**Anneli Lax New Mathematical Library**

Volume: 50;
2018;
275 pp;
Softcover

**Print ISBN: 978-1-4704-4783-0
Product Code: NML/50**

List Price: $48.00

AMS Member Price: $36.00

MAA Member Price: $36.00

**Electronic ISBN: 978-1-4704-4832-5
Product Code: NML/50.E**

List Price: $48.00

AMS Member Price: $36.00

MAA Member Price: $36.00

# Exercises in (Mathematical) Style: Stories of Binomial Coefficients

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*John McCleary*

MAA Press: An Imprint of the American Mathematical Society

Winner of a CHOICE Outstanding Academic Title Award for 2017!

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 well-known
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.

#### Reviews & Endorsements

The exercises are lucidly written; there is much beautiful mathematics to learn and enjoy.

-- Debra K. Borkovitz, Mathematics Teacher

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

# Table of Contents

## Exercises in (Mathematical) Style: Stories of Binomial Coefficients

- Cover Cover11
- Half-Title i2
- Copyright Page ii3
- Title iii4
- Preface vii8
- Contents xi12
- Notations 116
- Combinatorial thinking 318
- An algebraic relation 520
- Combinatorial consequences 722
- Downtown Carré 924
- Proof without words 1126
- A geometric representation 1227
- 6 3 tetrads 1429
- A footnote 1530
- Careful Choices 1833
- An explicit formula 2035
- Explicit counting 2237
- History 2338
- The diagonal club 2540
- The Chu-Vandermonde identity 2742
- Up and down 2944
- Mind the gaps 3146
- Recurrence 3348
- Rabbits 3550
- Repetition 3752
- Left out 3954
- Sets 4156
- The Ramsey game 4358
- The Principle of Inclusion and Exclusion 4661
- Inversion 4964
- Derangements 5166
- Seating the visiting dignitaries 5469
- Multinomials, passively 5772
- Don’t choose, distribute 5974
- Tanka 6277
- Ode to a little theorem 6378
- Divisibility by a prime 6580
- A far finer gambit 6883
- Congruence modulo a prime 7186
- Alchemy 7489
- Close reading 7792
- An algorithm to recognize primes 7994
- Shifting entries 8196
- DIY primes 8398
- Polynomial relations 86101
- The generalized binomial theorem 88103
- Four false starts 90105
- Protasis-apodosis 93108
- Matrices 96111
- Bourbaki 99114
- Generating repetitions 102117
- Dialogue concerning generating functions 104119
- Counting trees 107122
- q-analogues 109124
- A breakthrough 112127
- Partitions of numbers 115130
- Take it to the limit 118133
- q-binomial theorem 120135
- The quantum plane 123138
- Scrapsheet 126141
- Mathematical Idol 129144
- Symmetries 132147
- Sums of powers 135150
- Parts of proof 138153
- Rings and ideals 140155
- Mathmärchen 142157
- The binomial distribution 145160
- Wormhole points 147162
- You can’t always get what you want 150165
- Matt Hu, Graduate student 152167
- Seeking successes 155170
- TEXNO…AI•NIA 157172
- An area computation 158173
- Experimental mathematics 161176
- Telescopes 163178
- The Rechner 166181
- Lipogram 168183
- 18th century machinations 170185
- Recipe 173188
- Math talk 175190
- Averages and estimates 178193
- Equality 180195
- Pi, by parts 183198
- A macaronic sonnet 186201
- A hidden integral 187202
- Letter to a princess 189204
- Explicit Eulerian numbers 192207
- Mutperation satticsits 195210
- Review 197212
- Plus C 200215
- At the carnival 203218
- Indicators 206221
- Tweets 209224
- Beautiful numbers 210225
- Reminiscences 212227
- Winter journal 215230
- Cellular automata 218233
- Tiling 221236
- Lattice points 224239
- Afterlife 227242
- Matt Hu and the Euler caper 230245
- Hypergeometric musings 233248
- On the bus 236251
- Style notes 239254
- Index 271286
- Back cover 276291