Which first year Mathematics courses are right for me? | Computer and Mathematical Sciences

Information to help you decide which first year Mathematics course(s) to take.

The department of Computer and Mathematical Sciences offers ten introductory-level courses in Mathematics. It can sometimes be difficult for new students to decide which courses they should, or should not, take. This guide will help you to understand your options, and choose the course(s) that will benefit you the most. As a reminder you should also check the calendar regarding prerequisites and exclusions.

The Courses:

MATA02 – The Magic of Numbers 
This course is designed for students who are not pursuing a program in mathematics, statistics or computer science. It is an introduction to various topics in mathematics such as numerical notation, prime numbers, geometry and platonic solids and sequences. This course is an exclusion to all first year math courses. This means that a student taking MATA02 and any other math course will not get credit for both courses and in addition MATA02 will not count towards a degree requirement. This course has no prerequisites.

MATA22 – Linear Algebra I for Mathematical Sciences 
This core course is a conceptual and rigorous introduction to linear algebra. It is a required course for all students in a major or specialist program in mathematics, computer science, or statistics. It focuses on the logical development of fundamental structures, mathematical proofs, and essential computational techniques in linear algebra. This course will expose students to rigorous proofs and computational techniques about vectors, systems of linear equations, matrices and algebra, determinants, diagonalization, and complex numbers.

MATA23 – Linear Algebra I 
This course is an introduction to the main ideas and computational methods linear algebra. It is designed for students who are not in a major or specialist program in computer science, mathematics, or statistics. This course will discuss ideas and computational techniques pertaining to vectors, systems of linear equations, matrices, vector algebra, determinants and diagonalization.

MATA29 - Calculus for the Life Sciences
MATA29 is an introduction to diﬀerential calculus for students in specialist programs in biological sciences, life sciences, neurosciences, and most major programs in biological sciences and psycholo-gial and health sciences. It is not intended for students in any major or specialist program in computer science, mathematics, or statistics. MATA29 emphasizes techniques, applications, and computational aspects of diﬀerential calculus that are relevant to biological and life sciences and neurosciences.

MATA30 - Calculus I for Physical Sciences 
MATA30 is an introduction to diﬀerential and integral calculus. It is designed for students in a major or specialist program in chemistry, environmental sciences, physical sciences, and the major in mathematics. This courses is not intended for students in a major or specialist program in computer science or a specialist program in math. MATA30 emphasizes techniques, applications, and computational aspects of calculus that are relevant in chemistry, environmental sciences, and physical sciences. Some content of MATA30 is not covered in MATA31.

MATA31 – Calculus I for Mathematical Sciences 
This course provides a rigorous and theoretical introduction to differential and integral calculus. Students will be introduced to techniques of calculus and mathematical proofs and will build foundations in rigorous mathematical thinking. The course is intended for students in a major/specialist program in computer sciences, specialist program in mathematics and it is strongly recommended for students in major programs in math and major/specialist programs in statistics.

MATA32 – Calculus I for Management I 
MATA32 is an introduction to differential and integral calculus with significant business applications. Some of the content in this course is not covered in MATA30 or in MATA31. MATA32 is designed for students in all specialist programs in management. This course is not intended for students in any major or specialist program in computer science, mathematics or statistics.

MATA33 – Calculus I for Management II 
MATA33 follows directly from MATA32 and continues to use differential and integral calculus as well as introduce linear algebra with business applications. It is designed for students in all specialist programs in management. This course is not intended for students in any major or specialist program in computer science, mathematics or statistics.

MATA35 – Calculus II for Biological Sciences 
MATA35 is a continuation of MATA29 but also emphasizes computational techniques and applications in the biological and life sciences through the use of discrete probability, vectors, and matrices. It is intended for students in biological and life sciences. This course is not intended for students in any major or specialist program in computer science, mathematics, or statistics. MATA35 is not a prerequisite to any upper-level math course, thus a student taking this course will not be able to take any more math courses.

MATA36 – Calculus II for Physical Sciences 
MATA36 is a continuation of MATA30 intended to prepare students for physical sciences. It emphasizes techniques and applications of integrals and introduces students to sequences and series. This course is a requirement for all major and specialist programs in physical sciences and major programs in mathematics. This course is not intended for students in any major or specialist program in computer science, mathematics or statistics.

MATA37 – Calculus II for Mathematical Sciences 
This course is a continuation of MATA31. It is a theoretical course emphasizing proofs and techniques through the study of axioms and properties of real numbers, differential and integral calculus. The course is intended for students in a major/specialist program in computer sciences, specialist program in mathematics and it is strongly recommended for students in major programs in math and major/specialist programs in statistics.

