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Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion


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January 6th, 2008, 08:11 PM   #1
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Where should I start?

Hi all. First visit and post! I'm looking for direction more than anything. Here's my story...

I'm a programmer. Specifically, I develop web applications (in Ruby, if you were you curious).

All the apps I've worked on have been very light on any "real" math. That is, math beyond basic accounting -- prices, taxes, discounts, etc.

I recently got into game programming and hit a brick wall. Hard. I realized I couldn't do very much at all without running into math. Rotation, acceleration, collision detection, etc. All math.

I asked a programmer I respect how much math he suggested one learn to do roughly what he does. He suggested I learn algebra and geometry really well, as those are the primary skills he uses when writing games.

So I picked up a geometry book (Geometry, Seeing, Doing, Understanding by Harold R. Jacobs). Lo' and behold, the first chapter beats me over the head with this little bit:

Quote:
If the map is accurately drawn [12 cm wide from A to K] and the street from A to K is 6 miles long, how many miles is it from A to F?
I had no idea how to answer the question. I can find the conversion between 1 cm and 1 mile, but that's not what I'm being asked.

So my question is this... if a problem from the first chapter of a geometry gives me problems, where should I start?
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January 7th, 2008, 06:55 PM   #2
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A to K is how many letters? A to F is how many letters? What's the ratio?

Does that help?
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January 7th, 2008, 08:19 PM   #3
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Quote:
Originally Posted by cknapp
A to K is how many letters? A to F is how many letters? What's the ratio?

Does that help?
Hmm, not so much.

AK is just a line segment. The distance between each point between A and K is different, so the number of points between A and K won't help me.

I did some more research last night and think I shall begin by re-learning how to work with fractions and decimals, and then I'll move onto pre-algebra. From there I imagine I'll head into algebra and finally make my way back to geometry.

Are there any books anyone suggests for pre-algebra?
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January 9th, 2008, 03:33 PM   #4
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Quote:
Originally Posted by rabbit
AK is just a line segment. The distance between each point between A and K is different, . . .
Is it? The book is playing a game with you. The phrase "If the map is accurately drawn" is ambiguous. Does it mean "on the assumption that the map is already accurate, . . ." or does it mean "if the map were redrawn so that the points (or lines) A, B, . . . , J, K are regularly spaced, . . ."? The second interpretation would let you deduce easily that F is halfway from A to K (for the redrawn map), which leads directly to an answer. The information given about the map's scale isn't needed to obtain an answer; it's just a red herring put in to distract you.

I suspect you do know how to add and subtract numbers. You probably know how to multiply and divide them. Even if you do, though, that's not enough. It's no fun having to work out such things, so you have to work through the "no fun" stuff by doing loads of simple arithmetic until most of the answers are automatic, just as understanding this sentence is automatic; you don't have to "work out" how the words combine to give a particular meaning because you get the meaning almost instantly through familiarity with English. You can use a calculator to verify your answers; don't use it instead of working out answers for yourself. Are you ready and willing to give it a go? If not , why not?
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January 9th, 2008, 04:06 PM   #5
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Quote:
Originally Posted by skipjack
Is it? The book is playing a game with you. The phrase "If the map is accurately drawn" is ambiguous. Does it mean "on the assumption that the map is already accurate, . . ." or does it mean "if the map were redrawn so that the points (or lines) A, B, . . . , J, K are regularly spaced, . . ."? The second interpretation would let you deduce easily that F is halfway from A to K (for the redrawn map), which leads directly to an answer. The information given about the map's scale isn't needed to obtain an answer; it's just a red herring put in to distract you.
I didn't think I was being distracted by the wording of the question. I believe the question, written mathematically, is a basic algebra equation. A comparison of two ratios with different rates. Something similar to:



Is that accurate?

Quote:
Originally Posted by skipjack
I suspect you do know how to add and subtract numbers. You probably know how to multiply and divide them. Even if you do, though, that's not enough. It's no fun having to work out such things, so you have to work through the "no fun" stuff by doing loads of simple arithmetic until most of the answers are automatic, just as understanding this sentence is automatic; you don't have to "work out" how the words combine to give a particular meaning because you get the meaning almost instantly through familiarity with English. You can use a calculator to verify your answers; don't use it instead of working out answers for yourself. Are you ready and willing to give it a go? If not , why not?
I'm willing to do anything I need to do to become efficient at math. However, I don't think simple arithmetic drills are what I need.

Also, I understand that 6 and 12 are easy numbers to deal with. So for the sake of my question, let's assume 12cm represents 13 miles -- something not evenly divisible by 2.
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January 9th, 2008, 07:10 PM   #6
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I stopped by the library earlier and picked up a medium-sized tome: Prealgebra, Third Edition by K. Elayn Martin-Gay.

Top-level table of contents are...

1. Whole numbers and introduction to algebra
2. Integers
3. Solving equations and problem solving
4. Fractions
5. Decimals
6. Ratio and proportion
7. Percent
8. Graphic and introduction to statistics
9. Geometry and measurement
10. Polynomials

The entire book is about 800 pages, so each topic appears to be covered fairly thoroughly.

Skipjack will be happy to know that each section includes upwards of 50 sample problems -- repetition, repetition, repetition. Indeed.
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January 15th, 2008, 06:38 PM   #7
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The wording "something similar" is too vague for me to be able to comment as to whether what you gave is "accurate". The scaling information is irrelevant, so changing it makes no significant difference.

Arithmetic "drills" are more than just learning dull facts; you become used to the methods used and to handling numbers accurately. Hence drawing scale diagrams reasonably accurately becomes easier, and there are many other incidental benefits.
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