EPTA note on my car, and reviewing mathematics - Page 2
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targ
Malaysia445 Posts
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BirdKiller
United States428 Posts
Too many students simply read the concept portion and examples given, thinking so long as they understand the concept, then they've mastered the concept, skipping the problems at the end of the chapter. Absolutely stupid. Once you've done some problems on your own and have a good grasp of the concept you've learned, you're then better off using computational software like Mathematica, Mathlab, and MAPLE to solve such problems in the future. As for looking into references with more rigor, specifically analysis as a more rigorous form of calculus, I would caution you that while you'll be more challenged and have more solid foundation, such could be excessive if your goal is to simply learn and be proficient enough to apply calculus/geometry/algebra to other things that don't require such rigor and critical analysis. It's like a C++ programmer trying to understand the electrical circuits of the CPU in the hopes that he or she will program better in C++. *Be extremely careful of selecting an algebra book meant for college. The two standard algebra subjects (linear and abstract) in college is much different from the standard algebra in high school | ||
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SayfT
Australia298 Posts
"Right, here is a proof, this is how its done make sure you learn it because it will be examinable" and that is it, no how it was created nor why  . So I have decide to familiarise myself with logic, set theory and proofs using this book http://www.amazon.com/How-Prove-Structured-Daniel-Velleman/dp/0521675995 . I highly recommend this piece of knowledge giving contraption, it actually explains why, how and when to use particular proof techniques and starts off with introducing basic logic and set theory.I am not sure if this particular topic is of interest to you (perhaps you already know how to proof stuff very well) but if this is something of interest for you then I highly recommend buying it (note: for Australian people, buy it online if you can since this book costs upwards of $200+ at Dymmocks/Kinokunya!!! blasphemy!) | ||
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Lysenko
Iceland2128 Posts
On January 14 2013 16:12 targ wrote: Is partial fraction decomposition that technique where they split an integral of a fraction with some function as the denominator into two or more fractions with easier functions as the denominators? Partial fraction decomposition is taking the ratio of two polynomials and factoring either the numerator or denominator to write the expression with lower-order polynomials. It's a basic algebraic technique, though it can be useful as a step in integration. Regarding the comment about Spivak that it's not that great for learning computation, I suspect my memory of the techniques will come back pretty fast, and a more rigorous approach might be just what I need to push myself beyond where I was before in understanding. | ||
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synapse
China13814 Posts
On January 14 2013 15:54 Carbonyl wrote: i've taken 3 semesters and it never came up from what i remember. so i think you're good. It comes in handy for some integrations and laplace transforms mostly, iirc. | ||
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Lysenko
Iceland2128 Posts
On January 14 2013 16:16 BirdKiller wrote: Just about any widely used calculus/algebra*/geometry books for high school and freshmen college students are enough for you to understand the concept. Whether or not you can master or at least be competent in the subject depends on whether or not you're willing to solve problems and exercises on your own. It's this part that's the most frustrating and time consuming yet equally rewarding as well. Excellent point, and yes, I'm mainly looking to have problems to solve. Too many students simply read the concept portion and examples given, thinking so long as they understand the concept, then they've mastered the concept, skipping the problems at the end of the chapter. Absolutely stupid. I don't have a lot of sympathy for their point of view, myself.  As for looking into references with more rigor, specifically analysis as a more rigorous form of calculus, I would caution you that while you'll be more challenged and have more solid foundation, such could be excessive if your goal is to simply learn and be proficient enough to apply calculus/geometry/algebra to other things that don't require such rigor and critical analysis. It's like a C++ programmer trying to understand the electrical circuits of the CPU in the hopes that he or she will program better in C++. I think it's safe to say that my goal is simply to go back through the material that I learned in college and strive for a better understanding than I had the first time. As I was coming up on graduation, I achieved about a 60th percentile on the physics GRE. This tells me that I was doing a little better than average for physics majors serious about graduate study, but it also highlights that I had weak areas and I'm interested in trying to get back into those in more depth. | ||
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Ktk
Korea (South)753 Posts
On January 14 2013 14:07 UniversalSnip wrote: about to head into calculus, I haven't got a clue what partial fraction decomposition is D: was the same, no worries. I actually first learned about partial fraction decomp in calc ii, so far it's not a big deal for undergrad math requirements for engineering majors :/ | ||
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hypercube
Hungary2735 Posts
When I see something that I don't understand, but feel like I should, I review that exact technique. Then I try to think if there are some obvious related ideas I might want to go over. After I'm finished I make a mental note to go over these ideas again in a few days (spaced repetition). Review should mean writing out the material without using a reference. For example I might see something like sin(a/2) = +-sqrt((1-cosa)/2) I realize that I didn't remember this, so I do a google search for trig identities, and find that it comes from the identity cos2x = cos^2x-sin^2x = 1 - 2sin^2x. Substituting a/2 = x gives the first formula. This is nice, but I'm sure I'll forget it in a week, if not faster. So the plan is to learn the half-angle formulas, addition and difference formulas for sine and cosine (I actually still remember these so no extra work), double angle formulas for cosine (know this too) and the fact that they can be rewritten using the pythagorean theorem. So I have 4 formulas to learn (sin(a/2), cos(a/2), cos2x with RHS written only in terms of cos^2x or only in terms of sin^2x) and a few pieces of connections. A review should look something like writing: sin(a/2)= cos(a/2)= cos2x= (something with cos^2x) cos2x= (something with sin^2x) and finally the derivation of the first two lines from the last 2. This should take less than 3 minutes if you actually know what you're doing. Note that I'm writing the formula before the derivation because I want to remember it without having to derive it every time. BTW, if there's any misunderstanding, like where does the +- come from or what happens if the value under the square root is negative (it never is, do you see why?), those can be included in the review cycle too. | ||
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keioh
France1099 Posts
On January 14 2013 03:02 BrTarolg wrote: D: Anyone who loves those parts of maths is a freak (I'm such a freak T_T) No you're not. Perfectly normal to love what is beautiful to you eyes. First quoted post here summarized what is imo the most beautiful and interesting maths. Edit : OP you know that MIT has a moutain of free videos of lecture from 1st year to 3rd year in maths ? You should give it a shot. For litterature sadly the books we use in France are often unknown outside, as much as I don't know who the hell is Spivak nor what you do in calc i, calc ii, etc. A book of Rudin 'principle of mathematic analysis" is quite famous on basic real anlysis now that I think of it. I don't know what you're searching for in Algebra, but if you're giving me more informations I can search in my bibliography. | ||
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