Proofs 101

Author : Joseph Kirtland
Publisher : CRC Press
Page : 197 pages
File Size : 50,8 Mb
Release : 2020-11-21
Category : Mathematics
ISBN : 9781000227345

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Proofs 101 by Joseph Kirtland Pdf

Proofs 101: An Introduction to Formal Mathematics serves as an introduction to proofs for mathematics majors who have completed the calculus sequence (at least Calculus I and II) and a first course in linear algebra. The book prepares students for the proofs they will need to analyze and write the axiomatic nature of mathematics and the rigors of upper-level mathematics courses. Basic number theory, relations, functions, cardinality, and set theory will provide the material for the proofs and lay the foundation for a deeper understanding of mathematics, which students will need to carry with them throughout their future studies. Features Designed to be teachable across a single semester Suitable as an undergraduate textbook for Introduction to Proofs or Transition to Advanced Mathematics courses Offers a balanced variety of easy, moderate, and difficult exercises

Author : Joseph Kirtland
Publisher : CRC Press
Page : 164 pages
File Size : 53,9 Mb
Release : 2020-12-11
Category : Mathematics
ISBN : 9781000227383

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Proofs 101 by Joseph Kirtland Pdf

Proofs 101: An Introduction to Formal Mathematics serves as an introduction to proofs for mathematics majors who have completed the calculus sequence (at least Calculus I and II) and a first course in linear algebra. The book prepares students for the proofs they will need to analyze and write the axiomatic nature of mathematics and the rigors of upper-level mathematics courses. Basic number theory, relations, functions, cardinality, and set theory will provide the material for the proofs and lay the foundation for a deeper understanding of mathematics, which students will need to carry with them throughout their future studies. Features Designed to be teachable across a single semester Suitable as an undergraduate textbook for Introduction to Proofs or Transition to Advanced Mathematics courses Offers a balanced variety of easy, moderate, and difficult exercises

Author : Bachmair
Publisher : Springer Science & Business Media
Page : 142 pages
File Size : 41,6 Mb
Release : 2013-03-08
Category : Mathematics
ISBN : 9781468471182

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Canonical Equational Proofs by Bachmair Pdf

Equations occur in many computer applications, such as symbolic compu tation, functional programming, abstract data type specifications, program verification, program synthesis, and automated theorem proving. Rewrite systems are directed equations used to compute by replacing subterms in a given formula by equal terms until a simplest form possible, called a normal form, is obtained. The theory of rewriting is concerned with the compu tation of normal forms. We shall study the use of rewrite techniques for reasoning about equations. Reasoning about equations may, for instance, involve deciding whether an equation is a logical consequence of a given set of equational axioms. Convergent rewrite systems are those for which the rewriting process de fines unique normal forms. They can be thought of as non-deterministic functional programs and provide reasonably efficient decision procedures for the underlying equational theories. The Knuth-Bendix completion method provides a means of testing for convergence and can often be used to con struct convergent rewrite systems from non-convergent ones. We develop a proof-theoretic framework for studying completion and related rewrite based proof procedures. We shall view theorem provers as proof transformation procedures, so as to express their essential properties as proof normalization theorems.

Author : William Mawdesly BEST
Publisher : Unknown
Page : 910 pages
File Size : 48,9 Mb
Release : 1860
Category : Electronic
ISBN : BL:A0017637239

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A Treatise on the Principles of Evidence and Practice as to Proofs in Courts of Common Law; with elementary rules for conducting the examination and cross-examination of witnesses by William Mawdesly BEST Pdf

Author : Sol Azuelos-Atias
Publisher : John Benjamins Publishing
Page : 193 pages
File Size : 43,5 Mb
Release : 2007-07-26
Category : Language Arts & Disciplines
ISBN : 9789027292155

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A Pragmatic Analysis of Legal Proofs of Criminal Intent by Sol Azuelos-Atias Pdf

A Pragmatic Analysis of Legal Proofs of Criminal Intent is a detailed investigation of proofs of criminal intent in Israeli courtrooms. The book analyses linguistic, pragmatic, interpretative and argumentative strategies used by Israeli lawyers and judges in order to examine the defendant’s intention. There can be no doubt that this subject is worthy of a thorough investigation. A person’s intention is a psychological phenomenon and therefore, unless the defendant chooses to confess his intent, it cannot be proven directly – either by evidence or by witnesses’ testimonies. The defendant’s intention must be inferred usually from the overall circumstances of the case; verbal and situational contexts, cultural and ideological assumptions and implicatures should be taken into account. The linguistic analysis of these inferences presented here is necessarily comprehensive: it requires consideration of a variety of theoretical frameworks including speech act theory, discourse analysis, argumentation theory, polyphony theory and text linguistics.

