Revamping university level mathematics knowledge.
Category: Science > Math
Asked by: knowledgeseeker7-ga
List Price: $55.00
22 Jan 2005 14:04 PST
Expires: 21 Feb 2005 14:04 PST
Question ID: 461654
I am a college student with an excellent GPA, but: I struggle with math intensive courses (Differential Equations, Physics, etc.) Not because the new material is difficult to comprehend, but becuase my math background is spotty - I spend a lot of time staring at problems trying to remember how to solve them. I just dont know how (exactly) it's spotty. I need a good way to pinpoint my exact problem areas, in mathematics, so that I can efficiently improve my ability and technique in this area. I have already asked math professors, counselors, etc; the answers I get are not answers at all: "keep working hard and practice." I need to know *where* to focus my efforts. My question, in brief, is: what systems exist (books, computer programs, learning centers) that I can use to maximize my mathematics ability without doing what I currently do (spending 8 hours a day on the weekends practicing integrations.) Any good system should have at least the following: an excellent (and fast!) feedback mechanism so that I can quickly notice (and pinpoint) what I'm doing wrong, and: a method for comparing personal relative skill levels before and after using the said system. Links to said programs, or books or whatever would be great. Phone numbers will do as well. But I can't use something like a full-time 8 week course (unless it's at night), because I need to attend my college classes concurrently. Thanks. P.S. This is a very important topic for me. I'm paying my own way through school, so I've done the best I could on the price - but I will also tip well for an excellent answer. For purposes of answering the question with regard to education programs, I live in Northern California.
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Re: Revamping university level mathematics knowledge.
From: mathtalk-ga on 22 Jan 2005 17:03 PST
Integration is a challenging skill to master. There are a number of "techniques" to learn, and the ability to recognize "what is useful when" is part of the learning curve. The good news is that really math doesn't get any tougher than the integration and solution of differential equations (which is an extension or generalization of integration). [At least it will seem like good news _after_ you get through this.] You have the gist of a great idea in "an excellent (and fast!) feedback mechanism so that I can quickly notice (and pinpoint) what I'm doing wrong." You have to be that mechanism. Each time you do a problem, check your answer. For the case of doing indefinite integration, the check is usually to take the derivative and make sure you get back to where you started. If you don't, there's a mistake someplace. Track it down and reflect carefully on how you came to make that mistake, and how closely it resembles past mistakes. This is just one variation on the broad theme of taking your answer and plugging it back in to make sure it's right. The solution of an initial value problem in differential equations, for example, must satisfy not only the differential equation but the initial conditions as well. Practice at verification is time well spent. You'll find that too is a skill that improves with repetition, and the effort will motivate you to get things right the first time around. Success in mathematics is a matter of making lots of mistakes and remembering their names (yes, give them humorous names to aid in recall). Make a mental catalog of your mistakes as you discover them. Consider for yourself how to most efficiently guard against such mistakes in the future. For example, you make discover (after checking a few dozen worked exercises), that you have trouble remembering exactly where the minus sign goes in the integration by parts technique (I know I do!), and decide how you plan to keep that source of error under control. (I go off to the margin of the page and rederive the integration of parts rule from the rule for derivative of a product, but you may have a different idea!) A tutor is a possibility, or perhaps a study group connected to the classes you are taking. If you invest in a tutor, it should perhaps be someone not much futher along in mathematics than yourself, but at any rate someone who can relate to your degree of confusion with knowledgeable suggestions about how to find a clear path through the woods when you see the same material at exam time. regards, mathtalk-ga
Re: road to mathematics knowledge.
From: hedgie-ga on 23 Jan 2005 16:03 PST
I would recommended as one of the remedies supplementary reading. Look at the bottom of http://answers.google.com/answers/threadview?id=447747 Asimov also has books on general science and math http://www.asimovonline.com/oldsite/asimov_catalogue.html For more advanced, for calculus, and instant feedback I would suggest interactive software, such as http://www.hut.fi/cc/applications/math.html good luck Hedgie
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