Fall 2006
Topics |
Date(s) |
Reading |
|
Class Overview
Basics: Sets and
Numbers
|
Mon, Aug 21
|
|
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Propositions
Direct Proofs |
Wed, Aug 23
|
Reading: (1) Intro Lecture from Berkeley Class, (2) Rosen, pp. 75-102 (I suggest reading all of Chapter 1.) |
|
Direct proofs |
Fri, Aug 25
|
Same as before |
|
No lecture |
Mon,
Aug 28 |
|
|
Proofs by contrapositive,
cases |
Wed, Aug 30 |
Same as before
|
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Proofs by contradiction
|
Fri,
Sept 1 |
Same as before
|
|
Functions |
Wed,
Sept 6 |
Rosen, Chapter 2
|
|
Functions |
Fri,
Sept 8 |
Same as before
|
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Countable and uncountable sets
|
Mon,
Sept 11 |
Same as before
|
|
Propositional logic
|
Wed,
Sept 13 |
Rosen, Chapter 1, Sections 1.1-1.5 |
|
Induction
|
Fri, Sept 15
|
Rosen, Chapter 4,
Pages 263-298 |
|
Induction
|
Mon,
Sept 18
|
Same as before |
|
Review for Quiz 1
|
Wed,
Sept 20
|
|
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Review for Quiz 1
|
Fri,
Sept 22
|
|
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Quiz 1
|
Mon,
Sept 25 |
|
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Review of quiz solutions
|
Wed,
Sept 27 |
|
|
Induction
|
Fri,
Sept 29
|
Rosen, Chapter 4,
Pages 263-298
|
|
Induction
|
Mon, Oct 2 |
Same as before
|
|
Recursively defined functions |
Wed,
Oct 4 |
|
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Recursively defined functions |
Fri, Oct 6 |
|
|
Solving a special type of
recurrence
Fibonacci numbers
|
Mon,
Oct 9
|
|
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Sorting, Bubble sort
|
Wed,
Oct 11
|
Rosen, Chapter 3, Pages 167-175 |
|
Insertion sort, Binary search
|
Fri,
Oct 13
|
Same as before |
|
Merge Sort
|
Mon,
Oct 16
|
Same as before
|
|
Asymptotic growth of functions |
Wed, Oct 18 |
Rosen, Chapter 3, Pages 180-188 |
|
Asymptotic growth of functions |
Fri, Oct 20 |
Same as before |
|
Review for Quiz-2
|
Mon,
Oct 23
|
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Review for Quiz-2
|
Wed,
Oct 25
|
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Quiz-2
|
Fri, Oct 27 | |
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Big-Oh notation |
Mon, Oct 30 |
Rosen, Chapter 3, Pages 180-188 |
|
Number theory and number theoretic algorithms: Euclid's GCD algo. |
Wed, Nov 1 |
Rosen, Chapter 3, Pages 227-237 |
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Properties of GCD |
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Mod notation, its properties |
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Modular exponentiation |
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Fermat's little theorem, RSA Cryptosystem |
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|
Introduction to Graph Theory |
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