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

Math 1200: Problems, Conjectures and Proofs - Fall 2018/Winter 2019 - Section B and Section D - Zabrocki

Contact information:

Mike Zabrocki
Office: DB (TEL) 2026
office hours: Mondays 12-1pm, Thursdays 2:30-3:30pm and by appointment

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. Prerequisite: 12U Advanced Functions (MHF4U) or Advanced Functions and Introductory Calculus (MCB4U). NCR note: Not open to any student who is taking or has passed a MATH course at the 3000 level or higher.

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.

Course references:

The course textbook is
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.

Course components:

The evaluation will be based on the following criteria
Tutorial presentations
based on attendance and in class assignments
assigned throughout the term
During December exam period
Final Examination
During April exam period

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.

Participation: You are expected to show your commitment to this course and your fellow students by sharing your mathematical knowledge of the material. Attendance at the weekly classes and the tutorials is obligatory. The TAs will be calling on people at random from their class list to show solutions to the problems that you have been working on and they will be grading the presentation and solution of those problems. Non participation in these assignments will result in a lowering of your tutorial presentation grade.

Assignments: There will be roughly one assignment 3-4 weeks. Most assignments will require explanation beyond a simple one or two word/numerical answer. It is good practice to RECOPY THE QUESTION EVERY SINGLE TIME when you do the assignment. This makes it possible to understand what the assignment when it is handed back to you and it attempts to reduce the error of answering a different question than is on the assignment. Full credit is given to papers which demonstrate deep understanding of the problem by providing multiple solutions and considers variations based on the original question when this is appropriate. Your assignment should include complete sentences and explanations and not just a few equations or numbers. A solution will not receive full credit unless you explain what your answer represents and where it came from. You may discuss the homework with other students in the class, but please write your own solutions.

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.

Note: Late assignments will be penalized by 10% per day. This will apply to any homework handed in after the class time in which it is due. In addition, assignments which are handed in late are unlikely to be marked in a timely manner.

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.


(September 6, 2018) Welcome! I am teaching two sections of math 1200 each with about 30ish students.
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 LaTeX, Matlab and R.

The workshop will run twice a week, on Mondays and Wednesdays, for three weeks (September 17 - October 3, 2018), the duration of each session will be 90 minutes (11:30am - 1:00pm). The sessions will take place in the Gauss Lab, Ross S110.

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:

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
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).