# Decided on math major but I don't have good study skills

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## Main Question or Discussion Point

Hi

I've recently decided to become a math major, as it's the subject that I've enjoyed the most and had the most exposure to during high school.

During high school, the AP Calc classes and a Calc III course I took at a local CC came to me quite naturally. I just followed along to the lectures, did the homework problems, reviewed my notes before tests and got an A in those classes.

I took linear algebra last semester and am taking topology and differential equations this semester. These classes are more challenging and I can't just read the chapters once or twice, write down formulas, and get started on the problems.

What are some good study habits that you use when you study math?

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Hi

I've recently decided to become a math major, as it's the subject that I've enjoyed the most and had the most exposure to during high school.

During high school, the AP Calc classes and a Calc III course I took at a local CC came to me quite naturally. I just followed along to the lectures, did the homework problems, reviewed my notes before tests and got an A in those classes.

I took linear algebra last semester and am taking topology and differential equations this semester. These classes are more challenging and I can't just read the chapters once or twice, write down formulas, and get started on the problems.

What are some good study habits that you use when you study math?
Hi squelchy,

The "message to the student" in my abstract algebra (Hungerford) text has some great advice about how to study abstract mathematics. I'll quote/paraphrase it here:

Read the text with pencil and paper in hand before looking at the exercises. When you read the statement of a theorem, be sure you know the meaning of all the terms in the statement of the theorem. For example, if it says "every finite integral domain is a field," review the definitions of "integral domain" and "field" -- if necessary, look up the definitions online or in another text.

Once you understand what the theorem claims is true, then turn to the proof. Remember, there is a big difference between understanding a proof in the text and constructing one yourself. ... Begin by skimming through the proof to get a general idea of its outline before worrying about the details in each step. It's easier to understand an argument if you know approximately where it's headed. Then go back to the beginning of the proof and read it carefully, line by line. If it says "such-and-such is true by theorem 5.18," go back and check to see just what Theorem 5.18 says and make sure you understand why it applies here. When you get stuck, take that part on faith and finish the proof. If you still get stuck after that, ask a professor.
There is another quote from Sheldon Axler. Here's an excerpt from his well-regarded linear algebra text:

You cannot expect to read mathematics the way you read a novel. If you zip through a page in less than an hour, you are probably going too fast. When you encounter the phrase “as you should verify”, you should indeed do the verification, which will usually require some writing on your part. When steps are left out, you need to supply the missing pieces. You should ponder and internalize each definition. For each theorem, you should seek examples to show why each hypothesis is necessary.
These guidelines have been very effective for me. Best of luck to you in your studies!