At this time of year, our first students are about one month into their required math class: enough time to learn something, enough time to wonder whether it will be useful and to ask “is this course an arbitrary barrier to my career?”. The purpose of this blog posting is to say “Yes, math class teaches important ideas” and “Listen carefully to discover the really useful stuff”.
It may help to start by making some silly questions disappear. If you think that the mathematics used in advanced classes or on the job is about entering numbers into a spreadsheet and making sure that the answer is calculated correctly, then you misunderstand the value added of a job. If you think that calculus is about fancy symbols that were developed a couple of hundred years ago for use by scientists (but not people in business) then you misunderstand the questions that business people need to answer.
This table lists a couple of familiar subjects, the contents of such courses and why there are costs to not understanding them.
||Misunderstanding a concept opens the door to …
||1, 2, 3, -100, 0, …, +, -, *, /, ( ), …
||Creative accounting, misleading consulting reports with excessive jargon , poor number sense
||x, y, =, y= mx+ b, α, π, …
||Being unable to understand trade offs or system-based thinking, confusing anecdotes for logic, unable to recognize equivalencies
||slope, curvature, change, functions, optimization (with and without constraints), …
||“Model risk”, being unprepared when market conditions change, confusing marginal costs and fixed costs
Technology makes computation incredibly easy now if you know what needs to be computed.
Good math classes develop problem solving skills. Accounting classes explore particular examples of accounting problems and marketing classes explore examples of problems faced by marketers. But, like a magician pulling a rabbit out of a hat, the solution to many of these problems is as obvious as if the hat had two floppy ears sticking out.
In upper year classes, we teach net present value (NPV) or sensitivity analysis. Students think that the class teaches how to make investment decisions and that is not completely wrong: they are taught how to show whether a project’s financial sensitivity coefficient is more or less than 5. A better student would recognize that NPV is a type of function with inputs and an output, and that sensitivity analysis is an example of calculus (which quants in finance disguise with jargon such as “delta”, “vega” and “rho”). With math class providing a solid foundation, upper year classes can spend less time on boring review and more time on advanced ideas.
A university education is about obtaining a more general perspective so that, without being taught directly, you can see that the problem of tipping restaurant staff is related to the problem of giving incentives to corporate executives. Or, you can use your perspective to extend the textbook examples to solve a type of problem which is too new to be in any textbook: somebody will, why not you?
The goal of learning is to develop a level of comfort with the concepts, not the ability to calculate the answer to a known formula using known inputs. A student who only learns to calculate an answer can be tempted to torture a formula and to change planning assumptions to produce the “right” answer (such as demonstrating profit is high by ignoring certain costs). A better student would know that the right decision for a business is not yet known and would know when to ask hard questions of any answer.
There are many worthy articles on why it is good for your soul to study this or that subject but a blog posting on the Scientific American website argues: math is fun. By playing with math tools, you will realize the value of having learned time tables or calculus. When used to them, they complement the application of creativity. Stimulated by the real world, you can play with puzzles and patterns that nobody else has noticed. With the added clarity, you can proactively provide solutions before people realize that they have a problem. It sounds like good math leads to a happy customer.