Mathematical Problems And Proofs PDF Download
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Author | : Branislav Kisacanin |
Publisher | : Springer Science & Business Media |
Total Pages | : 219 |
Release | : 2007-05-08 |
Genre | : Mathematics |
ISBN | : 0306469634 |
Download Mathematical Problems and Proofs Book in PDF, ePub and Kindle
A gentle introduction to the highly sophisticated world of discrete mathematics, Mathematical Problems and Proofs presents topics ranging from elementary definitions and theorems to advanced topics -- such as cardinal numbers, generating functions, properties of Fibonacci numbers, and Euclidean algorithm. This excellent primer illustrates more than 150 solutions and proofs, thoroughly explained in clear language. The generous historical references and anecdotes interspersed throughout the text create interesting intermissions that will fuel readers' eagerness to inquire further about the topics and some of our greatest mathematicians. The author guides readers through the process of solving enigmatic proofs and problems, and assists them in making the transition from problem solving to theorem proving. At once a requisite text and an enjoyable read, Mathematical Problems and Proofs is an excellent entrée to discrete mathematics for advanced students interested in mathematics, engineering, and science.
Author | : Branislav Kisačanin |
Publisher | : Springer Science & Business Media |
Total Pages | : 219 |
Release | : 1998-10-31 |
Genre | : Education |
ISBN | : 0306459671 |
Download Mathematical Problems and Proofs Book in PDF, ePub and Kindle
Introduces the various fields of discrete mathematics to talented high school students and to undergraduates who would like to see illustrations of abstract mathematical concepts and learn a bit about their historic origin. Also teaches how to read mathematical literature in general, which is, always with pencil and paper to hand. Annotation copyrighted by Book News, Inc., Portland, OR
Author | : Richard S. Millman |
Publisher | : Springer |
Total Pages | : 230 |
Release | : 2015-02-09 |
Genre | : Mathematics |
ISBN | : 3319144278 |
Download Problems and Proofs in Numbers and Algebra Book in PDF, ePub and Kindle
Focusing on an approach of solving rigorous problems and learning how to prove, this volume is concentrated on two specific content themes, elementary number theory and algebraic polynomials. The benefit to readers who are moving from calculus to more abstract mathematics is to acquire the ability to understand proofs through use of the book and the multitude of proofs and problems that will be covered throughout. This book is meant to be a transitional precursor to more complex topics in analysis, advanced number theory, and abstract algebra. To achieve the goal of conceptual understanding, a large number of problems and examples will be interspersed through every chapter. The problems are always presented in a multi-step and often very challenging, requiring the reader to think about proofs, counter-examples, and conjectures. Beyond the undergraduate mathematics student audience, the text can also offer a rigorous treatment of mathematics content (numbers and algebra) for high-achieving high school students. Furthermore, prospective teachers will add to the breadth of the audience as math education majors, will understand more thoroughly methods of proof, and will add to the depth of their mathematical knowledge. In the past, PNA has been taught in a "problem solving in middle school” course (twice), to a quite advanced high school students course (three semesters), and three times as a secondary resource for a course for future high school teachers. PNA is suitable for secondary math teachers who look for material to encourage and motivate more high achieving students.
Author | : Martin Aigner |
Publisher | : Springer Science & Business Media |
Total Pages | : 194 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 3662223430 |
Download Proofs from THE BOOK Book in PDF, ePub and Kindle
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 | : Imre Lakatos |
Publisher | : Cambridge University Press |
Total Pages | : 190 |
Release | : 1976 |
Genre | : Mathematics |
ISBN | : 9780521290388 |
Download Proofs and Refutations Book in PDF, ePub and Kindle
Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.
Author | : Steven Galovich |
Publisher | : Cengage Learning |
Total Pages | : 344 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : |
Download Doing Mathematics Book in PDF, ePub and Kindle
Prepare for success in mathematics with DOING MATHEMATICS: AN INTRODUCTION TO PROOFS AND PROBLEM SOLVING! By discussing proof techniques, problem solving methods, and the understanding of mathematical ideas, this mathematics text gives you a solid foundation from which to build while providing you with the tools you need to succeed. Numerous examples, problem solving methods, and explanations make exam preparation easy.
Author | : George Polya |
Publisher | : Lushena Books |
Total Pages | : 0 |
Release | : 2023-02-22 |
Genre | : Computers |
ISBN | : 9781639235919 |
Download Mathematics and Plausible Reasoning Book in PDF, ePub and Kindle
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 | : Daniel J. Velleman |
Publisher | : Cambridge University Press |
Total Pages | : 401 |
Release | : 2006-01-16 |
Genre | : Mathematics |
ISBN | : 0521861241 |
Download How to Prove It Book in PDF, ePub and Kindle
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 | : Branislav Kisacanin |
Publisher | : |
Total Pages | : 240 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9781475771411 |
Download Mathematical Problems and Proofs Book in PDF, ePub and Kindle
Author | : Gary Chartrand |
Publisher | : Pearson |
Total Pages | : 0 |
Release | : 2013 |
Genre | : Proof theory |
ISBN | : 9780321797094 |
Download Mathematical Proofs Book in PDF, ePub and Kindle
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.