Introduction To Mathematical Proofs

Introduction to Mathematical Proofs PDF
Author: Charles Roberts
Publisher: CRC Press
ISBN: 1482246880
Size: 34.40 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : un
Pages : 414
View: 5758

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Introduction to Mathematical Proofs helps students develop the necessary skills to write clear, correct, and concise proofs. Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive mathematical systems and the systems of natural numbers, integers, rational numbers, and real numbers. It also covers elementary topics in set theory, explores various properties of relations and functions, and proves several theorems using induction. The final chapters introduce the concept of cardinalities of sets and the concepts and proofs of real analysis and group theory. In the appendix, the author includes some basic guidelines to follow when writing proofs. This new edition includes more than 125 new exercises in sections titled More Challenging Exercises. Also, numerous examples illustrate in detail how to write proofs and show how to solve problems. These examples can serve as models for students to emulate when solving exercises. Several biographical sketches and historical comments have been included to enrich and enliven the text. Written in a conversational style, yet maintaining the proper level of mathematical rigor, this accessible book teaches students to reason logically, read proofs critically, and write valid mathematical proofs. It prepares them to succeed in more advanced mathematics courses, such as abstract algebra and analysis.

Mathematical Proofs

Mathematical Proofs PDF
Author: Gary Chartrand
Publisher:
ISBN: 9781292040646
Size: 17.44 MB
Format: PDF
Category : Mathematics
Languages : un
Pages : 418
View: 4326

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Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition, prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own. Written in a clear, conversational style, this book provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory. It is also a great reference text that students can look back to when writing or reading proofs in their more advanced courses.

Math Proofs Demystified

Math Proofs Demystified PDF
Author: Stan Gibilisco
Publisher: McGraw Hill Professional
ISBN: 0071469923
Size: 52.48 MB
Format: PDF, ePub
Category : Mathematics
Languages : un
Pages : 290
View: 4597

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Almost every student has to study some sort of mathematical proofs, whether it be in geometry, trigonometry, or with higher-level topics. In addition, mathematical theorems have become an interesting course for many students outside of the mathematical arena, purely for the reasoning and logic that is needed to complete them. Therefore, it is not uncommon to have philosophy and law students grappling with proofs. This book is the perfect resource for demystifying the techniques and principles that govern the mathematical proof area, and is done with the standard “Demystified” level, questions and answers, and accessibility.

Introduction To Mathematical Proofs

Introduction to Mathematical Proofs PDF
Author: Charles Roberts
Publisher: CRC Press
ISBN: 9781420069563
Size: 66.36 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 433
View: 6081

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Shows How to Read & Write Mathematical Proofs Ideal Foundation for More Advanced Mathematics Courses Introduction to Mathematical Proofs: A Transition facilitates a smooth transition from courses designed to develop computational skills and problem solving abilities to courses that emphasize theorem proving. It helps students develop the skills necessary to write clear, correct, and concise proofs. Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive mathematical systems and the systems of natural numbers, integers, rational numbers, and real numbers. It also covers elementary topics in set theory, explores various properties of relations and functions, and proves several theorems using induction. The final chapters introduce the concept of cardinalities of sets and the concepts and proofs of real analysis and group theory. In the appendix, the author includes some basic guidelines to follow when writing proofs. Written in a conversational style, yet maintaining the proper level of mathematical rigor, this accessible book teaches students to reason logically, read proofs critically, and write valid mathematical proofs. It will prepare them to succeed in more advanced mathematics courses, such as abstract algebra and geometry.

Mathematical Proofs

Mathematical Proofs PDF
Author: Gary Chartrand
Publisher: Addison-Wesley
ISBN:
Size: 45.82 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 289
View: 7172

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Mathematical Proofs is designed to prepare students for the more abstract mathematics courses that follow calculus. This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise providing solid introductions to relations, functions, and cardinalities of sets.

Metamath A Computer Language For Mathematical Proofs

Metamath  A Computer Language for Mathematical Proofs PDF
Author: Norman Megill
Publisher: Lulu.com
ISBN: 0359702236
Size: 37.67 MB
Format: PDF, Kindle
Category :
Languages : en
Pages : 248
View: 3989

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Metamath is a computer language and an associated computer program for archiving, verifying, and studying mathematical proofs. The Metamath language is simple and robust, with an almost total absence of hard-wired syntax, and we believe that it provides about the simplest possible framework that allows essentially all of mathematics to be expressed with absolute rigor. While simple, it is also powerful; the Metamath Proof Explorer (MPE) database has over 23,000 proven theorems and is one of the top systems in the ?Formalizing 100 Theorems? challenge. This book explains the Metamath language and program, with specific emphasis on the fundamentals of the MPE database.

Logic Sets And The Techniques Of Mathematical Proofs

LOGIC  SETS AND THE TECHNIQUES OF MATHEMATICAL PROOFS PDF
Author: Brahima MBODJE, Ph.D.
Publisher: Author House
ISBN: 1463429665
Size: 28.84 MB
Format: PDF, Kindle
Category : Education
Languages : en
Pages : 356
View: 761

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As its title indicates, this book is about logic, sets and mathematical proofs. It is a careful, patient and rigorous introduction for readers with very limited mathematical maturity. It teaches the reader not only how to read a mathematical proof, but also how to write one. To achieve this, we carefully lay out all the various proof methods encountered in mathematical discourse, give their logical justifications, and apply them to the study of topics [such as real numbers, relations, functions, sequences, fine sets, infinite sets, countable sets, uncountable sets and transfinite numbers] whose mastery is important for anyone contemplating advanced studies in mathematics. The book is completely self-contained; since the prerequisites for reading it are only a sound background in high school algebra. Though this book is meant to be a companion specifically for senior high school pupils and college undergraduate students, it will also be of immense value to anyone interested in acquiring the tools and way of thinking of the mathematician.

