WARNING THIS IS AN OLDER WEB PAGE FROM A COURSE GIVEN IN 2018/19 AND REMAINS POSTED HERE FOR REFERENCE ONLY

The course webpage for the Fall 2019 version of the course.

Office: DB (TEL) 2026

office hours: Mondays 12-1pm, Thursdays 2:30-3:30pm and by appointment

Most High School mathematics problems are solved using algorithmic methods or via reference to model solutions. One purpose of this course is to enable students to develop the confidence and ability to attack richer and more demanding problems. The attempt to check work and to explain one’s discoveries to others leads naturally to the need for explanation. Learning how to present convincing reasoning — or proof — is one of the course outcomes.

With an emphasis on communication/convincing argument, there is a critical contribution to be made by: group work, reading a proposed 'proof' including other student's work, presenting and discussing as a whole class. There is also value in working through several different approaches to solve a problem, and taking the time to understand an alternative approach offered by a peer in the class. Doing mathematics well includes talking and listening to mathematics and there will be assignments that require collaborative work with another student in the class, as well as support for forming study groups.

The main goal of this course is to develop skills that lead to understanding and communicating a convincing argument. Support will be given for proof presentation, especially for the kinds of proofs that students are expected to produce in their second year and higher level courses. This includes inductions, and arguments with counting and with inequalities. Formal proof writing exercises will be introduced in the second half of the course, once problem solving and informal justification skills reach an acceptable level.

Class and tutorial attendance is mandatory and active participation is expected of all students.

Martin Liebeck, A Concise Introduction to Pure Mathematics, Third Edition.

It is recommended, but not required. We will plan to cover the following topics from that text: 4. Inequalities

5. $n^th$ roots and rational powers

6. complex numbers

8. induction

10. the integers

11. prime factoriziation

13. congruences of integers

16. counting and choosing

21. Infinity

Other useful references are

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.

Tutorial presentations |
based on attendance and in class assignments |
10% |

Assignments |
assigned throughout the term |
35% |

Midterm |
During December exam period |
20% |

Final Examination |
During April exam period |
35% |

Do your own work. Don't look for a solution on the web or take one from another student's work unless you already have found your own solution and intend to review another to make a comparison. Work that is not original will be graded accordingly. Presenting someone else's work as your own without proper citation is academic dishonesty. You must cite any internet sources which you have consulted. I recommend that you look carefully at the York University Academic Integrity Tutorial.

You should prepare your assignments in LaTeX and hand them in on the online Moodle. LaTeX is a program that was designed for writing mathematics. Information about how to do this is provided on this page and we will discuss it more in class.

There are typically two types of assignments that I will ask you do work on for the homework in this class. Sometimes they will consist of smaller problems related to the discussion that we have in class. Other times the assignments will ask you to write and explain a problem that will require careful analysis and understanding by dividing a long solution into smaller, more manageable steps.

Here is a breakdown of some aspects that I plan to evaluate your solutions. Before you hand in your assignment, I recommend that you read it though carefully and try to address the points from this list.:

(1) The discussion begins with an explanation of the problem

(2) The explanation should convince the reader that the meaning of the question is understood (e.g. small examples, a clearly labeled table of data, and/or a discussion of the meaning of the question)

(3) diagrams, tables or images that are drawn to aid the reader in understanding the problem are well labeled and explained

(4) Clear statements are made of conjectures that are believed to be true

(5) Explanations of why those conjectures are true are included

(6) An explanation of how the problem solving process proceeded is clear from the explanation

(7) The entries consist of writing which is clear and grammatically correct

(8) A conclusion about the solution to the problem is reached

Note that to receive full credit you must go beyond simply solving the problem as posed. Learn to think of your solutions as a starting point.

Midterm and Final Examination: There will a midterm during the December exam period and a final exam during the April exam period. The time and date of these exams will be announced mid way through each term.

If your class is Monday evening 5:30pm-6:45pm you are in section B.

If your class is on Thursday morning at 8:30am-10:15am, you are in section D.

Both of these classes are divided further into Tutorial 01 and Tutorial 02.

(September 6, 2018) I am posting a LaTeX template (this is what it looks like once you compile it) that you can use for your homework. Feel free to borrow other headers of files (but not the content!).

(September 10, 2018) (*) This class will use LaTeX for assignments. I will give you some minimal instruction about how to get started, but if you are looking for additional information, there is an upcoming workshop.

(November 14, 2018) The midterm exam will take place Thursday December 6 from 7-10pm. The location is still to be determined.

The Association for Women in Mathematics (AWM) Student Chapter, York University, will be organizing a technical workshop that aim to give undergraduate students the basics they need to get started on a variety of different software platforms that are commonly used by mathematics and statistics majors, namely

The workshop will run twice a week, on

If you are an undergraduate student, we would like to invite you to register to any, or all, of the sessions on the following link:

awm.info.yorku.ca/technical-workshop/

Please share this email with any interested students. We hope to see you at the workshop!

Best wishes,

Yohana and Allysa (On behalf of the AWM committee)

(November 14, 2018) (*) The exam schedule was announced and we will have a midterm December 6, 2018 7-10pm (location is still TBD). I'll send out another announcement when we get the location. UPDATE (Nov 23): The exam is in the Aviva centre. This is a large space with lots of classes in the same room at the same time.

(November 23, 2018) I will be out of town November 26-30. There are people who will replace me during class, but my office hours are cancelled for that week. For the class and tutorial I'm providing you with practice problems for the midterm. Please do these problems and make sure that you have others read your explanations if you are unsure. The midterm will be very similar (not quite so long).

(January 4, 2019) You should have received your midterm exam by email so that it can be accessed through the crowdmark system. If you did not, it is possible that there was a glitch and you should notify me ASAP.

(January 14, 2019) I will be out of town January 21-25, 2019. Office hours for that week are unfortunately cancelled. I will also need to displace my office hours on January 17, 2019 and they will be from 10am-11am (and not the usual 2:30pm-3:30pm).

(February 28, 2019) (*) A tentative date for the exam has been assigned by the registrar for Saturday, April 13, 2019. I will let you know here if there are changes on subsequent updates.

(Feb 28, 2019) (*) You are required to do a presentation as part of your grade for this class. The TAs will be assigning a single problem from assignment 9 to each student (that is, you won't be required to write up all of them, just one that you will present in the tutorial). You should attend tutorial and make sure that you are assigned a problem as well as a date to present it (you will be assigned the problem one day and should present it in the following weeks).

I just wanted to let everyone know that it is each person's individual responsibility that they are assigned a problem from assignment 9 by the TA and to make sure that she/he attends on the right day and has a time to present it in tutorial.

(Mar 11, 2019) (*) When you do your presentation the TAs will be evaluating you on these criteria.

(Mar 26, 2019) I like this:

(Mar 26, 2019) Here is a list of topics that the final will be focused on:

rationals and irrationals

complex numbers

induction

quantifiers

Euclidean algorithm and applications

modular arithmetic

counting and binomial theorem

Remark: announcements on this page marked with an (*) will also be sent to registered students via Moodle.

(Mar 30, 2019) (*) I have to push back my Monday office hours this coming week. Here are my scheduled office hours for the next two weeks:

Tuesday, April 1, 2:30-3:30pm

Thursday April 4, 2:30-3:30pm

Monday April 8, 12-1pm

Thursday April 11, 2:30-3:30pm

(Apr 1, 2019) I've added more problems to the practice. The TAs and I can answer these questions in class tonight (but not the ones posted on the Moodle).