**Student Mathematical Library**

Volume: 65;
2012;
504 pp;
Softcover

MSC: Primary 05; 11; 33;

**Print ISBN: 978-0-8218-8795-0
Product Code: STML/65**

List Price: $58.00

Individual Price: $46.40

**Electronic ISBN: 978-0-8218-9167-4
Product Code: STML/65.E**

List Price: $58.00

Individual Price: $46.40

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#### Supplemental Materials

# Numbers and Functions: From a classical-experimental mathematician’s point of view

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*Victor H. Moll*

New mathematics often comes about by probing what is already known.
Mathematicians will change the parameters in a familiar calculation or
explore the essential ingredients of a classic proof. Almost
magically, new ideas emerge from this process. This book examines
elementary functions, such as those encountered in calculus courses,
from this point of view of experimental mathematics. The focus is on
exploring the connections between these functions and topics in number
theory and combinatorics. There is also an emphasis throughout the
book on how current mathematical software can be used to discover and
prove interesting properties of these functions.

The book provides a transition between elementary mathematics and
more advanced topics, trying to make this transition as smooth as
possible. Many topics occur in the book, but they are all part of a
bigger picture of mathematics. By delving into a variety of them, the
reader will develop this broad view. The large collection of problems
is an essential part of the book. The problems vary from routine
verifications of facts used in the text to the exploration of open
questions.

#### Readership

Undergraduate and graduate students interested in number theory, combinatorics, analysis, and experimental mathematics.

#### Reviews & Endorsements

On the whole, this is an extraordinarily interesting book overflowing with (mostly) elementary non-routine mathematics. It's well-written and a pleasure to read. I've been keeping it on my desk for the ease of access; it's going to stay there for some while. I recommend it wholeheartedly to math instructors, teachers, and students, especially those who have only a slight interest in the subject. The book is bound to expand their horizons.

-- MAA Reviews

#### Table of Contents

# Table of Contents

## Numbers and Functions: From a classical-experimental mathematician's point of view

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface xiii14 free
- The number systems 126 free
- Factorials and binomial coefficients 5782
- The Fibonacci numbers 105130
- Polynomials 133158
- Binomial sums 159184
- Catalan numbers 179204
- The Stirling numbers of the second kind 191216
- Rational functions 211236
- Wallis’ formula 245270
- Farey fractions 255280
- The exponential function 269294
- Trigonometric functions 309334
- Bernoulli polynomials 355380
- A sample of classical polynomials: Legendre, Chebyshev, and Hermite 387412
- Landen transformations 411436
- Three special functions: Γ,𝜓, and 𝜁 445470
- Bibliography 473498
- Index 493518 free
- Back Cover Back Cover1530