Lecture Notes

Discrete Mathematics

While a statement (a claim) in natural sciences is validated by observations or experiments, in mathematics it is done by proofs using principles of logical reasoning. We discuss various techniques of proofs that will be useful in studying mathematics and computer science. (Recall that computers are built upon the same sytem of logic that is the foundation of mathematics.) In addition, we also discuss some topics of finite and discrete mathematics, which will be important not only for the students of mathematics but also for the students of computer science. Those topics include: Basic Proof Techniques, Proof by Mathematical Induction, Sets, Logic, Graphs, Automata, Languages, Probability, Modular Arithmetics and Public Key Cryptography. The target readers of these lecture notes are freshmen undergraduates in mathematics and computer science.