University of British Columbia Okanagan

Course outline

MATH 220 Mathematical Proof

Last updated: November 18, 2008

General

Lectures: Tuesdays and Thursdays, 9:30AM - 10:50AM, in ARTS 118
Web page to watch: This course is WebCT supported; the current version of this page is http://people.ok.ubc.ca/bauschke/220.html; To login to WebCT, go to http://www.vista.ubc.ca (This has little to do with the Microsoft Operating System of the same name.)
Text books: Daniel Solow: How to read and do proofs (4th edition)
Seymour Lipschutz: Set theory and related topics (2nd edition)
Instructor: Dr. Heinz Bauschke
Office: SCIENCE 108
Email: heinz.bauschke@ubc.ca. Use MATH 220 in the Subject line of your email.
Evaluation: Midterms 30%; Homework 30%; Final Exam 40%.
Office hours: Varies weekly or by appointment.
Visit http://ical.me.com/bauschke/public to see my public current calendar.
Teaching Assistant: Liangjin Yao; SCIENCE 105.
See Liangjin's calendar for his office hours.
Cheating and Plagiarism: I shall assume that you have read the corresponding pages on academic misconduct in the current calendar, as well as general information about academic integrity. The academic enterprise is founded on honesty, civility, and integrity. As members of this enterprise, all students are expected to know, understand, and follow the codes of conduct regarding academic integrity. At the most basic level, this means submitting only original work done by you and acknowledging all sources of information or ideas and attributing them to others as required. This also means you should not cheat, copy, or mislead others about what is your work. Violations of academic integrity (i.e., misconduct) lead to the breakdown of the academic enterprise, and therefore serious consequences arise and harsh sanctions are imposed. For example, incidences of plagiarism or cheating may result in a mark of zero on the assignment or exam and more serious consequences may apply if the matter is referred to the President’s Advisory Committee on Student Discipline. Careful records are kept in order to monitor and prevent recurrences. A more detailed description of academic integrity, including the policies and procedures, may be found at http://web.ubc.ca/okanagan/faculties/resources/academicintegrity.html
If you have any questions about how academic integrity applies to this course, consult with your professor.
Disability Services: If you require disability-related accommodations to meet the course objectives, please contact the Coordinator of Disability Resources located in the Student Development and Advising area of the student services building. For more information about Disability Resources or academic accommodations, please visit the website at: http://okanagan.students.ubc.ca/current/disabilities.cfm

Contents of the course

I aim to work with you through Solow's book completely and through some sections of Lipschutz's book.
Bring your copy of Solow with you, for possible occassional class work.

Midterm Examinations

Two midterm examinations will be given (in class).

Thursday, October 16, 2008.
Know and understand the material in Chapters 1-8. Understand all assigned homework ("on your own" and "hand in") for the dates up to and including October 16, 2008.
Thursday, November 6, 2008.
Know and understand the material in Chapters 1-12. Understand all assigned homework ("on your own" and "hand in") for the dates up to and including November 6, 2008. More emphasis is placed on the material from Chapters 9-12.

Absolutely no make-up exams will be given. The weight for each midterm that was missed and for which you have a medical certificate will be transferred to the final exam. (Example: if you missed 1 midterm and have a medical certificate for it, then the midterm portion of your course grade is 15%, and your final exam is worth 55% of your course grade.) Student identification cards are required for all tests and examinations.

Final examination

The final exam will be given during the final exam period. You will need at least 50% on this examination in order to pass this course.

Date: Monday, December 15, 2008; Time: 9:00AM-noon; Room: GYM. Odd Rows 1-5, Blue Sheet.

Homework

You are encouraged to discuss problems with others, but I expect you to write up solutions on your own. You are expected to work at least 4 hours every week on homework problems. The "hand in" portion of your homework is due at the beginning of class. The following list will be updated regularly throughout the term. Only a selection of the homework problems may be marked. Only your best 9 homeworks count - your worst homework score will automatically be excluded!

