198: 205; Spring 2004

• Classes: MW 6:10-7:30pm, HHB4

• Instructor: Matthew Stone
  Contact and meeting information

• Text: Kenneth H. Rosen, Discrete Mathematics and its Applications, 5th edition, McGraw-Hill, September 2002 This book has a companion web site

• Syllabus: Logic and proofs, sets, functions. Boolean algebra. Integers, division, and algorithms. Mathematical reasoning and program correctness. Finite state machines and regular expressions. Relations.

Requirements and Grading:

• There will be two midterm exams and a final exam. Each of the three exams will be graded on the scale 0 -- 100. An overall score for the course will be computed from the scores (M1,M2) on the two midterms and the score (F) on the final as the maximum of four quantities:
  • .25 M1 + .25 M2 + .5 F,
  • .33 M1 + .67 F,
  • .33 M2 + .67 F,
  • F.
  There will be no makeup exams for missed midterms.

• All three exams will be closed-book exams: no books, no notes, and no calculators will be allowed. The final will be cumulative (meaning that it will cover everything taught in the course). Rutgers University Policy on Academic Integrity

• Students with overall score of less than 25 will fail the course. The remaining letter grades will be assigned to give roughly 10 % A, 15 % B+, 20 % B, 20 % C+, 20 % C, 15 % D. These percentages may be adjusted so as not to give students with very close numerical scores differing letter grades.

• Five sets of homework questions will be given out during the term in order to provide the students with (i) an opportunity to practice for the exams and (ii) a feedback on their progress. Students will be under no obligation to do these homeworks, but may submit them, on a specified date, for grading; late homeworks will not be graded. (As specified by the grading scheme, homework grades will have no influence at all on the overall grades for the course.)

News

• Jan 28
  Initial revision of this web page.

Lecture Schedule, Events, Notes

• Jan 21
  Introduction and overview.

• Jan 26
  Material covered: Section 1.1: Propositions, truth tables, translation.
  Suggested Exercises: 1.1 (pp16-18) #9, #11, #15, #23, #28.
  

• Jan 28
  Material covered: Section 1.1-1.2: Implication and equivalence.
  Suggested Exercises: 1.2 (pp26-27) #7, #8, #20-25, #34-37.

• Feb 2
  Material covered: Section 1.3: Introduction to quantifiers.
  Suggested Exercises: 1.3 (pp40-43) #12-14, #27, #29, #37, #39.

• Feb 4
  Material covered: Sections 1.3-1.4: quantifier scope; negation.
  Suggested Exercises: 1.4 (pp51-56) #11, #16, #19, #27, #31.

• Feb 9
  Material covered: Sections 1.4 and start of 1.5: multiple quantifiers; introducing arguments and inference.
  Homework 1 out; accepted for grading 2/18

• Feb 11
  Material covered: informal and formal proofs (Sec. 1.5).
  

• Feb 16
  Material covered: formal proofs, mechanical proofs, proof strategies (Sec. 1.5).
  Suggested exercises: 1.5 (pp73-77) #11, #17, #19, #25, #27, #45, #49, #52, #59.

• Feb 18
  Material covered: Sets: member, subset, empty, power set (Sec. 1.6).
  Homework 1 due.

• Feb 23
  Material covered: Sets: union, intersection, difference (Sec. 1.7).
  Answers to homework 1.
  Homework 2 out.

• Feb 25
  Material covered: Ordered pairs, Cartesian products, relations (Sec. 1.6).
  

• Mar 1
  Homework 2 due.
  For reference, some notes about proofs to supplement Rosen
  Answers to homework 2
  

• Mar 3
  Midterm 1.
  Midterm 1 answers.
  Homework 3 delayed till after break.

• Mar 8
  Material covered: Representations and specification of functions (Sec. 1.8).
  Extra: $\lambda$-calculus.

• Mar 10
  Material covered: Properties of functions, constructing functions (Sec. 1.8).
  

• Mar 15-Mar 19
  Spring Break!

• Mar 22
  Material covered: Functions and cases; floor and ceiling (Sec. 1.8).
  Homework 3 out. Accepted for grading March 31
  

• Mar 24
  Material covered: Division, primes (Sec. 2.4).
  

• Mar 29
  Material covered: GCD and modular arithmetic (Sec. 2.4 and 2.6).
  Slight fix to Homework 3.
  

• Mar 31
  Material covered: Mathematical induction and the well-ordering property (Sec 3.3).
  

• Apr 5
  Material covered: Divisibility, GCD, and primes, again. (Parts of Sec 2.4, 2.6 and 3.3)
  Answers to homework 3.

• Apr 7
  Material covered: Program correctness. (Sec 3.6)
  A quick set of problems.
  These problems will be covered in class Monday and answers will be posted. There's not much time but give them a try!
  

• Apr 12
  Review: Led by Weilei Zhang.
  Review notes
  Answers to homework 4.
  MS's office hours for April 13 will be moved: 4-6pm, Core 328.
  

• Apr 14
  Midterm 2.
  Answers.

• Apr 19
  Material covered: Strings and languages (from Sec 11.1 and 11.4).
  Homework 5, due April 28

• Apr 21
  Material covered: Finite state machines (from Sec 11.3).
  

• Apr 26
  Material covered: Regular expressions (from Sec 11.4).
  

• Apr 28
  Material covered: Nondeterministic finite automata; equivalences between NFAs, DFAs and REs. (from Sec 11.3 and 11.4).
  

• May 3
  Review: Led by Weilei Zhang.
  MS's office hours for May 4 are cancelled.
  

• May 10
  Final Exam: 8pm-11pm.
  Held in our regular classroom: HHB4
  Answers