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Gamersez

Finding the beauty in mathematics

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''Attitude is everything - it''s your guide to life.'' -Anonymous Reading that quote on the homepage really puts things into perspective. A nice segue here, if you will I am wondering...how many of you used to hate math and physics? How many of you had math and physics anxiety? For me, it is challenging. Starting today, I am retaking Math and Physics again in my chosen course of game development. My attitude towards it was lax. I didn''t put in enough hours of study. The main reason was my ^attitude^ towards it. That attitude being, boredom and hatred towards learning it because it seems so foreign to English, History, Art, etc. So different. The ugly logical stepchild of learning subjects. What I am trying to get at is this- I have a natural curiosity towards programming because it resembles a little bit of English. Yet, we all know mathematics is the foundation for computer science. It needs to learned first to build on learning game programming. So I am seeking some of your reasons why you love or like math so much? Or if you didn''t at first, how did you come about to like it? Through your suggestions and experiences, I am hoping to find a temporary motive to keep me going till I find out why I love math so much. Which I don''t right now. Though my belief towards liking it and soon, remains steadfast. Once, I find my true motive, that wind will help me catch fast sail towards having a natural curiosity towards learning MORE of math. As we know natural curiosity = growth in learning. I don''t care. Give a Top Ten list. Be funny Be creative. I am eagerly awaiting your reasons why you love math! "I Vanna Fryyyy Skyyyy Hiiiiiiigh! Vroooll to get Vyyy!" -Sega''''s "Daytona USA"

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quote:
Original post by Gamersez
I am eagerly awaiting your reasons why you love math!



I grew up always enjoying mathematics, doing well at it in school and getting a degree in college in both comp sci and applied math. Some of my reasons:

- As you state, computer science is based fully in mathematics. My curiosity for both helped to reinforce my interest in each other.

- Mathematics in nature. Some would say we read too much into things, but the truth is that there are some very predictable and beautiful patterns in nature that have very elegant mathematical properties. Many rates of growth can map to a function of e , other shapes define the golden ratio (a number I really enjoy!)...

- A strong foundation in mathematics and logic can go a long way to improve your skills in logic, thinking, and reasoning for many things in life.

- You can tell mathematical jokes and laugh while all your friends wonder at your sanity... wait a sec...


---- --- -- -
Blue programmer needs food badly. Blue programmer is about to die!

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The first geometry course I took dramatically changed my view of math. Until then (through grade school), math had seemed to be mostly arithmatic. I hate arithmatic; I'm still bad at it. When I took geometry, however, I saw the logical basis of math; it no longer seemed arbitrary. When I got a TI-83+ the arithmatic part disappeared altogether and it became even more enjoyable! Now that I'm beginning to look into things like number theory a little bit though, arithmatic doesn't seem so arbitrary after all!

Edited by - TerranFury on February 5, 2002 4:58:55 PM

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Maths was always something I had a talent for, perhaps because that talent was measured relative to my other classes. I suspect it was because from an early age I enjoyed the challenge that mathematics offered. Writing an essay is a rather nebulous affair with success very subjectively determined by a teacher/tutor. Mathematics on the other hand offers (in general) an immediate evaluation of your ability. Many people dislike mathematics because they are turned off by the black and white of being either right or wrong. It''s hard to be partly correct and therefore partly encouraged when doing mathematics. Most people are discouraged early on because they get things wrong. Maths takes practice, just like any other language... and you have to continually use it to remember it.

So, my talent and enthusiasm grew into a First Class Honours degree in Applied Mathematics(Astrophysics) (but then I also obtained majors in Physics and Philosophy!) and a PhD in Artificial Intelligence (maths/comp sci) basically because I love to be continually challenged and stimulated.

Most people find their motivation through success, or the desire to achieve success. If you look at the long term goal of maths applied to game programming you may see maths as a hurdle you must overcome to achieve your goal. Instead, view learning mathematics as the goal and take pride in your successes in mathematics. Once you have achieved that, then achieving goals that depend on knowning mathematics will be that much easier!

Cheers,

Timkin

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Very thought provoking Timkin!

"Mathematics on the other hand offers (in general) an immediate evaluation of your ability." Very true. I enjoy instant feedback. Good point.

"Instead, view learning mathematics as the goal and take pride in your successes in mathematics." Agreed.

Timkin, and btw, congrats on your successes so far. I have an interest in AI as well, particularily with programming.

As for everyone else''s reply, I REALLY appreciate you posting also. I''ve read them.

Please feel free to keep your reasons why you love math coming. The more suggestions, the more I enjoy reading them, the more the ideas (as well as many other prospective would-be programmers) help.