MATA67 - Discrete Mathematics 
This course provides an introduction to discrete mathematics that computer and mathematical science students will need, both to introduce fundamental topics that are used extensively in upper year courses, and to build foundations in rigorous mathematical thinking. The course is intended for students in a major/specialist program in computer sciences, major/specialist program in mathematics. This course is the same as CSCA67H3 i.e. it has two identifiers course codes.

Frequently Asked Questions

What are the various calculus sequences and what is the difference between them?

There are four sequences:

MATA29+MATA35: for biology and environmental sciences students; it emphasizes computational techniques and applications in bio/environmental sciences.
MATA30+MATA36: for physical sciences/math major students; it also emphasizes computational techniques and applications in physical sciences.
MATA31+MATA37: for math/computer science students. This sequence is challenging with emphasis on theory. Students without very strong mathematical background will find it difficult.
MATA32+MATA33: for management students; the emphasis is on techniques and applications in business and economics

Each sequence of calculus has content unique to that sequence. That is, even though they are all calculus courses, each sequence contains topics, applications and skills (relevant to the programs they are required) that are not found in the other sequences.

If I’m intending to take a program in mathematics, which mathematics courses should I take?

For a specialist program you should take MATA31, MATA37, MATA67 and MATA22. For a major program you can take MATA30 and MATA36 instead of MATA31 and MATA37.

What if I take MATA32 but then change my mind. Can I take MATA36 or MATA37?

You should take MATA30 (if interested in MATA36) or MATA31(if interested in MATA37) as a non-credit course or discuss this with a math program supervisor. If you did extremely well in MATA32, you may be allowed into MATA36 or MATA37.

What if I take MATA30 or MATA29, but then change my mind. Can I then take MATA37 after MATA29 or MATA30?

You should take MATA31 as a non-credit course or discuss this with a math program supervisor. If you did extremely well in MATA30 or MATA29, you may be allowed in MATA37.

My program requires MATA37, can I substitute MATA36 instead?

No. You should take the course required by your program.

I do not have the high school prerequisite for MATA29/MATA30/MATA32/MATA23. Can I still take calculus and linear algebra at UTSC?

You can complete a high school prerequisite over the summer or take the Math Development Course provided by the Math and Stats Learning Centre. This course is available online over the fall term and upon successful completion you can take the calculus or linear algebra course you want in the winter term.

What are the risks of choosing the wrong first year calculus sequence?

If you complete a sequence of calculus that is not designed for your program, then you will have to take the ones required by your program for no credit.
If you take MATA31+MATA37 even though it is not a requirement for your program, you will have to deal with a challenging theoretical course and risk low marks or failure.
MATA37 does not contain some applications and topics that MATA35 and MATA36 contain that are useful and crucial to the programs for which they are required. Taking MATA37 instead of MATA35/36 will be a disadvantage to students in those programs.

What calculus course prerequisites do upper level math courses have?

The following courses have MATA37 or MATA36 as a prerequisite: MATB41H3 Techniques of the Calculus of Several Variables I, MATB44H3 Differential Equations I, and MATC01H3 Groups and Symmetry. MATA37 is a prerequisite to MATB43H3 Introduction to Analysis (but MATA36 does not suffice). Finally, note that MATA35 or MATA33 are terminal courses in the sense that these courses are not prerequisites to any other math course. Thus students taking only these courses will not be able to take any further math courses.

What is the difference between a major and a specialist program in mathematics?

A major program in math requires a total of 8.5 (out of 20) credits in mathematics, where a specialist program requires 13-13.5 (out of 20) credits in mathematics. A student needs a double major, or a major and a double minor, or a single specialist program for UTSC degree requirements. A student in a specialist math program must take MATA31+MATA37 (along with the other required courses) where a student in a major program can take MATA30+MATA36 instead.

Is there a minor program in mathematics?

No there is not.

Note on Pre-requisites & Exclusions

Please pay special attention to pre-requisites, co-requisites and exclusions when you enroll in courses:

To enroll in a course you must have successfully completed all pre-requisites. If you have not satisfied pre-requisite, even if the computer system allows you to enroll, you will be removed from the course before the course begins.
Co-requisites are courses that must be taken in the same session.
When one course is an exclusion of another, then you will not get credit for both courses. If you take both then one of the two will not count toward the 20 credits needed to graduate. In some cases exclusions are not both ways. That is, it is ok to take course A before course B, but not course B before course A. Pay attention to this so you are not surprised by having too few credits when you apply to graduate.