Introduction To Proof Through Number Theory

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Introduction To Proof Through Number Theory

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Author : Bennett Chow
language : en
Publisher: American Mathematical Society
Release Date : 2023-02-09

Introduction To Proof Through Number Theory written by Bennett Chow and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-09 with Mathematics categories.

Lighten up about mathematics! Have fun. If you read this book, you will have to endure bad math puns and jokes and out-of-date pop culture references. You'll learn some really cool mathematics to boot. In the process, you will immerse yourself in living, thinking, and breathing logical reasoning. We like to call this proofs, which to some is a bogey word, but to us it is a boogie word. You will learn how to solve problems, real and imagined. After all, math is a game where, although the rules are pretty much set, we are left to our imaginations to create. Think of this book as blueprints, but you are the architect of what structures you want to build. Make sure you lay a good foundation, for otherwise your buildings might fall down. To help you through this, we guide you to think and plan carefully. Our playground consists of basic math, with a loving emphasis on number theory. We will encounter the known and the unknown. Ancient and modern inquirers left us with elementary-sounding mathematical puzzles that are unsolved to this day. You will learn induction, logic, set theory, arithmetic, and algebra, and you may one day solve one of these puzzles.

Introduction To Proof In Abstract Mathematics

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Author : Andrew Wohlgemuth
language : en
Publisher: Courier Corporation
Release Date : 2011-02-17

Introduction To Proof In Abstract Mathematics written by Andrew Wohlgemuth and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-17 with Mathematics categories.

Originally published: Philadelphia: Saunders College Pub., c1990.

Book Of Proof

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Author : Richard H. Hammack
language : en
Publisher:
Release Date : 2013-05

Book Of Proof written by Richard H. Hammack and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05 with Mathematics categories.

This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

Introduction To Proof Through Number Theory

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Author : BENNETT. CHOW
language : en
Publisher:
Release Date : 2023

Introduction To Proof Through Number Theory written by BENNETT. CHOW and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Electronic books categories.

Lighten up about mathematics! Have fun. If you read this book, you will have to endure bad math puns and jokes and out-of-date pop culture references. You'll learn some really cool mathematics to boot. In the process, you will immerse yourself in living, thinking, and breathing logical reasoning. We like to call this proofs, which to some is a bogey word, but to us it is a boogie word. You will learn how to solve problems, real and imagined. After all, math is.

Number Theory

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Author : George E. Andrews
language : en
Publisher: Courier Corporation
Release Date : 2012-04-30

Number Theory written by George E. Andrews and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-30 with Mathematics categories.

Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.

Handbook Of Proof Theory

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Author : S.R. Buss
language : en
Publisher: Elsevier
Release Date : 1998-07-09

Handbook Of Proof Theory written by S.R. Buss and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-07-09 with Mathematics categories.

This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth.The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.

An Introduction To Proof Through Real Analysis

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Author : Daniel J. Madden
language : en
Publisher: John Wiley & Sons
Release Date : 2017-08-14

An Introduction To Proof Through Real Analysis written by Daniel J. Madden and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-14 with Education categories.

An engaging and accessible introduction to mathematical proof incorporating ideas from real analysis A mathematical proof is an inferential argument for a mathematical statement. Since the time of the ancient Greek mathematicians, the proof has been a cornerstone of the science of mathematics. The goal of this book is to help students learn to follow and understand the function and structure of mathematical proof and to produce proofs of their own. An Introduction to Proof through Real Analysis is based on course material developed and refined over thirty years by Professor Daniel J. Madden and was designed to function as a complete text for both first proofs and first analysis courses. Written in an engaging and accessible narrative style, this book systematically covers the basic techniques of proof writing, beginning with real numbers and progressing to logic, set theory, topology, and continuity. The book proceeds from natural numbers to rational numbers in a familiar way, and justifies the need for a rigorous definition of real numbers. The mathematical climax of the story it tells is the Intermediate Value Theorem, which justifies the notion that the real numbers are sufficient for solving all geometric problems. • Concentrates solely on designing proofs by placing instruction on proof writing on top of discussions of specific mathematical subjects • Departs from traditional guides to proofs by incorporating elements of both real analysis and algebraic representation • Written in an engaging narrative style to tell the story of proof and its meaning, function, and construction • Uses a particular mathematical idea as the focus of each type of proof presented • Developed from material that has been class-tested and fine-tuned over thirty years in university introductory courses An Introduction to Proof through Real Analysis is the ideal introductory text to proofs for second and third-year undergraduate mathematics students, especially those who have completed a calculus sequence, students learning real analysis for the first time, and those learning proofs for the first time. Daniel J. Madden, PhD, is an Associate Professor of Mathematics at The University of Arizona, Tucson, Arizona, USA. He has taught a junior level course introducing students to the idea of a rigorous proof based on real analysis almost every semester since 1990. Dr. Madden is the winner of the 2015 Southwest Section of the Mathematical Association of America Distinguished Teacher Award. Jason A. Aubrey, PhD, is Assistant Professor of Mathematics and Director, Mathematics Center of the University of Arizona.

Journey Into Mathematics

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Author : Joseph J. Rotman
language : en
Publisher: Courier Corporation
Release Date : 2013-01-18

Journey Into Mathematics written by Joseph J. Rotman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-18 with Mathematics categories.

This treatment covers the mechanics of writing proofs, the area and circumference of circles, and complex numbers and their application to real numbers. 1998 edition.

How To Prove It

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Author : Daniel J. Velleman
language : en
Publisher: Cambridge University Press
Release Date : 2006-01-16

How To Prove It written by Daniel J. Velleman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-16 with Mathematics categories.

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.

A Classical Introduction To Modern Number Theory

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Author : Kenneth Ireland
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

A Classical Introduction To Modern Number Theory written by Kenneth Ireland and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

Bridging the gap between elementary number theory and the systematic study of advanced topics, A Classical Introduction to Modern Number Theory is a well-developed and accessible text that requires only a familiarity with basic abstract algebra. Historical development is stressed throughout, along with wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. An extensive bibliography and many challenging exercises are also included. This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordell-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curves.