"I Vanna Fryyyy Skyyyy Hiiiiiiigh! Vroooll to get Vyyy!" -Sega''''s "Daytona USA"

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quote:
Original post by TerranFury
The first geometry course I took dramatically changed my view of math. Until then (through grade school), math had seemed to be mostly arithmatic. I hate arithmatic; I''m still bad at it. When I took geometry, however, I saw the logical basis of math; it no longer seemed arbitrary. When I got a TI-83+ the arithmatic part disappeared altogether and it became even more enjoyable! Now that I''m beginning to look into things like number theory a little bit though, arithmatic doesn''t seem so arbitrary after all!

Edited by - TerranFury on February 5, 2002 4:58:55 PM


I had always done well in math, but didn''t neccesarily like it. "Yeah, yeah, opposite interior angles equal. Whatever. Crank up the Soundgarden." It wasn''t until I took physics in high school and I realized "So that is the point of trigonometry!" that I started to have more of an appreciation for it.

I would argue that hardcore math is not that important for general programming anymore. For games, it definitely is. For engineering applications, it is. But I participated in building a pretty complex course manager with some other students last summer, and I can''t think of one instance where we needed math (except maybe Boolean arithmetic, which is pretty much everywhere).

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Hi all!

I did poorly in math in high school, never took math in college, then got into the computer thing and realized that I had a serious hole in my education.

I think it was when I realized that, without math, the only games I would EVER be able to make would be text adventures, that I sat down and taught myself what I know of trigonometry, geometry, calculus, logic, and physics.

Inspirations? Chaos theory, astronomy, PI (the movie).

If possible, learn math in school. It is much easier than learning it in your spare time.

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According to me, mathematics have to be considered as a tool which allow you to modelize and resolve a problem, but maths for maths is a real boring task (too abstract) that a few people can handle due to complexity...

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According to me, mathematics have to be considered as a tool which allow you to modelize and resolve a problem, but maths for maths is a real boring task (too abstract) that a few people can handle due to complexity...

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um...Bloodscourge, you said that twice. Good point though. I am really starting to like math now! Woohoo!



"I Vanna Fryyyy Skyyyy Hiiiiiiigh! Vroooll to get Vyyy!" -Sega''''s "Daytona USA"

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Yep, thats a recursion equation of complex numbers:

Z[n] = Z[n-1] * Z[n-2] + P

(zoomed in on a very small area)

P is a constant and the point in the plane, Z is looped up to n= 499 to check if it converge or diverge. The white areas are where it converges.

I calculate the light effects by making approx normals by using |Z| as a heightmap when it exits the loop.

My post up, your post down, my site here


Edited by - Jesper T on February 8, 2002 7:27:41 PM

Edited by - Jesper T on February 8, 2002 7:30:23 PM

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I used to just count maths and physics like any other subject, albeit ones i was good at, i got a good grade in physics GCSE(im in england) so i went on to take physics A level (in year two at the moment) but about september i realised that i found EVERY aspect of physics incredibly interesting, and have now applied for Physics Masters degrees at university.

In a way, i suppose it is because Physics Runs the universe, so there is not a much more fundamental Science. (incidentally, i believe that this is why i originally was interested in programming, to know how things worked.)

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For me, math is the basis of all learning.

-Math is absolute. While other courses can be open to instructor biased (ie. English, Social Studies), if a math teacher asked you to add 50+1, and you answer 51, it''s right, no question about it.

I love math simply because it''s logical and I did better in it than any other subject through High School.

Just my personal opinion.

''''You shall be as Gods!'''' Xenogears
''''You work on the salads until you get killed!'''' Space Ghost C2C

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I''ve always liked maths because it''s so precise. You''re either right or wrong not like when writing an essay. I still like history don''t get me wrong but I prefer maths because it makes more sense to me, it''s more definate.

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I used to like math a lot. I was also very good at it, doing multiplication and division when the rest of my class was still learning addition... Then once I hit fourth grade, all interest suddenly dropped... I think its because we changed our math books, which resulted in more homework.

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Here's why I love math...

For a while I did great in math but simply didn't like it. I don't know why, maybe because the teacher was stupid, or because it was going WAAAAAAAAAY too slow. Anyway, my point is, I write code since the age of 12 (ok, I REALLY started at 16, but I wrote little apps before) and I soon became attracted by 3D programming, especially games and movies (wow, Jurassic Park, I mean, SoftImage rules !) and I knew I wanted to work in this field. But after learning OpenGL and C++ and a lot of other things, I realized that I wanted to go further and investigate really interesting things like Bézier surfaces, illumination models, etc. I had always been fascinated by how we can use computers to create realistic, yet virtual, images. When I saw Jurassic Park (I was about 13 or 14) I realized how fascinating it was. BUT... now came the troubles. Every time I wanted to do something, there was that problem. Math. Every time I had to think in order to solve a problem, I realized that it was in fact a pure math problem and that I was completely stuck due to my lack of knowledge. So... I began to learn mathematics. And to like them. And now... hey, last week in my linear algebra class, we calculated orthogonal projection matrices... and in my other class we use triple integrals to find the volume of 3D shapes (rigid bodies, anyone?), etc... and now when I come back to programming, I find everything so easy I almost laugh. Want to display a Bézier surface with an optimized polygons set without partial derivatives? Hehehe... GOOD LUCK ! Using a constant tesselation interval for "t" in the formula is not exactly optimized Math is just the base of computer science. Once you understand it, you will find everything else in computer science a lot easier. You can always ignore math in general programming. But you won't be able to avoid math in the game programming industry unless you really want to avoid engine and physics code. So... if you like game programming, thats a very good motivation, isn't it? :-)

