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Exercises in (Mathematical) Style: Stories of Binomial Coefficients
 
John McCleary
Exercises in (Mathematical) Style
MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN:  978-1-4704-4783-0
Product Code:  NML/50
List Price: $65.00
MAA Member Price: $48.75
AMS Member Price: $48.75
eBook ISBN:  978-1-4704-4832-5
Product Code:  NML/50.E
List Price: $50.00
MAA Member Price: $37.50
AMS Member Price: $37.50
Softcover ISBN:  978-1-4704-4783-0
eBook: ISBN:  978-1-4704-4832-5
Product Code:  NML/50.B
List Price: $115.00 $90.00
MAA Member Price: $86.25 $67.50
AMS Member Price: $86.25 $67.50
Add to cart
Exercises in (Mathematical) Style
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Exercises in (Mathematical) Style: Stories of Binomial Coefficients
John McCleary
MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN:  978-1-4704-4783-0
Product Code:  NML/50
List Price: $65.00
MAA Member Price: $48.75
AMS Member Price: $48.75
eBook ISBN:  978-1-4704-4832-5
Product Code:  NML/50.E
List Price: $50.00
MAA Member Price: $37.50
AMS Member Price: $37.50
Softcover ISBN:  978-1-4704-4783-0
eBook ISBN:  978-1-4704-4832-5
Product Code:  NML/50.B
List Price: $115.00 $90.00
MAA Member Price: $86.25 $67.50
AMS Member Price: $86.25 $67.50
Add to cart
  • Book Details
     
     
    Anneli Lax New Mathematical Library
    Volume: 50; 2018; 275 pp
    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.
  • Table of Contents
     
     
    • Chapters
    • Notations
    • Combinatorial thinking
    • An algebraic relation
    • Combinatorial consequences
    • Downtown Carré
    • Proof without words
    • A geometric representation
    • $\binom {6}{3}$ 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$^{\ast \ast }$
    • Ode to a little theorem$^{\ast \ast }$
    • Divisibility by a prime$^{\ast \ast }$
    • A far finer gambit$^{\ast \ast }$
    • Congruence modulo a prime$^{\ast \ast }$
    • Alchemy$^{\ast \ast }$
    • Close reading$^{\ast \ast }$
    • An algorithm to recognize primes$^{\ast \ast }$
    • Shifting entries$^{\ast \ast }$
    • DIY primes$^{\ast \ast }$
    • Polynomial relations
    • The generalized binomial theorem
    • Four false starts
    • Protasis-apodosis$^{\ast \ast }$
    • Matrices$^{\ast \ast }$
    • Bourbaki
    • Generating repetitions
    • Dialogue concerning generating functions
    • Counting trees
    • $q$-analogues
    • A breakthrough$^{\ast \ast }$
    • Partitions of numbers
    • Take it to the limit
    • $q$-binomial theorem
    • The quantum plane$^{\ast \ast \ast }$
    • Scrapsheet
    • Mathematical Idol
    • Symmetries
    • Sums of powers$^{\ast }$
    • Parts of proof
    • Rings and ideals$^{\ast \ast \ast }$
    • Mathmärchen$^{\ast \ast \ast }$
    • The binomial distribution
    • Wormhole points
    • You can’t always get what you want
    • Matt Hu, Graduate student
    • Seeking successes
    • \Russian{TEH}N\Russian{OPA}\Russian{ĪG}N\Russian{ĪA}$^{\ast }$
    • An area computation$^\ast $
    • Experimental mathematics
    • Telescopes
    • The Rechner
    • Lipogram
    • 18th century machinations
    • Recipe$^\ast $
    • Math talk$^\ast $
    • Averages and estimates
    • Equality$^{\ast \ast \ast }$
    • $\pi $, by parts$^\ast $
    • A macaronic sonnet$^\ast $
    • A hidden integral$^\ast $
    • Letter to a princess$^\ast $
    • Explicit Eulerian numbers
    • Mutperation satticsits$^{\ast \ast \ast }$
    • Review$^\ast $
    • Plus $C^\ast $
    • At the carnival$^{\ast \ast }$
    • Indicators$^{\ast \ast }$
    • Tweets$^{\ast \ast }$
    • Beautiful numbers$^{\ast \ast }$
    • Reminiscences$^{\ast \ast \ast }$
    • Winter journal$^{\ast \ast }$
    • Cellular automata
    • Tiling
    • Lattice points$^\ast $
    • Afterlife
    • Matt Hu and the Euler caper$^{\ast \ast \ast }$
    • Hypergeometric musings$^{\ast \ast \ast }$
    • On the bus$^{\ast \ast \ast }$
  • Reviews
     
