Topics

DISCRETE COMPUTATIONAL STRUCTURES
Com S 330

Course Topics

The following is a tentative schedule of the topics we will be covering in class.

 

Week	Date	Book Chapters	Topics
1	Jan 10	Rosen 1.1	Introduction and Course Policies Introduction to Logic Logical Operators, Truth Tables
1	Jan 12	Rosen 1.1	Conditional Satements Translating English Sentences
1	Jan 14	Rosen 1.2	Logical Equivalences
2	Jan 17	-	University Holiday
2	Jan 19	Rosen 1.3	Predicates and Quantifiers
2	Jan 21	Rosen 1.4	Nested Quantifiers
3	Jan 24	Rosen 1.4	Translating between English and Logical Expressions with Quantifiers
3	Jan 26	Rosen 1.5	Rules of Inference
3	Jan 28	Rosen 1.5	Valid Arguments
4	Jan 31	Rosen 1.6	Direct and Indirect Proofs
4	Feb 2	Rosen 1.7	Proof Methods and Strategy
4	Feb 4	Rosen 2.1	Introduction to Sets
5	Feb 7	Rosen 2.1	Countable and Uncountable Sets Power Sets, Cartesian Products
5	Feb 9	Rosen 2.2	Set Operations, Set Identities
5	Feb 11	Rosen 2.2	Proofs of Set Properties
6	Feb 14	Rosen 2.2	Generalized Unions and Intersections Computer Representation of Sets
6	Feb 16	Rosen 2.3	Introduction to Functions One-to-one and Onto Functions
6	Feb 18	Rosen 2.3	Inverse, Converse and Composition of Functions
7	Feb 21	Rosen 2.3	Proving Properties of Functions
7	Feb 23	Rosen 8.1	Relations Properties of Relations
7	Feb 25	-	Exam I: Sets & Logic
8	Feb 28	Rosen 8.5	Equivalence Relations Equivalence Classes and Partitions
8	Mar 2	Rosen 8.6	Partial Orders
8	Mar 4	Rosen 2.4	Sequences and Summations
9	Mar 7	Rosen 2.4	Proving Sets Countable by Dovetailing
9	Mar 9	Rosen 2.4	Proving Sets Uncountable by Diagonalization
9	Mar 11	-	Some Problems are Unsolvable
-	Mar 14	-	Spring Break
-	Mar 16	-	Spring Break
-	Mar 18	-	Spring Break
10	Mar 21	Rosen 4.1	Mathematical Induction
10	Mar 23	Rosen 4.2	Strong Induction Strengthening the Inductive Hypothesis
10	Mar 25	Rosen 4.3	Inductive and Recursive Definitions
11	Mar 28	Rosen 4.3	Structural Induction
11	Mar 30	Rosen 5.1	Basic Counting Techniques
11	Apr 1	Rosen 5.2	PigeonHole Principle
12	Apr 4	Rosen 5.3	Permutations
12	Apr 6	Rosen 5.3	Combinations
12	Apr 8	-	Exam II: Functions, Relations & Induction
13	Apr 11	Rosen 5.4	Binomial Theorem
13	Apr 13	Rosen 5.5	Generalized Permutations and Combinations
13	Apr 15	Rosen 5.5	Combinations with Repetitions Permutations with Indistinguishable Objects
14	Apr 18	Rosen 6.1	Introduction to Probability
14	Apr 20	Rosen 6.2	Finite and Infinite Sample Space Conditional Probability
14	Apr 22	Rosen 6.2, 7.5	Independence in Probability Inclusion-Exclusion Principle
15	Apr 25	Rosen 9.1, 9.2, 9.4, CLRS B.4	Introduction to Graphs
15	Apr 27	Rosen 10.1, CLRS B.5	Introduction to Trees
15	Apr 29	Rosen 10.1, CLRS B.5	Properties of Trees and Graphs
-	May 4	-	Exam III: Counting, Probability & Graph Theory

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