Lectures and Reading

Make sure to go over key terms and results (at the end of each chapter in book) and relevant review questions.
1/23/02 : Overview of the course, policies, examples of set theory, induction, insertion sort Vs merge sort, recurrences, logic etc.
1/28/02 : Propositional Logic : Truth tables, and, or , not, exor, implication, biconditional operators, translating english sentences.

          Sec 1.1 , suggested problems :7,8,15,23

1/30/02 : Logical Equivalences : Tautologies, contradictions, contingency, logical equivalence table (page 17), proving logical equivalences by truth table/ by rules, Abstract Boolean Algebra

         Sec 1.2 , suggested problems : 10,11,13,15

         Sec 9.1, suggested propblems : 25,27,29

2/04/02 : Boolean Algebra and Prop. Logic :  Similarity between BA and PL, Normal Forms,

CNF = POS, DNF = SOP, deriving DNF from truth table, functional completeness, Minimizing DNF/CNF for majority circuit, Abstract Boolean Algebra repeated

        Sec 1.2, suggested problems: 27-35

        Sec 9.2, suggested problems: 3,11,19

2/06/02 : More Boolean Algebra: Problems similar to homework 1, Duality (from 9.1,1.2),

Deriving DNF, CNF from the truth table, Minimizing DNF using K-maps, K-maps with don't cares,

BCD representation, drawing circuit corresponding to the boolean function, also funcational completeness repeated.

        Sec 9.4, suggested problems: 3,7,13,19,23

2/11/02 : More K-maps, K-maps for BCDs with/without don't cares,

                Predicate Logic: predicate, quantifiers: universal/existential, examples, when true/false?

Laws for negation

        Sec 1.3, suggested problems: 21,33,47,48,49

2/13/02 :  Quantification of predicates in more than one variables, binding, more examples,

equivalences, prenex normal form (Notes on PNF) (Pdf format)

 2/18/02 : Sets (1.4) suggested problems : 1, 5, 7, 13, 15, 22

2/20/02 : Set Operations (1.5) suggested problems : 1,3,5,9,13,21,25,29,31

2/25/02 : Methods of proof (3.1)

2/27/02 : recap, homework2 Q&A session

3/4/02 : Midterm Review

3/6/02 : Midterm 1

3/11/02 : Methods of  Proof(3.1) , divisibility (2.3) suggested problems : (3.1) 7,11,17,25,27,59

3/13/02 : Induction (3.2), fibonacci numbers

spring break

3/25/02 : Induction (3.2) suggested problems : almost all from 3.2

                    solving recurrences

3/27/02 : recursively defined functions, recursively defined sets, fibonacci numbers, GCD algorithm (3.3) (and some 2.3)

4/1/02 : Solving recurrences, fibonacci numbers, recursive structures

4/3/02 :  Induction over strings, two dimensional functions

4/8/02 : more structural induction, functions

4/10/02: functions

4/15/02 : midterm review

4/17/02 : Midterm 2

4/22/02: cardinality, bijections

4/24/02: Growth functions, logarithms

4/29/02: Relations

5/1/02: Relations

5/6/02: Final review

5/13/02: Final Exam