Spring 2009. CS 1050 B Constructing Proofs
| Topics |
Dates
|
Reading
|
|---|---|---|
| Course overview. Administrative stuff. Introduction. |
01.08
|
Course
rules.
Rosen textbook, Chapter 1, pp.1-43. |
| Rules of inference. Direct proofs. |
01.13
|
(1) Intro
Lecture
from Berkeley Class, (2) Intro Lecture from MIT Class. (3) Rosen textbook, pp. 1-43,63-69. |
| Inderect proofs. Proofs by contraposition and by contradiction. Proofs by cases. |
01.15
|
Same as above, |
| Existence proofs. Basics of induction. |
01.20
|
(1)
Berkeley
Lectures,
(2) Rosen textbook, Chapter 4, pp 91-100, 263-279. |
| More on induction. |
01.22
|
(1) Berkeley
Lectures,
(2) Rosen textbook, Chapter 4, pp 263-279. |
| Strong induction. Induction and recursion: an algorithmic perspective. |
01.27
|
(1) MIT
Lectures,
(2) Rosen textbook, Chapter 4, pp 283-291. |
| Sort and search algorithms. Finding MIN and MAX in a list of elements. |
01.29
|
Rosen
textbook, Chapter 4, pp 294-300.
|
| More on sort and search algorithms. Solving recurrences. |
02.03
|
|
| MergeSort. |
02.05
|
|
| Review for Quiz 1. |
02.10
|
|
| Quiz 1. |
02.12
|
|
| Review
of the solutions for Quiz 1. Asymptotic notation: Big-O. |
02.17
|
|
| Asymptotic notation:
Big-O. |
02.19
|
Rosen textbook, Chapter 3,
pp.180-190.
|
| Principles of counting. |
02.24
|
Rosen textbook, Chapter 5,
pp.335-344, 347-353,
355-360. |
| Choice, permutations, combinations. |
02.26
|
Rosen textbook, Chapter
5.1.
|
| Choice, permutations, combinations. Practice problems on counting. |
03.03
|
Rosen textbook, Chapter
5.3-5.5
|
| Binomial coefficients. Pigeonhole principle. |
03.05
|
Rosen textbook, Chapter
5.2
|
| Quiz 2. |
03.10
|
|
| Introduction to probability. Conditional probability. |
03.12
|
Rosen textbook, Chapter 6,
pp. 393-398,
404-406,
|
| Bayes' theorem. |
03.24
|
Rosen textbook, Chapter 6,
pp. 417-423
|
| Spring break. | ||
| Random variables. Expectation. |
03.26
|
Rosen textbook, Chapter 6,
pp. 426-433 |
| Variance. Markov's inequality. Chebyshev's inequality. |
03.31
|
Berkeley
Lectures
Chapter 6,
pp.
434-439
|
| Hash tables. Birthday paradox. |
04.02
|
Rosen textbook, Chapter 6,
pp. 409-411
UCSD Lectures |
| Basics of cryptography. |
04.07
|
|
| Basics of number theory. Euclid's GCD algorithm. Extended GCD. |
04.09
|
Lecture
by B. Pinkas Rosen textbook, Chapter 3, pp. 201-205,
210-244 |
| Practice for the quiz. |
04.14
|
|
| Quiz
3.
|
04.16
|
|
|
Review of the solutions for Quiz 3. More on number theory and crypto.
|
04.21
|
|
|
|
04.23
|
|
|
|
