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Discrete Mathematics by Arthur T Benjamin

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Discrete Mathematics written by Arthur T Benjamin
Discrete mathematics can be described as an advanced look at the mathematics that we learned as children. In elementary school, we learned to count, did basic arithmetic, and amused ourselves with solving puzzles, ranging from connecting the dots, to coloring, to more sophisticated creative pursuits.
So what exactly is discrete mathematics? Perhaps it is easier to first say what it is not. Most of the mathematics that we are taught in high school from geometry through calculus—is continuous mathematics. Think of the second hand of a wristwatch or the path traveled by a ball as it is thrown in the air. These objects are typically described by real numbers and continuous functions. By contrast, discrete mathematics is concerned with processes that occur in separate chunks, such as how the seconds or minutes change on a digital watch, or the way the path of the ball would look if we took a few snapshots of its journey. The numbers used in discrete mathematics are whole numbers. Discrete mathematics is the foundation of computer science, where statements are true or false, numbers are represented with finite precision, and every piece of data is stored in a specific place.
In this course, we concentrate on 3 major fields of discrete mathematics: combinatorics, number theory, and graph theory. Combinatorics is the mathematics of counting. How many ways can we rearrange the letters of “Mississippi”? How many different lottery tickets can be printed? How many ways can we be dealt a full house in poker? Central to the answers to these questions is Pascal’s triangle, whose numbers contain some amazingly beautiful patterns, which we shall explore.

Book Detail :-
Title: Discrete Mathematics
Edition:
Author(s): Arthur T Benjamin
Publisher:
Series: The Great Courses: Science & Mathematics
Year: 2009
Pages: 160
Type: PDF
Language: English
ISBN: 1598035789,9781598035780
Country: US

Author Arthur T. Benjamin is a Professor of Mathematics at Harvey Mudd College. He graduated from Carnegie Mellon University in 1983, where he earned a B.S. in Applied Mathematics with university honors. He received his Ph.D. in Mathematical Sciences in 1989 from Johns Hopkins University, where he was supported by a National Science Foundation graduate fellowship and a Rufus P. Isaacs fellowship. Since 1989, Dr. Benjamin has been a faculty member of the Mathematics Department at Harvey Mudd College, where he has served as department chair. He has spent sabbatical visits at Caltech, Brandeis University, and University of New South Wales in Sydney, Australia.
1999, Professor Benjamin received the Southern California Section of the Mathematical Association of America (MAA) Award for Distinguished College or University Teaching of Mathematics, and in 2000, he received the MAA Deborah and Franklin Tepper Haimo National Award for Distinguished College or University Teaching of Mathematics. He was named the 2006í2008 George Pólya Lecturer by the MAA.
Dr. Benjamin’s research interests include combinatorics, game theory, and number theory, with a special fondness for Fibonacci numbers. Many of these ideas appear in his book (co-authored with Jennifer Quinn), Proofs That Really Count: The Art of Combinatorial Proof published by the MAA. In 2006, that book received the Beckenbach Book Prize by the MAA. Professors Benjamin and Quinn are the co-editors of Math Horizons magazine, published by MAA and enjoyed by more than 20,000 readers, mostly undergraduate math students and their teachers.
Professor Benjamin is also a professional magician. He has given more than 1,000 “mathemagics” shows to audiences all over the world (from primary schools to scienti¿ c conferences), where he demonstrates and explains his calculating talents. His techniques are explained in his book Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks. Proli¿ c math and science writer Martin Gardner calls it “the clearest, simplest, most entertaining, and best book yet on the art of calculating in your head.” An avid games player, Dr. Benjamin was winner of the American Backgammon Tour in 1997.
Professor Benjamin has appeared on dozens of television and radio programs, including the Today Show, CNN, and National Public Radio. He has been featured in Scienti¿ c American, Omni, Discover, People, Esquire, The New York Times, the Los Angeles Times, and Reader’s Digest. In 2005, Reader’s Digest called him “America’s Best Math Whiz.”

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Book Contents :-
Discrete Mathematics written by Arthur T Benjamin cover the following topics.
1. What Is Discrete Mathematics?
2. Basic Concepts of Combinatorics
3. The 12-Fold Way of Combinatorics
4. Pascal’s Triangle and the Binomial Theorem
6. The Principle of Inclusion-Exclusion
7. Proofs—Inductive, Geometric, Combinatorial
8. Linear Recurrences and Fibonacci Numbers
9. Gateway to Number Theory—Divisibility
10. The Structure of Numbers
11. Two Principles—Pigeonholes and Parity
12. Modular Arithmetic The Math of Remainders
13. Enormous Exponents and Card Shuffling
14. Fermat’s “Little” Theorem and Prime Testing
15. Open Secrets—Public Key Cryptography
16. The Birth of Graph Theory
17. Ways to Walk Matrices and Markov Chains
18. Social Networks and Stable Marriages
19. Tournaments and King Chickens
20. Weighted Graphs and Minimum Spanning Trees
21. Planarity—When Can a Graph Be Untangled?
22. Coloring Graphs and Maps
23. Shortest Paths and Algorithm Complexity
24. The Magic of Discrete Mathematics
Timeline
Glossary
Biographical Notes
Bibliography

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