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E-raamat: Discrete Encounters

(York College of Pennsylvania, Physical Sciences Department, USA)
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Eschewing the often standard dry and static writing style of traditional textbooks, Discrete Encounters provides a refreshing approach to discrete mathematics. The author blends traditional course topics and applications with historical context, pop culture references, and open problems. This book focuses on the historical development of the subject and provides fascinating details of the people behind the mathematics, along with their motivations, deepening readers appreciation of mathematics.

This unique book covers many of the same topics found in traditional textbooks, but does so in an alternative, entertaining style that better captures readers attention. In addition to standard discrete mathematics material, the author shows the interplay between the discrete and the continuous and includes high-interest topics such as fractals, chaos theory, cellular automata, money-saving financial mathematics, and much more. Not only will readers gain a greater understanding of mathematics and its culture, they will also be encouraged to further explore the subject. Long lists of references at the end of each chapter make this easy.

Highlights:











Features fascinating historical context to motivate readers





Text includes numerous pop culture references throughout to provide a more engaging reading experience





Its unique topic structure presents a fresh approach





The texts narrative style is that of a popular book, not a dry textbook





Includes the work of many living mathematicians





Its multidisciplinary approach makes it ideal for liberal arts mathematics classes, leisure reading, or as a reference for professors looking to supplement traditional courses





Contains many open problems

Profusely illustrated
Acknowledgments ix
Introduction xi
Author xiii
0 Continuous vs. Discrete
1(20)
1 Logic
21(32)
2 Proof Techniques
53(32)
3 Practice with Proofs
85(16)
4 Set Theory
101(34)
5 Venn Diagrams
135(24)
6 The Functional View of Mathematics
159(18)
7 The Multiplication Principle
177(20)
8 Permutations
197(22)
9 Combinations
219(24)
10 Pascal and the Arithmetic Triangle
243(34)
11 Stirling and Bell Numbers
277(24)
12 The Basics of Probability
301(26)
13 The Fibonacci Sequence
327(30)
14 The Tower of Hanoi
357(28)
15 Population Models
385(20)
16 Financial Mathematics (and More)
405(22)
17 More Difference Equations
427(26)
18 Chaos Theory and Fractals
453(62)
19 Cellular Automata
515(56)
20 Graph Theory
571(70)
21 Trees
641(22)
22 Relations, Partial Orderings, and Partitions
663(28)
Index 691
Craig P. Bauer is a professor of mathematics at York College of Pennsylvania. Hes the

editor-in-chief of Cryptologia and was the 20112012 Scholar-in-Residence at the National

Security Agencys Center for Cryptologic History. He loves to carry out research, write,

and lecture. His previous books are Secret History: The Story of Cryptology and Unsolved!

The History and Mystery of the Worlds Greatest Ciphers from Ancient Egypt to Online Secret

Societies. With the present book he stays true to his style, blending mathematics and

history. Craig earned his Ph.D. in mathematics from North Carolina State University

and did his undergraduate work at Franklin & Marshall College.