Mathematical Induction

Author : Titu Andreescu,Vlad Crisan
Publisher : Unknown
Page : 432 pages
File Size : 41,9 Mb
Release : 2017-03-15
Category : Induction (Mathematics)
ISBN : 0996874593

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Mathematical Induction by Titu Andreescu,Vlad Crisan Pdf

This book serves as a very good resource and teaching material for anyone who wants to discover the beauty of Induction and its applications, from novice mathematicians to Olympiad-driven students and professors teaching undergraduate courses. The authors explore 10 different areas of mathematics, including topics that are not usually discussed in an Olympiad-oriented book on the subject. Induction is one of the most important techniques used in competitions and its applications permeate almost every area of mathematics.

Author : Harris Kwong
Publisher : Open SUNY Textbooks
Page : 298 pages
File Size : 45,8 Mb
Release : 2015-11-06
Category : Mathematics
ISBN : 1942341164

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A Spiral Workbook for Discrete Mathematics by Harris Kwong Pdf

A Spiral Workbook for Discrete Mathematics covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions,relations, and elementary combinatorics, with an emphasis on motivation. The text explains and claries the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a nal polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a dierent perspective or at a higher level of complexity, in order to slowly develop the student's problem-solving and writing skills.

Author : Hantao Zhang
Publisher : Springer Science & Business Media
Page : 223 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9789400916753

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Automated Mathematical Induction by Hantao Zhang Pdf

It has been shown how the common structure that defines a family of proofs can be expressed as a proof plan [5]. This common structure can be exploited in the search for particular proofs. A proof plan has two complementary components: a proof method and a proof tactic. By prescribing the structure of a proof at the level of primitive inferences, a tactic [11] provides the guarantee part of the proof. In contrast, a method provides a more declarative explanation of the proof by means of preconditions. Each method has associated effects. The execution of the effects simulates the application of the corresponding tactic. Theorem proving in the proof planning framework is a two-phase process: 1. Tactic construction is by a process of method composition: Given a goal, an applicable method is selected. The applicability of a method is determined by evaluating the method's preconditions. The method effects are then used to calculate subgoals. This process is applied recursively until no more subgoals remain. Because of the one-to-one correspondence between methods and tactics, the output from this process is a composite tactic tailored to the given goal. 2. Tactic execution generates a proof in the object-level logic. Note that no search is involved in the execution of the tactic. All the search is taken care of during the planning process. The real benefits of having separate planning and execution phases become appar ent when a proof attempt fails.

Author : David S. Gunderson
Publisher : Chapman & Hall/CRC
Page : 921 pages
File Size : 48,7 Mb
Release : 2016-11-16
Category : Induction (Mathematics)
ISBN : 113819901X

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Handbook of Mathematical Induction by David S. Gunderson Pdf

Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics. In the first part of the book, the author discusses different inductive techniques, including well-ordered sets, basic mathematical induction, strong induction, double induction, infinite descent, downward induction, and several variants. He then introduces ordinals and cardinals, transfinite induction, the axiom of choice, Zorn's lemma, empirical induction, and fallacies and induction. He also explains how to write inductive proofs. The next part contains more than 750 exercises that highlight the levels of difficulty of an inductive proof, the variety of inductive techniques available, and the scope of results provable by mathematical induction. Each self-contained chapter in this section includes the necessary definitions, theory, and notation and covers a range of theorems and problems, from fundamental to very specialized. The final part presents either solutions or hints to the exercises. Slightly longer than what is found in most texts, these solutions provide complete details for every step of the problem-solving process.

