##### PROBLEM, CONJECTURES AND PROOFS

**Office**: Tel 2036**Email**: vnika@yorku.ca**Lectures**: Tuesdays 5:30 – 7:00 in Ross South 136**Tutorial**: Mondays 7:00 – 8:00 pm in either VH 3000 (tutorial 1) or VH 2000 (tutorial 2). (See the campus map for the location of these rooms.) You are enrolled in one of these.**Office Hours:**Book an appointment with me via email.**Text**:*A concise introduction to Pure Mathematics*by Martin Liebeck. We will cover Sections 1-6, 8, 10, 11, 13, 17-19, 21, and 22 of the text.

**Course Description:** An extended exploration of elementary problems leading to conjectures, partial solutions, revisions, and convincing reasoning, and hence to proofs. Emphasis on problem-solving, reasoning, and proving. Regular participation is required.

**Main Objectives**: This course is designed for first-year mathematics majors to develop basic skills essential for more advanced courses in mathematics. An emphasis will be placed on writing proofs. There are two main aspects to proofs that we will focus on, problem solving and exposition. One of the challenges in the mathematics courses is to come up with proofs to problems that are not familiar or similar to problems presented in lectures or in the textbook. This requires a variety of problems solving techniques and lots of practice to develop the confidence to attack a problem without yet knowing how to solve it. Once one has solved a problem, or come up with a proof, one must then clearly communicate that solution in a clear and concise manner. Learning how to present convincing reasoning (aka a proof) is the main objective of this course. We will be learning the language of mathematical exposition. Of course, this means a lot of hard work on your part. You will not succeed in this course if you do not actively engage in solving problems, writing proofs, and working through examples each and every week. If you fall behind one week, it can be very difficult to get caught up. E.g., attend the tutorials and start work on the homework assignments early!!

**Prerequisites:** 12U Advanced Functions (MHF4U) or Advanced Functions and Introductory Calculus (MCB4U). Course credit exclusion 2200 3.00. NCR note: Not open to any student who is taking or has passed a MATH course at the 3000 level or higher. (or equivalent).

**Important Dates:**

- First class: Sept. 12, 2017
- Last date to enroll
**without my permission:**Sept. 20, 2017 - Last date to enroll
**with my permission:**Oct. 18, 2017 - Fall reading week: Oct. 26-29, 2017
- Last lecture of fall term: Nov. 28, 2017
- Fall examinations: Dec. 6 - 21
- Winter break – University closed: Dec. 23, 2017 – Jan. 2, 2018
- Winter reading week: Feb.17 – 23, 2018
- Last date to drop the course without receiving a grade: Feb. 9, 2018
- Course Withdrawal Period (withdraw from a course and receive a grade of “W” on transcript): Feb. 10, 2017
- Last day of class: April 3, 2018
- Final exam: April 9 – 23, 2018

**Attendance: **If you do miss a class, it is your responsibility to find out what was covered and whether any important announcement was made. Class participation is strongly encouraged. You can participate both by asking some questions and by answering others. __Please don’t hesitate to ask for clarification__.

**Evaluation:**

**Assignment**35%**Fall Exam**25%**Final Exam**40%

Homework will be assigned more or less weekly. There also will be 7 assignments based on the current material being covered in class. Each assignment counts 5% of your final grade. The due date for each assignment will be announced on Moodle. The fall exam will be given in December during the exam period. The fall exam **MUST** be written in ink. The final exam can be written in pencil.

**Academic Honesty: **Students are responsible for familiarizing themselves with policies regarding academic honesty as set out by the Senate of York University. Please Cheating and/or impersonation is dealt with severely. Please read the Senate Policy on Academic Honesty (which can be found in the University Policies and Regulations section of the York University Undergraduate Programs Calendar. http://secretariat-policies.info.yorku.ca/policies/academic-honesty-senate-policy-on/.

**In-Class Behaviour: **All cell phones and pagers are to be turned off during lectures. Cheating and/or impersonation will not be tolerated. Photo identification and signing-in are required at all tests and examination. DO NOT CHEAT. Read carefully and keep this document for future reference. If you stay in the course then you are agreeing to accept them.

**Tentative Homework Suggestions: **Below is a list of suggested homework problems from the end of each section and perhaps from other sources. Do as many of these as you can. I might select them for assignments, fall, and the final exam. If you have trouble with any of them, bring your questions to class and your tutorial.

- Chapter 1: All of them
- Chapter 2: 1-5, 7, 8
- Chapter 3: All of them
- Chapter 4: 1-8
- Chapter 5: all of them
- Chapter 6: all of them
- Chapter 8: all of them
- Chapter 10: 1-9
- Chapter 11: 1-9
- Chapter 13 All of them
- Chapter 17 1-8, 10
- Chapter 18 1-8
- Chapter 19. All of them
- Chapter 21. 1, 2b, 3, 4
- Chapter 22. 1-7