The Nuts and Bolts of Proofs PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download The Nuts and Bolts of Proofs PDF full book. Access full book title The Nuts and Bolts of Proofs by Antonella Cupillari. Download full books in PDF and EPUB format.
Author: Antonella Cupillari
Publisher: Academic Press
ISBN: 9780121994518
Category : Mathematics
Languages : en
Pages : 166
Get Book Here
Book Description
This book leads readers through a progressive explanation of what mathematical proofs are, why they are important, and how they work, along with a presentation of basic techniques used to construct proofs. The Second Edition presents more examples, more exercises, a more complete treatment of mathematical induction and set theory, and it incorporates suggestions from students and colleagues. Since the mathematical concepts used are relatively elementary, the book can be used as a supplement in any post-calculus course. This title has been successfully class-tested for years. There is an index for easier reference, a more extensive list of definitions and concepts, and an updated bibliography. An extensive collection of exercises with complete answers are provided, enabling students to practice on their own. Additionally, there is a set of problems without solutions to make it easier for instructors to prepare homework assignments. * Successfully class-tested over a number of years * Index for easy reference * Extensive list of definitions and concepts * Updated biblography
Author: Antonella Cupillari
Publisher: Academic Press
ISBN: 9780121994518
Category : Mathematics
Languages : en
Pages : 166
Get Book Here
Book Description
This book leads readers through a progressive explanation of what mathematical proofs are, why they are important, and how they work, along with a presentation of basic techniques used to construct proofs. The Second Edition presents more examples, more exercises, a more complete treatment of mathematical induction and set theory, and it incorporates suggestions from students and colleagues. Since the mathematical concepts used are relatively elementary, the book can be used as a supplement in any post-calculus course. This title has been successfully class-tested for years. There is an index for easier reference, a more extensive list of definitions and concepts, and an updated bibliography. An extensive collection of exercises with complete answers are provided, enabling students to practice on their own. Additionally, there is a set of problems without solutions to make it easier for instructors to prepare homework assignments. * Successfully class-tested over a number of years * Index for easy reference * Extensive list of definitions and concepts * Updated biblography
Author: Neil R. Nicholson
Publisher: CRC Press
ISBN: 0429522002
Category : Mathematics
Languages : en
Pages : 465
Get Book Here
Book Description
A Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of the proof takes place: thought processes, scratch work and ways to attack problems. Readers will learn not just how to write mathematics but also how to do mathematics. They will then learn to communicate mathematics effectively. The text emphasizes the creativity, intuition, and correct mathematical exposition as it prepares students for courses beyond the calculus sequence. The author urges readers to work to define their mathematical voices. This is done with style tips and strict "mathematical do’s and don’ts", which are presented in eye-catching "text-boxes" throughout the text. The end result enables readers to fully understand the fundamentals of proof. Features: The text is aimed at transition courses preparing students to take analysis Promotes creativity, intuition, and accuracy in exposition The language of proof is established in the first two chapters, which cover logic and set theory Includes chapters on cardinality and introductory topology
Author: Imre Lakatos
Publisher: Cambridge University Press
ISBN: 9780521290388
Category : Mathematics
Languages : en
Pages : 190
Get Book Here
Book Description
Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.
Author: Tom Kenny
Publisher: John Wiley & Sons
ISBN: 1444357077
Category : Medical
Languages : en
Pages : 462
Get Book Here
Book Description
Nothing is more perplexing to the clinician new to device therapy than having to deal with cardiac electrocardiograms from a device patient. Pacemakers and other implantable cardiac rhythm management devices leave their “imprint” on ECGs and can significantly change what clinicians see - or expect to see. Evaluating paced ECGs can be challenging, yet nowhere is it taught in any sort of comprehensive manner. Designed specifically for clinicians new to device therapy, The Nuts and Bolts of Interpreting Paced ECGs and EGMs offers practical, reliable and objective information on paced cardiac electrograms. Written in a lively, intelligent and easy to navigate style, emphasizing real-life clinical practice and practical tips, this book includes illustrated paced ECGs by skilled artists to help minimize “fuzzy” lines and emphasize key points. Each chapter concludes with a checklist of key points from each subject (“Nuts and Bolts”).
