MTH U230 - Discrete Mathematics

Fall 2007

Course Information


Course:	MTH U230, Discrete Mathematics
Time and place:	MWTh 9:15-10:20 AM, 431 Ryder Hall (#24 on map)
Textbook:	K. Rosen, Discrete Mathematics and Its Applications, Sixth Edition. WCB/McGraw-Hill, 2006
Instructor:	Professor Andrei Zelevinsky
Office and phone:	431 LA, x5648
Email:	andrei (at) neu (dot) edu
Office hours:	MWTh 11:40 - 12:45, or by appointment

Course Description

The course provides the discrete portion of the mathematical background needed by students in electrical and computer engineering. Here is an (approximate) list of topics we are planning to cover (the numbers refer to sections in Rosen's book):

1.1 Propositional logic
1.2 Propositional equivalences
2.1 Sets
2.2 Set operations
2.3 Functions
11.1 Boolean functions
11.2 Representing Boolean functions
11.3 Logic gates
2.4 Sequences and summations
4.1 Mathematical induction
4.3 Recursive definitions and structural induction
5.1 The basics of counting
5.3 Permutations and combinations
5.4 Binomial coefficients
7.1 Recurrence relations
7.2 Solving linear recurrence relations
7.5 Inclusion-exclusion
7.6 Applications of inclusion-exclusion
9.1 Graphs and graph models
9.2 Graph terminology
9.3 Representing graphs and graph isomorphism
9.4 Connectivity
10.1 Introduction to trees
10.4 Spanning trees

The grading will be based on several half-hour quizzes (40%), the midterm (20%), and the final exam (40%). Homework will be regularly assigned and discussed in class. Although the homework is not counted in grading, the quizzes and tests will consist of similar problems so doing it is very essential.

It is your responsibility to be aware of any changes in the syllabus announced in class. Students are responsible for all information given when they are absent.

If you have a concern about the course or the instructor that cannot be resolved by speaking with the instructor, please contact Professor Alex Martsinkovsky (undergraduate director), 471 LA, x5510, alexmart@neu.edu.

It is University policy that no grade, including an incomplete, can be changed after one year. Exceptions must be authorized by the Academic Standing Committee.

All students without legitimate conflicts will take the final exam at the scheduled time. Do not make travel plans that conflict with the final exam.

Homework:
Sep. 5: read Section 1.1 (pp.1-5); pp. 16-18, #2 (e,f), 3 (c,d), 5 (a,b,c,h), 7 (b,d), 17.
Sep. 6: read Section 1.2; pp. 17-19, #7 (a-f), 23, 27; p. 28, #9, 15.
Sep. 10: read Section 2.1; pp. 119-120, #1, 4, 12, 24, 29.
Sep. 12: read Section 2.2; pp. 130-132, #1-3, 29, 50-52.
Sep. 13: pp. 130-132, #18, 19, 30, 53; read Section 2.3 up to Example 5; p. 146, #1, 3, 7.
Sep. 17: read Section 2.3, Definitions 5, 7-10 and corresponding examples; pp. 146-147, #10-13, 17, 19 (a-c), 29-31.
Sep. 19: p. 147, #15, 16, 32, 35.
Sep. 20: read Section 11.1; p. 756, #1, 5(a,b), 9, 10, 13.
Sep. 24: read Section 11.2; p. 760, #1, 3, 12-14.
Sep. 26: read Section 11.3; pp. 765-766, #1, 3, 6, 7, 8.
Sep. 27: read (relevant parts of) Section 2.4; pp. 161-162, #3, 7, 13, 15, 16, 19, 20.
Oct. 1: p. 162, #21, 23; read (relevant parts of) Section 4.1; pp. 279-280, #3-7.
Oct. 3: p. 280, #10, 15, 19, 21.
Oct. 4: p. 280, #23, 25; read Section 4.3 up to Example 6; p. 308, #1d), 3a), 12, 13.
Oct. 10: review Sections 4.1, 4.3; p. 280, #13, 16, 22; p. 308, #15, 16.
Oct. 11: read Section 5.1; pp. 344-345, #1, 7, 8, 11, 12, 16, 21.
Oct. 15: p. 345, #27, 31-33; read Section 5.3; pp. 360-361, #2, 3, 5, 6, 13, 17.
Oct. 17: pp. 361-362, #19, 20, 27, 30, 31.
Oct. 18: read Section 5.4; p. 369, #3, 4, 7, 9, 13.
Oct. 22: review the material in Chapters 1, 2 and 11 (including old homeworks and quizzes 1-3).
Oct. 24: review the material in Chapters 4 and 5 (including old homeworks and quizzes 4-5).
Oct. 25: read Section 7.1; pp. 456-457, #1 (a,b), 5 (a-e), 9 (a, c, e, g).
Oct. 29: pp. 458-459, #25, 27, 29, 40, 41.
Oct. 31: pp. 457-459, #14, 42; read Section 7.2 (up to Example 5); p. 471, #3(c,d,e), 4(a,b).
Nov. 1: p. 471, #3(f), 4(c,d,e,f), 7, 8, 11.
Nov. 5: read Section 7.5; pp. 504-505, #1, 3, 5, 10, 11, 13.
Nov. 7: p. 505, #17, 18; read Section 7.6; p. 513, #5, 6.
Nov. 8: p. 513, #8, 9, 13, 15, 25, 26.
Nov. 14: read Section 9.1; pp. 596-597, #13, 15, 21.
Nov. 15: read Section 9.2; pp. 608-610, #1, 5, 7, 13, 17, 23, 25, 26, 29, 31-33.
Nov. 19: p.610, #34-37; read Section 9.3; pp. 618-619, #5, 9, 11, 34-37.
Happy Thanksgiving!
Nov. 26: pp. 619-620, #39, 41, 57, 67; read Section 9.4; pp. 629-630, #1, 5.
Nov.28: p. 631, #18-21.
Nov.29: pp. 693-694, #1, 11a), 12a), 17-19 (read relevant parts of Section 10.1).

Quizzes and tests:
Quiz 1: Thursday, Sep. 13 (on Logic, Sets, sections 1.1, 1.2, 2.1). Solutions.
Quiz 2: Sep. 20 (on Set Operations, Functions, sections 2.2, 2.3). Solutions.
Quiz 3: Sep. 27 (on Boolean Algebra, sections 11.1, 11.2). Solutions.
There will be no quiz on October 4.
Quiz 4: Oct. 11 (on Summations, Mathematical Induction, Recursive Definitions, sections 2.4, 4.1, 4.3). Solutions.
Quiz 5: Oct. 18 (on Basics of Counting, Permutations and Combinations, sections 5.1, 5.3). Solutions.
Midterm: October 25 (on all the topics covered so far). Solutions.
Quiz 6: Nov. 1 (on Recurrence Relations, section 7.1). Solutions.
Quiz 7: Nov. 8 (on Recurrence Relations, Inclusion-Exclusion Principle, sections 7.2, 7.5). Solutions.
Quiz 8: Monday, Nov. 19 (on Inclusion-Exclusion, Graphs, sections 7.6, 9.1, 9.2). Solutions.
Quiz 9: Nov. 29 (on Graph Isomorphism, Connectivity, sections 9.3, 9.4). Solutions.

I will be available for last minute questions on Thursday December 6 at 10:00 AM - 12:00 PM.

Final Exam: Friday December 7 at 8:00 AM in 15 SL (Snell Library)
(allowed: calculators, one sheet of notes). Solutions.

GRADES (Two lowest quiz grades have been dropped).

Created: August 28, 2007. Last modified: December 14, 2007.