So, in conclusion, that's why I used to avoid math and why I'm right now a math addict.


Edited by - ET on February 16, 2002 11:19:15 AM

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Math is wonderful... it's built upon a complete and logical concept that a singular object is one. Take a singular object and stick it with another object and we get two. Take this "two" and put it with another "two" and woohoo, we just multiplied! And yet, with this simple concept we can compute from orbital trajectories and celestial interception points right down to double root quadratics. It's incredible to say the least! Okay, I'm done preaching now...
-Jesse

| The Hitchhiker''s Guide to Programming |
"That is not dead which can eternal lie,
And with strange aeons even death may die."
-H.P. Lovecraft

Edited by - Aphelion on February 17, 2002 1:26:00 AM

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I appreciate you sharing your experiences and reasons why you like math so much. If you wish to continue to do so, by all means post away. I can only hope that this thread will help others who hate math, to love math.

Here is my conclusion. Take a programmer such as John Carmack. Yes, forgive me, he is overused as an example programmer. But we mostly admit, he is very skilled at coding. So, please, indulge me for a moment with him being the example. Why is he so proficient or good? It makes you wonder, doesn''t it? Especially since he is SELF-TAUGHT! To me, being self-taught is amazing considering others (such as myself) who are going into debt with in$titutions of higher learning to practice the same stuff he knows. The answer is quite simple. He sees learning information about math and programming a joy, a hobby, much like Einstein enjoyed physics so much. In fact, he "consumes all 3D information" like Pac-Man consumes ghosts, power pellets, and fruit.

They both have what is known as an autotelic discipline. It means "self goal" in Greek. In English, it means a goal within itself. The desire is not to get good grades, money, or any other outside factor than just learning those studies as play, not work, though they may be challenging. After all, the desire for good grades or a better job is poor fuel for study. From what I read of your posts, it seems many of you are like this as well, autotelic.

I read on some threads that early in his career, John Carmack would spend up to around 80 hours a week just studying programming and 3D math. 80 frickin'' hours a week!

Now I know some of us here may or may not have that time. Let''s scale this time down to moments. Well, what about before you go to sleep? Or what about before you get to school? Or stand in line at the bank? What are you thinking then? My point in this paragraph is that we have at least small opportunities throughout the day to make learning fun in otherwise boring everyday situations where we are not using our minds much. We can quiz ourselves to sleep. We can make a game saying that you will not get out of the car to eat at Dunkin Donuts until you remember the distance formula. You know, little fun, challenging things like that. Heck, make a full fledged board game if it helps. In the end, our minute daily habits build up to gigantic achievements or gigantic failures.


So I derived a little formula for myself that will help me (and hopefully help others as I keep reiterating). The reason why I hate math is because I am prejudice against it. It looks ugly. It makes little sense. The reason why it looks ugly and makes little sense is because I haven''t put in the time to get to know it better. And that has a direct affect on my attitude towards it. I''d rather play many hours of Half-Life mods than study vectors, scalars, and matrices. So I have put up the addicting games in the closet, the most incovenient place possible for which to get them out again. I am devoting my time, effort and energy much like Carmack, since I have the time, to math. And from here on out, I am looking at math as a fun game instead of some torture, though it may be hard at times. In those times of torture I may post around. Hehehe.

By the way, of these thoughts, a book in particular, really helped me see learning as fun. You may want to pick it up and read it. It''s called the Einstein Factor, by Richard Poe and Win Wenger, Ph.D.







"I Vanna Fryyyy Skyyyy Hiiiiiiigh! Vroooll to get Vyyy!" -Sega''''s "Daytona USA"

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It''s good to see that you''ve found the desire to learn Gamersez! Now I have a little challenge for you (and any others trying to learn math for game/graphics programming)! When you can answer this question, you should have gained enough understanding of maths to be able to solve most math-related programming problems you will encounter in graphics programming.

My question is: Why is the derivative of a vector NOT a vector ?

For bonus points: What is the derivative of a vector ?

For extra bonus points: Why do we teach students that the derivative of a vector IS a vector ?

Enjoy!

Timkin

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