The following is a tentative schedule of the topics we will be covering in class.
Date Book Chapters Topics Mon, Aug 24 Rosen 1.1 Introduction and Course Policies
Introduction to Logic
Logical Operators, Truth TablesWed, Aug 26 Rosen 1.1 Conditional Satements
Translating English SentencesFri, Aug 28 Rosen 1.2 Logical Equivalences Mon, Aug 31 Rosen 1.2 Proving New Logical Equivalences Wed, Sept 2 Rosen 1.3 Predicates and Quantifiers Fri, Sept 4 Rosen 1.4 Nested Quantifiers
Translating from Nested Quantifiers into EnglishMon, Sept 7 - University Holiday Wed, Sept 9 Rosen 1.4 Translating from English into Nested Quantifiers
Negating Nested QuantifiersFri, Sept 11 Rosen 1.5 Rules of Inference
Using Rules of Inference to Build ArgumentsMon, Sept 14 Rosen 1.5 Rules of Inference for Quantified Statements Wed, Sept 16 Rosen 1.6, 1.7 Direct and Indirect Proofs
Proof Methods and StrategyFri, Sept 18 Rosen 2.1 Introduction to Sets Mon, Sept 21 Rosen 2.1 Countable and Uncountable Sets
Power Sets, Cartesian ProductsWed, Sept 23 Rosen 2.2 Set Operations, Set Identities Fri, Sept 25 Rosen 2.2 Proofs of Set Properties Mon, Sept 28 Rosen 2.2, 2.3 Generalized Unions and Intersections
Computer Representation of Sets
Introduction to FunctionsWed, Sept 30 Rosen 2.3 One-to-one and Onto Functions
Inverse Functions; Composition of FunctionsFri, Oct 2 Rosen 2.3 Proving Properties of Functions Mon, Oct 5 Rosen 8.1 Relations
Properties of RelationsWed, Oct 7 Rosen 8.5 Equivalence Relations Fri, Oct 9 - Exam I: Sets & Logic Mon, Oct 12 Rosen 8.5 Equivalence Classes and Partitions Wed, Oct 14 Rosen 8.6 Partial Orders Fri, Oct 16 Rosen 2.4 Sequences and Summations Mon, Oct 19 Rosen 2.4 Proving Sets Countable and Uncountable
DovetailingWed, Oct 21 Rosen 2.4 Diagonalization Fri, Oct 23 Rosen 4.1 Mathematical Induction Mon, Oct 26 Rosen 4.2 Strong Induction
Strengthening the Inductive HypothesisWed, Oct 28 Rosen 4.3 Inductive and Recursive Definitions Fri, Oct 30 Rosen 4.3 Structural Induction Mon, Nov 2 Rosen 5.1 Basic Counting Techniques Wed, Nov 4 Rosen 5.2 PigeonHole Principle Fri, Nov 6 Rosen 5.3 Permutations Mon, Nov 9 Rosen 5.3 Combinations Wed, Nov 11 Rosen 5.4 Binomial Theorem Fri, Nov 13 - Exam II: Functions, Relations, Induction
& Basics of CountingMon, Nov 16 Rosen 5.5 Generalized Permutations and Combinations Wed, Nov 18 Rosen 5.5 Combinations with Repetitions
Permutations with Indistinguishable ObjectsFri, Nov 20 Rosen 6.1 Introduction to Probability Mon, Nov 23 - Fall Break Wed, Nov 25 - Fall Break Fri, Nov 27 - Fall Break Mon, Nov 30 Rosen 6.2 Finite and Infinite Sample Space
Conditional ProbabilityWed, Dec 2 Rosen 6.2, 7.5 Independence in Probability
Inclusion-Exclusion PrincipleFri, Dec 4 Rosen 9.1, 9.2, 9.4, CLRS B.4 Introduction to Graphs Mon, Dec 7 Rosen 10.1, CLRS B.5 Introduction to Trees Wed, Dec 9 Rosen 10.1, CLRS B.5 Properties of Trees and Graphs Fri, Dec 11 - Review Mon, Dec 14 - Exam III: Counting, Probability
& Graph Theory
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