<p>I'm trying to find a simple but thorough pure math book or series of books good for self-study. Goal is to be able to do research.</p>
<p>Thanks.</p>
<p>There are a gazillion good math textbooks. Why don’t you tell us a bit about your background and the subject you would like to study, and maybe we can suggest some accessible stand-alone textbooks?</p>
<p>I’m a freshman undergrad student - I don’t have any research experience or anything, but I’m pretty sure that I want to do pure math research and possibly teach at the university level. I don’t have any specific areas of interest in pure math - I kind of just want to have a broad overview of everything and then choose an area of research later on - I’m wondering which books give the best all-encompassing overview of pure math while being detailed enough for me to pick out an area of research along the way. </p>
<p>Thanks.</p>
<p>Want to know what math is?</p>
<p>Stochastic Calculus by Richard Durret</p>
<p>[Stochastic</a> calculus: a practical … - Google Books](<a href=“Stochastic Calculus: A Practical Introduction - Richard Durrett - Google Books”>Stochastic Calculus: A Practical Introduction - Richard Durrett - Google Books)</p>
<p>Maybe you don’t like that. Why not try Differential Geometry?</p>
<p>Differential Geometry by Edwin K.</p>
<p>[Differential</a> geometry - Google Books](<a href=“Differential Geometry - Erwin Kreyszig - Google Books”>Differential Geometry - Erwin Kreyszig - Google Books)</p>
<p>These are upper division classes but you should get the idea of what studying math is.</p>
<p>You are trying to do too much at once. It’s the purpose of second- and third-year graduate courses to introduce you to different fields of research. As an undergraduate student, you should focus on getting a good foundation. In fact, most undergraduate students will never learn enough math in their undergraduate career to work on a research project worth mentioning. (There are open problems accessible to undergraduates, but few professional mathematicians would care about their solution.)</p>
<p>If your library has a copy of the book “A Mathematician’s Survival Guide” by Steven Krantz, I recommend that you read the chapter on undergraduate research.</p>