Am I Reading Math Textbooks Efficiently?

[bacte2013]

Dear Physics Forum friends,

I am an undergraduate at US actively pursuing mathematics and microbiology. Recently, I started to evaluate my methodology of reading books in the mathematics, which raised me some concerns and worry that I want to share with you, and seek advice from you.

Whenever reading math books, I tend to focus more on the concepts presented in the books rather than their corresponding problem set. The way I am reading math book is that I always try to translate the understanding in my own words, doubt everything in the book and come up with reasons to disprove my doubt, try to prove theorems and lemmas by myself without looking any additional source, try to come up with counterexamples, and come up with my own ideas and questions. Also I enjoy formulating my own questions and try to solve them.

The main problem is that I am able to devote enough time for problem sets in each corresponding chapter in the book I am reading. For most of time, I had to skip 40% of the problems since I spent majority of my time on the expositions. Also, my other commitments like undergraduate research and club officials take some of my time too.

My main question is that Is it okay to spend more time on the expositions of the book rather than corresponding problem set? Is it okay to not solve every problem in the book? Should I not try to formulate my own questions and just focus on problem sets? Sometimes, questions I formulated while reading are strikingly similar to problems in the book, but not always.

Do you also take extensive notes per textbook? I used to do so, which ended up consuming a lot of time. I started to take notes inside the book (started when I read Rudin and Dugundji). Recently, I decided to use LaTeX to write notes I took to supplement the book (lectures, my own ideas while reading, etc.).

I apologize for this long post, and I look forward to hear back from you.

 

[Dr. Courtney]

It is more important to be able to work all the problems assigned by the instructor rather than all the problems in the chapter that are not assigned.

I would recommend spending 45-60 minutes reading the book for each hour the class meets and 90-135 minutes working on the homework problems.

I usually focused my note taking on the lecture rather than on the book, but if there are important definitions and theorems in the book, that would be what you want to write down.

 

[chiro]

Hey bacte2013.

In line with with what Dr. Courtney mentioned above, I would suggest you realize that the assessment and grading of your work will be on what the faculty has set and not so much what the material or field encapsulates in terms of knowledge and expectations for answering questions outside of what is assessed.

It's basically a game and they are not testing all material - just what they deem relevant.

You can extend your learning later on either in your own time or in later endeavors but for university and college, it's about meeting assessment criteria and not so much being able to comprehend everything set out in a textbook or a given field.

 

[Dr. Courtney]

It's basically a game and they are not testing all material - just what they deem relevant.

It's not a game, it's just that the learning objectives approved by the department and the accrediting agencies may not have a 1:1 correspondence with the book.

The book is one tool among many that faculty use to move students toward learning objectives laid out in the syllabus and other course documents.

 

[chiro]

It's a game where you maximize your "points" relative to what rules they set.

You may think a game refers to something like monopoly or something different but the truth is that they set the rules and students who want to maximize marks do so by understanding the rules, so called "winning" conditions and use their energies to maximize their "points" (i.e. grade).

The nature of a game doesn't make it less serious and I think you are making an interpretation problem based on this.

Also - they can't test all material and the game involves things that they are testing.

 

[IGU]

It's a game where you maximize your "points" relative to what rules they set.

It's your life. You are investing time and money. You should be looking to come out of the experience with what you want. If you let others define what you want (e.g. good grades), then you have already lost.

Time to level up. That stuff is for middle school.

 

[chiro]

The grading system is just that - a system.

I think people have the idea that a game has certain motivational constraints - it doesn't have to.

People do things for many reasons and I acknowledge that - but the fact is that university is a point based system and often even has rank in some form.

It's like a sport - you have rules and play the game to score points. Winning is not the same as a normal sport but it has the same dynamics.

Unfortunately many people have to be motivated by this system of points and it just reflects something deeper psychologically about this planet.