A compilation of notes, typeset in LaTeX, from my time teaching CS70: Discrete Mathematics and Probability Theory at the University of California, Berkeley. These notes aim to provide more background for the Discrete Mathematics part of the class. The planned structure of the book is as follows:
- Numbers, Sets & Functions
- Quadratic Equations
- Inequalities
- Sets
- Functions
- Fields
- Exercises
- Language and Proofs
- Statements and Connectives
- Predicates and Quantifiers
- Proving Existential Statements
- Unary Proofs
- Conditional Proofs
- Biconditional Proofs (TODO)
- Mathematical Induction
- Sum and Product Notation
- The Natural Numbers
- Inductive Proofs
- Sequences and Recurrences
- Extending Induction
- Strong Induction
- Strengthening the Hypothesis (TODO)
- The Well-Ordering Principle
- Bijections and Cardinality (TODO)
- Divisibility (TODO)
- Modular Arithmetic (TODO)