"Proof" has been and remains one of the concepts which characterises mathematics. Covering basic propositional and predicate logic as well as discussing axiom systems and formal proofs, the book seeks to explain what mathematicians understand by proofs and how they are communicated. The authors explore the principle techniques of direct and indirect proof including induction, existence and uniqueness proofs, proof by contradiction, constructive and non-constructive proofs, etc. Many examples from analysis and modern algebra are included. The exceptionally clear style and presentation ensures that the book will be useful and enjoyable to those studying and interested in the notion of mathematical "proof."
Author: Rowan Garnier,John Taylor
If you believe in Heaven and Hell you believe in Multiple Universes and Parallel Dimensions EVIDENCE CONFIRMS * Jesus' Biblical and Sacred Gnostic Teachings * New Jerusalem of Revelation 21 * The Sign of Son of Man * The Seal of God * The Gates of the Heavens * Multiple Universes and Parallel Dimensions * The Seventh Heaven of Muhammad's Night Journey - The Seventh Heaven is confirmed as a portal of the multiverse of divine realms, which Jesus was able to control and pass through without aid. BOOK OPTIONS Paperback, PDF download, and Evidence DVD available at http://amencode.com Companion Book, "Advancian - Systemic Reform Movement" available at http://Advancian.org OVERVIEW The bible is the Hebrew tales. It includes the old and new testaments and speaks mainly of the material realm. The Pistis Sophia and the Sophia (Wisdom) of Jesus Christ are the Coptic (Greek/Egyptian) sacred scriptures that reveal in full detail the heavenly realm Jesus came from. Within it, Jesus tells of the angels and gods, the process of reincarnation, and the consummation – the end of the material world. The evidence in the Amen Code outlines the process for decoding the sacred texts. It confirms the existence of multiple universes, parallel dimensions, the Heavens, New Jerusalem, reincarnation, and the afterlife with the “Predictive Result Standard” science requires. The evidence exposes and at times invalidates the traditional teachings of organized religion. Then, we explore the biblical prophecies that reveal the reason the bible was written and decipher the plans that were coded into the Bible. Do the plans reveal a New World Order? the means to stabilize and secure our global social and economic systems? the end of the elite? -- Yes.
Mathematical Proof of the Existence of God, Multiple Universes, and Parallel Dimensions Based on Jesus' Biblical and Gnostic Teachings
Author: W. Iamwe Ph.D.
Category: Body, Mind & Spirit
The notion of proof is central to mathematics yet it is one of the most difficult aspects of the subject to teach and master. In particular, undergraduate mathematics students often experience difficulties in understanding and constructing proofs. Understanding Mathematical Proof describes the nature of mathematical proof, explores the various techniques that mathematicians adopt to prove their results, and offers advice and strategies for constructing proofs. It will improve students’ ability to understand proofs and construct correct proofs of their own. The first chapter of the text introduces the kind of reasoning that mathematicians use when writing their proofs and gives some example proofs to set the scene. The book then describes basic logic to enable an understanding of the structure of both individual mathematical statements and whole mathematical proofs. It also explains the notions of sets and functions and dissects several proofs with a view to exposing some of the underlying features common to most mathematical proofs. The remainder of the book delves further into different types of proof, including direct proof, proof using contrapositive, proof by contradiction, and mathematical induction. The authors also discuss existence and uniqueness proofs and the role of counter examples.
Author: John Taylor,Rowan Garnier
Publisher: CRC Press
This text is designed to teach students how to read and write proofs in mathematics and to acquaint them with how mathematicians investigate problems and formulate conjecture.
The Mathematician's Toolbox
Author: Robert S. Wolf
Publisher: St. Martin's Press
The amazing story of one of the greatest math problems of all time and the reclusive genius who solved it In the tradition of Fermat’s Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri Poincaré developed the Poincaré Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldn’t prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found. Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius.
