Topics


DISCRETE COMPUTATIONAL STRUCTURES
Com S 330


Course Topics


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

 

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

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