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I am curious why Computer Science majors have to learn Calculus to receive their Bachelors Degrees. My father worked as a Software Engineer for twenty years and never used it. It seems to have little more value in programming than other forms of mathematics. What is it about Calculus that makes it a requirement for Computer Science majors? Is it just that it's a tradition in STEM fields?

There are several answers:

Answer 1: Not all CS programs

First, not all CS programs require calculus in order to get a bachelor's degree. The Bachelor of Arts (BA) program at Mills College, where I teach, does not require calculus. Instead, we require two semesters of discrete mathematics, which we consider far more useful to computer scientists, because it (at least the way we teach it) includes:

• inductive proofs


• Boolean logic


• proof by contradiction


• sets


• combinatorics


• basic probability


• recurrence relations


• graph theory


• matrices


• regular expressions


• finite state automata


• formal languages

Answer 2: Scientific foundations
That said, getting a Bachelor of Science (BS) degree from Mills or just about any other school requires calculus as part of general scientific knowledge, along with introductory chemistry, biology, physics, etc., none of which we claim someone will necessarily be useful to a computer scientist. These courses are part of the college-wide BS core, not specified by any individual department. The idea is that anyone holding a BS degree should understand the fundamentals of major scientific fields even if they will never apply them in their careers. (Similarly, most colleges require students to take classes in history, even though they are unlikely to become time travelers.)

Answer 2: Historical reasons

Computer science as an academic discipline has not been around that long. Most CS programs started within either Mathematics or Electrical Engineering programs. Both of those fields legitimately require calculus. I went to MIT, where CS was added to the EE department. All CS majors were required to learn both digital and analog electronics, the latter of which requires calculus.

Personal thoughts

In my decades as a computer scientist, including in industry, I never used any of what I learned in the required calculus (I, II, and III), linear algebra, or differential equations. That said, they did give me the background to go into computer graphics, electrical engineering, or machine learning, had I later chosen to.

Whether programs should require calculus is another question.

This isn't really an answer, but I'd like to say a few things about calculus. I think that what is needed by a CS major from that realm and what is needed by a math major are very different. As such, I think that if calculus is taught to CS majors, and to history majors, for that matter, might be a different sort of course than that taken by the math majors.

First, not a lot of people who have taken Elementary Calculus (i.e. Calc I, II, and III) actually have much insight into what is really the point. It is easy to get lost in details of differentiation and integration and techniques and such without realizing that it is really a study of the relationship between what happens locally with a function (differential calc) and what happens globally (integral calc). It is all tied together by the Fundamental Theorem.

But even the nature of the derivative is poorly understood for a long while - it took me several years of graduate study in math to really grok it. The derivative you study in Elementary Calculus is really only one specific form of a wide variety of possibilities. The limit used in Elementary Calculus could be replaced by alternatives. The difference quotient in the derivative could be replaced by another "average ratio of change". This would result in a different theory.

However, the standard version of Elementary Calculus (note that I keep writing Elementary")

Sorry. I have to interrupt. I'll be back.

Much of the material one learns in school has no direct utility in one's job as a software engineer. Conversely, much of the working knowledge one needs as an industry practitioner is not gained in school. What school is supposed to do is provide some basic knowledge and a basic framework for learning, out of which an individual is going to actively retain a small-ish portion for their day-to-day use on the job.

However, much engineering work is multi-disciplinary, and therefore "surplus" knowledge is not exactly useless: it can provide a useful bridge to other disciplines. Calculus in particular occurs in the math that describes physical processes.

In today's global economy, it is likely that one will switch employers and job specializations multiple times in one's career. At the start of one's career it is impossible to foresee what knowledge is going to come in handy later on. About twenty-five years into my career, I found myself interfacing to domain specialists whose bread and butter are differential equations. When I was in school, studying for a CS degree, I could have taken optional classes to learn about differential equations, but decided not to as I was already struggling with my math workload. So late in my career I came to regret my earlier decision, as it put me at a disadvantage relative to colleagues with a working knowledge of differential equations.

The exact nature and number of math classes required in a CS program may in part be driven by departmental tradition. For example, in the school I attended, the CS program had grown out of the math program in the early 1970s. Therefore, math was heavily emphasized. In fact, as an undergrad I took exactly the same math classes as students in the math program. Out of those, linear algebra turned out to be useful for computer graphics, and numerics turned out to be useful for high-performance computing. Multi-dimensional analysis and statistics I never needed again, but it might have been quite different had my career taken me in a data science direction.