The Positive Impact of a University Calculus Preparation Course

university calculus preparation

High school math alone does not adequately prepare students for the intensive curriculum of university calculus. In university, your professor expects you to have already acquired the confidence and substantial knowledge of the basics of math, allowing you to learn more advanced concepts towards forming a deeper understanding. In addition, many college majors and medical schools expect prospective students to take a university calculus course. Students, without the necessary preparation and proficiency in math basics, risk failing the needed calculus course as they struggle to keep up with the demands of a university curriculum and expectations of math skills. A University Calculus Preparation Course (UCPC) is designed to ensure your confidence in developing a concrete understanding of fundamental math concepts, giving you a head start in achieving a successful post-secondary career. 

To provide further insight into the importance of a UCPC, we interviewed Dev Gokal – a University of Toronto math specialist student. Along with his experience as a teaching assistant, he has seen firsthand the struggles of being ill-prepared for university calculus:

Q1: What is the difference between high school math and university math?

D. Gokal: High school calculus only scratches the surface of the subject; MCV4U0 only covered basic notions of limits and derivatives, before moving on to linear algebra during the second half of the term. In university, first-year calculus is generally a full-year course or offered as a split between two courses. All of high school calculus is covered within a quarter of the time in a university calculus course before moving on to new concepts. 

Another significant difference between high school and university is that students are expected to study the material before attending the lecture. This expectation ensures that the lecture dedicates itself not only to teaching but also to providing students with the opportunity to ask questions and gain a deeper understanding of challenging parts.

An important point to consider is that, given the large class size, professors may find it challenging to address every student’s needs. Therefore, professors encourage students to read ahead to avoid feeling overwhelmed during lectures. University lectures move faster than high school, focusing mostly on instruction rather than dividing time for exercises.

In high school, calculus relies on memorizing and applying formulas for problem-solving. In university, you delve into the deeper underlying theory, encompassing mathematical definitions, theorems, and lemmas.

You will see the tools that you have been using in high school developed in a new light and rigorous manner that will help you form a deeper understanding of those tools. We will rigorously define elementary functions like sine, cosine, exponential, and the logarithm using their Taylor series expansions.

Testing will also differ, as they will require you to not only show your understanding of the material by making you compute integrals and derivatives but also prove certain statements by using definitions and theorems. A high school test question may look like this:

Calculate the following derivative: 

Whereas in a first year calc course you may see something like this: 

(Chapter 9, Q15 from Spivak)

It’s easy to discern that answering such questions demands a certain level of mathematical maturity and comprehension of theory, in contrast to the relatively simple computational problems frequently encountered in high school.

Q2: Why is this relevant for computer science and engineering students?

D. Gokal: Engineers and computer science students are natural problem solvers. 

In engineering, the challenge often involves devising novel, optimal solutions to meet unique client needs, solutions that may not yet exist. While it’s tempting to rely on existing standards, this approach isn’t always viable. As an engineering student, it’s your responsibility to innovate and find new problem-solving methods. This demands a deep understanding of not just how things work, but also why they function as they do. The ability to think logically with abstraction is crucial for generating fresh ideas and solutions. This skill is equally valuable for troubleshooting, as abstract analysis allows you to dissect a problem into its individual components and quickly identify the root cause.

Many mistakenly assume that a computer science degree revolves around coding and software design with minimal theory. In reality, the first year introduces basic coding, while the remainder emphasizes understanding computer and program functioning. By the second year, the theory of computation is explored, covering inductive reasoning and computability. These concepts often require proof techniques from first-year math courses, highlighting the importance of a strong foundation. Upper-level computer science courses, especially in fields like machine learning and artificial intelligence, prioritize theory, mathematics, and strong abstract and logical thinking skills—nurtured in first-year math courses.

Q3: What benefit will I get from a University Calculus Preparation Course?

D. Gokal: By doing this UCPC, it will allow you to sharpen your critical thinking skills, as it forces you to understand the basics. The use of mathematical logic and reasoning in the program is easily transferable to other subjects; the more exercises and proofs you write, the better you will get at explaining your ideas in a logical and rigorous way. In addition, learning to be precise and rigorous when expressing your ideas is a necessity in any STEM-related field. Studying calculus rigorously at the university level equips you with analytical thinking tools that transform problem-solving and learning approaches.

In high school, students often rely on examples to grasp the material. However, those with strong skills habitually delve into the fundamental levels, comprehending the building blocks that constitute the big picture. This ability to work with these “fundamental building blocks” is crucial for those interested in research.

In STEM fields, especially math and computer science, many problems are conceptually easy to grasp and break down. However, the ability to rigorously convey these ideas in a clear and understandable manner is an essential skill that many should possess but often lack.

Q4: Why does it matter now?

D. Gokal: This is probably the best time to learn and to do a UCPC.

Amid the current COVID-19 restrictions, there’s no better time to acquire these valuable skills. Establishing a strong foundation is more achievable with the extra time available, enabling you to enhance problem-solving and critical thinking abilities. This preparation will ease the stress of future high school or university courses, as you’ll possess a deeper understanding of the material, allowing you to grasp the “why” and rigorously demonstrate concepts, rather than passively accepting propositions and theorems.


At MathProject, we have our University Calculus Preparation Course in Mississauga, Brampton, and Oakville to help students achieve calculus proficiency before university. Within two months of our university calculus preparation course, our students gain the confidence and skills needed to excel in university calculus and in any STEM field. Enroll now with our math programs by visiting our contact page or calling +1 844 628 4243 to book a free assessment.

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