Download or read book Essential Permutations Combinations written by Tim Hill and published by Createspace Independent Publishing Platform. This book was released on 2018-04-29 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematics of counting permutations and combinations is required knowledge for probability, statistics, professional gambling, and many other fields. But counting is hard. Students find it hard. Teachers find it hard. And in the end the only way to learn is to do many problems. Tim Hill's learn-by-example approach presents counting concepts and problems of gradually increasing difficulty. If you become lost or confused, then you can back up a bit for clarification. With practice, you'll develop the ability to decompose complex problems and then assemble the partial solutions to arrive at the final answer. The result: learn in a few weeks what conventional schools stretch into months. Teaches general principles that can be applied to a wide variety of problems. Avoids the mindless and excessive routine computations that characterize conventional textbooks. Treats counting as a logically coherent discipline, not as a disjointed collection of techniques. Restores proofs to their proper place to remove doubt, convey insight, and encourage precise logical thinking. Omits digressions, excessive formalities, and repetitive exercises. Provides exceptional preparation for probability and statistics courses. Includes problems (with all solutions) that extend your knowledge rather than merely reinforce it. Contents 1. The Sum Rule and Product Rule 2. Permutations 3. Combinations 4. The Binomial Theorem 5. Combinations with Repetition 6. Summary and Solutions About the Author Tim Hill is a statistician living in Boulder, Colorado. He holds degrees in mathematics and statistics from Stanford University and the University of Colorado. Tim has written self-teaching guides for Algebra, Trigonometry, Geometry, Precalculus, Advanced Precalculus, Permutations & Combinations, Mathematics of Money, and Excel Pivot Tables. When he's not crunching numbers, Tim climbs rocks, hikes canyons, and avoids malls.
Download or read book Essential Permutations Combinations written by Tim Hill and published by Questing Vole Press. This book was released on 2018-06-12 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematics of counting permutations and combinations is required knowledge for probability, statistics, professional gambling, and many other fields. But counting is hard. Students find it hard. Teachers find it hard. And in the end the only way to learn is to do many problems. Tim Hill's learn-by-example approach presents counting concepts and problems of gradually increasing difficulty. If you become lost or confused, then you can back up a bit for clarification. With practice, you'll develop the ability to decompose complex problems and then assemble the partial solutions to arrive at the final answer. The result: learn in a few weeks what conventional schools stretch into months. - Teaches general principles that can be applied to a wide variety of problems. - Avoids the mindless and excessive routine computations that characterize conventional textbooks. - Treats counting as a logically coherent discipline, not as a disjointed collection of techniques. - Restores proofs to their proper place to remove doubt, convey insight, and encourage precise logical thinking. - Omits digressions, excessive formalities, and repetitive exercises. - Provides exceptional preparation for probability and statistics courses. - Includes problems (with all solutions) that extend your knowledge rather than merely reinforce it. Contents 1. The Sum Rule and Product Rule 2. Permutations 3. Combinations 4. The Binomial Theorem 5. Combinations with Repetition 6. Summary and Solutions
Download or read book Probability written by Duo Code and published by Createspace Independent Publishing Platform. This book was released on 2017-07-26 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: Never worry about understanding permutations and combinations again!!! Are you ready to master permutations and combinations?If you answered "YES!" then you'll want to download this book today Here's a brief overview of the chapters... Chapter one of the book reviews the basics of permutations and combination to provide you with a big picture view of counting problems Chapter two delves deeper to provide you a solid understanding of permutations Chapter three focuses on exploring combinations and how it is different from permutations In chapter four, you'll learn how to solve more difficult mixed problems of permutations and combinations Chapter five dives deeper to provide a complete understanding of how permutations and combinations are applied in the lottery Finally, in chapter six, you'll learn how combinations can help you solve more complex poker problems. (insert bullet point) Much, much more! Download your copy today!
