double post
Nowadays, I think most colleges and universities offer a different “version” of Calculus to Business majors (called something like “Business Calculus” or “Calculus for Social Science”) than the traditional STEM Calculus.
My own suspicion (and that’s all it is) is that, of business-related majors who take calculus, very few will ever need to use most of the specific, nitty-gritty details (like how to compute the derivative or integral of a complicated function), but many of them will benefit from gaining some familiarity with the basic ideas and concepts studied in such a course (e.g. rates of change, absolute vs relative maxima and minima, the fact that not everything’s linear or even continuous, etc.).
Not to get too much in the weeds on double entry, but:
Accounting is based on four basic account types that generate two basic reports. The reports are the Balance Sheet, and the Profit and Loss. The Balance sheet account are Assets (the dollar amount of everything you own, and all the money that you are owed) and Liabilities (the dollar amount of everything you owe to others). The P&L accounts are Income (all the money you have earned over a set period) and expenses (all the money you have spent over the same period).
The natural sign of these accounts are Assets positive (debit), Liabilities negative (credit), which makes sense to most people, and Income negative, and Expense positive, which most people find counter intuitive.
The way the double entry goes:
You create an invoice for a customer, the entry is credit income, debit asset, typically Accounts Receivable. When your customer pays you credit AR, debit cash, typically a bank account. When you get a bill from a vendor, debit expense, credit liability, typically Accounts Payable. When you pay that invoice debit AP, credit cash, typically a bank account.
The balance sheet report always balances to zero. All of your Assets plus all your Liabilities equals zero. The way this is achieved is through a type of liability account called an equity account (how much the business owes to its owners). If the company is profitable it will have a credit balance in equity, if it is not profitable it will have a positive balance, helpfully called negative equity.
I took Business Calculus at Villanova in the 1990s. It should have been called “Using math to screw people, a nickel at a time.”
The best take away was the calculus of pricing and maximizing profit. It makes it clear that the idea that companies will pass their expenses (increased taxes, increased wages) onto their customers is a complete myth for any mid to large size business. A big box retailer is not going to increase its prices in response to a higher minimum wage because expenses do not enter into how prices are determined. If the market would bear a six pack of socks at $12 instead of $11, then the price would already be $12. Knowing the calculus of pricing also explains how a company can sell a $200 pair of shoes at 80% off and still make money hand over fist.
You have to be smart to learn calculus, being smart may make you a better programmer, but that is it. I never thought about Calculus again after leaving the class, and when I went to computer school I never had any thought that calculus was related in any way.
Since the purpose of college is to certify intelligence and conscientiousness I think calculus classes could definitely help do that but it is not useful for 95-99% of students.
That is fine if you’re absolutely sure that you won’t go into those fields. However, there is a slight risk that if you change your mind partway through college, you’ll have to backtrack and take the calculus courses and delay your graduation. I never said calculus is for everyone, but for some it is essential.
How often? I’ve used calculus, differential equations, etc. in work before. But you are right, it’s rare. That said understanding the math behind a lot of the software is very useful.
OK, maybe I expressed myself wrong, but I’m interested in teaching kids stuff like this: If there’s a certain probability of A given B, what’s the probability of B given A? You don’t need calculus to solve that. You need algebra and an understanding of conditional probability.
More to the point, I want kids to come away with a knowledge of logic, fundamental logical arguments (syllogism, for example), logical fallacies formal and informal, and statistics in that context, not the more formal statistics which is just a sub-field of measure theory.
And this is where I differ: You can learn calculus to the extent of your interest in the physical sciences, but the true foundation of being a functional adult is being able to use logical arguments and determine risk. That is what elevated us from mere superstition, and that is what’s needed in our and every society.
This is, simply, wrong: Both because programming at the bare metal level has absolutely no bearing on what kinds of math you use to analyze your programs, and because programmers do indeed need to know what kind of runtime behavior their program is going to have on the kinds of inputs they expect it to see. Big-O notation is a tiny amount of calculus (limits, to be precise) and a lot of creating the formula to take a limit of, which is done using counting arguments.
Seriously… where did you get the idea that assembly language programmers are in special need of theoretical computer science concepts?
It is impossible to predict in advance what knowledge will be important or necessary- occasionally it is a surprise- so the more you learn, the better, but at the same time one cannot learn everything in the first year or even a multi-year curriculum. Therefore, administrators always make compromises. So whether computer science is approached as a branch of mathematics or of engineering, students get a decent grounding in mathematical techniques including infinitesimal calculus and differential equations; your psychologists, economists, and physicians a perhaps more abbreviated one, and pure classics majors may end up taking a lot of philosophy instead.
All other things being equal, though, it would be a strange argument to make that ignorance equals bliss in a scholarly environment, or that any harm is done to anyone by accidentally taking an introductory mathematics class.
You don’t have to be smart to learn calculus. Anyone can learn it. You don’t have to be smart to read Ulysses, you just need time to kill.
My own take:
Basic math and practical math (including basic financial math, how to half or double a recipe, etc) should be required for everyone - this is through what is called Algebra 1 (which in my experience is a middle school subject).
At that point we are off the rails. MOST jobs won’t need calculus - for those that do its critical - but a middle schooler knows if they like math enough and are driven enough to get through calculus. Most jobs don’t need trig, or Algebra II. The only time I’ve FOILED in my adult life is teaching my own kids how to FOIL.
Likewise, MOST people will not need the skills you develop analyzing The Great Gatsby or The Scarlet Letter.
Most PEOPLE do need critical thinking skills. They need logic skills (which is what geometric proofs are). They need statistics.
By high school, school should not be as much about check boxes (have you taken four years of math) and more about making sure you get the skills that are going to help you along your anticipated life path. For some people that will be two years of Calc in high school. For some that plus detailed level Science coursework. For others, it will be four of a foreign language or developing research and writing skills to get them through a liberal arts degree. For others that is going to be learning to weld or clean a carburetor.
For everyone that will involve enough History, Economics, Sociology to be able to make intelligent informed decisions when it comes to voting. It will be enough Science to be able to call bullshit on obvious bullshit. It will be enough statistics to be able to tell when someone is lying with it. Enough math to do your taxes. Enough computer skills to be able to submit resumes online. And, if you change your mind on what you want to do, thats what remedial college or intro college work is for.
I REALLY hate the four years of math, four of English, three of foreign language, three of Science of the college admissions process.
You can’t tell. I used graph theory and automata theory more than any of the stuff above, though I’ve taken it, but that might be because I never enjoyed it. If I did I could have moved in different directions.
That’s the argument for teaching a wide range of math, even if most people only use a fraction of it.