**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

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**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

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 11
- Half-Title 22
- Copyright Page 33
- Title 44
- Preface 88
- Contents 1212
- Notations 1616
- Combinatorial thinking 1818
- An algebraic relation 2020
- Combinatorial consequences 2222
- Downtown Carré 2424
- Proof without words 2626
- A geometric representation 2727
- 6 3 tetrads 2929
- A footnote 3030
- Careful Choices 3333
- An explicit formula 3535
- Explicit counting 3737
- History 3838
- The diagonal club 4040
- The Chu-Vandermonde identity 4242
- Up and down 4444
- Mind the gaps 4646
- Recurrence 4848
- Rabbits 5050
- Repetition 5252
- Left out 5454
- Sets 5656
- The Ramsey game 5858
- The Principle of Inclusion and Exclusion 6161
- Inversion 6464
- Derangements 6666
- Seating the visiting dignitaries 6969
- Multinomials, passively 7272
- Don’t choose, distribute 7474
- Tanka 7777
- Ode to a little theorem 7878
- Divisibility by a prime 8080
- A far finer gambit 8383
- Congruence modulo a prime 8686
- Alchemy 8989
- Close reading 9292
- An algorithm to recognize primes 9494
- Shifting entries 9696
- DIY primes 9898
- Polynomial relations 101101
- The generalized binomial theorem 103103
- Four false starts 105105
- Protasis-apodosis 108108
- Matrices 111111
- Bourbaki 114114
- Generating repetitions 117117
- Dialogue concerning generating functions 119119
- Counting trees 122122
- q-analogues 124124
- A breakthrough 127127
- Partitions of numbers 130130
- Take it to the limit 133133
- q-binomial theorem 135135
- The quantum plane 138138
- Scrapsheet 141141
- Mathematical Idol 144144
- Symmetries 147147
- Sums of powers 150150
- Parts of proof 153153
- Rings and ideals 155155
- Mathmärchen 157157
- The binomial distribution 160160
- Wormhole points 162162
- You can’t always get what you want 165165
- Matt Hu, Graduate student 167167
- Seeking successes 170170
- TEXNO…AI•NIA 172172
- An area computation 173173
- Experimental mathematics 176176
- Telescopes 178178
- The Rechner 181181
- Lipogram 183183
- 18th century machinations 185185
- Recipe 188188
- Math talk 190190
- Averages and estimates 193193
- Equality 195195
- Pi, by parts 198198
- A macaronic sonnet 201201
- A hidden integral 202202
- Letter to a princess 204204
- Explicit Eulerian numbers 207207
- Mutperation satticsits 210210
- Review 212212
- Plus C 215215
- At the carnival 218218
- Indicators 221221
- Tweets 224224
- Beautiful numbers 225225
- Reminiscences 227227
- Winter journal 230230
- Cellular automata 233233
- Tiling 236236
- Lattice points 239239
- Afterlife 242242
- Matt Hu and the Euler caper 245245
- Hypergeometric musings 248248
- On the bus 251251
- Style notes 254254
- Index 286286
- Back cover 291291