Due Thursday, September 11:
On your own:
- Read Chapter 1.
- Practice Exercises 1.3 and 1.10.
- Read Lipschutz, page 237, Examples 10.6 and 10.7.
Hand in: Exercises 1.2,1.5,1.7,1.9.
Due Thursday, September 18:
On your own: Read Chapters 2 and 3. Read Section 1.12 in Lipschutz.
Hand in: Exercises 2.2,2.4,2.12.a,2.16.b,3.2.c&d,3.4.b,3.6.d,3.8,3.11.
Due Thursday, September 25:
On your own: Read Chapters 4 and 5.
Hand in: Exercises 4.4,4.8,4.10,4.14,5.2,5.6,5.9. The proofs of 4.8 and 4.10 must contain an analysis of the proof (forward-backward method exposing your thinking) and a condensed short proof.
Due Thursday, October 2:
On your own: Read Chapters 5 and 6.
Hand in: Exercises 5.14,5.15,6.4.a-c,6.6.a,6.10,6.16.
Due Thursday, October 9:
On your own: Read Chapters 7 and 8.
Hand in: Exercises 7.2,7.8,7.12,8.2,8.4,8.6,8.8.a&c.

Due Thursday, October 16:
On your own (practice for midterm 1):
- Review Chapters 1-8.
- Review all previously assigned homework questions.
- Practice and understand: Exercises 1.6,1.8,1.10,2.3,2.5,2.19.a,3.5,3.10,4.9,5.1,5.3,5.16,6.7,6.9,6.15,7.1,7.5,8.1,8.7.

Due Thursday, October 23:
On your own: Read Chapters 9 and 10.
Hand in: Exercises 9.10,9.12,9.14,10.2,10.14,10.16.
Due Thursday, October 30:
On your own: Read Chapter 11.
Hand in: Exercises 11.2,11.7,11.11,11.17,11.24,11.27.

Due Thursday, November 6:
On your own (practice for midterm 2):
- Read and review Chapters 1-12, with more emphasis on 9-12.
- Review all previously assigned homework questions.
- Practice and understand: Exercises 9.7,9.13,9.18,10.5,10.7,10.15,11.10,11.14,11.25,12.7,12.11,12.15.

Due Thursday, November 13:
On your own: Read Chapters 12 and 13.
Hand in: Exercises 12.2,12.10,12.14,13.4.
Due Thursday, November 20:
On your own: Read Sample Solutions for Midterm 2. Read Solow Appendix A. Read Lipschutz Sections 1.1-1.10 (pp. 1-14), and 4.1-4.4 (pp. 94-100).
Hand in: Solow Exercises A.3,A.6,A.9,A.11,A.13. Lipschutz Problem 1.51.(a)-(b) (p. 28).
Due Thursday, November 27:
On your own: Read Lipschutz Sections 6.1-6.6 (pp. 141-144), and 4.1-4.4 (pp. 94-100).
Hand in: Lipschutz Problems 5.42 and 5.43 (p. 137), 6.35 (p. 163), find the typos in Problems 6.19 (p. 159) and 6.22 (p. 160). Finally, denote by S the set of points in the Euclidean plane whose coordinates are integers. Partition S into two sets H and V such that (i) the intersection of H with any horizontal line is finite and (ii) the interection of V with any vertical line is finite.

Due Monday, December 15:
On your own (practice for final examination):
- Read and review in Solow: Chapters 1-13, Appendix A and Definition 31 on page 183 in Appendix C.2.
- Review all previously assigned homework ("hand in") and practice questions ("on your own").
- Practice and understand: Solow Exercises A.10, A.12, A.16, C.1, C.6.
  Lipschutz: 4.21, 4.22, 5.4, 5.6, 6.5, 6.8, and all the material from Lipschutz we did in class.
- Fully understand the Practice Final Examination!!

Important dates

Thursday, September 4, 2008: First MATH 220 class.
Friday, October 10, 2008: Last day for "W" withdrawal.
Tuesday, November 11, 2008: Remembrance Day. University closed.
Thursday, November 27, 2008: Last MATH 220 class.
December 3-17, 2008: Final examination period.

The present syllabus is tentative, and subject to change according to the needs of the class.