     

    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Anneli Lax New Mathematical Library
Volume: 50; 2018; 275 pp
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.
  • Chapters
  • Notations
  • Combinatorial thinking
  • An algebraic relation
  • Combinatorial consequences
  • Downtown Carré
  • Proof without words
  • A geometric representation
  • $\binom {6}{3}$ 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$^{\ast \ast }$
  • Ode to a little theorem$^{\ast \ast }$
  • Divisibility by a prime$^{\ast \ast }$
  • A far finer gambit$^{\ast \ast }$
  • Congruence modulo a prime$^{\ast \ast }$
  • Alchemy$^{\ast \ast }$
  • Close reading$^{\ast \ast }$
  • An algorithm to recognize primes$^{\ast \ast }$
  • Shifting entries$^{\ast \ast }$
  • DIY primes$^{\ast \ast }$
  • Polynomial relations
  • The generalized binomial theorem
  • Four false starts
  • Protasis-apodosis$^{\ast \ast }$
  • Matrices$^{\ast \ast }$
  • Bourbaki
  • Generating repetitions
  • Dialogue concerning generating functions
  • Counting trees
  • $q$-analogues
  • A breakthrough$^{\ast \ast }$
  • Partitions of numbers
  • Take it to the limit
  • $q$-binomial theorem
  • The quantum plane$^{\ast \ast \ast }$
  • Scrapsheet
  • Mathematical Idol
  • Symmetries
  • Sums of powers$^{\ast }$
  • Parts of proof
  • Rings and ideals$^{\ast \ast \ast }$
  • Mathmärchen$^{\ast \ast \ast }$
  • The binomial distribution
  • Wormhole points
  • You can’t always get what you want
  • Matt Hu, Graduate student
  • Seeking successes
  • \Russian{TEH}N\Russian{OPA}\Russian{ĪG}N\Russian{ĪA}$^{\ast }$
  • An area computation$^\ast $
  • Experimental mathematics
  • Telescopes
  • The Rechner
  • Lipogram
  • 18th century machinations
  • Recipe$^\ast $
  • Math talk$^\ast $
  • Averages and estimates
  • Equality$^{\ast \ast \ast }$
  • $\pi $, by parts$^\ast $
  • A macaronic sonnet$^\ast $
  • A hidden integral$^\ast $
  • Letter to a princess$^\ast $
  • Explicit Eulerian numbers
  • Mutperation satticsits$^{\ast \ast \ast }$
  • Review$^\ast $
  • Plus $C^\ast $
  • At the carnival$^{\ast \ast }$
  • Indicators$^{\ast \ast }$
  • Tweets$^{\ast \ast }$
  • Beautiful numbers$^{\ast \ast }$
  • Reminiscences$^{\ast \ast \ast }$
  • Winter journal$^{\ast \ast }$
  • Cellular automata
  • Tiling
  • Lattice points$^\ast $
  • Afterlife
  • Matt Hu and the Euler caper$^{\ast \ast \ast }$
  • Hypergeometric musings$^{\ast \ast \ast }$
  • On the bus$^{\ast \ast \ast }$

  • 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
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