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

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

#131

Post by jimmaswell »

ajuc wrote: post #105
jimmaswell wrote: post #65

Earlier quoted context omitted.

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 ga…

>trying to calculate if enemy can see you

Send a raytrace from the bot to the player and see if it hits something other than the player, which is just one line

Pathtaking beyond simply moving towards the player is a lot harder, yeah.

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

#132

Post by ajuc »

jimmaswell wrote: post #131
ajuc wrote: post #105

Earlier quoted context omitted.

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 ga…

>trying to calculate if enemy can see you Send a raytrace from the bot to the player and see if it hits something other than the player, which is just one line Pathtaking beyond simply moving towards the player is a lot harder, yeah.

If you just send 1 ray from eye towards the center of the enemy (or head, or whatever) - and this particular part of the body is occluded by a wall or a chair, but the rest isn't - the result will be wrong.

You can accept that, use many rays, or do proper view frustum/body model(simplified probably) intersection, after cutting the view frustum with the terrain.

You can also consider lighting (so enemy can't see you hiding in a dark corner), or even dynamic lighting (and give enemies light sources).

Everything becomes hard after you think about it enough :)

But I agree simple solutions + some tinkering with parameters works most of the time (and gamers probably won't notice).

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

#133

Post by SpaceManNabs »

jeffreyrogers wrote: post #74
cbgb wrote: post #66

Earlier quoted context omitted.

This may be true for mathematics in the analytical tradition (things like Topology, Measure Theory, Real/Complex Analysis), but Linear Algebra is far more important in, unsurprisingly, algebraic disciplines. These include Number Theory, Field Theory, and Mathematical Logic. While studying mathematics in college, once I had finished my Real Analysis requirement, I jumped headfirst into the algebraic side of things and…

That's a good point, my own studies have been biased towards the analytical side of mathematics, but I can definitely see how calculus could be less useful in other fields, e.g. I don't remember ever needing to do an integral when learning algorithms. And the opinions of my professors are of course biased as well, since they've spent their entire careers on analysis.

When analyzing algorithms, I have used calculus as a shortcut to many calculations. I believe that learning calculus is not just about its direct applications. Calculus often comes up when just dealing with your set-up.

You might make a discrete model for a problem and end up using calculus for approximations, equivalent calculations, or reasoning.

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

#134

Post by eli_gottlieb »

mathattack wrote: post #110
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?

> Too much focus on preparing people for careers in Engineering? Or preparing them for more abstract concepts like Analysis and Analytic Geometry?

Yes. Computer Science curricula tend to focus overmuch on preparing students to work as software engineers, and Mathematics curricula tend to focus overmuch on analysis (to the point that once you get past Calc 1+2+3, Linear Algebra, Differential Equations, Mathematical Analysis/Epsilon-Delta Calculus-with-proofs, and Real Analysis, things like Algebra and Topology are senior-year electives).

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

#135

Post by eli_gottlieb »

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…

> They have enough trouble understanding functions in Calculus I: linear algebra's "functions are basically matrix multiplication" feature would NOT help.

What do they have trouble understanding about functions?

Actually, it took me until just a few minutes ago to realize that one of the major differences between my CS-centric way of thinking and the proper mathematician's way of thinking: mathematicians treat all coextensive representations of the same object as identical, while a computer scientist tends to treat only provable intensional equality as actual identity.

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

#136

Post by mannykannot »

ams6110 wrote: post #59
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…

As a programmer, I've used calculus and linear algebra exactly never in my professional (20+ years) career. It just doesn't really come up doing web apps, sysadmin or dba work.

Mechanics don't use calculus, even many engineers don't, but those working in R&D, especially towards the R side, do.

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

#137

Post by mathattack »

eli_gottlieb wrote: post #134
mathattack wrote: post #110

Earlier quoted context omitted.

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?

> Too much focus on preparing people for careers in Engineering? Or preparing them for more abstract concepts like Analysis and Analytic Geometry? Yes. Computer Science curricula tend to focus overmuch on preparing students to work as software engineers, and Mathematics curricula tend to focus overmuch on analysis (to the point that once you get past Calc 1+2+3, Linear Algebra, Differential Equations, Mathematical An…

Yes - it's too bad they keep the fun stuff for the end. I've been rediscovering the fun of number theory via Project Euler.
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