Fall 2005
Topics |
Date(s) |
Reading |
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Class Overview |
Mon, Aug 22
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Direct and Indirect Proofs. |
Wed, Aug 24
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Reading: (1) Intro Lecture from Berkeley Class, (2) Rosen, pp. 56-65 (I suggest reading all of Chapter 1.) |
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Proofs by contradiction. |
Fri, Aug 26
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Same as last lecture |
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Proofs by cases and Non-constructive proofs. Induction |
Mon, Aug 29
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More on Induction
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Wed, Aug 31
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Variants on Standard Induction: (1) Strong Induction with primes example (See Example 14 from Rosen Chapter 3, or the beginning of Berkeley notes.) and (2) Induction over pairs of natural numbers with Knight's moves example (see the end of the Berkeley notes). |
Fri, Sep 2
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(1) Rosen, end of Section 3.3 (pp. 249-251), (2) Berkeley Notes (We covered Strong Induction with the primes example from the beginning of the notes, and the knight's moves at the end. The rest may be useful to read, but you are not obligated.) |
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Asymptotic Notation: Big-O
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Wed, Sept 7 and Fri, Sept 9 |
Rosen, Chapter 2.2, especially pp. 131-140 |
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Algorithm Analysis and Recursion: Linear Search and Binary Search |
Mon, Sep 12 |
Rosen, Chapter 2.1,2.3 |
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BubbleSort and MergeSort Simultaneous Min and Max (Recursive and iterative algorithm) |
Wed, Sep 14, Fri, Sep 16, Mon, Sep 19, |
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Solving Recurrences |
Wed, Sep 21, Wed, Sep 28 |
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Quiz 1 and review of solutions |
Fri, Sep 23, Mon, Sep 26 |
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Strassen's Multiplication |
Fri, Sep 30 |
See pargraphs 1,2, & 3 in these
Berkeley notes |
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Counting |
Mon, Oct 3 Wed, Oct 5 |
Rosen, Chapter 4
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Introduction to Probability |
Fri, Oct 7 |
Rosen pp. 355-371
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Expectation Linearity of Expectation Conditional Probability |
Mon, Oct 10 |
Rosen pp. 379-388
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Markov's Inequality Variance Chebychev's Inequality Estimating Sample Size |
Wed, Oct 12, Fri, Oct 14 |
Rosen pp. 388-392 and these Berkeley notes |
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Randomized Median |
Wed, Oct 19 |
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Practice Problems on Counting and Probability |
Fri, Oct 21 |
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Hash Tables Birthday Paradox |
Mon, Oct 24 |
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Review for the quiz
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Wed, Oct 28
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Study Recurrence Relations,
Counting and Probability. Homeworks 4-7 |
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Quiz 2
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Fri, Oct 28
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Review of Quiz 2
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Mon, Oct 31
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Naive Primality Testing Algorithms Euclid's GCD Algorithm Properties of Modular Arithmetic Modular Exponentiation Inverses Extended Euclid Algorithm |
Wed, Nov 2 Fri, Nov 4 Mon, Nov 7 |
Berkeley notes (also see Section 2.4 (and some of 2.5) of Rosen) |
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Fermat's Little Theorem Primality Testing Algorithm |
Mon, Nov 7 |
Berkeley notes (also see Rosen, p. 189-191) |
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Generating Random Primes RSA Cryptosystem |
Wed, Nov 9 |
Berkeley notes
(especially sections 4 and 5)
(also see Rosen, p. 191-194) |
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Digital Signature |
Fri, Nov 11 |
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Chinese Remainder Theorem Diffie Hellman Secret Key Exchange |
Mon, Nov 14 |
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Polynomials and Secret Sharing |
Wed, Nov 16 |
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Review for Quiz |
Fri, Nov 18 |
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Quiz 3
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Mon, Nov 21
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Countably Infinite Uncountably Infinite Diagonalization Proof Limitations of Computation |
Mon, Nov 28
Wed, Nov 30 Fri, Dec 2 |
