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

In summary, the student has recently decided to become a math major and has had success in previous math classes but is struggling with more challenging ones. They are seeking advice on good study habits for math and have received helpful tips such as thoroughly understanding theorems and definitions, taking time to understand proofs and verifying steps, and actively seeking out examples to solidify understanding.
  • #1
squelchy451
25
0
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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  • #2
squelchy451 said:
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! :smile:
 

1. What are some effective study strategies for a math major?

Effective study strategies for a math major include creating a study schedule, practicing regularly, seeking help from professors or tutors, working on practice problems, and reviewing lecture notes and textbooks.

2. How can I improve my math study skills?

Some ways to improve math study skills include breaking down complex problems into smaller parts, using visual aids and diagrams, and actively engaging with the material by asking questions and explaining concepts to others.

3. What resources are available to help me with my math studies?

Most universities have tutoring centers or study groups specifically for math students. You can also seek help from your professors during office hours or join a study group with classmates. Online resources, such as Khan Academy or YouTube tutorials, can also be helpful.

4. How can I stay motivated while studying for my math major?

Staying motivated can be challenging, but setting achievable goals, rewarding yourself for progress, and finding a study group or study partner can help keep you motivated. It can also be helpful to remind yourself of your long-term goals and the importance of mastering math skills for your future career.

5. What steps can I take to prevent burnout while studying for my math major?

Burnout is a common issue for students, especially in demanding majors like math. To prevent burnout, make sure to take breaks and prioritize self-care. Additionally, try to balance your workload by breaking up study sessions and not leaving everything until the last minute. Remember to also ask for help when needed and not be too hard on yourself for mistakes.

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