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6.042J | Spring 2015 | Undergraduate
Mathematics for Computer Science

Lecture Notes

Asymptotics: Asymptotic Blunders
Asymptotics: Asymptotic Notation
Asymptotics: Asymptotic Properties
Binary Relations: Finite Cardinality
Binary Relations: Relational Mapping
Binary Relations: Relations
Coloring & Connectivity: Coloring
Coloring & Connectivity: Connectivity
Coloring & Connectivity: k-Connectivity
Conditional Probability: Bayes' Theorem
Conditional Probability: Conditional Probability Definitions
Conditional Probability: Law Of Total Probability
Conditional Probability: Monty Hall Conditional Confusions
Congruences: Congruence Mod N
Congruences: Inverses Mod N
Counting with Bijections: Bijections
Counting with Bijections: Sum and Product Rules
Degrees and Isomorphism: Degrees
Degrees and Isomorphism: Isomorphism
Deviation: Markov & Chebyshev Bounds: Chebyshev Bounds
Deviation: Markov & Chebyshev Bounds: Deviation From The Mean
Deviation: Markov & Chebyshev Bounds: Markov Bounds
Deviation: Markov & Chebyshev Bounds: Variance
Digraphs: Walks & Paths: Digraphs: Connected Vertices
Digraphs: Walks & Paths: Digraphs: Walks & Paths
Directed Acyclic Graphs & Scheduling: DAGs
Directed Acyclic Graphs & Scheduling: Scheduling
Directed Acyclic Graphs & Scheduling: Time vs Processors
Euler's Theorem: Modular Exponentiation: Euler’s Function
Euler's Theorem: The Ring Z_n
Expectation: Expectation
Expectation: Expected Number Of Heads
Expectation: Linearity Of Expectation
Expectation: Mean Time To Failure
Expectation: Total Expectation
GCDs: Die Hard Primes
GCDs: Euclidean Algorithm
GCDs: GCDs and Linear Combinations
GCDs: The Pulverizer
GCDs: Unique Factorization
Independence & Causality: Independence
Independence & Causality: Mutual Independence
Induction: Bogus Induction
Induction: Induction
Induction: Strong Induction
Induction: WOP vs Induction
Infinite Sets: Cantor's Theorem
Infinite Sets: Cardinality
Infinite Sets: Countable Sets
Infinite Sets: Russell's Paradox
Infinite Sets: Set Theory Axioms
Infinite Sets: The Halting Problem
Intro to Discrete Probability: Sample Spaces
Intro to Discrete Probability: Simplified Monty Hall Tree
Intro to Discrete Probability: Tree Model
Intro to Proofs: Introduction to Proofs
Logic and Propositions: Digital Logic
Logic and Propositions: Implies
Logic and Propositions: Propositional Logic
Logic and Propositions: Propositional Operators
Logic and Propositions: Truth Tables
Partial Orders and Equivalence: Equivalence Relations
Partial Orders and Equivalence: Partial Orders
Partial Orders and Equivalence: Representing Partial Orders As Subset Relations
Pigeonhole Principle, Inclusion-Exclusion: Inclusion-Exclusion
Pigeonhole Principle, Inclusion-Exclusion: Inclusion-Exclusion Example
Pigeonhole Principle, Inclusion-Exclusion: The Pigeonhole Principle
Proof Methods: Proof by Cases
Proof Methods: Proof by Cases Example
Proof Methods: Proof by Contradiction
Random Variables, Density Functions: Bigger Number Game
Random Variables, Density Functions: Random Variables: Independence
Random Variables, Density Functions: Random Variables: Uniform & Binomial
Random Walks & Pagerank: Pagerank
Random Walks & Pagerank: Random Walks
Random Walks & Pagerank: Stationary Distributions
Recursive Definition: Recursive Data
Recursive Definition: Recursive Functions
Recursive Definition: Structural Induction
Repetitions & Binomial Theorem: Binomial Theorem
Repetitions & Binomial Theorem: Bookkeeper Rule, Multinomial Theorem
Repetitions & Binomial Theorem: Generalized Counting Rules
Repetitions & Binomial Theorem: Two Pair Poker Hands
RSA Encryption: Reducing Factoring to SAT
RSA Encryption: RSA Public Key Encryption
Sampling & Confidence: Birthday Matching
Sampling and Confidence: Independent Sampling Theorem
Sampling and Confidence: Law of Large Numbers
Sampling and Confidence: Sampling and Confidence
Sets: Sets Definition
Sets: Sets Operation
Stable Matching: Bipartite Matching
Stable Matching: Hall's Theorem
Stable Matching: Mating Ritual
Stable Matching: Optimal Stable Matching
Stable Matching: Stable Matching
State Machines – Invariants: Derived Variables
State Machines – Invariants: State Machine Invariants
Sums & Products: Arithmetic Sums
Sums & Products: Book Stacking
Sums & Products: Geometric Sums
Sums & Products: Integral Method
Sums & Products: Stirling's Formula
Trees: Spanning Trees
Trees: Tree Coloring
Trees: Trees
Quantifiers & Predicate Logic: Predicate Logic 1
Well Ordering Principle: Well Ordering Principle 1
Quantifiers & Predicate Logic: Predicate Logic 2
Well Ordering Principle: Well Ordering Principle 2
Quantifiers & Predicate Logic: Predicate Logic 3
Well Ordering Principle: Well Ordering Principle 3
Intro to Proofs: Welcome to 6.042
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Spring 2015
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Undergraduate
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