This is an archived course. A more recent version may be available at ocw.mit.edu.

Lecture Notes

This section contains slides, in-class problems, and solutions. Students work in groups to solve the in-class problems; see the Syllabus for more information.

Powerpoint and LaTeX source files and LaTeX macros are available to instructors by request: email Prof. Albert Meyer at meyer at csail dot mit dot edu.

LEC # TOPICS SLIDES PROBLEMS SOLUTIONS
Week 1
1 Good and bad proofs (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
2 Proof by contradiction (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
Week 2
3 Well ordering principle (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
4 Propositional logic (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
5 Sets and relations (This resource may not render correctly in a screen reader.PDF - 2.0MB) (PDF) (PDF)
Week 3
6 Size of sets, mapping lemma (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
7 Predicates and quantifiers (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
8 Set theory, Russell paradox (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
Week 4
9 Induction and strong induction (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
10 Partial orders (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
11 Partial orders and scheduling (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
Week 5
12 Digraphs (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
13 State machines, preserved invariants (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
14 Derived variables, termination (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
Week 6
15 Stable matching (This resource may not render correctly in a screen reader.PDF - 2.5MB) (PDF) (PDF)
16 Simple graphs, degrees, isomorphism (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
17 Graph connectedness, trees (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
Week 7
18 Graph coloring, bipartite matching (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
19 Recursive data (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
20 Planar graphs (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
Week 8
21 GCD and integer linear combinations (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
22 Modular arithmetic (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
23 Inverses (mod n), RSA encryption (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
Week 9
24 Harmonic sums, Stirling's approximation (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
25 Asymptotics (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
26 Counting with bijections (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
Week 10
27 Pigeonhole and division rules (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
28 Counting repetitions, card magic (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
29 Inclusion-exclusion, counting practice (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
Week 11
30 Binomial theorem, combinatorial identities (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
31 Generating functions: for counting (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
Week 12
32 Generating functions: for recurrences (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
33 Introduction to probability (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
34 Conditional probability, independence (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
Week 13
35 Random variables (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
36 Expectation (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
37 Variance (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
Week 14
38 Sampling and confidence (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)
39 Random processes (This resource may not render correctly in a screen reader.PDF) (PDF) (PDF)