How To Solve It: A New Aspect of Mathematical Method G. Polya. This isn't a "math book." It's a book about how to think about problems in a way that leads to solutions. To paraphrase the author, if you want to learn to swim, you have to get wet; if you want to learn to solve problems, you have to solve problems. This book guides the reader through solving problems in a step-by-step fashion. The goal isn't to solve the particular problems given, but to learn the general approaches. (The Princeton Science Library edition of this book is less expensive than the edition in the link, if you can find it.)
The Deluxe Transitive Vampire: The Ultimate Handbook of Grammar for the Innocent, the Eager, and the Doomed Karen Elizabeth Gordon. The most important ideas that college students – and college graduates – have will be presented in writing. This book, and the next two, have to do with writing and the use of the English language. It's a crucial skill because bad writing kills good ideas. College writing courses often assume that students have learned the basics in elementary and high school. That isn't always the case, and even when it is, sometimes a refresher is needed. If I were asked the difference the future progressive tense and the future perfect progressive, I'd have to turn to my copy of Transitive Vampire. (Future perfect progressive implies completion at a time in the future.) This isn't a book about learning the rules, though; it's about using the language effectively.
The examples and accompanying illustrations are ever so slightly risqué.The section on dependent clauses has an engraving of a Victorian maiden holding the paw of a bear and saying, "If this is love, I've made a terrible mistake."
The Elements of Style (4th Edition) William Strunk and E. B. White. While Transitive Vampire is about writing correct English, Strunk and White is about writing English with style. It's about how to put words into sentences that convey one's ideas effectively. The first part of the book consists of 22 rules for effective writing: rules like omit needless words and use the proper case of pronoun. (If you need a refresher about case, see Transitive Vampire.) There's a short section on form, followed by a few pages of advice on commonly misused words. The book concludes with 21 more rules. This time, they're about style rather than effective writing. The student should skim this book early on, then refer to it when she has questions.
A Handbook for Scholars Mary-Claire VanLeunen. This one may be hard to find, but it's worth looking for. The two books listed above are about writing well, but there are rules for scholarly writing that are different from writing other types of prose. Sometimes professors assume that students know the rules, and often that's not the case. The publisher says, "Custom, propriety, and a quest for certainty hem the scholar in on all sides. But while it is necessarily formal, allusive, and accurate, scholarly writing does not have to be – nor should it be – wooden, pedantic, and cryptic." Van Leunen will help students stay within the rules and avoid the mistakes.
There's a section at the back about preparing manuscripts for publication. It's out of date in the age of computers and laser printers. Just ignore it; the rest of the book is worth the price.
The Impoverished Students' Book Of Cookery Drinkery And Housekeepery Jay F. Rosenberg. I've saved the best for last. College students do not live on problem solving and writing alone, and the author of this little book realized that early on. This book was written over fifty years ago when the late Dr. Rosenberg was an undergraduate at Reed College. Do not let "impoverished" in the title put you off. The book says, "We may provisionally define an Impoverished Student as an individual who loves to eat, hates to cook, and cannot really afford to do either. It is important to distinguish between the merely Impoverished Student and the really Impoverished Student. The really Impoverished Student is poor!"
This book contains solid advice for the merely Impoverished: "You cannot afford to buy top quality food, so buy top quality spices. No one will know the difference." The recipes can be prepared by a college student with no experience in cookery, are made from inexpensive ingredients like chicken, are at least mostly healthy, and taste good! There's a sample recipe here. You will, however, have to caution your Impoverished Student that the prices given in the book are from a half century ago. At 47 pages, this is the shortest of the books I've recommended; it's really more of a pamphlet than a book. That may make the $10 price seem high. Buy it anyway, and take comfort in the fact that 40% of the price goes to the Reed College scholarship fund.
Books Every College Student Should Have by Bob Brown is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.
Full disclosure: Some of the links above go to Amazon. If you buy using those links, I earn a few pennies. If that bothers you, just go direct to Amazon and search by title or author. To put this into perspective, my total earnings from the Amazon Associates program over the last five years are one dollar and seventy-six cents.