Mathematical Induction
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Mathematical Induction
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Author : Titu Andreescu
language : en
Publisher:
Release Date : 2017-03-15
Mathematical Induction written by Titu Andreescu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-15 with Induction (Mathematics) categories.
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.
Handbook Of Mathematical Induction
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Author : David S. Gunderson
language : en
Publisher: Chapman & Hall/CRC
Release Date : 2016-11-16
Handbook Of Mathematical Induction written by David S. Gunderson and has been published by Chapman & Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-16 with Induction (Mathematics) categories.
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.
Mathematical Reasoning
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Author : Theodore A. Sundstrom
language : en
Publisher:
Release Date : 2003
Mathematical Reasoning written by Theodore A. Sundstrom and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Proof theory categories.
Focusing on the formal development of mathematics, this book demonstrates how to read and understand, write and construct mathematical proofs. It emphasizes active learning, and uses elementary number theory and congruence arithmetic throughout. Chapter content covers an introduction to writing in mathematics, logical reasoning, constructing proofs, set theory, mathematical induction, functions, equivalence relations, topics in number theory, and topics in set theory. For learners making the transition form calculus to more advanced mathematics.
Mathematical Induction
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Author : Jianlun Xu
language : en
Publisher: Independently Published
Release Date : 2020-04-08
Mathematical Induction written by Jianlun Xu and has been published by Independently Published this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-08 with categories.
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.
Induction In Geometry
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Author : L.I. Golovina
language : en
Publisher: Courier Dover Publications
Release Date : 2019-10-16
Induction In Geometry written by L.I. Golovina and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-16 with Mathematics categories.
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.
Discrete Maths And Its Applications Global Edition 7e
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Author : Kenneth Rosen
language : en
Publisher: McGraw Hill
Release Date : 2012-09-16
Discrete Maths And Its Applications Global Edition 7e written by Kenneth Rosen and has been published by McGraw Hill this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-16 with Mathematics categories.
We are pleased to present this Global Edition which has been developed specifically to meet the needs of international students of discrete mathematics. In addition to great depth in key areas and a broad range of real-world applications across multiple disciplines, we have added new material to make the content more relevant and improve learning outcomes for the international student.This Global Edition includes: An entire new chapter on Algebraic Structures and Coding Theory New and expanded sections within chapters covering Foundations, Basic Structures, and Advanced Counting Techniques Special online only chapters on Boolean Algebra and Modeling Computation New and revised problems for the international student integrating alternative methods and solutions.This Global Edition has been adapted to meet the needs of courses outside of the United States and does not align with the instructor and student resources available with the US edition.
A Readable Introduction To Real Mathematics
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Author : Daniel Rosenthal
language : en
Publisher: Springer
Release Date : 2019-04-02
A Readable Introduction To Real Mathematics written by Daniel Rosenthal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-02 with Mathematics categories.
Designed for an undergraduate course or for independent study, this text presents sophisticated mathematical ideas in an elementary and friendly fashion. The fundamental purpose of this book is to teach mathematical thinking while conveying the beauty and elegance of mathematics. The book contains a large number of exercises of varying difficulty, some of which are designed to help reinforce basic concepts and others of which will challenge virtually all readers. The sole prerequisite for reading this text is high school algebra. Topics covered include: * mathematical induction * modular arithmetic * the Fundamental Theorem of Arithmetic * Fermat's Little Theorem * RSA encryption * the Euclidean algorithm * rational and irrational numbers * complex numbers * cardinality * Euclidean plane geometry * constructibility (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass)* infinite series * higher dimensional spaces. This textbook is suitable for a wide variety of courses and for a broad range of students of mathematics and other subjects. Mathematically inclined senior high school students will also be able to read this book. From the reviews of the first edition: “It is carefully written in a precise but readable and engaging style... I thoroughly enjoyed reading this recent addition to the Springer Undergraduate Texts in Mathematics series and commend this clear, well-organised, unfussy text to its target audiences.” (Nick Lord, The Mathematical Gazette, Vol. 100 (547), 2016) “The book is an introduction to real mathematics and is very readable. ... The book is indeed a joy to read, and would be an excellent text for an ‘appreciation of mathematics’ course, among other possibilities.” (G.A. Heuer, Mathematical Reviews, February, 2015) “Many a benighted book misguidedly addresses the need [to teach mathematical thinking] by framing reasoning, or narrowly, proof, not as pervasive modality but somehow as itself an autonomous mathematical subject. Fortunately, the present book gets it right.... [presenting] well-chosen, basic, conceptual mathematics, suitably accessible after a K-12 education, in a detailed, self-conscious way that emphasizes methodology alongside content and crucially leads to an ultimate clear payoff. ... Summing Up: Recommended. Lower-division undergraduates and two-year technical program students; general readers.” (D.V. Feldman, Choice, Vol. 52 (6), February, 2015)
Discrete Mathematics
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Author : Iyengar, N.Ch. S.N./Chandrasekaran V.M./Venkalesh K.A. & Arunachalam P.S.
language : en
Publisher: Vikas Publishing House
Release Date : 2003-11-01
Discrete Mathematics written by Iyengar, N.Ch. S.N./Chandrasekaran V.M./Venkalesh K.A. & Arunachalam P.S. and has been published by Vikas Publishing House this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-01 with Computers categories.
Student-friendly and comprehensive, this book covers topics such as Mathematical Logic, Set Theory, Algebraic Systems, Boolean Algebra and Graph Theory that are essential to the study of Computer Science in great detail.
Oswaal Isc Question Bank Class 11 Mathematics Chapterwise Topicwise Solved Papers For 2025 Exams
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Author : Oswaal Editorial Board
language : en
Publisher: Oswaal Books
Release Date : 2024-03-02
Oswaal Isc Question Bank Class 11 Mathematics Chapterwise Topicwise Solved Papers For 2025 Exams written by Oswaal Editorial Board and has been published by Oswaal Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-02 with Study Aids categories.
Description of the Product: • 100% Updated with Latest 2025 Syllabus & Typologies of Questions for 2024 • Crisp Revision with Topic wise Revision Notes & Smart Mind Maps • Extensive Practice with 1000+ Questions & Self Assessment Papers • Concept Clarity with 500+ Concepts & 50+ Concept Videos • 100% Exam Readiness with Answering Tips & Suggestions
Introduction To Discrete Mathematics Via Logic And Proof
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Author : Calvin Jongsma
language : en
Publisher: Springer Nature
Release Date : 2019-11-08
Introduction To Discrete Mathematics Via Logic And Proof written by Calvin Jongsma and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-08 with Mathematics categories.
This textbook introduces discrete mathematics by emphasizing the importance of reading and writing proofs. Because it begins by carefully establishing a familiarity with mathematical logic and proof, this approach suits not only a discrete mathematics course, but can also function as a transition to proof. Its unique, deductive perspective on mathematical logic provides students with the tools to more deeply understand mathematical methodology—an approach that the author has successfully classroom tested for decades. Chapters are helpfully organized so that, as they escalate in complexity, their underlying connections are easily identifiable. Mathematical logic and proofs are first introduced before moving onto more complex topics in discrete mathematics. Some of these topics include: Mathematical and structural induction Set theory Combinatorics Functions, relations, and ordered sets Boolean algebra and Boolean functions Graph theory Introduction to Discrete Mathematics via Logic and Proof will suit intermediate undergraduates majoring in mathematics, computer science, engineering, and related subjects with no formal prerequisites beyond a background in secondary mathematics.