ECS 20 - Lecture-by-Lecture Topic Summaries
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| Lecture |
Title |
Recommended reading |
| Lect 1 Th 1/4 |
Introduction. Mathematical symbols you should know. Type of problems we will solve: counting, proofs, ... |
Table of mathematical symbols
Tower of Hanoi
|
| Lect 2 T 1/9 |
Logic. Propositions. Compound propositions: conjunction, disjunction, exclusive or. Logical equivalences. De Morgan's laws. Implications. Biconditionals |
Textbook: pages 1-15 & 21-27
Liar's paradox
Important logical equivalences
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| Lect 3 Th 1/11 |
Implications. Biconditionals. Proofs. Rules of inference.
| Textbook: pages 63-72
Rules of inference
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| Lect 4 T 1/16 |
Proofs. Methods of proof: direct, indirect, contradiction
| Textbook: pages 75-83
|
| Lect 5 Th 1/18 |
Proofs. Methods of proof: proof by cases; existence proofs. Non constructive proofs. Quantifiers | Textbook: pages 84-100
|
| Lect 6 T 1/23 |
(Basic) Set theory. Definition of sets. Terminology: eleme
nts, union, intersection. Set identities. Computer representation of sets |
Textbook: pages 111-130. See also Wikipedia's articles on Russell's paradox and the Barber paradox
|
| Lect 7 Th 1/25 |
Quiz 1..
Functions. Injection, Surjection, Bijection.
Floor and Ceiling functions. |
| Lect 8 T 1/30 |
Growth of functions. |
See Wikipedia article on Big-O notation which contains properties of Big-O. |
| Lect 9 Th 2/1 |
Algorithms. |
See Wikipedia's articles on Binary Search |
| Lect 10 T 2/6 |
Number theoryDivisions. Prime numbers. Sieve of Eratosthenes. |
See Wikipedia's articles on Eratosthenes's sieve |
| Lect 11 Th 2/8 |
Number theorygcd(a,b), lcm(a,b). Bezout's identity. Proof that gcd(a,b)*lcm(a,b)=ab |
See Wikipedia's articles on Prime numbers. Check also the Music of the Primes
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| Lect 12 T 2/13 |
Number theoryCongruence; Fermat's little theorem
Sequences The symbol "sum". Sum of geometric progressions. |
| Lect 13 Th 2/15 |
Midterm |
| Lect 14 T 2/20 |
Induction Proof by induction. Validity. Examples |
See Wikipedia's article on Mathematical induction
|
| Lect 15 Th 2/22 |
Induction- Recurrence Proof by induction (continued). Recurrences. Fibonacci' s numbers |
See Wikipedia's article on Fibonacci numbers
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| Lect 16 T 2/27 |
Counting Sum rule; Product rule |
| Lect 17 Th 3/1 |
Counting Pigeonhole principle |
See Wikipedia's article in the Pigeonhole principle, or this web site
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| Lect 18 T 3/6 |
Quiz 2: Induction
Counting Permutations
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| Lect 19 Th 3/8 |
Counting Permutations, Combinations. Binomial theorem.
Pascal's identity. |
See article in Wikipedai on Pascal's triangle
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