Temptation to read many books on same topics

[bacte2013]

Dear Physics Forum advisers,

I am a college sophomore in US with a major in mathematics and an aspiring mathematician in the computational complexity theory. I have been reading some math books on different topics, such as analysis and abstract algebra. As a former microbiology major, it is very surprising that the mathematics has more books for different topics than biological science. Currently, I am studying Apostol-Mathematical Analysis and Pugh for the introductory analysis, Artin and Hoffman/Kunze for the algebra, and Halmos for the set theory. I also have been checking out various real analysis textbooks to get an exposure to the basics of measure theory and approximation for my upcoming math undergraduate research in the computational theory and wireless communications. I noticed that there are near-countless number of books dedicated for the introductory analysis and abstract algebra, which causes me a temptation to read all of them and also an anxiety that I will miss something from other books if I dedicated myself to read the books I mentioned above. How should I overcome such temptation and anxiety? After you finish reading a book on a certain mathematical topic (let's say the real analysis), then do you proceed to another book on the same level as your previous book to get a different approach, or do you proceed to an advanced book with more vigorous treatment of the subject?

 

[DEvens]

There is probably more math than any normal human can possibly learn. Life is finite.

Pick the subjects you are interested in that will help you move forward. If you find that you have an insufficient understanding of a topic to do the work you want, then get a text at the level that you can understand but that will stretch you. Don't read a bunch of texts at the same level. Two or three at a given level should be sufficient.

There is an old saying. Do you want ten years experience? Or do you want one year experience ten times?

 

[ewp]

I usually try to do the following:
1: look up two or three books on the subject I'm interested in, usually I can get good recommendations from syllabi for courses covering the same subject.

2: get the two or three books from the library, look through them and their tables of contents, and pick the one that seems to cover the subject in a way I find appealing or readily comprehensible.

3: use that book and plow through until I encounter a roadblock or something I don't understand at which time I consult one of the others. Another important point is to solve the problems.

As a biophysics student, I understand the desire to be comprehensive but its really more important with math to understand the concepts and work problems. On a given subject there's only so much that can be said. Math is math. Also, depending on which direction you want to go, half of the things in a textbook will end up being useless for you unless you want to become a mathematician so there's no need for the sort of exhaustive reading like there is in biology.

 

[atyy]

There is nothing wrong with reading many books, In fact, my statistical mechanics teacher recommended we read many books to get many different viewpoints. There are two problems with reading too much:

1) You only read and don't do problems. This can be solved by doing problems

2) It is expensive to read many books if you have to buy them. This can be solved by going into finance. Kidding. I don't know how to solve it. Access to a good library is the best. Nowadays, for the amateur, many free sources are available on the internet.

 

[MidgetDwarf]

for math. I do 2 books at the same level. Followed by a russian text. Then a higher one after that one and use a second book as a reference.

You have to get into the habit of relying on at least 2 good tex and not rely so much on online videos. The further you go, the less video lectures there are.

 

[bacte2013]

Thank you all for great advice! I decided to stick to a methodology of choosing three books: two for expositions with different approach, and one for the challenging problem sets. There are huge number of books for introductory analysis. Will it be a safe idea to read the sections of Apostol and Courant for additional knowledge when studying the analysis?

Mr. MidgetDwarf, I really do not like the video lectures and online courses as they are not suited for my learning. I learn the best when I teach myself with the books. By the way, I often hear great reviews about Russian texts (I heard that they have very interesting exposition). In fact, I just purchased Rosenlicht and Kolmogorov to learn more about the metric space and get different treatment.