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.

NB allows you to annotate PDFs for yourself or for sharing with others. We are piloting NB on this course and will use the results of this pilot to decide whether this tool will be useful for other courses.

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