1. Chapter 10: Mathematical proofs
Introduction
10.1 Preliminaries
10.2 Mathematical deduction
10.3 Specific fields
10.4 Conclusion

2. Introduction One of few ways to demonstrate absolute truth
Research that proves assertions mathematically is highly regarded

3. 10.1 Preliminaries Need for mathematical notation
Sets, functions, and relations
Propositional logic (p59)
First-order predicate logic
Automata
Petri nets
Formal grammars
Specification languages

4. 10.2 Mathematical deduction
Definitions describe what is meant by a specific term
Axioms express truths that are either obvious or assumed
Theorems represent interesting or useful derived facts
Lemmas are similar to theorems but are only used as stepping stones to derive more general or more powerful theorems
Corollaries are rephrased theorems or lemmas

5. 10.3 Specific fields Computability and algorithmic complexity
Can a given problem be solved by a computer?
If so, prove it by means of an algorithm.
Algorithmic complexity refers to time and/or memory requirements of an algorithm for a computable problem
Correctness: Proving a program correct
Combinatorics and graph theory
Formal languages and automata theory

6. 10.4 Conclusion
A little mathematics increase other people’s regard of your work