Presents some common problems in mathematics and how they can be investigated using the Mathematica computer system. Problems and exercises include the calendar, sequences, the n-Queens problems, digital computing, blackjack and computing pi. This book is for those that would like to see how Mathematica is applied to real-world mathematics.
Author(s): Ilan Vardi
Edition: 1
Publisher: Addison-Wesley Professional
Year: 1991
Language: English
Commentary: Cover, OCR, bookmarks, paginated
Pages: 303
Tags: Библиотека;Компьютерная литература;Mathematica;
1 Elegant Programs in Mathematica
1.1 An algebraic method in Mathematica programming
1.1.1 Answer to Question 1
1.1.2 Answer to Question 2
1.2 Efficient Mathematica programs
1.2.1 Answer to Question 3
1.2.2 Answer to Question 4
1.3 Conclusion: Answer to Question 5
1.4 Notes
2 Digital Computing
2.1 The digits of 2 n in base three
2.1.1 Some facts about powers of 2 mod 3 k
2.1.2 The algorithm
2.2 Application to Binomial coefficients
2.3 Niven numbers
2.3.1 A lower bound
2.3.2 An upper bound
2.4 Notes
3 The Calendar
3.1 The calendar as a number system
3.2 Positional Number Systems
3.3 Mixed radix representations
3.4 Generalizing to lists
3.5 Rules for Some Calendars
3.5.1 The Julian Calendar
3.5.2 The Gregorian Calendar
3.5.3 The Islamic Calendar
3.5.4 The French Revolutionary Calendar
3.6 Implementation of the calendars
3.6.1 The Gregorian Calendar
3.6.2 The Islamic calendar
3.7 Notes
4 Searching for Numbers
4.1 Binomial Coefficients
4.2 A class of solutions
4.3 Computing binomial coefficients
4.4 Binomials modulo an integer
4.5 The search method
4.6 Notes
5 How Not to Use Mathematica
5.1 Are all Euclid numbers squarefree?
5.2 PowerMod to the rescue
5.3 American Science
5.4 Wieferich
5.4.1 The program
5.5 Notes
6 The n-Queens Problem
6.1 Permanents
6.2 Toroidal Semiqueens
6.3 Determinants and permanents
6.4 Notes
7 The 3x + 1 Problem
7.1 Using some ideas of Terras
7.2 The algorithm
7.3 The program
8 The Riemann Zeta Function
8.1 The distribution of primes
8.2 A more pedestrian application of (
8.3 The Euler-Maclaurin formula
8.3.1 Implementing the formula
8.4 Khinchin's constant
8.5 Notes
9 The Running Time of TAK
9.1 The lower bound
9.2 Asymptotics of the lower bound
9.3 The running time of TAKy
9.4 The running time of TAKz
10 The Condom Problem
10.1 The work of Hajnal and Lovasz
10.1.1 The algorithm
10.1.2 The lower bound
10.2 The algorithm
10.3 The general case
10.4 Lower bounds
A Answers to Exercises
A.0 Preface
A.1 Elegant Programs in Mathematica
A.2 Digital Computing
A.3 The Calendar
A.4 Searching for Numbers
A.5 How Not to Use Mathematica
A.6 The n-Queens Problem
A.8 The Riemann Zeta Function
A.9 The Running Time of TAK
A.10 The Condom Problem
B Glossary of Functions
Bibliography
Index
