Preparing for Graduate Studies in Mathematics: Tips and Resources

[Stlgeek]

I will be heading into my 2nd semester of junior year as a mathematics major. I am curious about grad studies and how to prepare or to discover if i am capable of such a rigorous course.

the video below is ment for humor but i believe the advise coould still be solid.

a funny video on youtube, "so you want a phd in mathematics" sorry cannot post links yet due to being new.

I have a bit more education than the student in the video, however that does not mean I know more about what is in-store for me.

any reading material on a larger view of mathematics as a whole and/or how to ensure a solid foundation of mathematics would be amazing. Besides working problems of my mathematical level till I am blue in the face, any other suggestions or helpful texts would be great.

I do not have the education to quite decide on a field yet.

Thank You.

 

[theorem4.5.9]

I have a couple reading recommendations. Though they really are suggestions for pure mathematics, as that's what I'm more versed in.

All the mathematics you missed but need for graduate school - Garrity

This book is a very well written overview of undergraduate mathematics, pretty much just what you are asking. The most important aspect of it is the reference list at the end of every chapter. Whatever pieces you find interesting, you should follow these sources. I think the strongest section of the book is the chapters building up to the general stokes theorem, which adds to my bias of the book (I like analysis and geometry). This book is also great in helping you find your interests.The Princeton Companion to Mathematics - edited by timothy gowers

This is one of my favorite books I own. It's like wikipedia for math, but better written. I think it's best suited toward serious undergraduates in math who want to see some "real" mathematics. I can spend all day jumping between topics (plenty of which are written by world class experts - plenty of abel winners, fields medalists etc). There is a little applied mathematics in it, I know this only because I remember the section on wavelettes by Ingrid Daubechies. This book won't prepare you for the rigor of graduate school, but it will definitely help in broadening you scope.And the last book recommendation I have is to get the princeton review's book on the math subject GRE. Actually, I hated this book and the GRE in general, but it's mildly important for getting into a good grad school. I'm going to skip my rant about the GRE and say *most* successful Ph.D. applicants do well on the GRE (80 percentile), and to get there you must start early, give yourself at least a year of continuous work (a few times of week). Building speed and familiarity is what the GRE tests (not traits particularly useful in graduate school).

To sum up: The first two books are some of my favorites, the third is a necessary evil to prepare for graduate school.

NOTE: Apparently I am too new to this forum to post links. Sorry, you will have to google them!

 

[micromass]

I will be heading into my 2nd semester of junior year as a mathematics major. I am curious about grad studies and how to prepare or to discover if i am capable of such a rigorous course.

the video below is ment for humor but i believe the advise coould still be solid.

a funny video on youtube, "so you want a phd in mathematics" sorry cannot post links yet due to being new.

I have a bit more education than the student in the video, however that does not mean I know more about what is in-store for me.

any reading material on a larger view of mathematics as a whole and/or how to ensure a solid foundation of mathematics would be amazing. Besides working problems of my mathematical level till I am blue in the face, any other suggestions or helpful texts would be great.

I do not have the education to quite decide on a field yet.

Thank You.

What are you planning to do in grad school??

 

[Stlgeek]

Thank You very much, I will check these titles out on amazon. I have always been keen on building a resourceful library. Also it seems you supported your choices with exactly what i was looking for thank you. For anyone else reading this post, please feel free to add food for thought or your own suggestions. there is no such thing as enough resources.

 

[theorem4.5.9]

You're welcome! If you end up reading them, let me know what you think and if you would recommend them to others =)