



-
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 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.
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Table of Contents
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cover
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Exercises in (Mathematical) Style
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Preface
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Contents
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Notations
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Combinatorial thinking
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An algebraic relation
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Combinatorial consequences
-
Downtown Carré
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Proof without words
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A geometric representation
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(6 choose 3) tetrads
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A footnote
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Fancy evaluations
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Careful choices
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An explicit formula
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Explicit counting
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History
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The diagonal club
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The Chu-Vandermonde identity
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Up and down
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Mind the gaps
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Recurrence
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Rabbits
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Repetition
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Left out
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Sets
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The Ramsey game
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The Principle of Inclusion and Exclusion
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Inversion
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Derangements
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Seating the visiting dignitaries
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Multinomials, passively
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Don't choose, distribute
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Tanka**
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Ode to a little theorem**
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Divisibility by a prime**
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A far finer gambit**
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Congruence modulo a prime**
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Alchemy**
-
Close reading**
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An algorithm to recognize primes**
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Shifting entries**
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DIY primes**
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Polynomial relations
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The generalized binomial theorem
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Four false starts
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Protasis-apodosis**
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Matrices**
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Bourbaki
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Generating repetitions
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Dialogue concerning generating functions
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Counting trees
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q-analogues
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A breakthrough**
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Partitions of numbers
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Take it to the limit
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q-binomial theorem
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The quantum plane***
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Scrapsheet
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Mathematical Idol
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Symmetries
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Sums of powers*
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Parts of proof
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Rings and ideals***
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Mathmärchen***
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The binomial distribution
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Wormhole points
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You can't always get what you want
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Matt Hu, Graduate student
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Seeking successes
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TEXNOΠAIΓNIA*
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An area computation*
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Experimental mathematics
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Telescopes
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The Rechner
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Lipogram
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18th century machinations
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Recipe*
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Math talk*
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Averages and estimates
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Equality***
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pi, by parts*
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A macaronic sonnet*
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A hidden integral*
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Letter to a princess*
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Explicit Eulerian numbers
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Mutperation satticsits***
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Review*
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Plus C*
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At the carnival**
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Indicators**
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Tweets**
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Beautiful numbers**
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Reminiscences***
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Winter journal**
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Cellular automata
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Tiling
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Lattice points*
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Afterlife*
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Matt Hu and the Euler caper***
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Hypergeometric musings***
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On the bus***
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Style notes
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Index
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Additional Material
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Reviews
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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 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.
-
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 Chu-Vandermonde 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
-
Protasis-apodosis**
-
Matrices**
-
Bourbaki
-
Generating repetitions
-
Dialogue concerning generating functions
-
Counting trees
-
q-analogues
-
A breakthrough**
-
Partitions of numbers
-
Take it to the limit
-
q-binomial 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