Student Resources

This page constitutes a new addition to this website, and as such is still very much work in progress. I intend to expand the individual sections as time goes on, and always welcome suggestions for additions so please don't hesitate to contact me.

DISCLAIMER: The opinions expressed below are my personal opinions, and do not necessarily reflect the position of my employer. I derive absolutely no benefit whatsoever from you buying one of the books or using one of the services or products mentioned below.

At Rutgers

If mathematics in general and calculus in particular is causing you headaches, then you should make use of the many learning resources that Rutgers has available for its students. For example, the Rutgers Learning Centers offer small group tutoring in all the mainstream mathematics courses in the undergraduate curriculum, including calculus and linear algebra. This valuable offering seems to be much underused - where else can you get highly qualified help for free?

If you are at the other end of the spectrum and found your calculus class unbearable because you never really got to see exactly why a formula was true beyond some hand-waving heuristic attempt at an explanation, and you generally didn't find it quite challenging enough, then consider talking to your instructor about taking one of the honors sections of the calculus sequence next semester. If you generally take your math seriously, the undergraduate mathematics honors track at Rutgers may be for you. Applications are very competitive, but if accepted you will no doubt find the program extremely rewarding. At the very least you may consider participating in the problem solving seminar if you have a taste for challenging questions.

Mathematics on the Web

While anything out there should be consumed with caution, I have generally found Wikipedia to be a reliable resource for most things mathematical, and on average much more useful than dedicated mathematics sites such as Wolfram Mathworld or Planet Math. Having said that, I occasionally use the Wolfram Online Integrator to check my calculations.

A few months ago Tim Gowers started an online project called the Tricki. Its aim is to collect accessible articles on problem solving techniques written by mathematicians for an audience with all kinds of mathematical backgrounds. Topics range from elementary ones such as "how to integrate by parts" to rather abstract and sophisticated questions such as "how to compute derived functors". Throughout, the emphasis is on concrete examples and hands-on advice. The project is still very much in its infancy, but is likely to grow rapidly in the near future and already fun to browse!

The Tricki grew out of Tim Gowers's mathematical discussions on undergraduate topics including algebra, analysis and geometry, which continue to be available from his website.

Career

Terry Tao maintains a wonderful page with career advice for people at all stages of their mathematical careers, from high school students through young postdoctoral researchers. He's also written up some interesting personal thoughts on time management.

The American Mathematical Society has a careers page containing a myriad of useful links for current undergraduate students, including advice on jobs, graduate school, internships, fellowships etc. If you are considering becoming a teacher of mathematics, Mathematics for America appears to be an excellent opportunity.

Research Opportunities

The American Mathematical Society also collects research opportunities for undergraduates across the US that you might want to consider applying for. The list includes one program that is very close to home, the Rutgers Summer REU, which is run in collaboration with DIMACS.

There are a large number of mathematics summer camps on offer for enthusiastic high-school students, which are again helpfully listed by the American Mathematical Society. In particular, if puzzle-type problem solving is your cup of tea, you may wish to participate in the Rutgers Young Scholars program in discrete mathematics next year.

Typesetting Mathematics

Ever wondered how to typeset mathematics the way it's done in books and scientific journals? Find out all you ever wanted to know about the software LaTeX and how to install it. The Cambridge Engineering Department maintains an accessible tutorial and provides many useful links. This NASA reference is not a tutorial but simply a listing of available commands, which may come in handy once you have a bit of experience.

If you want to go one step further and present mathematics in front of an audience, slides produced using the LaTeX package Beamer will look most professional. A Beamer Quickstart tutorial and a directory of Beamer themes are also available. Go to my talks page to see some examples of mine. (Incidentally, the word "Beamer" is one of those wonderfully incorrect anglicisms that the German language seems to be teeming with these days. It is meant to mean "projector".)

Book Recommendations

The books I am about to discuss are of a very general mathematical nature. I intend to add some more subject-specific ones that lie somewhat outside the standard undergraduate curriculum in the very near future.

How to solve it by George Polya. This book is a classic amongst mathematicians, especially those of the problem-solving kind, packed with strategies, tips and tactics to employ when one is trying to solve a mathematical problem. You could have guessed it from the title. These general techniques are skillfully illustrated by way of elementary but meaningful examples. I have a slight feeling that the book may be even more useful to the teacher of mathematics than the student, and you may well hear me quote from it ad nauseam next semester.

Solving mathematical problems - a personal perspective by Terence Tao. This is a beautiful book that talks about lots of beautiful problems. More importantly, it is an amazingly lucid and intuitive discussion on how to find non-obvious solutions to those problems. This is all the more impressive as the author wrote this book when he was 15 years old. Alright, at age 13 he became the youngest person ever to win a gold medal at the International Mathematical Olympiad, so you'd kind of suspect he has something worthwhile to say about problem solving... (Some sample chapters are available from his website as a ps file.)

A very short introduction to mathematics by Timothy Gowers. This is an excellent book to give to friends or family members who greet your interest in mathematics by raising an eyebrow or shaking their head. My mother, who cannot recollect any positive mathematical experiences prior to reading this book, absolutely loved it. It has the added advantage of living up to its title: it is indeed very short.

The Cauchy-Schwarz master class by J. Michael Steele. An entire book devoted to a single inequality may seem to be a recipe for guaranteed boredom, but nothing could be further from the truth. I generally believe that the importance of inequalities is not sufficiently emphasized in the undergraduate curriculum, and this inequality in particular is absolutely central to a number of areas of mathematics (and not just my own research). It gives rise to many other useful and elegant inequalities, and the book beautifully illustrates these (sometimes subtle) connections. It's a book I wish I'd read as an undergraduate.

About Me

For what it's worth, here is a quick link to the results of my Student Instructional Rating Survey at Rutgers. You will need your Rutgers NetID to log on. Some comments that students leave on ratemyprofessors.com should be taken with a pinch of salt (or a large dose of humour).

My name appears in the credits of the movie Proof, starring Gwyneth Paltrow and Jake Gyllenhaal. You literally have to wait until the VERY end though.