The Problem Solvers are an exceptional series of books that are thorough, unusually well-organized, and structured in such a way that they can be used with any text. No other series of study and solution guides has come close to the Problem Solvers in usefulness, quality, and effectiveness. Educators consider the Problem Solvers the most effective series of study aids on the market. Students regard them as most helpful for their school work and studies. With these books, students do not merely memorize the subject matter, they really get to understand it. Each Problem Solver is over 1,000 pages, yet each saves hours of time in studying and finding solutions to problems. These solutions are worked out in step-by-step detail, thoroughly and clearly. Each book is fully indexed for locating specific problems rapidly. Thorough coverage is given to the fundamental concepts of topology, axiomatic set theory, mappings, cardinal numbers, ordinal numbers, metric spaces, topological spaces, separation axioms, Cartesian products, the elements of homotopy theory, and other topics. A comprehensive study aid for the graduate student and beyond.

This text contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment. Proofs of theorems are separated from their formulations and are gathered at the end of each chapter, making this book appear like a problem book and also giving it appeal to the expert as a handbook. The book includes about 1,000 exercises.

An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.

This book constitutes the refereed proceedings of the 7th International Conference on Parallel Problem Solving from Nature,PPSN 2002, held in Granada, Spain in September 2002. The 90 revised full papers presented were carefully reviewed and selected from 181 submissions. The papers are organized in topical sections on evolutionary algorithms theory, representation and codification, variation operators, evolutionary techniques and coevolution, multiobjective optimization, new techniques for evolutionary algorithms, hybrid algorithms, learning classifier systems, implementation of evolutionary algorithms, applications, and cellular automata and ant colony optimization.

We are proud to introduce the proceedings of the Seventh International C- ference on Parallel Problem Solving from Nature, PPSN VII, held in Granada, Spain, on 7–11 September 2002. PPSN VII was organized back-to-back with the Foundations of Genetic Algorithms (FOGA) conference, which took place in Torremolinos, Malaga, Spain, in the preceding week. ThePPSNseriesofconferencesstartedinDortmund,Germany[1].Fromthat pioneering meeting, the event has been held biennially, in Brussels, Belgium [2], Jerusalem, Israel [3], Berlin, Germany [4], Amsterdam, The Netherlands [5], and Paris, France [6]. During the Paris conference, several bids to host PPSN 2002 were put forward; it was decided that the conference would be held in Granada with Juan J. Merelo Guerv ́ os as General Chairman. The scienti?c content of the PPSN conference focuses on problem-solving paradigms gleaned from natural models, with an obvious emphasis on those that display an innate parallelism, such as evolutionary algorithms and ant-colony optimization algorithms. The majority of the papers, however, concentrate on evolutionary and hybrid algorithms, as is shown in the contents of this book and itspredecessors.Thiseditionoftheconferenceproceedingshasalargesectionon applications,betheytoclassicalproblemsortoreal-worldengineeringproblems, which shows how bioinspired algorithms are extending their use in the realms of business and enterprise.

Thorough coverage is given to fluid properties, statics, kinematics, pipe flow, dimensional analysis, potential and vortex flow, drag and lift, channel flow, hydraulic structures, propulsion, and turbomachines.