Study Tips and Techniques for Self-Oriented Students

Solution 1:

You question is waay too many questions in one for this website. Just FYI. Anyway...

"... real mathematics is usually done where you understand 2 or 3 pages a day of a text on your first reading of it. Is this true for graduate-level work for the average student??"

• This completely depends on what the reading is and the person's background in it. Learning something completely new? Then yes, its probably true.

"Do students who follow my immersive way of studying tend to have an advantage over those who don't when we get to grad school?"

• Sure, students who know more math upon entering graduate school have an advantage over the students who were content with just the details given in class. It's probably the self-motivation of the student more so than the actual knowledge that puts the student at an advantage to do well.

"In terms of learning theory and doing exercises, how much importance is recommended I place on each?"

• Exercises confirm that theory was actually learned and understood. If you are doing exercises and you find them "easy", well then you probably have a very solid grasp of the theory. Do what feels right. Learn some theory, go back and see if you understand the theory.

"Are there study techniques used in more advanced math courses (like engaging in discourse with peers, focusing more on memorization before attempting to do problem sets, taking notes in a particular way) that are more fruitful than others?"

• I've found that reading the book and taking notes (well) before class and then paying close attention in class is almost always sufficient to understand the material. I've also found that graduate students many times do not keep up with this regime of reading before the class, whether due to workload or general dislike for the material.

In summary, do what feels right, you'll learn a lot if you stay motivated, and enjoy.

Solution 2:

I found benefit in reading two books by Lara Alcock:

How to Study as a Mathematics Major

and

How to Think About Analysis