First Year Information

  1. MAT133Y5 - Intended for Commerce and Management students.
  2. MAT132H5 + MAT134H5 - Intended for Life Sciences students.
  3. MAT135H5 + MAT136H5 - A general calculus course useful for an array of Science and other students.
  4. MAT137Y5 - A proof-focused calculus course primarily for mathematical sciences students. 
  5. MAT157Y5 - A highly abstract and rigorous course primarily for students aiming at the Mathematical Sciences Specialist program or mathematics graduate studies.

*Note: Effective September 1, 2023, in the Fall 2023 – Winter 2024 academic session, MAT137Y5 and MAT157Y5 will be split into two one-semester H courses. MAT137Y5 will be split into MAT137H5 and MAT139H5, and MAT157Y5 will be split into MAT157H5 and MAT159H5.

Check out this video to help you choose your first year calculus courses.

  1. MAT133Y5 - This is a calculus and linear algebra course for students intending to pursue a Commerce or Management Program. We recommend that students in Commerce or Management who intend to also do an MCS program (for example a Mathematical Sciences Minor or Major, or a Computer Science Minor, etc.) take MAT135H5 + MAT136H5 instead of MAT133Y5. This is because MAT133Y5 cannot be used as a prerequisite for any other 200+ level math course. Nonetheless, if you change your mind and have a 75 per cent or higher mark in MAT133Y5, you can take the course MAT233H5 to fulfill MAT course prerequisites.
  2. MAT132H5 + MAT134H5 - These two courses are designed for students in Life Sciences (for example, those aiming for a Biology program). MAT132H5 and MAT134H5 focus on conceptual understanding and computations, with little or no focus on proofs. MAT132H5 + MAT134H5 are directly substitutable for MAT135H5 + MAT136H5 as prerequisites for MAT courses at UTM, and can be used to complete MCS programs. However, MAT135H5 + MAT136H5 would give a stronger foundation for students who plan on taking many MCS courses. 
    • Students must complete MAT132H5 before taking MAT134H5 (they cannot be taken in the other order or simultaneously). 
    • MAT135H5 + MAT136H5 - These are the calculus courses taken by the vast majority of first year UTM students taking calculus. MAT135H5 and MAT136H5 focus on conceptual understanding and computations, with little or no focus on proofs. The material covered is similar to MAT132H5 + MAT134H5, but is typically covered in a bit more depth or assessed a bit more intensely. The courses MAT135H5 + MAT136H5 may together be used to satisfy prerequisites for all 200+ level MCS courses and programs at UTM except the Mathematical Sciences Specialist program and the course MAT257Y5. (At U of T St. George, some other advanced or 200+ level mathematics courses will not accept MAT135H5 + MAT136H5 for prerequisites.)
      • Students must complete MAT135H5 before taking MAT136H5 (they cannot be taken in the other order or simultaneously). 
  3. MAT137Y5 - This course is for students who intend to study Mathematics. In particular, while Mathematical Sciences Major students can take either MAT132H5 + MAT134H5 or MAT135H5 + MAT136H5 to satisfy program requirements and 200+ level MAT course prerequisites, they will be better prepared for advanced MAT courses having taken MAT137Y5 or MAT157Y5. Furthermore, students in the Mathematical Sciences Specialist program are required to take either MAT137Y5 or MAT157Y5. Students in Computer Science, Applied Statistics, Physics or Economics who are mathematically inclined should consider this course. Students who think they might pursue graduate studies in statistics should consider taking MAT137Y5. MAT137Y5 emphasizes geometry and physical intuition but also gives attention to the theoretical foundations of calculus and will develop your analytical thinking. While proofs will form a significant component of the course, no previous experience with proofs is required. Students will be introduced to the language and techniques of proofs in the beginning of the course, with further development as the course progresses.
  4. MAT157Y5 - This is the most advanced of the first year mathematics courses offered. It gives students the opportunity to experience the beauty of a theoretical approach to calculus with the mathematical rigour and depth that will prepare them for graduate studies in mathematics. Advanced conceptual thinking and proofs form the bulk of the course. In that regard, MAT157Y5 is similar to MAT137Y5, but the depth of abstraction and expectations on students are higher in MAT157Y5. Students in the Mathematical Sciences Specialist program are required to take either MAT137Y5 or MAT157Y5 and we recommend taking MAT157Y5.
    • Note that MAT102H5 (information can be found below) is a co-requisite for MAT157Y5. This means that you must take MAT102H5 concurrently with MAT157Y5 (preferably taking MAT102H5 in the Fall term of the year when you are enrolled in MAT157Y5). That said, you will not be removed from MAT157Y5 if you do not fulfill this requirement. So effectively, it is our strong recommendation that you take MAT102 concurrently with MAT157Y5. If you have taken MAT102H5 prior to taking MAT157Y5, then that also fulfills the requirement.

