| Softcover ISBN: | 978-0-8218-8795-0 |
| Product Code: | STML/65 |
| List Price: | $59.00 |
| Individual Price: | $47.20 |
| eBook ISBN: | 978-0-8218-9167-4 |
| Product Code: | STML/65.E |
| List Price: | $49.00 |
| Individual Price: | $39.20 |
| Softcover ISBN: | 978-0-8218-8795-0 |
| eBook: ISBN: | 978-0-8218-9167-4 |
| Product Code: | STML/65.B |
| List Price: | $108.00 $83.50 |
| Softcover ISBN: | 978-0-8218-8795-0 |
| Product Code: | STML/65 |
| List Price: | $59.00 |
| Individual Price: | $47.20 |
| eBook ISBN: | 978-0-8218-9167-4 |
| Product Code: | STML/65.E |
| List Price: | $49.00 |
| Individual Price: | $39.20 |
| Softcover ISBN: | 978-0-8218-8795-0 |
| eBook ISBN: | 978-0-8218-9167-4 |
| Product Code: | STML/65.B |
| List Price: | $108.00 $83.50 |
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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.
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Table of Contents
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Chapters
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Chapter 1. The number systems
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Chapter 2. Factorials and binomial coefficients
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Chapter 3. The Fibonacci numbers
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Chapter 4. Polynomials
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Chapter 5. Binomial sums
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Chapter 6. Catalan numbers
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Chapter 7. The Stirling numbers of the second kind
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Chapter 8. Rational functions
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Chapter 9. Wallis’s formula
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Chapter 10. Farey fractions
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Chapter 11. The exponential function
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Chapter 12. Trigonometric functions
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Chapter 13. Bernoulli polynomials
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Chapter 14. A sample of classical polynomials: Legendre, Chebyshev, and Hermite
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Chapter 15. Landen transformations
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Chapter 16. Three special functions: $\Gamma $, $\psi $, and $\zeta $
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Additional Material
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Reviews
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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
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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 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
