# Course Outline for Math 220 (September- December, 2012)

Textbook:

Mathematical Proofs - A Transition to Advanced Mathematics (Second Edition) by Gary Chartrand, Albert D. Polimeni and Ping Zhang. Pearson / Addison Wesley, 2008. ISBN 978-0321390530

The course will (mostly) follow the text and the homework will also be assigned from it. We will mostly cover material in the same order as the text.

Drop-in Math Help: Tutors are available, at no charge, to answer questions on a drop-in basis, starting the second week of classes and continuing through the final-exam period until the final exam. Times scheduled are available by clicking the link:

Exams and Grades: There will be a common final exam for all sections of Math 220. The Final Exam (2.5 hours) will be held in December. The date of the final examination will be announced by the Registar later in the term. Attendance at the final examination is required, so be careful about making other committments (such as travel) before this date is confirmed. Your course mark will be based on homework (10%), two midterms (20% each), and the final exam (50%). No make-up tests will be given for midterms. All examinations will be strictly closed-book: no formula sheets, calculators, or other aids will be allowed. The instructor reserves the right to revise or round off gradeds if circumstances warrant. In order to make course grade standards consistent across sections the raw final grade will be scaled.

Course Outline: The main aim of the course is to learn how to write clear and correct mathematical proofs. It provides the gateway to more advanced mathematics. The topics we will cover are as follows:

1. Sets - definitions, set operations (chapter 1: 1.1-1.6)

2. Logic - logical connectives, quantifiers (chapter 2: 2.1-2.10)

3. Proofs - direct and contrapositive. (chapters 3: 3.1-3.5 and chapters 4: 4.1-4.6)

4. Proofs - existence and contradiction (chapter 5:5.1-5.5)

5. Induction (chapter 6: 6.1, 6.2, 6.4)

6. Equivalence realtions (chapter 8: 8.1-8.4 if there is time)

7. Functions - injective, surjective, bijective, inverses and compositions (chapter 9: 9.1-9.6)

8. Cardinality of sets - finite sets and different types of infinite sets (chapter 10: 10.1-10.5)

9. Elementary real analysis - limits of sequences and series (chapter 12: 12.1-12.6). Also supplement this with extra material on supremums.

The learning goals for this course are detailed here
.

Hand-in Homeworks: There will be weekly hand-in homework assigmnents, which will be assigned by your instructor. Late assignments will not be accepted. To allow for minor illnesses and other emergencies, the lowest 2 homework scores will be dropped.

Guidelines for writing and submitting your homework: Write clearly and legibly, in complete sentences. Remember that you will be graded both on your command of the material and on the quality of your writing. Do all problems in sequence if possible. For each solution, identify clearly the section and problem number (e.g. 1.2, 1.30). Staple your assignment. You may discuss the homework with other students, but the final write-up must be your own. If you cannot come to class, ask a friend to hand in your assignment or drop it off at your instructor's office before 12 noon on the due date. Late homework will not be accepted.

Suggested Problems: You are strongly advised to work out the following suggested problems in detail. These are not to be turned in, but they will give you practice in the techniques learned in class and provide valuable assistance in preparing for the common final examination.

Chapter 1: 1.3, 1.7, 1.9, 1.15, 1.17, 1.19, 1.27, 1.31, 1.33, 1.39, 1.43, 1.47

Chapter 2: 2.1, 2.3, 2.5, 2.13, 2.17, 2.21, 2.23, 2.25, 2.29, 2.31, 2.33, 2.35, 2.39, 2.45, 2.49

Chapter 3: 3.1, 3.3, 3.7, 3.11, 3.15, 3.17, 3.19, 3.21, 3.23, 3.25, 3.27, 3.29

Chapter 4: 4.5, 4.9, 4.15, 4.19, 4.27, 4.33, 4.35, 4.43, 4.45

Chapter 5: 5.5, 5.9, 5.17, 5.21, 5.33, 5.35

Chapter 6: 6.1, 6.9, 6.11, 6.17, 6.25, 6.33

Chapter 8: 8.5, 8.9, 8.13, 8.15, 8.17, 8.25

Chapter 9: 9.1, 9.3, 9.7, 9.13, 9.17, 9.21, 9.25, 9.29, 9.37

Chapter 10: 10.1, 10.3, 10.13, 10.15, 10.19, 10.23, 10.25

Chapter 12: 12.1, 12.3, 12.7, 12.9, 12.13, 12.17, 12.25, 12.27, 12.29