Download or read book Introduction to Counting and Probability written by David Patrick and published by . This book was released on 2007-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Combinatorics written by Peter Jephson Cameron and published by Cambridge University Press. This book was released on 1994-10-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics is a subject of increasing importance because of its links with computer science, statistics, and algebra. This textbook stresses common techniques (such as generating functions and recursive construction) that underlie the great variety of subject matter, and the fact that a constructive or algorithmic proof is more valuable than an existence proof. The author emphasizes techniques as well as topics and includes many algorithms described in simple terms. The text should provide essential background for students in all parts of discrete mathematics.
Download or read book Combinatorics A Very Short Introduction written by Robin Wilson and published by Oxford University Press. This book was released on 2016-04-28 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: How many possible sudoku puzzles are there? In the lottery, what is the chance that two winning balls have consecutive numbers? Who invented Pascal's triangle? (it was not Pascal) Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects, works to answer all these questions. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics such as graph theory, partitions of numbers, block designs, design of codes, and latin squares. In this Very Short Introduction Robin Wilson gives an overview of the field and its applications in mathematics and computer theory, considering problems from the shortest routes covering certain stops to the minimum number of colours needed to colour a map with different colours for neighbouring countries. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Download or read book Applied Discrete Structures written by Ken Levasseur and published by Lulu.com. This book was released on 2012-02-25 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: ''In writing this book, care was taken to use language and examples that gradually wean students from a simpleminded mechanical approach and move them toward mathematical maturity. We also recognize that many students who hesitate to ask for help from an instructor need a readable text, and we have tried to anticipate the questions that go unasked. The wide range of examples in the text are meant to augment the "favorite examples" that most instructors have for teaching the topcs in discrete mathematics. To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs. Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete. The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words. An Instructor's Guide is available to any instructor who uses the text. It includes: Chapter-by-chapter comments on subtopics that emphasize the pitfalls to avoid; Suggested coverage times; Detailed solutions to most even-numbered exercises; Sample quizzes, exams, and final exams. This textbook has been used in classes at Casper College (WY), Grinnell College (IA), Luzurne Community College (PA), University of the Puget Sound (WA).''--
Download or read book Mathematics of Choice written by Ivan Niven and published by MAA. This book was released on 1965 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Combinatorics The Art of Counting written by Bruce E. Sagan and published by American Mathematical Soc.. This book was released on 2020-10-16 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature which has never before appeared in print, such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set, or the connection between quasisymmetric functions and pattern avoidance. The book assumes minimal background, and a first course in abstract algebra should suffice. The exposition is very reader friendly: keeping a moderate pace, using lots of examples, emphasizing recurring themes, and frankly expressing the delight the author takes in mathematics in general and combinatorics in particular.
Download or read book Essential Trigonometry written by Tim Hill and published by Questing Vole Press. This book was released on 2013-10-16 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: This no-nonsense guide provides students and self-learners with a clear and readable study of trigonometry's most important ideas. Tim Hill's distraction-free approach combines decades of tutoring experience with the proven methods of his Russian math teachers. The result: learn in a few days what conventional schools stretch into months. - Teaches general principles that can be applied to a wide variety of problems. - Avoids the mindless and excessive routine computations that characterize conventional textbooks. - Treats trigonometry as a logically coherent discipline, not as a disjointed collection of techniques. - Restores proofs to their proper place to remove doubt, convey insight, and encourage precise logical thinking. - Omits digressions, excessive formalities, and repetitive exercises. - Covers all the trigonometry needed to take a calculus course. - Includes problems (with all solutions) that extend your knowledge rather than merely reinforce it. Contents 1. A Few Basics 2. Radian Measure 3. The Trig Functions 4. Trig Values for Special Angles 5. Graphs of Trig Functions 6. The Major Formulas 7. Inverse Trig Functions 8. The Law of Cosines (and Sines) 9. Solutions 10. Trig Cheat Sheet
Download or read book Principles and Techniques in Combinatorics written by Chuan-Chong Chen and published by World Scientific. This book was released on 1992 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook suitable for undergraduate courses. The materials are presented very explicitly so that students will find it very easy to read. A wide range of examples, about 500 combinatorial problems taken from various mathematical competitions and exercises are also included.
