Source: http://www.math.union.edu/~dpvc/courses/advice/perseverance.html

# Comments on Perseverance:

One source of confusion for students when they reach college and begin to do college-level mathematics is this: in high school, it is usually pretty apparent what formula or technique needs to be applied, as much of the material in high school is computational or procedural. In college, however, mathematics becomes more conceptual, and it is much harder to know what to do when you first start a problem. As a consequence of this, many students give up on a problem too early.

If you don’t immediately know how to attack a problem, this doesn’t mean you are stupid,

If you already know how to do it, it’s not really a problem.

or that you don’t understand what’s going on; that’s just how real problems work. After all, if you already know how to do it, it’s not really a problem, is it? You should

expectto be confused at first. There’s no way you can know ahead of time how to solve every problem that you will face in life. You’re only hope, and therefore your goal as a student, is to get experience with working through hard problems on your own. That way, you will continue to be able to do so once you leave college.One of the first steps in this is to realize that not knowing how, and the frustration that accompanies that, is part of the process. Then you have to start to figure out the questions that you can ask to help you to break down the problem, so that you can figure out how it really works. What’s really important in it? What is the central concept? What roles do the definitions play? How is this related to other things I know?

Continue reading at http://www.math.union.edu/~dpvc/courses/advice/perseverance.html

Yes. Do not be discouraged when transitioning from high-school math to university math, notably the abstract algebra, less so in Analysis (except the epsilon-delta).

If still at loss, go back to basic definitions and theorems, most likely you have been ‘bluffed’ by the arcane math language. Try to relate it to more concrete concept to visualize it. Also helpful is to think of special cases.

Example: Instead of reading the Ring’s “Ideal” formal definition, think of an analogy in plain language:

“something inside x anything outside still comes back inside”.

Concrete example for Ideal is Even number. Even x any number is still Even.

Special case: 0, 2

While trying to remember the Ring axioms, think of Integer as concrete Ring example. All operations in Z is the Ring’s operations.

It is good for you to collect a list of concrete example for each math object (group, ring, field, vector space, algebras, etc).

Same applies to internalize the definition of eigenvector. And eigenvalue of a matrix in a linear transformation. A matrix does some operation (eg. Rotation) to the vectors, among which one particular vector (eigenvector) will stay ‘unchanged’ except being stretched by a scalar (eigenvalue).

A good college math professor should be able to tell you the above learning techniques.

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Reblogged this on Math Online Tom Circle.

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