MTH U165 - Introduction to Mathematical Reasoning

Fall 2007

Course Information


Course:	MTH U165, Introduction to Mathematical Reasoning
Time and place:	MWTh 1:35 PM-2:40 PM, 130 Forsyth Building (#55 on map)
Textbook:	E. Scheinerman, Mathematics: A Discrete Introduction, Second edition. Brooks/Cole, 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 main objective of the course is to prepare incoming math majors for more challenging mathematical courses at Northeastern by covering the basics of mathematical reasoning and problem solving. The course focuses on learning to write logically sound mathematical arguments and to analyze such arguments. We will attempt to cover most of the material in the first five chapters of Scheinerman's book, and (if time allows) in Chapter 7. Here is a more detailed list of topics to be discussed:

Chapter 1: fundamentals of a mathematical argument (definitions, theorems, proofs, counterexamples, elements of Boolean Algebra).

Chapter 2: lists, sets, combinatorial proofs.

Chapter 3: equivalence relations, partitions of sets, binomial coefficients.

Chapter 4: mathematical induction, recurrence relations.

Chapter 5: functions, the pigeonhole principle.

Chapter 7: basic number theory (divisibility of integers, modular arithmetic, prime factorizations).

The grading will be based on periodic quizzes and written assignments (60%), and the final exam (40%). For the take-home assignments you are encouraged to consult with other students. However, ALL WRITTEN ASSIGNMENTS MUST BE WRITTEN INDIVIDUALLY, IN YOUR OWN WORDS.

Attendance will be taken and you are expected to be present for every class. 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 "To the Student" preface (pp. xv-xvii), Sections 1 and 2; p.2, #1.1; pp.5-7, #2.1-2.3, 2.6-2.8.
Sep. 6: read Section 3; p.15, #3.1-3.5, 3.8.
Sep. 10: read Section 4; p. 25, #4.2, 4.5, 4.8, 4.9, 4.13.
Sep. 12: review all previous topics and problems; p. 25, #4.1, 4.3, 4.4.
Sep. 13: read Section 5; p. 27, #5.1-5.9.
Sep. 17: read Section 6; pp. 32-33, #6.1, 6.3, 6.4, 6.9, 6.10(a,b), 6.11(a,b).
Sep. 19: review Sections 5 and 6; pp. 32-33, #6.12, 6.14, 6.16, 6.19.
Sep. 20: read Section 7; pp.43-44, #7.1, 7.4, 7.6, 7.7, 7.9.
Sep. 24: p.45, #7.11, 7.13, 7.14; read Section 8; pp.48-49, #8.1, 8.3, 8.4, 8.5, 8.7.
Sep. 26: review sections 7 and 8; p.81, #2-6.
Sep. 27: read Section 9; pp.57-58, #9.1-9.3, 9.5-9.8.
Oct. 1: read Section 11; p. 74, #11.1, 11.2, 11.5-11.9.
Oct. 3: pp. 74-75, #11.12, 11.14, 11.16.
Oct. 4: p. 76, #11.19; read Section 12; p. 80, #12.1-12.3.
Oct. 10: review Sections 9 and 11; p. 82, #15-17.
Oct. 11: read Section 15: Definition 15.1, Example 15.2, then pp. 100-102; pp. 102-103, #15.1-15.4, 15.7, 15.8, 15.13.
Oct. 15: p. 103, #15.11-15.12; read Section 16; pp. 113-114, #16.2-16.4, 16.7.
Oct. 17: pp. 113-114, #16.8, 16.10, 16.12, 16.14.
Oct. 18: pp. 114-116, #16.11, 16.15, 16.18, 16.22-16.26.
Oct. 22: p. 116, #16.27, 16.28; read Section 21 up to Proposition 21.5 (you may skip Theorem 21.2 on p. 157); p. 168, #21.3.
Oct. 24: review Section 16 and all the homework problems in it.
Oct. 25: read Section 21, Propositions 21.5 - 21.7; pp. 168-169, #21.4, 21.7, 21.8.
Oct. 29: review previous homework on Section 21; p. 190, #5-7.
Oct. 31: p.191, #10-12; read Section 22 up to Proposition 22.3; p. 188, #22.1, 22.2 (b, f, h).
Nov. 1: pp. 188-190, #22.2 (a-h), 22.16(a-c).
Nov. 5: read Section 22 up to Theorem 22.9; p. 188, #22.2 (i-p).
Nov. 7: review Section 22; p. 191, #13-15, 18(a-c).
Nov. 8: read the rest of Section 22; pp. 188-189, #22.3, 22.5, 22.7, 22.8, 22.9.
Nov. 14: p.189, #22.10-22.12; p.192, #19.
Nov. 15: read Section 23; pp. 204-205, #23.2-23.4, 23.9, 23.11, 23.12.
Nov. 19: read Section 24; pp. 210-211, #24.1-24.3, 24.9, 24.10.
Happy Thanksgiving!
Nov. 26: review Sections 23 and 24; p. 205, #23.14-23.15; p. 210, #24.4-24.6.
Nov. 28: p. 243, #3(a,b), 4-6, 8.
Nov. 29: review quizzes 1-4 and related homework.

Quizzes and tests:
Quiz 1: Thursday, Sep. 13 (on Sections 2-4). Solutions.
Quiz 2: Thursday, Sep. 20 (on Sections 5-6). Solutions.
Quiz 3: Thursday, Sep. 27 (on Sections 7-8). Solutions.
There will be no quiz on October 4.
Quiz 4: Thursday, Oct. 11 (on Sections 9, 11). Solutions.
Quiz 5: Thursday, Oct. 18 (on Sections 15, 16). Solutions.
Quiz 6: Thursday, Oct. 25 (on Section 16). Solutions.
Quiz 7: Thursday, Nov. 8 (on Sections 21, 22). Solutions.
Quiz 8: Monday, Nov. 19 (on Section 22, last part). Solutions.
Quiz 9: Thursday, Nov. 29 (on Sections 23, 24). Solutions.

I will be available for last minute questions on Thursday December 6 at 10:00 AM - 12:00 PM, or by appointment on Friday or Monday.

Final Exam: Tuesday December 11 at 8:00 AM in 320 SH (Shillman Hall)
(allowed: calculators, one sheet of notes). Solutions.

GRADES (Two lowest quiz grades have been dropped).

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