Discrete Mathematics: Winter 2019

Lectures

Notes:

I provide copies (PDF format) of my notes for each lecture. Note that these notes are incomplete and do not replace the notes you will take during the lectures!
"Lecture" should be distinguished from the actual class. A lecture is more like a chapter; some of these lectures will require more than one class time.
Lecture notes may change as quarter progresses

Number	Topic	Notes	Further reading/Comments
Lect 1 T 01/08	Introduction. Topics we will cover. Mathematical symbols you should know. Good practices in Math, ...	PDF scan of hand written notes	Table of mathematical symbols
Lect 2 Th 01/10	Chapter 1. Logic. Propositions. Compound propositions. Logic puzzles	PDF scan of hand written notes	Wikipedia article: Liar's paradox Handout: Important logical equivalences
Lect 3 T 1/15- T 1/22	Chapter 2. Logic (2). Conditional. Biconditional. Proofs. Rules of inference.	PDF scan of hand written notes	Handout: Rules of inference Additional problems: Text (PDF format) and Solutions to odd problems (PDF format)
Lect 4 Th 1/24- T 1/29	Chapter 3. Set theory. Definition of sets. Terminology: elements, union, intersection. Set identities. Computer representation of sets	PDF scan of hand written notes	See articles on Russell's paradox and the Barber paradox Handout: Set identities Additional problems: Text (PDF format) and Solutions to odd problems (PDF format)
Lect 5 Th 1/31 - Th 2/07	Functions. Injection, Surjection, Bijection. Floor and Ceiling functions. Growth of functions	PDF scan of hand written notes	See Wikipedia article on Big-O notation which contains properties of Big-O. Additional problems on functions: Text (PDF format) and Solutions to odd problems (PDF format) Additional problems on growth of functions: Text (PDF format) and Solutions to odd problems (PDF format)
Lect 6 T 02/11 - 02/19	Number theory.	PDF scan of hand written notes	See Wikipedia's articles on Eratosthenes's sieve See Wikipedia's articles on Prime numbers Additional problems on number theory: Text (PDF format) and Solutions to odd problems (PDF format)
Chapter 7 Th 02/21 - Th 02/28	Sequences. Induction	PDF scan of hand written notes	Additional problems on Induction: Induction: Text (PDF format) Strong Induction: Text (PDF format) Recursions, Fibonacci: Text (PDF format) Solutions to odd problems (PDF format)
Chapter 8 T 03/05 - Th 03/07	Counting	PDF scan of hand written notes	See article in Wikipedia on Pascal's triangle Additional problems on Counting: Counting: Text (PDF format) Pigeonhole principle: Text (PDF format) Permutations, Combinations: Text (PDF format) Solutions to odd problems (PDF format)
Chapter 9 Th 03/14	Algorithms.	PDF scan of hand written notes	See Wikipedia article on Binary search. Additional problems on algorithms: Text (PDF format) and Solutions to odd problems (PDF format)