Northeastern University
Mathematics Department


MATH 1137: Discrete Math

Summer 2003

Hours: MWTh: 8:00-9:05
Location: 302 Kariotis; Key# 06067

Instructor: Stephen Lovett
Office: 535 Nightingale Hall (NI)
Office Hours: TBA
Phone: 373-2080
Email: slovett@lynx.neu.edu

   

Required Text: Discrete Mathematics and its Applications, fifth edition
by Kenneth Rosen


Course Objectives

This course introduces students to foundational structures in mathematics and how to reason rigorously. We will study logic, set theory, number theory, combinatorics and Boolean algebra. The concepts we will investigate underlie all of modern mathematics and the methods we present find applications not only in mathematical proving but also in analyzing and designing algorithms. Consequently, the material presented in this course is of critical importance in both mathematics and computer science.

Chap.TopicHomeworkComments
1.1Logic1,3,8,23,24,29,33,34 p.15 Answers
1.2Propositional Equivalences6,7,13,19,29 p.26 Answers
1.3Predicates and Quantifiers2,5,8,13,22,37,58 p.40 Answers
1.5Methods of Proof2,5,12,17,46,52 p.73 Answers
1.6Sets1,2,4,15,16,24 p. 85 Answers
1.7Set Operations1,3,11,12,15,19,21,24,25,41,42 p.92 Answers
1.8Functions1,4,8-12,16,26,27,60,65 p.108 Answers
2.1Algorithms2,5,9,17,25,34 p.129 Skipped
2.4The Integers and Division1,5,10,12-14,28,36,37 p.168 Answers
2.5Integers and Algorithms2,4,7,19,21,22,36,37 p.179 Answers
2.6Applications of Number Theory2,5,6,12,27a,28a p.194 Answers
3.1Proof Strategy1,4,7,17,27,28 p.223 Answers
3.2Sequences and Summation3,6,14,19,20,24,25 p.236 Answers
3.3Mathematical Induction 1-3,5-7,10,11,22,37,47,51,62,65 p.253 Answers
3.4Recursive Definitions1,2,4,5,8,12,14 p.270 Answers
4.1The Basics of Counting1,7,8,10,18,19,25,28,39,41,42 p.310 Answers
4.3Permutations and Combinations2,3,5,7,10,11,19,22,23,31,38 p.324 Answers
4.4Binomial Coefficients4,8,42,19,21 p.333 Answers
6.1Recurrence Relations1-3,6,19-21,25,27,42,43 p.409 Answers
6.2Solving Recurrence Relations3(a-d),4(d-f),17,18,21,24 p.423  
10.1Boolean Functions3,7,9,22,23,31,32,35 p.707  
10.2Representing Boolean Functions1,3,6,15-17 p.712  


Course Policies

  1. Help and Tutoring: There are many resources for improving your mathematics skills. The best way is to come see me. Otherwise free Math tutoring (on any subject) is available by appointment and drop-in. Location: 544 NI (Nightingale Hall); Times: 9:15AM-3:45PM; Phone: 617-373-2328. Check at that number for a list of summer hours.
  2. Attendance: I will not take attendance in this class but the student is responsible for staying abreast of assignments, tests and any modifications to the schedule.
  3. Excused Absences: In order to take a make-up a late quiz or exam you must have talked to me first. For any other emergency situations, you will need to bring me valid documentation (from court, doctor,…) of your absence. Notes from family members are not acceptable.
  4. There will be weekly quizzes (no matter how much material is covered), a one-hour midterm and a two-hour cumulative departmental final. The final course grade will be calculated as follows:

     
    Homeworks           5%
    Weekly Quizzes30%
    Midterm Exam25%
    Final Exam40%
  5. Cheating: Those who choose to cheat should consult the appropriate section their Student Handbook or read the university's Academic Integrity Policy prior to doing so. In this class, collaborating on homeworks is not considered cheating but each person must turn in his or her own write-up. Furthermore, the use of an advanced calculator is not considered cheating but encouraged when helpful.
  6. If you have any questions, please feel free to talk to me. If my office hours are not convenient for you, please contact me and we can find some other time to meet.