Bernhard Riemann was an underdog of sorts, a malnourished son of a parson who grew up to be the author of one of mathematics' greatest problems. In Prime Obsession, John Derbyshire deals brilliantly with both Riemann's life and that problem: proof of the conjecture, "All non-trivial zeros of the zeta function have real part one-half." Though the statement itself passes as nonsense to anyone but a mathematician, Derbyshire walks readers through the decades of reasoning that led to the Riemann Hypothesis in such a way as to clear it up perfectly. Riemann himself never proved the statement, and it remains unsolved to this day. Prime Obsession offers alternating chapters of step-by-step math and a history of 19th-century European intellectual life, letting readers take a breather between chunks of well-written information. Derbyshire's style is accessible but not dumbed-down, thorough but not heavy-handed. This is among the best popular treatments of an obscure mathematical idea, inviting readers to explore the theory without insisting on page after page of formulae.

In 2000, the Clay Mathematics Institute offered a one-million-dollar prize to anyone who could prove the Riemann Hypothesis, but luminaries like David Hilbert, G.H. Hardy, Alan Turing, André Weil, and Freeman Dyson have all tried before. Will the Riemann Hypothesis ever be proved? "One day we shall know," writes Derbyshire, and he makes the effort seem very worthwhile. —Therese Littleton

Excellent textbook provides undergraduates with an accessible introduction to the basic concepts of abstract algebra and to the analysis of abstract algebraic systems. Features many examples and a large number of problems of varying levels of difficulty at the end of each chapter.

Blending the spirit of Eats, Shoots & Leaves with the science of The Language Instinct, an original inquiry into the development of that most essential-and mysterious-of human creations: Language

Language is mankind's greatest invention-except, of course, that it was never invented." So begins linguist Guy Deutscher's enthralling investigation into the genesis and evolution of language. If we started off with rudimentary utterances on the level of "man throw spear," how did we end up with sophisticated grammars, enormous vocabularies, and intricately nuanced degrees of meaning?

Drawing on recent groundbreaking discoveries in modern linguistics, Deutscher exposes the elusive forces of creation at work in human communication, giving us fresh insight into how language emerges, evolves, and decays. He traces the evolution of linguistic complexity from an early "Me Tarzan" stage to such elaborate single-word constructions as the Turkish sehirlilestiremediklerimizdensiniz ("you are one of those whom we couldn't turn into a town dweller"). Arguing that destruction and creation in language are intimately entwined, Deutscher shows how these processes are continuously in operation, generating new words, new structures, and new meanings.

As entertaining as it is erudite, The Unfolding of Language moves nimbly from ancient Babylonian to American idiom, from the central role of metaphor to the staggering triumph of design that is the Semitic verb, to tell the dramatic story and explain the genius behind a uniquely human faculty.

In Journey through Genius, author William Dunham strikes an extraordinary balance between the historical and technical. He devotes each chapter to a principal result of mathematics, such as the solution of the cubic series and the divergence of the harmonic series. Not only does this book tell the stories of the people behind the math, but it also includes discussions and rigorous proofs of the relevant mathematical results.

This highly useful text for students and professionals working in the applied sciences shows how to formulate and solve partial differential equations. Realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems and numerical and approximate methods. Suggestions for further reading. Solution guide available upon request. 1982 edition.

Stephen Northcutt and his coauthors note in the superb Intrusion Signatures and Analysis that there's really no such thing as an attack that's never been seen before. The book documents scores of attacks on systems of all kinds, showing exactly what security administrators should look for in their logs and commenting on attackers' every significant command. This is largely a taxonomy of hacker strategies and the tools used to implement them. As such, it's an essential tool for people who want to take a scientific, targeted approach to defending information systems. It's also a great resource for security experts who want to earn their Certified Intrusion Analyst ratings from the Global Incident Analysis Center (GIAC)—it—it's organized, in part, around that objective.

The book typically introduces an attack strategy with a real-life trace—usually attributed to a real administrator—from TCPdump, Snort, or some sort of firewall (the trace's source is always indicated). The trace indicates what is happening (i.e., what weakness the attacker is trying to exploit) and the severity of the attack (using a standard metric that takes into account the value of the target, the attack's potential to do damage, and the defenses arrayed against the attack). The attack documentation concludes with recommendations on how defenses could have been made stronger. These pages are great opportunities to learn how to read traces and take steps to strengthen your systems' defenses.

