Textbooks on solidifying graduate knowledge

manpreet Best Answer 2 years ago

I am finishing my undergraduate program soon and start getting ready for graduate school. What I have realized is that although I have passed many subjects and with good grades I feel that mathematical knowledge is somewhat loose.

I am looking for books/textbooks that aim on "solidifying" my body of knowledge. For example, I found the books Geometry I & II by Marcel Berger a very nice way to use very basic facts about groups and vector spaces to study very intricate things (+it contains many excersises). Other books I have in mind (although I have read a small portion of them) are the books of Terrence Tao with excerpts from his blog. Or yet another example, the (somewhat old) book of Shlomo Sternberg on Calculus (since it provides a very concrecte organisation of a syllabus spanning 3 or more subjects in a standard undergraduate program).

Alternatively, sets of demanding problems (like those provided by Paul Siegel) are very, very welcome.

Let me state in another way my question: What are the books you wished you have read as an undergraduate. And since there are many Proffesors here: What are the books you wished your graduate students have read?