If you were to start over your mathematical education

[murmillo]

I found a list of books on Amazon from a graduate student in math, who made a list of books he/she would recommend to undergraduates considering graduate school in math. They are books that he/she would ideally have learned from in undergrad classes, or that would have benefited him/her greatly during undergrad years. Some of the books on the list were Artin's Algebra and Differential Topology by Pollack. So, I was wondering, do any math graduate students in this forum have books in mind that they found very good to learn from?

 

[jgm340]

Hmm... can you link to that list?

I'm an undergraduate myself.

I'm currently reading Andrew Wallace's "Introduction to Algebraic Topology", and I like the style very much. I can't say I have enough perspective to recommend it over any other book, however.

 

[JCVD]

For a first course in the following topics, I especially liked the following books:
"Complex Variables and Applications" by Brown and Churchill
"Elementary Number Theory and its Applications" by Rosen
"Contemporary Abstract Algebra" by Gallian
"Fourier Series and Boundary Value Problems" by Brown and Churchill

 

[murmillo]

jgm340: Here is the link to the list:

 

[rezeew]

I would highly recommend starting over your mathematical education by incorporating a diverse range of resources, including books such as those recommended by the graduate student in math. The books on the list, such as Artin's Algebra and Differential Topology by Pollack, are well-known and respected in the field of mathematics and would provide a strong foundation for further studies in graduate school.

In addition to these books, I would also suggest exploring other resources such as online courses, lectures, and hands-on practice problems. It is important to have a well-rounded understanding of mathematical concepts and techniques, and utilizing various resources can help to achieve this.

Furthermore, I would encourage seeking out guidance and mentorship from experienced mathematicians, whether it be through discussions, seminars, or research opportunities. Learning from those who have already gone through the educational journey can be invaluable in developing a deeper understanding of the subject.

Overall, my advice would be to approach mathematical education with an open mind and a willingness to explore various resources and seek guidance from others. This will not only enhance your understanding of the subject, but also help to develop critical thinking and problem-solving skills that are essential for success in graduate school and in the field of mathematics.