Author : Larry Gerstein
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 51,6 Mb
Release : 2013-11-21
Category : Science
ISBN : 9781468467086

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Introduction · to Mathematical Structures and · Proofs by Larry Gerstein Pdf

This is a textbook for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, and so on. Without such a "bridge" course, most upper division instructors feel the need to start their courses with the rudiments of logic, set theory, equivalence relations, and other basic mathematical raw materials before getting on with the subject at hand. Students who are new to higher mathematics are often startled to discover that mathematics is a subject of ideas, and not just formulaic rituals, and that they are now expected to understand and create mathematical proofs. Mastery of an assortment of technical tricks may have carried the students through calculus, but it is no longer a guarantee of academic success. Students need experience in working with abstract ideas at a nontrivial level if they are to achieve the sophisticated blend of knowledge, disci pline, and creativity that we call "mathematical maturity. " I don't believe that "theorem-proving" can be taught any more than "question-answering" can be taught. Nevertheless, I have found that it is possible to guide stu dents gently into the process of mathematical proof in such a way that they become comfortable with the experience and begin asking them selves questions that will lead them in the right direction.

Author : Larry J. Gerstein
Publisher : Springer Science & Business Media
Page : 401 pages
File Size : 53,7 Mb
Release : 2012-06-05
Category : Mathematics
ISBN : 9781461442653

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Introduction to Mathematical Structures and Proofs by Larry J. Gerstein Pdf

As a student moves from basic calculus courses into upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, and so on, a "bridge" course can help ensure a smooth transition. Introduction to Mathematical Structures and Proofs is a textbook intended for such a course, or for self-study. This book introduces an array of fundamental mathematical structures. It also explores the delicate balance of intuition and rigor—and the flexible thinking—required to prove a nontrivial result. In short, this book seeks to enhance the mathematical maturity of the reader. The new material in this second edition includes a section on graph theory, several new sections on number theory (including primitive roots, with an application to card-shuffling), and a brief introduction to the complex numbers (including a section on the arithmetic of the Gaussian integers). Solutions for even numbered exercises are available on springer.com for instructors adopting the text for a course.

Author : Reg Allenby
Publisher : Elsevier
Page : 288 pages
File Size : 53,8 Mb
Release : 1997-09-26
Category : Mathematics
ISBN : 9780080928777

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Numbers and Proofs by Reg Allenby Pdf

'Numbers and Proofs' presents a gentle introduction to the notion of proof to give the reader an understanding of how to decipher others' proofs as well as construct their own. Useful methods of proof are illustrated in the context of studying problems concerning mainly numbers (real, rational, complex and integers). An indispensable guide to all students of mathematics. Each proof is preceded by a discussion which is intended to show the reader the kind of thoughts they might have before any attempt proof is made. Established proofs which the student is in a better position to follow then follow. Presented in the author's entertaining and informal style, and written to reflect the changing profile of students entering universities, this book will prove essential reading for all seeking an introduction to the notion of proof as well as giving a definitive guide to the more common forms. Stressing the importance of backing up "truths" found through experimentation, with logically sound and watertight arguments, it provides an ideal bridge to more complex undergraduate maths.

Author : Joseph Kirtland
Publisher : Chapman & Hall/CRC
Page : 176 pages
File Size : 52,8 Mb
Release : 2020-11-21
Category : Mathematics
ISBN : 1003082920

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Proofs 101 by Joseph Kirtland Pdf

"Proofs 101: An Introduction to Formal Mathematics serves as an introduction to proofs for mathematics majors who have completed the calculus sequence (at least Calculus I and II) and Linear Algebra. It prepares students for the proofs they will need to analyse and write, the axiomatic nature of mathematics, and the rigors of upper-level mathematics courses. Basic number theory, relations, functions, cardinality, and set theory will provide the material for the proofs and lay the foundation for a deeper understanding of mathematics, which students will need to carry with them throughout their future studies Features Designed to be teachable across a single semester Suitable as an undergraduate textbook for Introduction to Proofs or Transition to Advanced Mathematics courses A balanced variety of easy, moderate, and difficult exercises"--

Author : Claudi Alsina,Roger B. Nelsen
Publisher : American Mathematical Soc.
Page : 295 pages
File Size : 40,6 Mb
Release : 2010-12-31
Category : Mathematics
ISBN : 9781614442011

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Charming Proofs by Claudi Alsina,Roger B. Nelsen Pdf

Theorems and their proofs lie at the heart of mathematics. In speaking of the purely aesthetic qualities of theorems and proofs, G. H. Hardy wrote that in beautiful proofs 'there is a very high degree of unexpectedness, combined with inevitability and economy.' Charming Proofs present a collection of remarkable proofs in elementary mathematics that are exceptionally elegant, full of ingenuity, and succinct. By means of a surprising argument or a powerful visual representation, the proofs in this collection will invite readers to enjoy the beauty of mathematics, to share their discoveries with others, and to become involved in the process of creating new proofs. Charming Proofs is organized as follows. Following a short introduction about proofs and the process of creating proofs, the authors present, in twelve chapters, a wide and varied selection of proofs they consider charming. Topics include the integers, selected real numbers, points in the plane, triangles, squares and other polygons, curves, inequalities, plane tilings, origami, colorful proofs, threedimensional geometry, etc. At the end of each chapter are some challenges that will draw the reader into the process of creating charming proofs. There are over 130 such challenges. Charming Proofs concludes with solutions to all of the challenges, references, and a complete index. As in the authors' previous books with the MAA (Math Made Visual and When Less Is More), secondary school, college, and university teachers may wish to use some of the charming proofs in their classrooms to introduce their students to mathematical elegance. Some may wish to use the book as a supplement in an introductory course on proofs, mathematical reasoning, or problem solving.

