Study Methods Poll for Upper Math.

[jmjlt88]

Browsing through the archives here, I have seen many, "how do you study for upper math?" threads. This is not so much one of those thread, but rather a poll question.

When approaching a new subject in mathematics, do you...

(a) Master the chapter first (this includes develop a deep understanding of the theorems, trying to prove them yourself before glancing at the proof, constructing examples and counterexamples, explaining concepts very carefully in your own words, etc, etc), then attempt the exercises,

or

(b) Try to work the chapter and the exercises in tandem.



I have notice that I used both. Sometimes I will learn the first defintion/propostion of a chapter, then find some appropiate exercises. But, I feel that I have had less fustration using (a) since I have been acquinted with the material for longer.

I would enjoy to read your views. Thanks!

 

[TonyG]

I believe in taking a systematic and thorough approach to studying any subject, including mathematics. Therefore, my recommendation would be to follow option (a) and master the chapter first before attempting the exercises. This approach allows for a deeper understanding of the concepts and theorems, which is crucial for success in mathematics.

I understand the appeal of working through the exercises while learning the material, as it can provide immediate practice and reinforcement. However, I have found that without a solid understanding of the underlying concepts, it can lead to frustration and potentially incorrect solutions.

In my experience, taking the time to fully comprehend the material before attempting the exercises has not only helped me to successfully complete the exercises, but also to retain the information for future use. This includes developing a deep understanding of the theorems, attempting to prove them on my own, and constructing examples and counterexamples to solidify my understanding.

Of course, every individual may have a different learning style and may find success with a different approach. However, as a scientist, I believe in the importance of mastering the fundamentals before moving on to more complex problems.