Logic Sets And The Techniques Of Mathematical Proofs

Logic  Sets and the Techniques of Mathematical Proofs PDF
Author: Brahima Mbodje Ph. D.
Publisher: AuthorHouse
ISBN: 1463429673
Size: 19.82 MB
Format: PDF, Docs
Category : Education
Languages : un
Pages : 356
View: 6788

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As its title indicates, this book is about logic, sets and mathematical proofs. It is a careful, patient and rigorous introduction for readers with very limited mathematical maturity. It teaches the reader not only how to read a mathematical proof, but also how to write one. To achieve this, we carefully lay out all the various proof methods encountered in mathematical discourse, give their logical justifications, and apply them to the study of topics [such as real numbers, relations, functions, sequences, fine sets, infinite sets, countable sets, uncountable sets and transfinite numbers] whose mastery is important for anyone contemplating advanced studies in mathematics. The book is completely self-contained; since the prerequisites for reading it are only a sound background in high school algebra. Though this book is meant to be a companion specifically for senior high school pupils and college undergraduate students, it will also be of immense value to anyone interested in acquiring the tools and way of thinking of the mathematician.

Das Buch Der Beweise

Das BUCH der Beweise PDF
Author: Martin Aigner
Publisher: Springer-Verlag
ISBN: 3662064545
Size: 22.30 MB
Format: PDF, ePub
Category : Mathematics
Languages : de
Pages : 247
View: 3759

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Die elegantesten mathematischen Beweise, spannend und für jeden Interessierten verständlich. "Der Beweis selbst, seine Ästhetik, seine Pointe geht ins Geschichtsbuch der Königin der Wissenschaften ein. Ihre Anmut offenbart sich in dem gelungenen und geschickt illustrierten Buch." Die Zeit

An Introduction To Mathematical Proofs

An Introduction to Mathematical Proofs PDF
Author: Nicholas A. Loehr
Publisher: CRC Press
ISBN: 1000709809
Size: 23.16 MB
Format: PDF
Category : Mathematics
Languages : un
Pages : 396
View: 1137

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An Introduction to Mathematical Proofs presents fundamental material on logic, proof methods, set theory, number theory, relations, functions, cardinality, and the real number system. The text uses a methodical, detailed, and highly structured approach to proof techniques and related topics. No prerequisites are needed beyond high-school algebra. New material is presented in small chunks that are easy for beginners to digest. The author offers a friendly style without sacrificing mathematical rigor. Ideas are developed through motivating examples, precise definitions, carefully stated theorems, clear proofs, and a continual review of preceding topics. Features Study aids including section summaries and over 1100 exercises Careful coverage of individual proof-writing skills Proof annotations and structural outlines clarify tricky steps in proofs Thorough treatment of multiple quantifiers and their role in proofs Unified explanation of recursive definitions and induction proofs, with applications to greatest common divisors and prime factorizations About the Author: Nicholas A. Loehr is an associate professor of mathematics at Virginia Technical University. He has taught at College of William and Mary, United States Naval Academy, and University of Pennsylvania. He has won many teaching awards at three different schools. He has published over 50 journal articles. He also authored three other books for CRC Press, including Combinatorics, Second Edition, and Advanced Linear Algebra.

100 Mathematical Proof

100  Mathematical Proof PDF
Author: Rowan Garnier
Publisher: John Wiley & Son Limited
ISBN:
Size: 78.14 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 317
View: 3020

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"Proof" has been and remains one of the concepts which characterises mathematics. Covering basic propositional and predicate logic as well as discussing axiom systems and formal proofs, the book seeks to explain what mathematicians understand by proofs and how they are communicated. The authors explore the principle techniques of direct and indirect proof including induction, existence and uniqueness proofs, proof by contradiction, constructive and non-constructive proofs, etc. Many examples from analysis and modern algebra are included. The exceptionally clear style and presentation ensures that the book will be useful and enjoyable to those studying and interested in the notion of mathematical "proof."

Mathematical Proofs

Mathematical Proofs PDF
Author: Gary Chartrand
Publisher: Pearson College Division
ISBN: 9780321797094
Size: 49.82 MB
Format: PDF, Mobi
Category : Mathematics
Languages : un
Pages : 400
View: 5325

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Normal 0 false false false Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition, prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own. Written in a clear, conversational style, this book provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory. It is also a great reference text that students can look back to when writing or reading proofs in their more advanced courses.

Q E D

Q E D PDF
Author: Burkard Polster
Publisher: Wooden
ISBN: 9781904263500
Size: 40.44 MB
Format: PDF
Category : Proof theory
Languages : un
Pages : 64
View: 3836

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'Q.E.D.' presents some of the most famous mathematical proofs in a charming book that will appeal to non-mathematicians and experts alike.