Seven problem-solving techniques include inference, classification of action sequences, subgoals, contradiction, working backward, relations between problems, and mathematical representation. Also, problems from mathematics, science, and engineering with complete solutions.
Based on Stanford University's well-known competitive exam, this excellent mathematics workbook offers students at both high school and college levels a complete set of problems, hints, and solutions. 1974 edition.
The Nuts and Bolts of Proofs instructs students on the primary basic logic of mathematical proofs, showing how proofs of mathematical statements work. The text provides basic core techniques of how to read and write proofs through examples. The basic mechanics of proofs are provided for a methodical approach in gaining an understanding of the fundamentals to help students reach different results. A variety of fundamental proofs demonstrate the basic steps in the construction of a proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems. New chapter on proof by contradiction New updated proofs A full range of accessible proofs Symbols indicating level of difficulty help students understand whether a problem is based on calculus or linear algebra Basic terminology list with definitions at the beginning of the text
This book presents methods of solving problems in three areas of elementary combinatorial mathematics: classical combinatorics, combinatorial arithmetic, and combinatorial geometry. Brief theoretical discussions are immediately followed by carefully worked-out examples of increasing degrees of difficulty and by exercises that range from routine to rather challenging. The book features approximately 310 examples and 650 exercises.
Accessible text features over 100 reality-based examples pulled from the science, engineering, and operations research fields. Prerequisites: ordinary differential equations, continuous probability. Numerous references. Includes 27 black-and-white figures. 1978 edition.
This workbook bridges the gap between lectures and practical applications, offering students of mathematics, engineering, and physics the chance to practice solving problems from a wide variety of fields. 2011 edition.
Fascinating approach to mathematical teaching stresses use of recreational problems, puzzles, and games to teach critical thinking. Logic, number and graph theory, games of strategy, much more. Includes answers to selected problems. Free solutions manual available for download at the Dover website.
Provide students with the tools to solve problems that are found on mathematical problem-solving exams.
Delve into the development of modern mathematics and match wits with Euclid, Newton, Descartes, and others. Each chapter explores an individual type of challenge, with commentary and practice problems. Solutions.
Zaubern mit Zahlen – wer dieses Buch gelesen hat, muss PISA nicht mehr fürchten Wer glaubt, Mathematik sei eine trockene Angelegenheit und Kopfrechnen eine unnötige Quälerei, der irrt sich gewaltig. Denn nach der Lektüre dieses Buches ist es für jeden ein Leichtes, Rechenoperationen mit vier- und fünfstelligen Zahlen in Sekundenschnelle im Kopf auszuführen. Und was wie Zauberei wirkt, ist letztendlich nichts anderes als mathematische Logik, die jedermann beherrschen kann und die dazu noch richtig Spaß macht. • So wird Kopfrechnen kinderleicht! • Mit zahlreichen Übungen und Lösungen
Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, more. Detailed solutions, as well as brief answers, for all problems are provided.
For the mathematics enthusiast of any age or level of sophisitcation, this stimulating treasury of unusual math problems offers unlimited opportunity for mind-biggling recreation. Carles W. Trigg, Dean Emeritus and Professor Emeritus at Los Angeles City College and one of the country's best-known problemists, has compiled nearly 300 mathematical brainteasers from the field of of arithmetic, algebra, plane and solid geometry, trigonometry, number theory, and such general recreational mathematics and dissections, cryptarithms and magic squares. The object of each problem is to find the quickest, most elegant solution - they are often unorthodox and there is usually and element of surprise in each. Ranging from the simple to complex, problems are both original with the author and the work of over 100 other qualified mathematicians. Most are rarely seen or entirely new; all challenge the reader to devise solutions more elegant than the ones provided.
Collection of 100 of the best submissions to a math puzzle column features problems in engineering situations, logic, number theory, and geometry. Most solutions include details of several different methods.
Collection of nearly 200 unusual problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency and more. Arranged in order of difficulty. Detailed solutions.
Choice puzzles by one of America's most ingenious creators of mathematical entertainments, ranging from simple exercises in arithmetic to complex calculus problems
Clear, concise compendium of about 150 time-saving math short-cuts features faster, easier ways to add, subtract, multiply, and divide. Each problem includes an explanation of the method. No special math ability needed.
Volume I of a two-part series, this book features a broad spectrum of 100 challenging problems related to probability theory and combinatorial analysis. Most can be solved with elementary mathematics. Complete solutions.
Treasury of challenging brainteasers includes puzzles involving numbers, letters, probability, reasoning, more: The Enterprising Snail, The Fly and the Bicycles, The Lovesick Cockroaches, many others. No advanced math needed. Solutions.
The noted expert selects 70 of his favorite "short" puzzles, including such mind-bogglers as The Returning Explorer, The Mutilated Chessboard, Scrambled Box Tops, and dozens more involving logic and basic math. Solutions.