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getting better in math

ranald

Joined
4/11/08
Messages
10
Points
11
What does an 800 on the math GRE/SAT mean (REALLY mean)?

I scored an 800 on these but feel rather slow quantitatively in many of my endeavors. My thinking is fragmented, non-linear, disorganized, and it generally seems that I solve problems through an inefficient brute force method. It may take me just as much time (too much) to grasp an easy concept as it is to grasp a more difficult one.

Do I just lack mathematical maturity? How can I improve my situation?
 
I don't think you lack mathematical maturity, but the problem is that most quants use a hammer to kill a little bug.

My best advice is to train in doing some brainteasers in math, and always try to find the simplest solution you can.
 
Let me assure you

You are not alone struggling with maths most of us have such fears and issues with the subject.

One thing I would like to emphasise here is that studying mathematics is unlike any other subject and thats not because of you the person but the subject itself. I am no authority on the subject but i know from some reading and experience that mathematics has an internal organic structure where deductive logic and formal rigorous proof play the most vital role. Ofcourse most of us use mathematics as merely a tool for solving practical world problems ranging from simple arithmatics/ algebra to calculus and more advanced areas and that invariably leaves gaps in our understanding of the subject( whose complete understanding is not possible a feat for mortals humans even the best of mathematicians can't explain how and why calculus works).

In other subjects/ sciences inductive reasoning is mostly applied and in my personal view its easier to study a large number of cases study a pattern consistent and genaralise it across a wast array of similar situations. For mathematics one must be equally good at formal mathematical methodolgy and its applications for solving real world problmes and in such like fields of study the best appraoch is hands on practise

I remember the fear I felt of mathematics all my school years while sciences and social subjects were always a piece of cake. Most people are generally better in verbal skills than math acumen and its very important to follow both the direct approach where one exposed themselves to as many varied math problmes as possible and a more foundational fundamental proof/theoretic methodology which polished the concepts regarding how the subject flows from within and finally, its important not to hasten through problems finding multiple solutions and learning how to arrive at better ones takes time and patience.

Am looking forward to hear from you soon so ill be happy if you could give me your email address for I face similar problmes regarding mathematics and perhaps we coluld find a collaborative solution to our math problems.
 
I scored an 800 on these but feel rather slow quantitatively in many of my endeavors. My thinking is fragmented, non-linear, disorganized, and it generally seems that I solve problems through an inefficient brute force method. It may take me just as much time (too much) to grasp an easy concept as it is to grasp a more difficult one.

Do I just lack mathematical maturity? How can I improve my situation?
Click to expand...

There's no one right way to solve a problem. Often the first way of solving a problem is brute force; later on better ideas, alternative approaches, and labor-saving devices come in. The first priority is to solve the problem however you can. Gauss's first proof of quadratic reciprocity was not the most beautiful one -- and he went on to prove it seven other ways (he was looking for ways to generalise quadratic reciprocity to cubic and higher reciprocity laws). His first priority was to prove it at all. Likewise, whenever he had a spare fifteen minutes, he would go through a thousand consecutive numbers and look for the primes. It was "brute force" but it led to his conjecture on the distribution of prime numbers (the prime number theorem), which was proved later by other mathematicians. Don't look down on brute force, as it gets the job done, and it often suggests other ideas. And don't look down on calculation. A mathematician is first and foremost a calculator. Forget the nonsense about rigorous proof and deductive reasoning. The Bourbaki approach to mathematics -- rigorous proof and long chains of abstract reasoning -- got flushed down the toilet a long time ago. Let yourself be guided by the examples of Euler and Gauss.

One book I might recommend is Engel's Problem-Solving Strategies. It's a fun book, published by Springer, and the author has trained Math Olympiad teams for many years.

Another piece of advice is to try to get exposed to different kinds of mathematics and to see the different modes of reasoning employed. Number theory, combinatorics, probability, theory of equations, abstract algebra, classical geometry, ...
 
thanks guys

Thank you for your responses everyone - they've cleared up some anxiety I had surrounding the issue. The notion that patience and practice are of utmost importance has been further solidified thanks to the all of you.
 
math is mostly practice, so i feel like just working out random (competition) math problems might help you gain that analytical thinking ability?
 
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