You should think carefully about your intended combination of programs in order to pick the right calculus course(s). 

  • MAT133Y5 is offered twice per year. Once in the Fall/Winter session (September - April) and then again the Summer session (May - August). In the summer, MAT133Y5 is taught at 'double speed' i.e. with six hours of lectures and two hours of tutorials per week.
  • MAT132H5, MAT134H5, MAT135H5 and MAT136H5 – The courses MAT135H5 and MAT136H5 are offered every term/session (Fall, Winter, Summer). However, please note that in any given term/session (including the Summer), you will only be able to take one of these courses. (In the Summer they are run at 'normal speed' taking place across both Summer terms, May - August)
    • Note that you could take MAT135H5 in the Fall, then MAT136H5 in the Winter; but you can also consider taking MAT136H5 in the Summer, and MAT135H5 in either the Fall or Winter.
    • MAT132H5 will be offered in the Fall and Winter terms. It may also be offered in the Summer session, depending on demand.
    • MAT134H5 will be offered in the Winter term, and possibly 1-2 times more per year, depending on demand.
  • MAT137Y5 and MAT157Y5 – these courses are only offered once per year in the Fall/Winter session (September - April).

  • If you are considering taking MAT132H5, MAT133Y5, or MAT135H5:
    • Check out (an app developed by one of our faculty) and join the Fundamentals of High School Math course for free (there may be ads). Complete the tasks there to help you prepare you for the Fall term, and also get a sense of your level of preparation. Note that an anonymous account will not necessarily save your progress.
  • If you are considering taking MAT137Y5 or MAT157Y5, the U of T St. George Mathematics department has a page with some resources here: Getting a head start on proofs.

This course is a prerequisite for many 200+ level Mathematical Sciences and Computer Science courses and is a program requirement for all MCS programs (Mathematical Sciences, Computer Science and Applied Statistics). Our programs may have a minimum final grade requirement in this course. You can find our MCS entry and program requirements here.

The course bridges the gap between high school and university mathematics by introducing students to the techniques of theorem proving, logical thinking around mathematical statements, and many other necessary background topics.

We recommend taking this course in your first year, though you can consider not taking it in your first term (i.e., you could take it in the Winter term or Summer session.)

If you are taking MAT137Y5 or MAT157Y5, we recommend taking it concurrently (and ideally, in the Fall term.) Since MAT102H5 is a prerequisite for MAT240H5 (which is offered in the Winter): if you plan to take MAT240H5 in your first year, you will need to take MAT102H5 in the Fall term. (See more about our Linear Algebra courses below.)

  1. MAT223H5 - An introduction to Linear Algebra, with an emphasis on computations and conceptual understanding.
  2. MAT224H5 - A second course in Linear Algebra, with an emphasis on proofs and rigour. MAT224H5 builds off MAT223H5, but students will also see the theoretical foundations for much of the material from MAT223H5.
  3. MAT240H5 - A highly rigorous first course in Linear Algebra great for students with a serious interest in mathematics (for instance those aiming at, or in the Mathematical Sciences Specialist or the Major program.) MAT240H5 covers much of the same material as MAT223H5 + MAT224H5 but at an accelerated pace and with greater abstraction, rigour and depth.
  4. MAT247H5 - A continuation of MAT240H5. It is intended primarily for students aiming at, or in the Mathematical Sciences Specialist program.

MAT223H5 is a prerequisite for a number of other courses and a requirement for some programs, so for that reason it is often taken in the first year, despite the 200-level course code. Note that there are no prerequisites other than High School math for the course. That said, many students choose to wait until the Summer after their first year or during their second year to take a linear algebra course.

Far fewer non-mathematics courses or programs require MAT224H5 compared to those that require MAT223H5. So MAT224H5 is typically taken by students interested in the Mathematical Sciences Minor or Major program, as a prerequisite for upper-year courses.

If you are aiming at the Mathematical Sciences Specialist program, we recommend you take MAT102H5 in the Fall term of your first year, and then MAT240H5 in the Winter term. We offer MAT240H5 in the Winter to make this combination possible, since achieving at least 60 percent in MAT102H5 is a prerequisite for MAT240H5.

Last updated 17-Nov-22

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