Author : Theodore A. Sundstrom
Publisher : Prentice Hall
Page : 0 pages
File Size : 48,8 Mb
Release : 2007
Category : Logic, Symbolic and mathematical
ISBN : 0131877186

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Mathematical Reasoning by Theodore A. Sundstrom Pdf

Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs.Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with “Preview Activities” at the start of each section. Includes “Activities” throughout that relate to the material contained in each section. Focuses on Congruence Notation and Elementary Number Theorythroughout.For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills. Mathematical Reasoning: Writing and Proof, 2/E Theodore Sundstrom

Author : Ilʹi︠a︡ Samuilovich Sominskiĭ
Publisher : Unknown
Page : 61 pages
File Size : 55,6 Mb
Release : 1983
Category : Induction (Mathematics)
ISBN : OCLC:606394337

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The Method of Mathematical Induction by Ilʹi︠a︡ Samuilovich Sominskiĭ Pdf

Author : Martin Aigner,Günter M. Ziegler
Publisher : Springer Science & Business Media
Page : 194 pages
File Size : 42,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662223437

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Proofs from THE BOOK by Martin Aigner,Günter M. Ziegler Pdf

According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.

Author : L.I. Golovina,I. M. Yaglom
Publisher : Courier Dover Publications
Page : 177 pages
File Size : 41,6 Mb
Release : 2019-10-16
Category : Mathematics
ISBN : 9780486838564

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Induction in Geometry by L.I. Golovina,I. M. Yaglom Pdf

Induction in Geometry discusses the application of the method of mathematical induction to the solution of geometric problems, some of which are quite intricate. The book contains 37 examples with detailed solutions and 40 for which only brief hints are provided. Most of the material requires only a background in high school algebra and plane geometry; chapter six assumes some knowledge of solid geometry, and the text occasionally employs formulas from trigonometry. Chapters are self-contained, so readers may omit those for which they are unprepared. To provide additional background, this volume incorporates the concise text, The Method of Mathematical Induction. This approach introduces this technique of mathematical proof via many examples from algebra, geometry, and trigonometry, and in greater detail than standard texts. A background in high school algebra will largely suffice; later problems require some knowledge of trigonometry. The combination of solved problems within the text and those left for readers to work on, with solutions provided at the end, makes this volume especially practical for independent study.

Author : Steven H. Weintraub
Publisher : Courier Dover Publications
Page : 128 pages
File Size : 41,6 Mb
Release : 2017-05-03
Category : Mathematics
ISBN : 9780486821238

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The Induction Book by Steven H. Weintraub Pdf

Mathematical induction — along with its equivalents, complete induction and well-ordering, and its immediate consequence, the pigeonhole principle — constitute essential proof techniques. Every mathematician is familiar with mathematical induction, and every student of mathematics requires a grasp of its concepts. This volume provides an introduction and a thorough exposure to these proof techniques. Geared toward students of mathematics at all levels, the text is particularly suitable for courses in mathematical induction, theorem-proving, and problem-solving. The treatment begins with both intuitive and formal explanations of mathematical induction and its equivalents. The next chapter presents many problems consisting of results to be proved by induction, with solutions omitted to enable instructors to assign them to students. Problems vary in difficulty; the majority of them require little background, and the most advanced involve calculus or linear algebra. The final chapter features proofs too complicated for students to find on their own, some of which are famous theorems by well-known mathematicians. For these beautiful and important theorems, the author provides expositions and proofs. The text concludes with a helpful Appendix providing the logical equivalence of the various forms of induction.

Author : Jianlun Xu
Publisher : Independently Published
Page : 57 pages
File Size : 41,5 Mb
Release : 2020-04-08
Category : Electronic
ISBN : 9798629868644

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Mathematical Induction by Jianlun Xu Pdf

The book is about mathematical induction for college students. It discusses the first principle and its three variations such as the second principle.. As a self-study guide, the book gives plenty of examples and explanations to help readers to grasp math concepts.

Author : Cordelia Hall,John O'Donnell
Publisher : Springer Science & Business Media
Page : 362 pages
File Size : 51,6 Mb
Release : 2000
Category : Computer science
ISBN : 9781852330897

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Discrete Mathematics Using a Computer by Cordelia Hall,John O'Donnell Pdf

This volume offers a new, hands-on approach to teaching Discrete Mathematics. A simple functional language is used to allow students to experiment with mathematical notations which are traditionally difficult to pick up. This practical approach provides students with instant feedback and also allows lecturers to monitor progress easily. All the material needed to use the book will be available via ftp (the software is freely available and runs on Mac, PC and Unix platforms), including a special module which implements the concepts to be learned.No prior knowledge of Functional Programming is required: apart from List Comprehension (which is comprehensively covered in the text) everything the students need is either provided for them or can be picked up easily as they go along. An Instructors Guide will also be available on the WWW to help lecturers adapt existing courses.

