Student Advice: Comments on Perseverance


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 expect to 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?

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Author: mathtuition88

2 thoughts on “Student Advice: Comments on Perseverance”

  1. 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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