Subject(s) 
Functions  Textbooks


Calculus  Textbooks

Physical Description 
xxiii, 504 p. : ill. ; 22 cm 
Note 
Includes bibliographical references (p. 473491) and index 
Contents 
The number systems  Factorials and binomial coefficients  The Fibonacci numbers  Polynomials  Binomial sums  Catalan numbers  The Stirling numbers of the second kind  Rational functions  Wallis' formula  Farey fractions  The exponential function  Trigonometric functions  Bernoulli polynomials  A sample of classical polynomials: Legendre, Chebyshev, and Hermite  Landen transformations  Three special functions 
Summary 
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 
NOTE 
531124 
Series 
Student mathematical library ; v. 65