Author: Daniel J. Velleman
Publisher: Cambridge University Press
ISBN: 0521861241
Category : Mathematics
Languages : en
Pages : 401
Get Book Here
Book Description
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
Author: Antonella Cupillari
Publisher: Academic Press
ISBN: 0080537901
Category : Mathematics
Languages : en
Pages : 193
Get Book Here
Book Description
The Nuts and Bolts of Proof instructs students on the basic logic of mathematical proofs, showing how and why proofs of mathematical statements work. It provides them with techniques they can use to gain an inside view of the subject, reach other results, remember results more easily, or rederive them if the results are forgotten.A flow chart graphically demonstrates the basic steps in the construction of any proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems.* The "List of Symbols" has been extended.* Set Theory section has been strengthened with more examples and exercises.* Addition of "A Collection of Proofs"
Author: Gary Chartrand
Publisher: Pearson
ISBN: 9780321797094
Category : Proof theory
Languages : en
Pages : 0
Get Book Here
Book Description
This book prepares students for the more abstract mathematics courses that follow calculus. The author introduces students to proof techniques, analyzing proofs, and writing proofs of their own. It also 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.
Author: Daniel P. Friedman
Publisher: MIT Press
ISBN: 0262330571
Category : Computers
Languages : en
Pages : 244
Get Book Here
Book Description
An introduction to writing proofs about computer programs, written in an accessible question-and-answer style, complete with step-by-step examples and a simple proof assistant. The Little Prover introduces inductive proofs as a way to determine facts about computer programs. It is written in an approachable, engaging style of question-and-answer, with the characteristic humor of The Little Schemer (fourth edition, MIT Press). Sometimes the best way to learn something is to sit down and do it; the book takes readers through step-by-step examples showing how to write inductive proofs. The Little Prover assumes only knowledge of recursive programs and lists (as presented in the first three chapters of The Little Schemer) and uses only a few terms beyond what novice programmers already know. The book comes with a simple proof assistant to help readers work through the book and complete solutions to every example.
Author: KRANTZ
Publisher: Birkhäuser
ISBN: 3034876440
Category : Science
Languages : en
Pages : 190
Get Book Here
Book Description
The subject of real analytic functions is one of the oldest in mathe matical analysis. Today it is encountered early in ones mathematical training: the first taste usually comes in calculus. While most work ing mathematicians use real analytic functions from time to time in their work, the vast lore of real analytic functions remains obscure and buried in the literature. It is remarkable that the most accessible treatment of Puiseux's theorem is in Lefschetz's quite old Algebraic Geometry, that the clearest discussion of resolution of singularities for real analytic manifolds is in a book review by Michael Atiyah, that there is no comprehensive discussion in print of the embedding prob lem for real analytic manifolds. We have had occasion in our collaborative research to become ac quainted with both the history and the scope of the theory of real analytic functions. It seems both appropriate and timely for us to gather together this information in a single volume. The material presented here is of three kinds. The elementary topics, covered in Chapter 1, are presented in great detail. Even results like a real ana lytic inverse function theorem are difficult to find in the literature, and we take pains here to present such topics carefully. Topics of middling difficulty, such as separate real analyticity, Puiseux series, the FBI transform, and related ideas (Chapters 2-4), are covered thoroughly but rather more briskly.
Author: James V. Stone
Publisher: MIT Press
ISBN: 9780262693158
Category : Computers
Languages : en
Pages : 224
Get Book Here
Book Description
A tutorial-style introduction to a class of methods for extracting independent signals from a mixture of signals originating from different physical sources; includes MatLab computer code examples. Independent component analysis (ICA) is becoming an increasingly important tool for analyzing large data sets. In essence, ICA separates an observed set of signal mixtures into a set of statistically independent component signals, or source signals. In so doing, this powerful method can extract the relatively small amount of useful information typically found in large data sets. The applications for ICA range from speech processing, brain imaging, and electrical brain signals to telecommunications and stock predictions. In Independent Component Analysis, Jim Stone presents the essentials of ICA and related techniques (projection pursuit and complexity pursuit) in a tutorial style, using intuitive examples described in simple geometric terms. The treatment fills the need for a basic primer on ICA that can be used by readers of varying levels of mathematical sophistication, including engineers, cognitive scientists, and neuroscientists who need to know the essentials of this evolving method. An overview establishes the strategy implicit in ICA in terms of its essentially physical underpinnings and describes how ICA is based on the key observations that different physical processes generate outputs that are statistically independent of each other. The book then describes what Stone calls "the mathematical nuts and bolts" of how ICA works. Presenting only essential mathematical proofs, Stone guides the reader through an exploration of the fundamental characteristics of ICA. Topics covered include the geometry of mixing and unmixing; methods for blind source separation; and applications of ICA, including voice mixtures, EEG, fMRI, and fetal heart monitoring. The appendixes provide a vector matrix tutorial, plus basic demonstration computer code that allows the reader to see how each mathematical method described in the text translates into working Matlab computer code.
