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**About this book :- **
**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

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**About Author :- **

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

5. Advanced Combinatorics—Multichoosing

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

Answers to Questions to Consider

Timeline

Glossary

Biographical Notes

Bibliography

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- Boolean Algebra
- Graph Theory
- Linear Algebra
- Number Theory
- Set Theory
- Mathematical Induction
- Discrete Geometry
- Discrete Probability

- Abstract Algebra
- Calculus
- Differential Equations
- Engineering Mathematics
- Linear Algebra
- Math Magic
- Real Analysis