Saturday, July 6, 2019

Discrete Mathematics: Elementary and Beyond

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For most students, the first and often only course in college mathematics is calculus. It is true that calculus is the single most important field of mathematics, whose emergence in the seventeenth century signaled the birth of modern mathematics and was the key to the successful applications of mathematics in the sciences and engineering.

But calculus (or analysis) is also very technical. It takes a lot of work even to introduce its fundamental notions like continuity and the derivative (after all, it took two centuries just to develop the proper definition of these notions). To get a feeling for the power of its methods, say by describing one of its important applications in detail, takes years of study.

If you want to become a mathematician, computer scientist, or engineer, this investment is necessary. But if your goal is to develop a feeling for what mathematics is all about, where mathematical methods can be helpful, and what kinds of questions do mathematicians work on, you may want to look for the answer in some other fields of mathematics.

1. Let’s Count!
2. Combinatorial Tools
3. Binomial Coefficients and Pascal’s Triangle
4. Fibonacci Numbers
5. Combinatorial Probability
6. Integers, Divisors, and Primes
7. Graphs
8. Trees
9. Finding the Optim
10. Matchings in Graphs
11. Combinatorics in Geometry
12. Euler’s Formula
13. Coloring Maps and Graphs
14. Finite Geometries, Codes, Latin Squares, and Other Pretty Creatures
15. A Glimpse of Complexity and Cryptography
16. Answers to Exercises

Author Details
"L. Lovász"

"J. Pelikán"

"K. Vesztergombi"

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