Author : Richard H. Hammack
Publisher : Unknown
Page : 314 pages
File Size : 44,6 Mb
Release : 2016-01-01
Category : Mathematics
ISBN : 0989472116

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Book of Proof by Richard H. Hammack Pdf

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.

Author : Ina Goy
Publisher : Walter de Gruyter GmbH & Co KG
Page : 322 pages
File Size : 51,5 Mb
Release : 2023-12-31
Category : Philosophy
ISBN : 9783110688962

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Kant on Proofs for God’s Existence by Ina Goy Pdf

This volume provides a highly needed, comprehensive analysis of Kant's views on proofs for God's existence and explains the radical turns of Kant's accounts. In the "Theory of Heavens" (1755), Kant intended to harmonize the Newtonian laws of motion with a physicotheological argument for the existence of God. But only a few years later, in the "Ground of Proof" essay (1763), Kant defended an ontological ('possibility' or 'modal') argument on the basis of its logical exactitude. Nevertheless he continued to praise the physicotheological argument. In the first "Critique" (1781/7), Kant replaced the traditional constitutive proofs with regulative theoretical and practical arguments. He continued to defend a moral argument in the second "Critique" (1788). But in the third "Critique" (1790), Kant reintroduced a physicotheological besides an ethicotheological argument in order to unify the critical system of philosophy. Kant developed further moral arguments in the "Theodicy" essay (1791) and the "Religion" (1793/4), and still continued to discuss proofs for God's existence in the "OP" (1796–1804). This volume speaks to Kant specialists in the fields of philosophy and theology, but can be used also as an introduction for non-academic readers.

Author : Nicholas A. Loehr
Publisher : CRC Press
Page : 483 pages
File Size : 49,5 Mb
Release : 2019-11-20
Category : Mathematics
ISBN : 9781000709803

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An Introduction to Mathematical Proofs by Nicholas A. Loehr Pdf

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.

Author : Jing-zhong Zhang,Shang-ching Chou,Xiaoshan Gao
Publisher : World Scientific
Page : 488 pages
File Size : 48,5 Mb
Release : 1994-04-06
Category : Mathematics
ISBN : 9789814502603

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Machine Proofs In Geometry: Automated Production Of Readable Proofs For Geometry Theorems by Jing-zhong Zhang,Shang-ching Chou,Xiaoshan Gao Pdf

This book reports recent major advances in automated reasoning in geometry. The authors have developed a method and implemented a computer program which, for the first time, produces short and readable proofs for hundreds of geometry theorems.The book begins with chapters introducing the method at an elementary level, which are accessible to high school students; latter chapters concentrate on the main theme: the algorithms and computer implementation of the method.This book brings researchers in artificial intelligence, computer science and mathematics to a new research frontier of automated geometry reasoning. In addition, it can be used as a supplementary geometry textbook for students, teachers and geometers. By presenting a systematic way of proving geometry theorems, it makes the learning and teaching of geometry easier and may change the way of geometry education.

Author : M. E. Szabo
Publisher : Elsevier
Page : 310 pages
File Size : 54,6 Mb
Release : 2016-06-03
Category : Mathematics
ISBN : 9781483275420

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Algebra of Proofs by M. E. Szabo Pdf

Algebra of Proofs deals with algebraic properties of the proof theory of intuitionist first-order logic in a categorical setting. The presentation is based on the confluence of ideas and techniques from proof theory, category theory, and combinatory logic. The conceptual basis for the text is the Lindenbaum-Tarski algebras of formulas taken as categories. The formal proofs of the associated deductive systems determine structured categories as their canonical algebras (which are of the same type as the Lindenbaum-Tarski algebras of the formulas of underlying languages). Gentzen's theorem, which asserts that provable formulas code their own proofs, links the algebras of formulas and the corresponding algebras of formal proofs. The book utilizes the Gentzen's theorem and the reducibility relations with the Church-Rosser property as syntactic tools. The text explains two main types of theories with varying linguistic complexity and deductive strength: the monoidal type and the Cartesian type. It also shows that quantifiers fit smoothly into the calculus of adjoints and describe the topos-theoretical setting in which the proof theory of intuitionist first-order logic possesses a natural semantics. The text can benefit mathematicians, students, or professors of algebra and advanced mathematics.