THE UNIVERSITY OF WESTERN ONTARIO

LONDON CANADA

DEPARTMENT OF MATHEMATICS

__Mathematics 1120B -- WINTER 2016__

2015-2016**
**

**INSTRUCTOR:** L.E. Renner, Middlesex College, Room 130. lex at uwo dot ca

**TEXTBOOK:*** Mathematical Proofs: A Transition to Advanced Mathematics, Third
Edition *by Gary Chartrand, Albert D. Polimeni and Ping Zhang, published
by Addison-Wesley, 2008.

**PREREQUISITES:** One or more of Ontario Secondary School MCV4U, the former Ontario
Secondary School MGA4U, Linear Algebra 1600A/B, or the former Mathematics 017A/B.

**ANTIREQUISITE: **Mathematics 2155A.

**COURSE OUTLINE: **Mathematics 1120B is an introduction to rigorous mathematical thinking.
The main purpose of the course is to teach students to understand
mathematical reasoning

and write mathematical proofs.
There will be regular
homework assignments to help the students acquire information and
develop the required analytical skills. There will also be

some discussion
of applications as time permits. e.g. proving the veracity of a computer program.

**TOPICS:** logic, proofs, induction, sets, functions, relations, limits, complex
numbers, divisibility, polynomials.

**LECTURES:** MWF 1:30-2:30, NCB 285.

**EVALUATION OF STUDENT PERFORMANCE:**
**Grades will be based on assignments, in-class midterms and the final exam.**
**Assignments:** 40%
**Two One-Hour, In-Class, Midterm Exams:** 10% each. February 12 and March 11, 2016.
**MIDTERM#1:** Four questions: 1. Set theory proof (4.4). 2. Statements (2.1).
3. Contrapositive and negation of quantified statements (2.10).

4. Two basic proofs about rational numbers;
one by direct proof, the other by finding an example (see 5.4)
**MIDTERM#2:** Four questions: 1. Induction, three parts [15]. 2. An ``odd-even'' proof [10].
3. A short contradiction proof [5]. 4. A basic proof with sets [5].

This exam is based on material from chapters 3,4,5 and 6.

** Final Examination:** 40%. Tuesday, April 12 at 9am. TC 201.

..........................................................................................................................................................................

**ASSIGNMENTS**

**Assignment # 1:** Pages 30--36: # 1.2, 1.4, 1.14, 1.26, 1.36, 1.40, 1.78. Due January 18@1:30 pm.
** Solutions #1. **.

**Assignment # 2:** Pages 64--74: # 2.14, 2.16, 2.46, 2.68, 2.72. Pages 93--97: # 3.6, 3.10, 3.20, 3.30, 3.60. Due February 1@1:30 pm.
** Solutions #2. **.

**Assignment # 3:** Pages 114--117: # 4.6, 4.14, 4.20, 4.30, 4.70. Pages 138--139: # 5.2, 5.26, 5.28, 5.42. Due February 24@1:30 pm.
** Solutions #3. **.

**Assignment # 4:** Pages 165--168: # 6.8, 6.10, 6.36, 6.62. Pages 210--215: # 8.12, 8.24, 8.30, 8.52, 8.58. Due March 16@1:30 pm.
** Solutions #4. **.

**Assignment # 5:** Pages 234-241: # 9.4, 9.6, 9.12 a), 9.26, 9.46. Pages 281-287: #11.32, 11.38 a), 11.68. Due April 4@1:30 pm.

......................................................................................................................................................................................

**REVIEW PROBLEMS**

CHAPTER 1: 1.4, 1.7, 1.13, 1.19, 1.41, 1.45

CHAPTER 2: 2.1, 2.4, 2.12, 2.13, 2.23, 2.46, 2.67

CHAPTER 3: 3.16, 3.23, 3.38, 3.50, 3.66

CHAPTER 4: 4.8, 4.16, 4.34, 4.44, 4.68

CHAPTER 5: 5.10, 5.16, 5.19, 5.38

CHAPTER 6: 6.6b), 6.11, 6.23, 6.43, 6.56

CHAPTER 8: 8.11, 8.15, 8.18, 8.27, 8.40, 8.50, 8.55

CHAPTER 9: 9.6, 9.9, 9.14, 9.23, 9.25, 9.29, 9.32, 9.51

CHAPTER 11: 11.7, 11.15, 11.39, 11.41, 11.50, 11.78a)

CHAPTER 12: 12.5, 12.6, 12.7, 12.12, 12.15, 12.17

OTHERS WILL BE ADDED AS APPROPRIATE

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**SECTIONS COVERED FOR THE FINAL (TENTATIVE)**

CHAPTER 1: ALL

CHAPTER 2: 2.1 -- 2.10

CHAPTER 3: 3.1 -- 3.4

CHAPTER 4: ALL

CHAPTER 5: ALL

CHAPTER 6: 6.1, 6.2

CHAPTER 8: ALL

CHAPTER 9: 9.1 -- 9.6

CHAPTER 11: 11.1, 11.2, 11.3, 11.5, 11.6

CHAPTER 12: 12.1, 12.2

OTHERS WILL BE ADDED AS APPROPRIATE

......................................................................................................................................................................................

**IMPORTANT SENATE POLICY:**

Students are responsible for ensuring that their selection of courses is appropriate and accurately recorded and that all course prerequisites have been successfully completed. If the student does not have the requisites for a course, and does not have written special permission from his or her Dean to enroll in the course, the student may be removed from the course and it will be deleted from the student's record. This decision may not be appealed. A student will receive no adjustment to his or her fees in the event that he or she is dropped from a course for failing to have the necessary prerequisites.

**STATEMENT ON ACADEMIC OFFENCES:**

** **"Scholastic offences are taken seriously and students are directed to read
the appropriate policy, specifically, the definition of what constitutes a
Scholastic Offence, at the following Web site:
http://www.uwo.ca/univsec/handbook/appeals/scholoff.pdf** "**

** "**Computer-marked multiple-choice tests and/or exams may be subject to
submission for similarity review by software that will check for unusual
coincidences in answer patterns that may indicate cheating."

**NEW MEDICAL EXCUSE REGULATIONS:**

If you are unable to meet a course requirement due to illness or other serious circumstances, you must provide valid medical or other supporting documentation to the Dean's Office as soon as possible and contact your instructor immediately. It is the student's responsibility to make alternative arrangements with their instructor once the accommodation has been approved and the instructor has been informed. In the event of a missed final exam, a "Recommendation of Special Examination" form must be obtained from the Dean's Office immediately.

For further information please see:

http://www.uwo.ca/univsec/handbook/appeals/medical.pdf

A student requiring academic accommodation due to illness, should use the Student Medical Certificate when visiting an off-campus medical facility or request a Record's Release Form (located in the Dean's Office) for visits to Student Health Services.

The form can be found here:

https://studentservices.uwo.ca/secure/medical_document.pdf