The book admirably argues that security administrators should take some responsibility for the greater good of the Internet by, for example, using egress filtering to prevent people inside their networks from spoofing their source address (thus defending other networks from their own users' malice). The authors (and the community of white-hat security specialists that they represent) have done and continue to do a valuable service to all Internet users. Supplement this book with Northcutt's excellent Network Intrusion Detection, which takes a more general approach to log analysis and is less focused on specific attack signatures. —David Wall

Topics covered:External attacks on networks and hosts, as they appear to administrators and detection systems monitoring log filesHow to read log files generallyHow to report attacks and interact with the global community of good-guy security specialistsThe most commonplace critical security weaknessesTraces that document reconnaissance probesDenial-of-service attacksTrojansOverflow attacksOther black-hat strategies

A series of anecdotes shouldn't by rights add up to an autobiography, but that's just one of the many pieces of received wisdom that Nobel Prize-winning physicist Richard Feynman (1918-88) cheerfully ignores in his engagingly eccentric book, a bestseller ever since its initial publication in 1985. Fiercely independent (read the chapter entitled "Judging Books by Their Covers"), intolerant of stupidity even when it comes packaged as high intellectualism (check out "Is Electricity Fire?"), unafraid to offend (see "You Just Ask Them?"), Feynman informs by entertaining. It's possible to enjoy Surely You're Joking, Mr. Feynman simply as a bunch of hilarious yarns with the smart-alecky author as know-it-all hero. At some point, however, attentive readers realize that underneath all the merriment simmers a running commentary on what constitutes authentic knowledge: learning by understanding, not by rote; refusal to give up on seemingly insoluble problems; and total disrespect for fancy ideas that have no grounding in the real world. Feynman himself had all these qualities in spades, and they come through with vigor and verve in his no-bull prose. No wonder his students—and readers around the world—adored him. —Wendy Smith

Java just keeps growing, adding features, functionality, complexity, and tempting developers to growl with frustration. The new 1.4 release of Java 2 Standard edition increases the size of the platform by 50%, to 2757 classes in 135 packages. How are you going to figure out what this means for your applications? As always, Java in a Nutshell has the answers. The new 4th edition still contains an accelerated introduction to the Java programming language and its key APIs so you can start writing code right away. And with more than 250 new pages, author David Flanagan quickly brings you up to speed on new features that come with version 1.4:High-performance NIO APISupport for pattern matching with regular expressionsA logging APIA user preferences APINew Collections classesAn XML-based persistence mechanism for Java BeansSupport for XML parsing using both the DOM and SAX APIsUser authentication with the JAAS APISupport for secure network connections using the SSL protocolSupport for cryptographyThe book contains O'Reilly's classic quick-reference for all the classes in the essential Java packages, so you can dive in and find what you need to make the new 1.4 version work for you. For as long as Java developers have existed, Java in a Nutshell has been ready, willing and able to take you right to the heart of the program, turning those frustrated grrrrss into purrrss of satisfaction. No wonder readers of Java Developer's Journal voted this the "Best Java Book" the past two years in a row!

For the intermediate to advanced Java developer, Java Enterprise in a Nutshell shows how to work with all of today's relevant Java APIs. Plus, it's a topnotch reference for all enterprise classes. Part tutorial and part reference work that you can use everyday at your desk, this title is a worthwhile resource for any Java developer building Web or enterprise software.

The practical, succinct focus here on actual Java enterprise APIs helps distinguish this text from the pack. Early sections provide short, clear examples along with just enough background to help you use APIs like JDBC, servlets and JSPs, EJBs, and others. Coverage of Java's ability to interface with legacy CORBA systems is just excellent, with a full tour of Java IDL, CORBA services, and Remote Method Invocation (RMI). Typically, readers will be familiar with some J2EE APIs and not others. This book can help fill in the gaps.

Updated with the latest standards from Sun, including JDBC 3.0, Servlet 2.3, and EJB 2.0, this is an essential primer for today's high-end (and high-paying) Java. The basic presentation of servlets/JSP and EJBs (among the most important APIs for current Java Web development) is concise and nicely digestible. We also liked the chapter on JMS for messaging (also a hotbed of Java job activity).

The second half of this text lists every J2EE class, along with methods and properties, in a very valuable reference section that makes good use of two-toned shading for easy access. Entries are organized by package name. (One small oversight here is that an index of cross-listed packages, classes, and methods omits page numbers.)