Author : George Polya
Publisher : Lushena Books
Page : 0 pages
File Size : 47,5 Mb
Release : 2023-02-08
Category : Computers
ISBN : 1639235663

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Mathematics and Plausible Reasoning by George Polya Pdf

This two volume classic comprises two titles: "Patterns of Plausible Inference" and "Induction and Analogy in Mathematics". This is a guide to the practical art of plausible reasoning, particularly in mathematics, but also in every field of human activity. Using mathematics as the example par excellence, Polya shows how even the most rigorous deductive discipline is heavily dependent on techniques of guessing, inductive reasoning, and reasoning by analogy. In solving a problem, the answer must be guessed at before a proof can be given, and guesses are usually made from a knowledge of facts, experience, and hunches. The truly creative mathematician must be a good guesser first and a good prover afterward; many important theorems have been guessed but no proved until much later. In the same way, solutions to problems can be guessed, and a god guesser is much more likely to find a correct solution. This work might have been called "How to Become a Good Guesser."-From the Dust Jacket.

Author : David Gries,Fred B. Schneider
Publisher : Springer Science & Business Media
Page : 517 pages
File Size : 49,6 Mb
Release : 2013-03-14
Category : Computers
ISBN : 9781475738377

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A Logical Approach to Discrete Math by David Gries,Fred B. Schneider Pdf

Here, the authors strive to change the way logic and discrete math are taught in computer science and mathematics: while many books treat logic simply as another topic of study, this one is unique in its willingness to go one step further. The book traets logic as a basic tool which may be applied in essentially every other area.

Author : Bertrand Russell
Publisher : Courier Corporation
Page : 230 pages
File Size : 55,7 Mb
Release : 1993-01-01
Category : Mathematics
ISBN : 0486277240

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Introduction to Mathematical Philosophy by Bertrand Russell Pdf

In the words of Bertrand Russell, "Because language is misleading, as well as because it is diffuse and inexact when applied to logic (for which it was never intended), logical symbolism is absolutely necessary to any exact or thorough treatment of mathematical philosophy." That assertion underlies this book, a seminal work in the field for more than 70 years. In it, Russell offers a nontechnical, undogmatic account of his philosophical criticism as it relates to arithmetic and logic. Rather than an exhaustive treatment, however, the influential philosopher and mathematician focuses on certain issues of mathematical logic that, to his mind, invalidated much traditional and contemporary philosophy. In dealing with such topics as number, order, relations, limits and continuity, propositional functions, descriptions, and classes, Russell writes in a clear, accessible manner, requiring neither a knowledge of mathematics nor an aptitude for mathematical symbolism. The result is a thought-provoking excursion into the fascinating realm where mathematics and philosophy meet — a philosophical classic that will be welcomed by any thinking person interested in this crucial area of modern thought.

Author : Ken Levasseur,Al Doerr
Publisher : Lulu.com
Page : 574 pages
File Size : 51,8 Mb
Release : 2012-02-25
Category : Applied mathematics
ISBN : 9781105559297

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Applied Discrete Structures by Ken Levasseur,Al Doerr Pdf

Applied Discrete Structures, is a two semester undergraduate text in discrete mathematics, focusing on the structural properties of mathematical objects. These include matrices, functions, graphs, trees, lattices and algebraic structures. The algebraic structures that are discussed are monoids, groups, rings, fields and vector spaces. Website: http: //discretemath.org Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative. For more information on open textbooks, visit http: //www.aimath.org/textbooks/. This version was created using Mathbook XML (https: //mathbook.pugetsound.edu/) Al Doerr is Emeritus Professor of Mathematical Sciences at UMass Lowell. His interests include abstract algebra and discrete mathematics. Ken Levasseur is a Professor of Mathematical Sciences at UMass Lowell. His interests include discrete mathematics and abstract algebra, and their implementation using computer algebra systems.