Lecture Slides

Lecture note files.

SES #	COURSEWARE	LECTURE SLIDES
Unit 1: Proofs
1	1.1 Intro to Proofs	Welcome to 6.042J (PDF) Introduction to Proofs (PDF)
2	1.2 Proof Methods	Proof by Contradiction (PDF) Proof by Cases (PDF) Proof by Cases Example (PDF)
3	1.3 Well Ordering Principle	Well Ordering Principle 1 (PDF) Well Ordering Principle 2 (PDF) Well Ordering Principle 3 (PDF)
4	1.4 Logic & Propositions	Propositional Operators (PDF) Digital Logic (PDF) Truth Tables (PDF) Implies (PDF) Propositional Logic (PDF)
5	1.5 Quantifiers & Predicate Logic	Predicate Logic 1 (PDF) Predicate Logic 2 (PDF) Predicate Logic 3 (PDF)
6	1.6 Sets	Sets Definition (PDF) Sets Operation (PDF)
7	1.7 Binary Relations	Relations (PDF) Relational Mapping (PDF) Finite Cardinality (PDF)
8	1.8 Induction	Induction (PDF) Bogus Induction (PDF - 1.2MB) Strong Induction (PDF) Ordinary Induction vs Strong Induction vs WOP (PDF)
9	1.9 State Machines - Invariants	State Machine Invariants (PDF) Derived Variables (PDF)
10	1.10 Recursive Definition	Recursive Data (PDF) Structural Induction (PDF) Recursive Functions (PDF)
11	1.11 Infinite Sets	Cardinality (PDF) Countable Sets (PDF) Cantor's Theorem (PDF) The Halting Problem (PDF) Russell's Paradox (PDF) Set Theory Axioms (PDF)
Unit 2: Structures
12	2.1 GCDs	GCDs and Linear Combinations (PDF) Euclidean Algorithm (PDF) The Pulverizer (PDF) Die Hard Primes (PDF) Prime Factorization (PDF)
13	2.2 Congruences	Congruence (PDF) Inverses Mod N (PDF)
14	2.3 Euler's Theorem	Modular Exponentiation: Euler's Function (PDF) The Ring Z_n (PDF)
15	2.4 RSA Encryption	RSA Public Key Encryption (PDF) Reducing Factoring to SAT (PDF)
16	2.5 Digraphs: Walks & Paths	Digraphs: Walks & Paths (PDF) Digraphs: Connected Vertices (PDF)
17	2.6 Directed Acyclic Graphs (DAGs) & Scheduling	DAGs (PDF) Scheduling (PDF) Time vs Processors (PDF)
18	2.7 Partial Orders and Equivalence	Partial Orders (PDF) Representing Partial Orders As Subset Relations (PDF) Equivalence Relations (PDF)
19	2.8 Degrees & Isomorphism	Degrees (PDF) Isomorphism (PDF)
20	2.9 Coloring & Connectivity	Coloring (PDF) Connectivity (PDF) k-Connectivity (PDF)
21	2.10 Trees	Trees (PDF) Tree Coloring (PDF) Spanning Trees (PDF)
22	2.11 Stable Matching	Stable Matching (PDF - 2.6MB) Mating Ritual (PDF) Optimal Stable Matching (PDF) Bipartite Matching (PDF) Hall's Theorem (PDF)
Unit 3: Counting
23	3.1 Sums & Products	Arithmetic Sums (PDF) Geometric Sums (PDF) Book Stacking (PDF) Integral Method (PDF) Stirling's Formula (PDF)
24	3.2 Asymptotics	Asymptotic Notation (PDF) Asymptotic Properties (PDF) Asymptotic Blunders (PDF)
25	3.3 Counting with Bijections	Sum and Product Rules (PDF) Counting with Bijections (PDF)
26	3.4 Repetitions & Binomial Theorem	Generalized Counting Rules (PDF) Two Pair Poker Hands (PDF) Binomial Theorem (PDF) Bookkeeper Rule, Multinomial Theorem (PDF)
27	3.5 Pigeonhole Principle, Inclusion-Exclusion	The Pigeonhole Principle (PDF) Inclusion-Exclusion: 2 Set Proof (PDF)
Unit 4: Probability
28	4.1 Intro to Discrete Probability	Tree Model (PDF) Simplified Monty Hall Tree (PDF) Sample Spaces (PDF)
29	4.2 Conditional Probability	Conditional Probability (PDF) Law Of Total Probability (PDF) Bayes' Theorem (PDF) Monty Hall Problem (PDF)
30	4.3 Independence & Causality	Independence (PDF) Mutual Independence (PDF)
31	4.4 Random Variables, Density Functions	Bigger Number Game (PDF) Random Variables: Independence (PDF) Random Variables: Uniform & Binomial (PDF)
32	4.5 Expectation	Expectation (PDF) Expected Number Of Heads (PDF) Total Expectation (PDF) Mean Time To Failure (PDF) Linearity Of Expectation (PDF)
33	4.6 Deviation: Markov & Chebyshev Bounds	Deviation From The Mean (PDF) Markov Bounds (PDF) Chebyshev Bounds (PDF) Variance (PDF)
34	4.7 Sampling & Confidence	Law of Large Numbers (PDF) Independent Sampling Theorem (PDF) Birthday Matching (PDF) Sampling and Confidence (PDF)
35	4.8 Random Walks & Pagerank	Random Walks (PDF) Stationary Distributions (PDF) Pagerank (PDF)