198: 205; Spring 2004

Introduction to discrete structures I

Sections 07 and 08

Web Site Contents
Contact
Schedule
Overview
Requirements
Announcements
Lectures

Overview


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