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Too Much Calculus – Gilbert Strang (2001) [pdf]

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Re: Too Much Calculus – Gilbert Strang (2001) [pdf]

#101

Post by AnimalMuppet »

tdfx wrote: post #93

I've never understood why Calculus is taught as a separate course. It seems so detached from practicality. I've always thought students should take perhaps 4-6 semesters of Physics -- and introduce derivatives, integrals, etc. as needed when they can be demonstrated to more easily solve the physics problems. If the physics content was more spread out, there would be ample time to introduce the necessary math concepts…

I remember, in my high school calculus class, the teacher said that there were six or seven applications of derivatives, and more like 40 applications of integrals. It's way more than just physics.

Re: Too Much Calculus – Gilbert Strang (2001) [pdf]

#102

Post by IndianAstronaut »

ekidd wrote: post #7

As a programmer, I've found far more uses for linear algebra than for calculus. It shows up in robotics, in machine learning, in game development, and in many other cool subfields. I didn't get very much out of my university linear algebra course. (It was pure theory with nearly zero applications.) I don't think I really developed a good intuition for linear algebra—and why it's so useful—until I read Jim Hefferon's…

For some coding puzzles I was given during interviews, I found that sometimes linear algebra solutions can be used. I submitted such a solution once to a company for a take home problem, they rejected me but it was still an interesting experience.

Re: Too Much Calculus – Gilbert Strang (2001) [pdf]

#104

Post by profinger »

peterfirefly wrote: post #84
vowelless wrote: post #67

Earlier quoted context omitted.

I agree although I work in robotics / computer vision. What I wish I had done a lot more of is statistics. Being able to reason about probabilities clearly, getting an idea of how a system performs given various variables, and most importantly, being able to communicate this to others has been very useful to me. I think anyone (front end, backend, etc) can benefit from learning about statistics.

But statistics and probability is really just integration. It's either that or stamp collection. And optimization is really just differentiation (+ some geometry). I'd say the problem is too little calculus and not too much.

I agree as well. Not sure why you're being downvoted. Maybe I don't know enough about linear algebra to judge but everything ML that I've ever worked in was spoken in calculus..

Re: Too Much Calculus – Gilbert Strang (2001) [pdf]

#105

Post by ajuc »

jimmaswell wrote: post #65
ajuc wrote: post #12

Earlier quoted context omitted.

Make them code simple wolfenstain 3d clone with opengl, directx or even unity3d. It was a revelation for me when I've tried to get into game programming, and half of the math taught in primary and secondary school became immediately useful, also linear algebra (which was only started at the final year of high school). Made linear algebra courses on the university a lot more interesting. There's a difference if you lo…

I can't see myself really needing to apply any Linear Algebra concepts writing a Wolfenstein clone in Unity3D. It does everything for you like that (shader graphics, collision detection, vector math, etc). All you'd have to do is code some simple AI for the enemy gameobjects and make the player gameobject in the standard FPS shooting format, which there are pre-built defaults for in the example projects. The majority…

Even "just" ai can teach you a lot. For example trying to calculate if enemy can see you, or which path he should take is interesting.

Of course you can go far with "turn towards player and shoot" ai, but where's the fun in that.

Actually it would be fun to give student's assigment like:

here's the AI interface, make a game using it, and write your bot. Then we will run all the bots in free for all mode on all the games (except your bot on your game), and we will grade by sum of the points.

Re: Too Much Calculus – Gilbert Strang (2001) [pdf]

#106

Post by Dudelander »

peterfirefly wrote: post #84
vowelless wrote: post #67

Earlier quoted context omitted.

I agree although I work in robotics / computer vision. What I wish I had done a lot more of is statistics. Being able to reason about probabilities clearly, getting an idea of how a system performs given various variables, and most importantly, being able to communicate this to others has been very useful to me. I think anyone (front end, backend, etc) can benefit from learning about statistics.

But statistics and probability is really just integration. It's either that or stamp collection. And optimization is really just differentiation (+ some geometry). I'd say the problem is too little calculus and not too much.

Totally agree, calculus is a prerequisite for understanding statistics, unless you're just plugging in numbers for an A-B test - and you don't really need a class to do that.

Linear Algebra is very useful too, but it's not really fair to say one is more valuable than another. It just depends on what kinds of applications you end up working on. Universities should just teach both.

Re: Too Much Calculus – Gilbert Strang (2001) [pdf]

#107

Post by peterfirefly »

Dudelander wrote: post #106
peterfirefly wrote: post #84

Earlier quoted context omitted.

But statistics and probability is really just integration. It's either that or stamp collection. And optimization is really just differentiation (+ some geometry). I'd say the problem is too little calculus and not too much.

Totally agree, calculus is a prerequisite for understanding statistics, unless you're just plugging in numbers for an A-B test - and you don't really need a class to do that. Linear Algebra is very useful too, but it's not really fair to say one is more valuable than another. It just depends on what kinds of applications you end up working on. Universities should just teach both.

Many interesting things require a combination of more than one area of math. I don't understand how you can do much within robotics or vision without using all three of calculus, linear algebra, and statistics :)

Re: Too Much Calculus – Gilbert Strang (2001) [pdf]

#108

Post by pm90 »

RogerL wrote: post #90
xamuel wrote: post #10

(Speaking from my experience as a calc teacher at a big U.S. state U.; mileage may vary elsewhere) Most non-STEM students won't see the 'Calculus I, Calculus II, Calculus III' that starts the essay so dramatically. Increasingly, liberal arts students are able to get by with no more than a "math appreciation" course and maybe what amounts to high school algebra. The "math appreciation" course might actually touch on v…

"Consider a spherical cow in a vacuum on a frictionless plane..." That joke comes from the analytic calculus tradition of physics. I took a lot of physics while an undergrad, and I came out unable to do any useful physics. This is because as soon as you try even very simple problems the partial differential equations that result have either no, or extremely difficult to find solutions, and it is usually the former. I…

I agree with your point that a lot of current STEM education focuses on things that don't really have any practical value. I think its more of a tradition for engineering students to be learning about this stuff, a legacy of the time when knowledge was not available at your fingertips.

There are a lot of programs that are experimenting with different approaches though, and I think this will only get better with time.

Re: Too Much Calculus – Gilbert Strang (2001) [pdf]

#109

Post by peterfirefly »

tel wrote: post #97
peterfirefly wrote: post #84

Earlier quoted context omitted.

But statistics and probability is really just integration. It's either that or stamp collection. And optimization is really just differentiation (+ some geometry). I'd say the problem is too little calculus and not too much.

Don't know why you're being downvoted. This is totally true.

Most of my downvotes so far, both here and on reddit, have been earned by writing things that are true but unpopular.

The weird thing is that I can't predict which things are going to be sufficiently unpopular amongst people impolite enough to downvote instead of coming up with a good counterargument (or even better: fact). I had /never/ expected something like this to get a single downvote (and I was down at -3).

Re: Too Much Calculus – Gilbert Strang (2001) [pdf]

#110

Post by mathattack »

ekidd wrote: post #7

As a programmer, I've found far more uses for linear algebra than for calculus. It shows up in robotics, in machine learning, in game development, and in many other cool subfields. I didn't get very much out of my university linear algebra course. (It was pure theory with nearly zero applications.) I don't think I really developed a good intuition for linear algebra—and why it's so useful—until I read Jim Hefferon's…

Linear Algebra is also important in Finance too. Stats are useful in almost every field, as well as for developing a probability-based state of mind.

I wonder why the imbalance exists. Too much focus on preparing people for careers in Engineering? Or preparing them for more abstract concepts like Analysis and Analytic Geometry?

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