Download or read book Guide to Essential Math written by Sy M. Blinder and published by Newnes. This book was released on 2013-02-14 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reminds students in junior, senior and graduate level courses in physics, chemistry and engineering of the math they may have forgotten (or learned imperfectly) that is needed to succeed in science courses. The focus is on math actually used in physics, chemistry, and engineering, and the approach to mathematics begins with 12 examples of increasing complexity, designed to hone the student's ability to think in mathematical terms and to apply quantitative methods to scientific problems. Detailed illustrations and links to reference material online help further comprehension. The second edition features new problems and illustrations and features expanded chapters on matrix algebra and differential equations. - Use of proven pedagogical techniques developed during the author's 40 years of teaching experience - New practice problems and exercises to enhance comprehension - Coverage of fairly advanced topics, including vector and matrix algebra, partial differential equations, special functions and complex variables
Download or read book A Path to Combinatorics for Undergraduates written by Titu Andreescu and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique approach to combinatorics is centered around unconventional, essay-type combinatorial examples, followed by a number of carefully selected, challenging problems and extensive discussions of their solutions. Topics encompass permutations and combinations, binomial coefficients and their applications, bijections, inclusions and exclusions, and generating functions. Each chapter features fully-worked problems, including many from Olympiads and other competitions, as well as a number of problems original to the authors; at the end of each chapter are further exercises to reinforce understanding, encourage creativity, and build a repertory of problem-solving techniques. The authors' previous text, "102 Combinatorial Problems," makes a fine companion volume to the present work, which is ideal for Olympiad participants and coaches, advanced high school students, undergraduates, and college instructors. The book's unusual problems and examples will interest seasoned mathematicians as well. "A Path to Combinatorics for Undergraduates" is a lively introduction not only to combinatorics, but to mathematical ingenuity, rigor, and the joy of solving puzzles.
Download or read book Discrete Mathematics written by Oscar Levin and published by Createspace Independent Publishing Platform. This book was released on 2018-07-30 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.While there are many fine discrete math textbooks available, this text has the following advantages: - It is written to be used in an inquiry rich course.- It is written to be used in a course for future math teachers.- It is open source, with low cost print editions and free electronic editions.
Download or read book Concrete Mathematics written by Ronald L. Graham and published by Addison-Wesley Professional. This book was released on 1994-02-28 with total page 811 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them.
Download or read book Probability with Permutations and Combinations written by Robert Tier and published by Createspace Independent Publishing Platform. This book was released on 2017-01-30 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: One thing is certain: statistics don't lie. Learning about probability with combinations and permutations gives you that competitive edge in ANY field of work or hobby you're into. Whether it's Poker, horse racing, weather forecasting, lottery betting, general mathematics or virtually any other field where odds need to be determined--this book will help you succeed!
Download or read book Permutation Design written by Kostas Terzidis and published by Routledge. This book was released on 2014-09-04 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: In design, the problems that designers are called upon to solve can be regarded as a problem of permutations. A permutation is an ordered arrangement of elements in a set. In our case, the set is design and the elements are design components, such as lines, shapes, forms, or spaces. Traditionally, such arrangements are done by human designers who base their decision-making process either on intuition or on random sampling until a valid solution is found. However, in both cases the solution found may be an acceptable one but cannot be labeled as "the best possible solution" due to the subjective or arbitrary nature of the selection process. In contrast, by harnessing the potential of computational design, these elements can be arranged in all possible ways and then the best ones are chosen based on specific criteria. By presenting a complete list of permutation-based arrangements the "best solution" will eventually reveal itself by excluding all other possible solutions. This book comprehensively addresses theories, techniques, and examples of permutation design in order to fully demonstrate to the reader the full range of possibilities this method represents. The significance of such an approach to design is enormous, paradigmatic, and far-reaching. It provides an alternative method for design analysis, synthesis, and evaluation that is based on computational force rather than pure human intelligence alone. In contrast to human-based random sampling or intuition, permutation-based design offers the assurance of an optimum design since any possible alternative design can be eliminated. From a practical point of view, this methodology offers a paradigmatic shift away from the current state of design practice where arbitrariness, repetition, and redundancy often exist. From a theoretical viewpoint, this new paradigm will offer alternative insights into the value of human creativity, intuition, and intelligence.