Overall, this book is truly indispensable for any working Java programmer. The second edition of Java Enterprise in a Nutshell is a fully up-to-date tutorial and reference that lives up to the standards of O'ReillyÂ’s Nutshell series. Both thorough and concise, it's a handy resource for anyone who works with the hundreds and thousands of Java enterprise APIs on a regular basis. —Richard Dragan

Topics covered: Introduction to enterprise computing with the Java 2 Enterprise Edition (J2EE), survey of Java enterprise APIs, JDBC 3.0 (including database connections, ResultSets, prepared statements, BLOB fields, transaction support, stored procedures), the JDBC Optional Package (and connection pooling), Remote Method Invocation (RMI) described (building stubs and skeletons, dynamically loaded classes and remote object activation, RMI over IIOP), in-depth tutorial for Java IDL (with CORBA) and designing remote objects, Java Servlet 2.3 APIs (basic servlet processing and the servlet lifecycle, chaining and filters, thread safety, managing state, cookies, servlets used with JDBC), JavaServer Pages (JSP): including custom tags, JNDI and directory tutorial (contexts, looking up objects, accessing and modifying directory entries), Enterprise Java Beans (EJB) 2.0 (conventions for entity, session and message beans, using transactions), Java XML APIs (DOM, SAX and XSLT), Java Message Service (JMS), point-to-point and publish-subscribe messaging models, message selectors, JavaMail, reference to SQL and relational databases, RMI tools, reference to all IDL keywords, data types and declarations; CORBA services, Java IDL tool reference, Enterprise JavaBeans Query Language (EJB QL) 2.0 query language, and an alphabetical listing of all APIs for Java enterprise programming (listing of classes, methods, and properties).

This top-selling, theorem-proof book presents a careful treatment of the principle topics of linear algebra, and illustrates the power of the subject through a variety of applications. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinite-dimensional case where appropriate. Chapter topics cover vector spaces, linear transformations and matrices, elementary matrix operations and systems of linear equations, determinants, diagonalization, inner product spaces, and canonical forms. For statisticians and engineers.

This delightful book leads you through the basic elements of programming in Scheme (a Lisp dialect) via a series of dialogues with well-chosen questions and exercises. Besides teaching Scheme, The Little Schemer teaches the reader how to think about computation. The authors focus on ten essential concepts of thinking about how to compute and demonstrate how to apply these concepts in inventive ways. The Little Schemer is an excellent book both for the beginner and for the seasoned programmer.

Friedman and Felleisen's The Seasoned Schemer picks up where their book, The Little Schemer, left off and focuses on the myriad uses of functions in Scheme. Using the same dialogue format as The Little Schemer, the authors demonstrate how Scheme's flexible facilities for handling functions give the program so much variety and power. Along the way, the authors also present a variety of other more sophisticated language constructs.

Enormous quantities of data go unused or underused today, simply because people can't visualize the quantities and relationships in it. Using a downloadable programming environment developed by the author, Visualizing Data demonstrates methods for representing data accurately on the Web and elsewhere, complete with user interaction, animation, and more. How do the 3.1 billion A, C, G and T letters of the human genome compare to those of a chimp or a mouse? What do the paths that millions of visitors take through a web site look like? With Visualizing Data, you learn how to answer complex questions like these with thoroughly interactive displays. We're not talking about cookie-cutter charts and graphs. This book teaches you how to design entire interfaces around large, complex data sets with the help of a powerful new design and prototyping tool called "Processing." Used by many researchers and companies to convey specific data in a clear and understandable manner, the Processing beta is available free. With this tool and Visualizing Data as a guide, you'll learn basic visualization principles, how to choose the right kind of display for your purposes, and how to provide interactive features that will bring users to your site over and over. This book teaches you: The seven stages of visualizing data — acquire, parse, filter, mine, represent, refine, and interact How all data problems begin with a question and end with a narrative construct that provides a clear answer without extraneous details Several example projects with the code to make them work Positive and negative points of each representation discussed. The focus is on customization so that each one best suits what you want toconvey about your data set The book does not provide ready-made "visualizations" that can be plugged into any data set. Instead, with chapters divided by types of data rather than types of display, you'll learn how each visualization conveys the unique properties of the data it represents — why the data was collected, what's interesting about it, and what stories it can tell. Visualizing Data teaches you how to answer questions, not simply display information.