I have taken up through ODE and multi-variable calc but by algebra is still pretty bad. Calc came easy to me, the hardest part was the algebra. Now that I am getting into stuff where I can actually use algebra it seems as though I have forgotten alot of it. The part I need help with is word problems basically. I can think though most of them but they take time. I want to be able to read a problem and think of it in terms of an equation almost instantly. Any ideas on how to do this, other than just picking up an algebra book and reading it?
I want to beef up my basic algebra
- Thread starter TheoPetro
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PhatoseAlpha
Platinum Member
- Apr 10, 2005
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A noble goal. Turning a real world problem into the equations that you need to solve it is a vital skill. I recommend:
1. Read through the entire question before writing anything down.
2. Determine what, exactly, you're being asked to produce. Make a note of the units it's expected to be in.
3. Make a pass through the question again to determine what quantities you're being given.
4. Determine what relationships exist between the given quantities and what you have to produce.
5. Calculate.
6. Double check, making sure your answer makes sense, and especially that it's in the correct units.
1. Read through the entire question before writing anything down.
2. Determine what, exactly, you're being asked to produce. Make a note of the units it's expected to be in.
3. Make a pass through the question again to determine what quantities you're being given.
4. Determine what relationships exist between the given quantities and what you have to produce.
5. Calculate.
6. Double check, making sure your answer makes sense, and especially that it's in the correct units.
Practice. Like PA said, the best thing to do until you get the hang of it (and probably even afterwards) is to find a systematic solution procedure. His is very good, but perhaps a more basic form that might be easier to remember would be:
1. Write down the 'knowns'
2. Write down the 'unknowns' (i.e. what you're actually trying to find)
3. Try to relate the knowns to the unknowns using equations
After you have practiced sufficiently, #3 will come naturally for problems in that area of study, which I think is what you said you wanted. Practice, practice, practice. This is the only thing that worked for me (but, then, I've always been a little on the slow side
). Solving lots of simple problems is a great way to get started, but don't waste your time doing the same problems over and over again. Make sure you add in some complications so that you're really getting the concepts.
1. Write down the 'knowns'
2. Write down the 'unknowns' (i.e. what you're actually trying to find)
3. Try to relate the knowns to the unknowns using equations
After you have practiced sufficiently, #3 will come naturally for problems in that area of study, which I think is what you said you wanted. Practice, practice, practice. This is the only thing that worked for me (but, then, I've always been a little on the slow side
). Solving lots of simple problems is a great way to get started, but don't waste your time doing the same problems over and over again. Make sure you add in some complications so that you're really getting the concepts.To solve a problem you need to understand the problem and what it is asking. Translating text to mathematical formulas can be very beneficial. Instead of trying to think through the problem I would be able to write down a few formulas and solve it in a fraction of the time.
Mathworld is an awesome site. I use it extensively. Half the time because, even after 40 semesters of math, I still run in to lots of things I've never heard of. The other half because it has solutions to complicated problems that I know how to solve, but it's very time consuming to solve by hand. I don't think I've ever found a single thing wrong on the site either, which is very reassuring.
While I've never noticed anything wrong per se, the terms "curious determinant equation" on this page always annoyed me. The determinant equation isn't at all curious, it generalizes for other orthogonal polynomials, and I had to figure that out for a homework assignment.
But other than that, mathworld wins at life... or math at least
The skill you are referring to, from elementary algebra, is a very important foundation for mathematical learning. Sorry, but I have to recommend "picking up an algebra book" and doing exercises.
After you feel comfortable, try doing some problems from:
http://www.kalva.demon.co.uk/
Meh... I never much cared for the Chebyshev polynomials... I like Legendre the best! It looks like the author is human after all - another math professor bored with (or way too excited by) the small details of math.Originally posted by: eLiu
While I've never noticed anything wrong per se, the terms "curious determinant equation" on this page always annoyed me. The determinant equation isn't at all curious, it generalizes for other orthogonal polynomials, and I had to figure that out for a homework assignment.
But other than that, mathworld wins at life... or math at least
MagnusTheBrewer
IN MEMORIAM
- Jun 19, 2004
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Everyone learns differently. I reccomend going to the library and finding a Algebra book that teaches in a style best suited for you. The best way to learn math and integrate the concepts is to practice, practice practice.
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