Formal Proofs In Maths PDF Download
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| Author | : Chris Lavranos |
| Publisher | : Createspace Independent Publishing Platform |
| Total Pages | : 122 |
| Release | : 2015-07-15 |
| Genre | : |
| ISBN | : 9781514634448 |
Download Formal Proofs in Maths Book in PDF, ePub and Kindle
The scope of Formal Proofs in Maths is to teach students between higher school classes and University undergraduate or postgraduate studies, how to write a formal proof with the true meaning of the concept, of simple theorems in Algebra, particulary in identities concerning equalities, equations and inequalities. This is accomplished by writing four different types of proof namely type(A), type(B), type(C) and type(D) for each theorem or exercise. In TYPE(A) ordinary proofs will be cited in the usual narrative style used by experienced mathematicians. In TYPE(B) a rigorous proof in steps will be introduced to the reader. Each line of that proof will be justified by an appropriate axiom, theorem or definition. In TYPE(C) we will try for a smooth transition from a rigorous proof to a formal proof exposing the way that the laws of logic apply on one or more statements of the proof. In TYPE(D) we will simply write in tabular stepwise form, the results of TYPE(C) mentioning both: 1) Axioms, theorems or definitions. 2) The laws of logic. Hence, finally producing a formal proof according to the definition given in the preface note of the book.
| 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 | : 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 | : Ethan D. Bloch |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 434 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1461221307 |
Download Proofs and Fundamentals Book in PDF, ePub and Kindle
The aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.
| Author | : Richard H. Hammack |
| Publisher | : |
| Total Pages | : 314 |
| Release | : 2016-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780989472111 |
Download Book of Proof Book in PDF, ePub and Kindle
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 | : Larry Gerstein |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 355 |
| Release | : 2013-11-21 |
| Genre | : Science |
| ISBN | : 1468467085 |
Download Introduction · to Mathematical Structures and · Proofs Book in PDF, ePub and Kindle
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 | : Lawrence C. Paulson |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 348 |
| Release | : 1994-07-28 |
| Genre | : Computers |
| ISBN | : 9783540582441 |
Download Isabelle Book in PDF, ePub and Kindle
This volume presents the proceedings of the First International Static Analysis Symposium (SAS '94), held in Namur, Belgium in September 1994. The proceedings comprise 25 full refereed papers selected from 70 submissions as well as four invited contributions by Charles Consel, Saumya K. Debray, Thomas W. Getzinger, and Nicolas Halbwachs. The papers address static analysis aspects for various programming paradigms and cover the following topics: generic algorithms for fixpoint computations; program optimization, transformation and verification; strictness-related analyses; type-based analyses and type inference; dependency analyses and abstract domain construction.
| Author | : Joseph J. Rotman |
| Publisher | : Courier Corporation |
| Total Pages | : 323 |
| Release | : 2013-01-18 |
| Genre | : Mathematics |
| ISBN | : 0486151689 |
Download Journey into Mathematics Book in PDF, ePub and Kindle
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.
| Author | : Richard Bornat |
| Publisher | : OUP Oxford |
| Total Pages | : 264 |
| Release | : 2005-07-21 |
| Genre | : Mathematics |
| ISBN | : 0191586765 |
Download Proof and Disproof in Formal Logic Book in PDF, ePub and Kindle
Proof and Disproof in Formal Logic is a lively and entertaining introduction to formal logic providing an excellent insight into how a simple logic works. Formal logic allows you to check a logical claim without considering what the claim means. This highly abstracted idea is an essential and practical part of computer science. The idea of a formal system—a collection of rules and axioms which define a universe of logical proofs—is what gives us programming languages and modern-day programming. This book concentrates on using logic as a tool: making and using formal proofs and disproofs of particular logical claims. The logic it uses—natural deduction—is very small and very simple; working with it helps you see how large mathematical universes can be built on small foundations. The book is divided into four parts: · Part I "Basics" gives an introduction to formal logic with a short history of logic and explanations of some technical words. · Part II "Formal syntactic proof" show you how to do calculations in a formal system where you are guided by shapes and never need to think about meaning. Your experiments are aided by Jape, which can operate as both inquisitor and oracle. · Part III "Formal semantic disproof" shows you how to construct mathematical counterexamples to show that proof is impossible. Jape can check the counterexamples you build. · Part IV "Program specification and proof" describes how to apply your logical understanding to a real computer science problem, the accurate description and verification of programs. Jape helps, as far as arithmetic allows. Aimed at undergraduates and graduates in computer science, logic, mathematics, and philosophy, the text includes reference to and exercises based on the computer software package Jape, an interactive teaching and research tool designed and hosted by the author that is freely available on the web.
