Math for Computer Science

  1.  Unit 1: Proofs
    1. 1.1 Introduction to Proofs
    2. 1.2 Proof Methods
    3. 1.3 Well Ordering Principle
    4. 1.4 Logic & Propositions
    5. Problem Set 1
    6. 1.5 Quantifiers & Predicate Logic
    7. 1.6 Sets
    8. Problem Set 2
    9. 1.7 Binary Relations
    10. 1.8 Induction
    11. Problem Set 3
    12. 1.9 State Machines—Invariants
    13. 1.10 Recursive Definition
    14. 1.11 Infinite Sets
    15. Problem Set 4
  2.  Unit 2: Structures
    1. 2.1 GCDs
    2. 2.2 Congruences
    3. 2.3 Euler’s Theorem
    4. Problem Set 5
    5. 2.4 RSA Encryption
    6. 2.5 Digraphs: Walks & Paths
    7. Problem Set 6
    8. 2.6 Directed Acyclic Graphs
    9. 2.7 Partial Orders and Equivalence
    10. 2.8 Degrees & Isomorphism
    11. Problem Set 7
    12. 2.9 Coloring & Connectivity
    13. 2.10 Trees
    14. 2.11 Stable Matching
    15. Problem Set 8
  3.  Unit 3: Counting
    1. 3.1 Sums & Products
    2. 3.2 Asymptotics
    3. Problem Set 9
    4. 3.3 Counting with Bijections
    5. 3.4 Repetitions & Binomial Theorem
    6. 3.5 Pigeonhole Principle, Inclusion-Exclusion
    7. Problem Set 10
  4.  Unit 4: Probability
    1. 4.1 Intro to Discrete Probability
    2. 4.2 Conditional Probability
    3. Problem Set 11
    4. 4.3 Independence & Causality
    5. 4.4 Random Variables, Density Functions
    6. 4.5 Expectation
    7. Problem Set 12
    8. 4.6 Deviation: Markov & Chebyshev Bounds
    9. 4.7 Sampling & Confidence
    10. 4.8 Random Walks & PageRank