mathematical Idol

Symmetries

Sums of powers*

Parts of proof

Rings and ideals***

Mathmärchen***

The binomial distribution

Wormhole points

You can't always get what you want

Matt Hu, Graduate student

Seeking successes

TEXNOΠAIΓNIA*

An area computation*

Experimental mathematics

Telescopes

The Rechner

Lipogram

18th century machinations

Recipe*

Math talk*

Averages and estimates

Equality***

pi, by parts*

A macaronic sonnet*

A hidden integral*

Letter to a princess*

Explicit Eulerian numbers

Mutperation satticsits***

Review*

Plus C*

At the carnival**

Indicators**

Tweets**

Beautiful numbers**

Reminiscences***

Winter journal**

Cellular automata

Tiling

Lattice points*

Afterlife*

Matt Hu and the Euler caper***

Hypergeometric musings***

On the bus***

Style notes

Index


Additional Material

Reviews

By examining and extending binomial coefficients from seemingly every possible direction, the author provides an amazing concoction of ideas, prompting readers to say "Wow, I forgot that connection," or "Wow, I did not know that," or just "Wow!..McCleary's effort is exceptional, as it reaches into the realm of élan, clearly demonstrating the energy and enthusiasm that can pervade mathematical writing and mathematics itself.
J. Johnson, CHOICE

 Book Details
 Table of Contents
 Additional Material
 Reviews
Reprinted edition available: NML/50
What does style mean in mathematics? Style is both how one does something and how one communicates what was done. In this book, the author investigates the worlds of the wellknown numbers, the binomial coefficients. The author follows the example of Raymond Queneau's Exercises in Style. Offering the reader 99 stories in various styles. The book celebrates the joy of mathematics and the joy of writing mathematics by exploring the rich properties of this familiar collection of numbers. For any one interested in mathematics, from high school students on up.

cover

Exercises in (Mathematical) Style

Preface

Contents

Notations

Combinatorial thinking

An algebraic relation

Combinatorial consequences

Downtown Carré

Proof without words

A geometric representation

(6 choose 3) tetrads

A footnote

Fancy evaluations

Careful choices

An explicit formula

Explicit counting

History

The diagonal club

The ChuVandermonde identity

Up and down

Mind the gaps

Recurrence

Rabbits

Repetition

Left out

Sets

The Ramsey game

The Principle of Inclusion and Exclusion

Inversion

Derangements

Seating the visiting dignitaries

Multinomials, passively

Don't choose, distribute

Tanka**

Ode to a little theorem**

Divisibility by a prime**

A far finer gambit**

Congruence modulo a prime**

Alchemy**

Close reading**

An algorithm to recognize primes**

Shifting entries**

DIY primes**

Polynomial relations

The generalized binomial theorem

Four false starts

Protasisapodosis**

Matrices**

Bourbaki

Generating repetitions

Dialogue concerning generating functions

Counting trees

qanalogues

A breakthrough**

Partitions of numbers

Take it to the limit

qbinomial theorem

The quantum plane***

Scrapsheet

Mathematical Idol

Symmetries

Sums of powers*

Parts of proof

Rings and ideals***

Mathmärchen***

The binomial distribution

Wormhole points

You can't always get what you want

Matt Hu, Graduate student

Seeking successes

TEXNOΠAIΓNIA*

An area computation*

Experimental mathematics

Telescopes

The Rechner

Lipogram

18th century machinations

Recipe*

Math talk*

Averages and estimates

Equality***

pi, by parts*

A macaronic sonnet*

A hidden integral*

Letter to a princess*

Explicit Eulerian numbers

Mutperation satticsits***

Review*

Plus C*

At the carnival**

Indicators**

Tweets**

Beautiful numbers**

Reminiscences***

Winter journal**

Cellular automata

Tiling

Lattice points*

Afterlife*

Matt Hu and the Euler caper***

Hypergeometric musings***

On the bus***

Style notes

Index

By examining and extending binomial coefficients from seemingly every possible direction, the author provides an amazing concoction of ideas, prompting readers to say "Wow, I forgot that connection," or "Wow, I did not know that," or just "Wow!..McCleary's effort is exceptional, as it reaches into the realm of élan, clearly demonstrating the energy and enthusiasm that can pervade mathematical writing and mathematics itself.
J. Johnson, CHOICE