Softcover ISBN:  9780821887950 
Product Code:  STML/65 
List Price:  $58.00 
Individual Price:  $46.40 
Electronic ISBN:  9780821891674 
Product Code:  STML/65.E 
List Price:  $58.00 
Individual Price:  $46.40 

Book DetailsStudent Mathematical LibraryVolume: 65; 2012; 504 ppMSC: Primary 05; 11; 33;
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.ReadershipUndergraduate and graduate students interested in number theory, combinatorics, analysis, and experimental mathematics.

Table of Contents

Chapters

Chapter 1. The number systems

Chapter 2. Factorials and binomial coefficients

Chapter 3. The Fibonacci numbers

Chapter 4. Polynomials

Chapter 5. Binomial sums

Chapter 6. Catalan numbers

Chapter 7. The Stirling numbers of the second kind

Chapter 8. Rational functions

Chapter 9. Wallis’s formula

Chapter 10. Farey fractions

Chapter 11. The exponential function

Chapter 12. Trigonometric functions

Chapter 13. Bernoulli polynomials

Chapter 14. A sample of classical polynomials: Legendre, Chebyshev, and Hermite

Chapter 15. Landen transformations

Chapter 16. Three special functions: $\Gamma $, $\psi $, and $\zeta $


Additional Material

Reviews

On the whole, this is an extraordinarily interesting book overflowing with (mostly) elementary nonroutine mathematics. It's wellwritten 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


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

Chapters

Chapter 1. The number systems

Chapter 2. Factorials and binomial coefficients

Chapter 3. The Fibonacci numbers

Chapter 4. Polynomials

Chapter 5. Binomial sums

Chapter 6. Catalan numbers

Chapter 7. The Stirling numbers of the second kind

Chapter 8. Rational functions

Chapter 9. Wallis’s formula

Chapter 10. Farey fractions

Chapter 11. The exponential function

Chapter 12. Trigonometric functions

Chapter 13. Bernoulli polynomials

Chapter 14. A sample of classical polynomials: Legendre, Chebyshev, and Hermite

Chapter 15. Landen transformations

Chapter 16. Three special functions: $\Gamma $, $\psi $, and $\zeta $

On the whole, this is an extraordinarily interesting book overflowing with (mostly) elementary nonroutine mathematics. It's wellwritten 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