Mathematical Induction
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Author |
: Titu Andreescu |
Publisher |
: |
Total Pages |
: 432 |
Release |
: 2017-03-15 |
ISBN-10 |
: 0996874593 |
ISBN-13 |
: 9780996874595 |
Rating |
: 4/5 (93 Downloads) |
Synopsis Mathematical Induction by : Titu Andreescu
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 |
: Hantao Zhang |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 223 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9789400916753 |
ISBN-13 |
: 9400916752 |
Rating |
: 4/5 (53 Downloads) |
Synopsis Automated Mathematical Induction by : Hantao Zhang
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 |
: Steven H. Weintraub |
Publisher |
: Courier Dover Publications |
Total Pages |
: 129 |
Release |
: 2017-05-03 |
ISBN-10 |
: 9780486821238 |
ISBN-13 |
: 0486821234 |
Rating |
: 4/5 (38 Downloads) |
Synopsis The Induction Book by : Steven H. Weintraub
Every mathematician and student of mathematics needs a familiarity with mathematical induction. This volume provides advanced undergraduates and graduate students with an introduction and a thorough exposure to these proof techniques. 2017 edition.
Author |
: David S. Gunderson |
Publisher |
: Chapman & Hall/CRC |
Total Pages |
: 921 |
Release |
: 2016-11-16 |
ISBN-10 |
: 113819901X |
ISBN-13 |
: 9781138199019 |
Rating |
: 4/5 (1X Downloads) |
Synopsis Handbook of Mathematical Induction by : David S. Gunderson
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 |
Total Pages |
: 0 |
Release |
: 2007 |
ISBN-10 |
: 0131877186 |
ISBN-13 |
: 9780131877184 |
Rating |
: 4/5 (86 Downloads) |
Synopsis Mathematical Reasoning by : Theodore A. Sundstrom
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 |
: Harris Kwong |
Publisher |
: Open SUNY Textbooks |
Total Pages |
: 298 |
Release |
: 2015-11-06 |
ISBN-10 |
: 1942341164 |
ISBN-13 |
: 9781942341161 |
Rating |
: 4/5 (64 Downloads) |
Synopsis A Spiral Workbook for Discrete Mathematics by : Harris Kwong
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 |
: Martin Aigner |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 194 |
Release |
: 2013-06-29 |
ISBN-10 |
: 9783662223437 |
ISBN-13 |
: 3662223430 |
Rating |
: 4/5 (37 Downloads) |
Synopsis Proofs from THE BOOK by : Martin Aigner
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 |
: NARAYAN CHANGDER |
Publisher |
: CHANGDER OUTLINE |
Total Pages |
: 18 |
Release |
: 2017-12-15 |
ISBN-10 |
: |
ISBN-13 |
: |
Rating |
: 4/5 ( Downloads) |
Synopsis MATHEMATICAL INDUCTION by : NARAYAN CHANGDER
THE MATHEMATICAL INDUCTION MCQ (MULTIPLE CHOICE QUESTIONS) SERVES AS A VALUABLE RESOURCE FOR INDIVIDUALS AIMING TO DEEPEN THEIR UNDERSTANDING OF VARIOUS COMPETITIVE EXAMS, CLASS TESTS, QUIZ COMPETITIONS, AND SIMILAR ASSESSMENTS. WITH ITS EXTENSIVE COLLECTION OF MCQS, THIS BOOK EMPOWERS YOU TO ASSESS YOUR GRASP OF THE SUBJECT MATTER AND YOUR PROFICIENCY LEVEL. BY ENGAGING WITH THESE MULTIPLE-CHOICE QUESTIONS, YOU CAN IMPROVE YOUR KNOWLEDGE OF THE SUBJECT, IDENTIFY AREAS FOR IMPROVEMENT, AND LAY A SOLID FOUNDATION. DIVE INTO THE MATHEMATICAL INDUCTION MCQ TO EXPAND YOUR MATHEMATICAL INDUCTION KNOWLEDGE AND EXCEL IN QUIZ COMPETITIONS, ACADEMIC STUDIES, OR PROFESSIONAL ENDEAVORS. THE ANSWERS TO THE QUESTIONS ARE PROVIDED AT THE END OF EACH PAGE, MAKING IT EASY FOR PARTICIPANTS TO VERIFY THEIR ANSWERS AND PREPARE EFFECTIVELY.
Author |
: Ilʹi︠a︡ Samuilovich Sominskiĭ |
Publisher |
: |
Total Pages |
: 61 |
Release |
: 1983 |
ISBN-10 |
: OCLC:606394337 |
ISBN-13 |
: |
Rating |
: 4/5 (37 Downloads) |
Synopsis The Method of Mathematical Induction by : Ilʹi︠a︡ Samuilovich Sominskiĭ
Author |
: Jianlun Xu |
Publisher |
: Independently Published |
Total Pages |
: 57 |
Release |
: 2020-04-08 |
ISBN-10 |
: 9798629868644 |
ISBN-13 |
: |
Rating |
: 4/5 (44 Downloads) |
Synopsis Mathematical Induction by : Jianlun Xu
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.