**MAT133Y5**- Intended for Commerce and Management students.**MAT132H5 + MAT134H5**- Intended for Life Sciences students.**MAT135H5 + MAT136H5**- General calculus courses useful for an array of Science and other students.**MAT137H5 + MAT139H5**- Proof-focused calculus courses primarily for mathematical sciences students, or any student with a serious interest in theoretical science.**MAT157H5 + MAT159H5**- Highly abstract and rigorous courses primarily for students aiming at the Mathematical Sciences Specialist program or mathematics graduate studies.

Use this table for a quick comparison between the five calculus sequences. The five sequences are as follows:

- MAT133Y5 - Calculus and Linear Algebra for Commerce
- MAT132H5 + MAT134H5 - Differential Calculus for Life Sciences + Integral Calculus for Life Sciences
- MAT135H5 + MAT136H5 - Differential Calculus + Integral Calculus
- MAT137H5 + MAT139H5 - Differential Calculus for Mathematical Sciences + Integral Calculus for Mathematical Sciences
- MAT157H5 + MAT159H5 - Analysis I + Analysis II

For a more detailed version of the table above, download a **PDF version of "What is the difference between the calculus sequences?" **

**Intended for students...**

**Description**

** Keep in mind...**

** MAT133Y5**

...looking to pursue Commerce, Management or Business programs.

- in addition to calculus topics, also covers range of other topics including probability and combinatorics.

- cannot be used for MCS programs (except in combination with MAT233H5)

** MAT132H5 + MAT134H5**

...looking to pursue life science programs.

- differential & integral calculus

- emphasis on computations, conceptual understanding, reasoning

- each pair of courses is similar except that 132 + 134 emphasize life science applications

- enrolment is restricted to students admitted to specific areas

**MAT135H5 + MAT136H5**

...looking to pursue most programs, except for MAT Specialist.

- see "MAT132H5 + MAT134H5" above

- these courses are most appropriate for most programs needing calculus

**MAT137H5 + MAT139H5**

...looking to pursue MAT Major or Specialist, or with serious interest in theoretical science.

- differential & integral calculus

- 137 starts with an introduction to proofs, logic, abstraction and mathematical rigour

- these are rewarding and advanced courses, so speak to our department if you have any questions if the courses are right for you

** MAT157H5 + MAT159H5**

...looking to pursue MAT Specialist.

...who are already comfortable with mathematical rigour, have interest in abstract math.

- differential & integral calculus/analysis

- lay a theoretical and rigorous foundation for mathematics

- compared to 137, 139: more complexity to proofs and deeper abstraction methods are covered

- see "MAT137H5 + MAT139H5" above

*You should think carefully about your intended combination of programs in order to choose the right calculus course(s). Note that if you change your mind, certain combinations of courses are allowed while others are not. For example, a student who completed MAT137H5 can then take MAT136H5. Check the prerequisites of each course carefully. *In addition, after completing MAT132H5/ MAT134H5/ MAT135H5/ MAT136H5/ MAT137H5/ MAT139H5, it would be possible to take MAT157H5 and/or MAT159H5 for credit in a later year. (However, this is rare.) Taking more than one sequence in the same year is not recommended as they cover very similar material. Speak to an Academic Advisor in MCS if you have questions about doing this.

**** 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.

**** MAT137H5, MAT139H5, MAT157H5 and MAT159H5 **- MAT137H5 and MAT157H5 will be offered in the Fall term of the Fall/Winter Session. MAT139H5 and MAT159H5 will be offered in the Winter term of the Fall/Winter Session.

- If you are considering taking MAT132H5, MAT133Y5, or MAT135H5:
- Check out
**MathMatize.com**(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.

- Check out
- If you are considering taking MAT137H5 + MAT139H5 or MAT157H5 + MAT159H5, the U of T St. George Mathematics department has a page with some resources here:
**Getting a 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 (MAT137H5 + MAT139H5) or (MAT157H5 + MAT159H5), we recommend taking MAT102H5 concurrently with MAT137H5 or MAT157H5 (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. Read more about our Linear Algebra courses below in the section "What about Algebra courses? (MAT223H5, MAT224H5, MAT240H5 & MAT247H5)".

**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 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 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.

**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 22-Sep-23