You took MAT137 this year and did very well on it. You are considering taking MAT257 instead of MAT237 next year, and maybe even becoming a Math Specialist. You are wondering if this is possible. If this describes you, then this page is written for you.
Yes! It is possible. Every year a handful of students accomplish this.
The differences between MAT137 and MAT157
MAT157 studies some concepts that do not appear in MAT137, most importantly uniform convergence and Cauchy sequences.
MAT157 proves more theorems than MAT137, such as the IVT, the EVT, or Lagrange's Theorem.
MAT157 goes more in depth in some topics.
The main difference, however, is of skill, rather than of content knowledge. In MAT137 we introduce you to proofs, and we ask you to do simple proofs, with emphasis on "simple". In MAT157 you are responsible for understanding and creating more complex and abstract proofs. This is the main skill you need to develop as a future mathematician.
How to prepare
The best way to prepare for MAT257 is to study MAT157 by yourself during the Summer.
The textbook is "Calculus" by Michael Spivak (ISBN: 978-0521867443).
Have a look at the syllabus for MAT157 in 2012-2013 (this will download a spreadsheet). It will tell you which chapters are covered and will give you a list of practice problems per chapter. Read the book and do the problems (it is very easy to mistakenly convince yourself that you understand things if you try to read the book without solving the problems).
As a complement, you can watch videos of all lectures in this course in the year 2012-2013 by professor Kumar Murty.
Alternatively
The course MAT138H1 can serve to bridge the gap from MAT137Y to MAT257Y. It is offered often in the Summer term or in the Winter term.
Questions?
For questions about the Math program, contact Undergrad Administrator Donna Birch.