First Year Information

Introduction to proofs course:

MAT102H5 Introduction to Mathematical Proofs - This course is required for students who wish to take higher level Mathematics and Computer Science courses. It bridges the gap between high school and university mathematics by introducing students to the techniques of theorem proving.

Calculus and analysis courses:

The department offers several different calculus courses, each one slightly different. As of September 2019, there are some changes to the calculus courses offered:

*The course MAT134Y5 has been replaced by MAT132H5 + MAT134H5.

* The course MAT135Y5 has been replaced by MAT135H5 + MAT136H5.

It is therefore extremely important to pay attention to the details in the course codes. For example, MAT135Y5 is not the same as MAT135H5. The Y indicates a full year course whereas the H indicates a one semester course. (The last digit indicates the campus, so for example MAT135H5 is offered at UTM whereas MAT135H1 is offered at the St George campus.)

Students should choose ONE of the following 5 options:

  1. MAT133Y5 - This is a calculus and linear algebra course for students committed to the Commerce Program. Large lecture sections are complemented by small tutorial groups. MAT133Y5 cannot be used as a prerequisite for any other math course. Students in commerce who want to do a Major or Minor in a mathematical subject should take MAT135H5 and MAT136H5 instead of MAT133Y5. The course MAT133Y5 is for students who are certain that they will not take any additional mathematics courses, or courses that rely heavily on mathematics. 
  2. MAT132H5 and MAT134H5 (replaces MAT134Y5) - These two courses are designed for students in Biology. The applications of calculus considered in these courses are primarily in the life sciences. MAT132H5 and MAT134H5 focus on conceptual understanding and computations, with little or no focus on proofs. Large lecture sections are complemented by small tutorial groups. Students who subsequently become interested in further study in Mathematics may use these courses for prerequisite purposes to take additional mathematics courses. Students must complete MAT132H5 before taking MAT134H5. 
  3. MAT135H5 and MAT136H5 (replaces MAT135Y5) - These are the standard courses taken by most first year UTM students. MAT135H5 and MAT136H5 focus on conceptual understanding and computations, with little or no focus on proofs. Applications of calculus to all the sciences and within mathematics are studied. Large lecture sections are complemented by small tutorial groups. The option MAT135H5+MAT136H5 may be used for prerequisite purposes for all subsequent courses and programs at UTM except the Mathematics Specialist program and MAT257Y5. (Also note that some advanced mathematics courses at the St George campus may not accept MAT135H5+MAT136H5 as a prerequisite.) Students must complete MAT135H5 before taking MAT136H5. 
  4. MAT137Y5 - This course is for students who know when they enter university that they wish to study Mathematics or Computer Science (including Bioinformatics). Students in the Mathematics Specialist program are required to take either MAT137Y5 or MAT157Y5.Students in Statistics or Physics or Economics who are mathematically inclined will also enjoy this course. MAT137Y5 emphasizes geometry and physical intuition but also gives attention to the theoretical foundations of calculus. 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; it offers the mathematical rigour, depth and advanced thinking that are required for advanced studies in mathematics. Advanced conceptual thinking and proofs will form a significant component of the course.Students in the Mathematics Specialist program are required to take either MAT137Y5 or MAT157Y5. MAT157Y is not required by any program or course offered at UTM other than MAT257Y5. However, students who might consider pursuing graduate studies or other advanced studies in mathematics in the future, are most strongly advised to take MAT157Y5. Others who are up for the challenge may wish to take MAT157Y5 to enjoy the beauty of its theoretical approach.

Students who are still unsure of which calculus course(s) to enroll in, should look at this flowchart.

When will the calculus courses be offered?

  1. 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.
  2. MAT132H5 and MAT134H5 – The course MAT132H5 is offered in the fall of 2019. Both MAT132H5 and MAT134H5 will be offered in winter 2020. Both MAT132H5 and MAT134H5 will be offered in summer 2020.

         Note that if lecture or tutorial sections are full, more sections may be added later.

         Some possible scenarios for completing these courses:

  •          MAT132H5 in the fall followed by MAT134H5 in the winter.
  •          MAT132H5 in the winter followed by MAT134H5 in the summer.
  •          MAT132H5 in the fall followed by MAT134H5 in the summer.

         Note that both will be running the entire length of the summer so students can not complete both courses in the summer.

         We plan to offer both courses in the fall of 2020.

  1. MAT135H5 and MAT136H5 – The course MAT135H5 is offered in the fall of 2019. Both MAT135H5 and MAT136H5 will be offered in winter 2020. Both MAT135H5 and MAT136H5 will be offered in summer 2020.

         Note that if lecture or tutorial sections are full, more sections may be added later.

         Some possible scenarios for completing these courses:

  •          MAT135H5 in the fall followed by MAT136H5 in the winter.
  •          MAT135H5 in the winter followed by MAT136H5 in the summer.
  •          MAT135H5 in the fall followed by MAT136H5 in the summer.

         (Note that both will be running the entire length of the summer so students can not complete both courses in the summer.)

         We plan to offer both courses in the fall of 2020.

  1. MAT137Y5 is only offered once per year; starting in September and ending in April.
  2. MAT157Y5 is only offered once per year; starting in September and ending in April

You can find our Mathematics program requirements here.