Problems, Conjectures and Proofs: MATH1200.03
Information for the academic year 2014-2015

No tutorials on Friday, January 9.

Course description

This course is designed to introduce students to techniques that will help them solve problems in later mathematics courses. Students who have successfully completed this course, when confronted with a problem in an upper level courses will have at their disposal a number of strategies for beginning to work on the problem. While this is no guarantee of coming up with a solution, it should save students from the exasperation leading to, "I don't know where to begin!".
Course times and rooms
The class meets Thursdays from 10:00 to 11:15 in Vari Hall 3009. There are tutorial meetings from 10:30 to 11:20 on Fridays in TEL 0009 and TEL 0004. (See the campus map for the location of these rooms.) The organization of the tutorials will be explained in class.
Office Hours
My office is N523 in the Ross building. Due to other commitments I am not able to provided a regular schedule of office hours, but you are welcome, indeed encouraged, to make an appointment to see me. My telephone number is 736-5250 (ask for me), however, I check my email frequently and often the best way of reaching me is to send me an email. Be sure to check your spelling and grammar before sending off your email though --- my response time to sloppy emails is much longer than to carefully written ones.
Text
This course will follow A concise introduction to Pure Mathematics by Martin Liebeck. The aim of the course is to cover Sections 1, 6, 8, 10, 11 and 18 as well as some other sections. These may include 9, 12, 16, 19 or 22. Problems and exercises from this text will supplemented by other material.

However, there are a number of other books covering much of the same material that you may find useful. I have listed just a few of them:

  • An Introduction to Mathematical Reasoning by Peter J. Eccles.
  • How to Prove It: A Structured Approach by Daniel J. Velleman.
  • Thinking Mathematically by John Mason has a good collection of problems.
  • Which Way Did the Bicycle Go?: ... and Other Intriguing Mathematical Mysteries by Joseph D. E. Konhauser, Dan Velleman and Stan Wagon also has a good collection of problems, requiring a bit more ingenuity.
  • How to Solve It: A New Aspect of Mathematical Method by G. Polya is a classic written by a master on the art of problem solving. While it may seem a bit dated, it has the most comprehensive coverage of actual problem solving strategies and tactics.
  • There is also a film, Let Us Teach Guessing, made by the American Mathematical Society about Polya's approach in action in a high school setting.
  • The Fields medalist Tim Gowers maintains an interesting blog on mathematical topics. While much of the material on which he writes is quite sophisticated, he also has postings on topics from undergraduate mathematics. Two that are especially relevant to this course are Proving the fundamental theorem of arithmetic and Why isn't the fundamental theorem of arithmetic obvious? . The various various posts on basic logic are also well worth reading.
  • Another Fields medalist, Terry Tao, also maintains a blog that, while not quite as relevant to this course, contains some material of general mathematical interest.

Course evaluation
There will be a problem solving assignment every two weeks there will also be examinations during the December examination period and at the end of the course during the April examination period. The final mark will consist of the following components:
  • December examination: 25%. The December examination will be held Wednesday, December 15th at 9:00 AM in the Rexall Tennis Centre. A list of exercise questions to be used in preparing for the mid term is now available. The mid term questions will be chosen from these.
  • April examination: 45%
  • Marked assignments: 30%

The marked assignments component will consist of marks for assignments done both in class and at home. Students must come to class prepared to write an assignment during the last 15 minutes.

Students of this course will be able to find their scores for the various components of the final grade posted here as they become available.


Important dates
Check the registrar's web pages for full information. Here are some important dates:
  • The first lecture is on Thursday, September 11.
  • First tutorials are on Friday, September 19.
  • There are no classes on October 30 and February 19.
  • There are no tutorials on October 31 and February 20.
  • The last date to drop courses without receiving a grade is February 6.
  • The last class for the Fall Term is on December 4.
  • The last class for the Winter Term is on April 2.


If you follow me on Twitter by clicking the following follow button you will receive tweets about changes or corrections to assignments, tests and deadlines.


Course materials
The assignments and additional materials can be found here --- simply click on the appropriate link. These will be updated throughout the course.
A web site devoted to all sorts of mathematical problems, including those encountered in undergraduate courses like this one, is Mathematics Stack Exchange. If you intend to use this site be sure to read the FAQ, especially the part about tagging homework questions. You are encouraged to use this site, but you should also know that I will also be looking in. Any assignment substantially similar to a Math Stack Exchange posting will be consdiered to be plagiarism.


The Class Representative Program at Bethune College is a new initiative designed to assign a class representative to each of the major courses in the Faculty of Science and Engineering. Class representatives serve as liaisons between the course instructor and other students in the course, providing general feedback and bringing any concerns that arise to the attention of the instructor. Please consider volunteering to be the class representative for this section.

Instructor

Juris Steprans
Email address: steprans@yorku.ca
Department of Mathematics and Statistics.
Ross 523 North
York University
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This page was last modified on Thursday, January 08, 2015 at 14:52:08.