Google Answers Logo
View Question
Q: Revamping university level mathematics knowledge. ( No Answer,   2 Comments )
Subject: Revamping university level mathematics knowledge.
Category: Science > Math
Asked by: knowledgeseeker7-ga
List Price: $55.00
Posted: 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.


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.
There is no answer at this time.

Subject: 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

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
Subject: 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

Asimov also has books on general science and math

 For more advanced, for calculus, and instant feedback I would suggest
  interactive software, such as

good luck


Important Disclaimer: Answers and comments provided on Google Answers are general information, and are not intended to substitute for informed professional medical, psychiatric, psychological, tax, legal, investment, accounting, or other professional advice. Google does not endorse, and expressly disclaims liability for any product, manufacturer, distributor, service or service provider mentioned or any opinion expressed in answers or comments. Please read carefully the Google Answers Terms of Service.

If you feel that you have found inappropriate content, please let us know by emailing us at with the question ID listed above. Thank you.
Search Google Answers for
Google Answers  

Google Home - Answers FAQ - Terms of Service - Privacy Policy