First Year Information

On this page we answer the following questions:

  • Which Calculus course should I take?
  • Do you have any suggestions to help me prepare for university Calculus?
  • What is MAT102?
  • Should I take MAT223? If so, when?

Calculus Courses

At UTM we offer five different Calculus courses:

  • MAT133Y5 - Intended for Commerce and Management students.
  • MAT132H5 + MAT134H5 - Intended for Life Sciences students.
  • MAT135H5 + MAT136H5 - A general Calculus course useful for an array of Science and other students.
  • MAT137Y5 - A proof-focused Calculus course primarly for Mathematics students (others are welcome!)
  • MAT157Y5 - A highly abstract and rigorous course primarly for students aiming at the Mathematics Specialist program or Mathematics graduate studies (others are welcome!)

While these are the defaults, as you'll see below, there is quite a lot of flexibility - you have options!

Here are some further details on our Calculus courses:

  1. MAT133Y5 - This is a calculus and linear algebra course for students committed to a Commerce or Management Program. We recommend that students in Commerce or Mangement who intend to do an MCS program (like a Math 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 math course. Nonetheless, if you change your mind and have a 75% 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 (e.g. aiming at a Biology program). MAT132H5 and MAT134H5 focus on conceptual understanding and computations, with little or no focus on proofs. We recommend that students who intend to also do an MCS program (like a Math Minor or Major, or a Computer Science Minor, etc.) take MAT135H5+MAT136H5 instead. That said, MAT132H5+MAT134H5 are directly substitutable for MAT135H5+MAT136H5 as prerequisites for MAT courses at UTM.
    • Students must complete MAT132H5 before taking MAT134H5 (they cannot be taken in the other order or simultaneously). You will be removed from MAT134H5 if you do not have MAT132H5 (or MAT135H5, or an equivalent from UTSG or UTSC.)
    • Note: as of 2019-20, these two courses directly replaced MAT134Y5, a full year course.
  3. MAT135H5 and 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 subsequent MCS courses and programs at UTM except the Mathematics Specialist program and the course MAT257Y5. (At UTSG, some other advanced 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). You will be removed from MAT136H5 if you do not have MAT135H5 (or MAT132H5, or an equivalent from UTSG or UTSC.)
    • Note: as of 2019-20, these two courses directly replaced MAT135Y5, a full year course.
  4. MAT137Y5 - This course is for students who intend to study Mathematics. In particular, while Mathematics Major students can take either MAT132H5+MAT134H5 or MAT135H5+MAT136H5 to satisfy program requirements and upper-level MAT course prerequisites, they will be better prepared for advanced MAT courses having taken MAT137Y5 or MAT157Y5. Furthermore, students in the Mathematics Specialist program are required to take either MAT137Y5 or MAT157Y5. Students in Computer Science, Statistics, Physics or Economics who are mathematically inclined should consider this course. In particular, 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.

  5. MAT157Y5 - This is the most advanced of the first-year Mathematics courses offered (not only of the first-year Calculus courses). 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. Students in the Mathematics Specialist program are required to take either MAT137Y5 or MAT157Y5 and we recommend that they take MAT157Y5.
    • Note that MAT102 (info below) is technically a "co-requisite" for MAT157Y5. This means that you should take MAT102 concurrently with MAT157Y5 (preferrably taking MAT102 in the Fall 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.

A quick breakdown of your options are available in a flowchart, here.

You should think carefully about your intended combination of programs in order to pick the right option!

When will these Calculus courses be offered?

  • MAT133Y5 is offered twice per year. Once in September-April and then again the summer (May-August). In the summer, MAT133Y5 is taught at 'double speed' i.e. with 6 hours of lectures and 2 hours of tutorials per week.
  • MAT132H5, MAT134H5, MAT135H5 and MAT136H5 – These courses are offered every semester (Fall, Winter, Summer). However, please note that in any given semester (including the Summer), you will only be able to take one of these courses. (In the Summer they are run at 'normal speed' taking up both Summer semesters, May-Aug.)
    • Note that you could take MAT135 in the Fall, then MAT136 in the Spring; but you can also consider planning to take MAT136 in the Summer, and MAT135 in either the Fall or Spring.
    • (The same options apply to MAT132 and MAT134.)
  • MAT137Y5 and MAT157Y5– these courses are only offered once per year, September-April.

Note about waitlists: if lecture or tutorial sections are full for your chosen course, typically more sections are added or enrollment caps are raised (slighly) in August and early September.

What can I do to prepare for university-level Calculus?

  • If you are considering taking MAT132H5, MAT133Y5, or MAT135H5:
    • Check out Ready For University Math?
    • You could also check out MathMatize.com (an app in development 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, 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 downtown (St. George) Mathematics department has a page with some resources here: Getting a head start on proofs.

MAT102 - Introduction to Proofs

This course is a prerequisite for all higher-level Mathematics and Computer Science courses and is a program requirement for all MCS programs (Math, Computer Science, Statistics). Various programs have minimum mark requirements in this course. You can find our Mathematics 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.

When should I take MAT102?

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

If you are taking MAT137Y5 or MAT157Y5, we recommend taking it concurrently (and ideally, in the Fall.) Similarly, since it 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 MAT102 in the Fall. (See more about our Linear Algebra courses below.)

Linear Algebra Courses:

At UTM we have four different Linear Algebra courses:

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

When should I take these courses?

MAT223 is a prerequisite for a number of other courses or 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, and we do not check those.) That said, many students choose to wait until the Summer of their first year or during their second year to take a linear algebra course.

Far fewer non-Mathematics courses or programs require MAT224H5 than require MAT223H5, so MAT224H5 is typically taken by studnets interested in the Mathematics Minor or Major programs, as a prerequisite for upper-year courses.

If you are aiming at the Mathematics Specialist program, we recommend you take MAT102H5 in the Fall of your first year, and then MAT240H5 in the Winter. (We offer MAT240H5 in the Winter to make this combination possible, since acheiving at least 60% in MAT102H5 is a prerequisite for MAT240H5.)