Instructor: Farid Aliniaiefard
Office: TEL 2037
Telephone: 416-736-2100 ext. 20869
Email: faridanf@mathstat.yorku.ca
Webpage: math.yorku.ca/~faridanf/
Office Hours: Tuesdays at 3:30pm or by appointment
Location: Mathlab (ROSS S 525)

ANNOUNCEMENTS: Test 2, Nov. 29


ABOUT:
Course description: 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.
Course Learning Objectives: This course will develop the student's processes of mathematical thinking, problem solving, reasoning, conjecturing, and proof formation. It will also get the student used to communicating these processes effectively to others. It will complement our other core mathematics and statistics courses, where specific subject knowledge is the primary focus.

CLASSES: Tuesdays at 17:30 - 19, Mathlab (ROSS S 525)

RECOMMENDED TEXT:
Martin Liebeck, A Concise Introduction to Pure Mathematics, Third Edition.
We will aim to engage with the material in chapters 1, 6, 8, 10.

ADDITIONAL RESOURCES:
John Mason, Leone Burton, Kaye Stacey, Thinking Mathematically, Second Edition. This book gives an approach to problem solving and the problem solving experience. It is also a source for rich and varied problems.
G. Polya, How to Solve It: A New Aspect of Mathematical Method.

PARTICIPATION: You are expected to attend the classes and tutorials and to participate actively. Participation is how you show your commitment to the course and to the other students taking the course with you. You are expected to share both of your mathematical knowledge and the feelings you have as you engage in doing mathematics.





LECTURES:

Sept. 13 :
☺ Basic definitions of Sets with a set of examples.
☺☺☺ Questions on boards for groups: The subsets of a set with 3 elements, and some related quetions.
☺ Explaining the following question: John and Jane live 2 miles apart. John walks towards Jane at the rate of 4 mph, and Jane walks towards John by ten mph. When and where they do meet?
☺☺☺ Question for groups on table: Hour minutes hands of an analog clock point in the same direction at noon. When does it happen again? How many times and when this occur in 12 hours.



Sept. 20 :
Dividing students into five random groups. A question was orally given to groups: What is the sum of the first n odd numbers, find it and prove your answer. Teams worked on the question for 1 hour, and in the end, each group had a presentation on his answer, after presenting the answer by each group, we vote for the best answer to give that one bonus marks. Also, we asked the students to submit the first homework which contains a question about sets (CLICK) and the above question (What is the sum of the first n odd numbers, find it and prove your answer), at the beginning of the next lecture.

Sept. 27 :
Dividing students into five random groups. They work on some feedbacks of last week question: What is the sum of the first n odd numbers, find and prove it.

Oct 4 : Implications
Students submit the "feedback" assignments. Also, we give them Assignment 2 (due date: October 11)CLICK. Dividing students into five random groups. First, we give an outline of the activities for today. Then we give the students some everyday examples of if/then statements. After that they work on some mathematics statements (CLICK). After that I explained how to prove statements directly (direct proof) or by contrapositive. In the end, the groups work on a problem on boards. We polished and marked their work. Slides

Oct 11 : Contrapositive
Today was the due date for Assignment 2. We went through "Contrapositive" for proving statements. Here is the Slides. Also we gave the students Sample Questions for Class Test 1
Hints for Sample Questions for Class Test 1

Oct 18 :
Students received three sample answers and gave feedbacks on them. We review directed proof and contrapositive. Also today we went through "proof by contradiction". In the end groups worked to show that square root of 2 is irrational. Slides
Readings for Test 1.

Oct 25 :
Test 1. Answers-Test 1.

Nov 1 :
Reviewing Directed proof, Contrapositive, and Contradiction. Groups disccussed on the multiplications and sumations of rational/irrational numbers, and they worked on boards to figure out the sum of two irrationals is irrational, and the sum of a rational and an irrational is irrational.

Nov 8 :
We reviewed Proof by Contradiction. Then we started Mathematical Induction. Students divided into 5 groups randomly and every group was given either question 3 or 4 of THIS LIST. Groups were asked to solve the questions on boards and then we randomly choose one member of each group to represent their work. We give each group a score base on their writings and presentations.

Nov 15 :
Assignment 4 (CLICK) was released, the due date is November 22. Students was divided into 5 groups randomly and every group worked on feedback assignments. In the end, we briefly went through the concept of "Strong Mathematical Induction."


Assignments:

Assignment 1: Contains this (click) and finding the sum of the first n odd numbers and proving it. Answers to Assignment 1

Assignment 2: CLICK Answers to Assignment 2

Assignment on Boards Oct. 4: CLICK

Assignment on Boards Oct. 11: CLICK

Assignment 3: CLICK Examplar

Assignment 4: CLICK



TUTORIALS: Tuesdays at 19 - 20, for exact time refer to the following table, PLACE: TBA

TUTORS: Allysa Lumley, Email: alumley@yorku.ca, Office: TEL 2034, Helen

The following schedule is tentative.
Sept. 27 Tutor: Allysa
Oct. 11 Tutor: Allysa
Oct. 25 Tutor: Helen
Nov. 8 Tutor: Allysa
Nov. 22 Tutor: Allysa
Jan. 10
Jan. 17
Jan 31
Feb. 14
Feb. 28
Mar. 14
Mar. 28
Apr. 4





IMPORTANT DATES:

The following schedule is tentative.
Sept. 13 First day of classes
Sept. 27 Due date for Homework #1
Oct. 11 Due date for Homework #2
Oct 25 Class test #1
Nov. 8 Due date for Homework #3
Nov. 22 Due date for Homework #4
Nov. 29 Class test #2, last day of Fall classes
Jan. 17
Jan 31
Feb. 7
Feb. 21
Feb. 28
Mar. 14
Mar. 21
Apr. 4
Apr. 7 - Apr. 24
Final Exam will be held during winter examination period; exact time: TBA


EVALUATION:

Homeworks and In Class Problem Activities 30%
Class Tests 40%
Final Examination 30%


HOMEWORK: You will be asked to complete the York University Academic Integrity Tutorial prior to handing in any homework. Work that shows evidence of having been copied will receive a grade of 0.


TIME TABLE:

The following schedule is tentative.
Sept. 13 First day of classes
Sept. 20 Helen and Farid run the class
Sept. 27 Tutorial and Due date for Homework #1 (Allysa)
Oct. 4 Helen and Farid run the class
Oct. 11 Tutorial and Due date for Homework #2 (Allysa)
Oct. 25 Class test #1
Oct. 25 Tutorial (Helen)
Nov. 1 Helen and Farid run the class
Nov. 8 Tutorial and Due date for Homework #3 (Allysa)
Nov. 15 Helen and Farid run the class
Nov. 22 Tutorial and Due date for Homework #4 (Allysa)
Nov. 29 Class test #2, last day of Fall classes
Jan. 10
Jan. 17
Jan. 24
Jan 31
Feb. 7
Feb. 14
Feb. 21
Feb. 28
Mar. 7
Mar. 14
Mar. 21
Mar. 28
Apr. 4
Apr. 7 - Apr. 24 Winter examinations
Final Exam will be held during winter examination period; exact time: TBA