The Hundred-Year Quest to Solve One of Math's Greatest Puzzles
Author: George G. Szpiro
In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, "Ramanujan's lost notebook." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony. This volume is the fourth of five volumes that the authors plan to write on Ramanujan’s lost notebook. In contrast to the first three books on Ramanujan's Lost Notebook, the fourth book does not focus on q-series. Most of the entries examined in this volume fall under the purviews of number theory and classical analysis. Several incomplete manuscripts of Ramanujan published by Narosa with the lost notebook are discussed. Three of the partial manuscripts are on diophantine approximation, and others are in classical Fourier analysis and prime number theory. Most of the entries in number theory fall under the umbrella of classical analytic number theory. Perhaps the most intriguing entries are connected with the classical, unsolved circle and divisor problems. Review from the second volume: "Fans of Ramanujan's mathematics are sure to be delighted by this book. While some of the content is taken directly from published papers, most chapters contain new material and some previously published proofs have been improved. Many entries are just begging for further study and will undoubtedly be inspiring research for decades to come. The next installment in this series is eagerly awaited." - MathSciNet Review from the first volume: "Andrews and Berndt are to be congratulated on the job they are doing. This is the first step...on the way to an understanding of the work of the genius Ramanujan. It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complete." - Gazette of the Australian Mathematical Society
Author: George E. Andrews,Bruce C. Berndt
Publisher: Springer Science & Business Media
Computer Security and Access Control
Author: Jerome Lobel
Publisher: McGraw-Hill Companies
Category: Computer security
In this must-have for anyone who wants to better understand their love life, a mathematician pulls back the curtain and reveals the hidden patterns—from dating sites to divorce, sex to marriage—behind the rituals of love. The roller coaster of romance is hard to quantify; defining how lovers might feel from a set of simple equations is impossible. But that doesn’t mean that mathematics isn’t a crucial tool for understanding love. Love, like most things in life, is full of patterns. And mathematics is ultimately the study of patterns—from predicting the weather to the fluctuations of the stock market, the movement of planets or the growth of cities. These patterns twist and turn and warp and evolve just as the rituals of love do. In The Mathematics of Love, Dr. Hannah Fry takes the reader on a fascinating journey through the patterns that define our love lives, applying mathematical formulas to the most common yet complex questions pertaining to love: What’s the chance of finding love? What’s the probability that it will last? How do online dating algorithms work, exactly? Can game theory help us decide who to approach in a bar? At what point in your dating life should you settle down? From evaluating the best strategies for online dating to defining the nebulous concept of beauty, Dr. Fry proves—with great insight, wit, and fun—that math is a surprisingly useful tool to negotiate the complicated, often baffling, sometimes infuriating, always interesting, mysteries of love.
Patterns, Proofs, and the Search for the Ultimate Equation
Author: Hannah Fry
Publisher: Simon and Schuster
Category: Family & Relationships
The heart of mathematics is its elegance; the way it all fits together. Unfortunately, its beauty often eludes the vast majority of people who are intimidated by fear of the difficulty of numbers. Mathematical Elegance remedies this. Using hundreds of examples, the author presents a view of the mathematical landscape that is both accessible and fascinating. At a time of concern that American youth are bored by math, there is renewed interest in improving math skills. Mathematical Elegance stimulates students, along with those already experienced in the discipline, to explore some of the unexpected pleasures of quantitative thinking. Invoking mathematical proofs famous for their simplicity and brainteasers that are fun and illuminating, the author leaves readers feeling exuberant—as well as convinced that their IQs have been raised by ten points. A host of anecdotes about well-known mathematicians humanize and provide new insights into their lofty subjects. Recalling such classic works as Lewis Carroll’s Introduction to Logic and A Mathematician Reads the Newspaper by John Allen Paulos, Mathematical Elegance will energize and delight a wide audience, ranging from intellectually curious students to the enthusiastic general reader.
An Approachable Guide to Understanding Basic Concepts
Author: Steven Goldberg
Publisher: Transaction Publishers
without a properly developed inconsistent calculus based on infinitesimals, then in consistent claims from the history of the calculus might well simply be symptoms of confusion. This is addressed in Chapter 5. It is further argued that mathematics has a certain primacy over logic, in that paraconsistent or relevant logics have to be based on inconsistent mathematics. If the latter turns out to be reasonably rich then paraconsistentism is vindicated; while if inconsistent mathematics has seri ous restriytions then the case for being interested in inconsistency-tolerant logics is weakened. (On such restrictions, see this chapter, section 3. ) It must be conceded that fault-tolerant computer programming (e. g. Chapter 8) finds a substantial and important use for paraconsistent logics, albeit with an epistemological motivation (see this chapter, section 3). But even here it should be noted that if inconsistent mathematics turned out to be functionally impoverished then so would inconsistent databases. 2. Summary In Chapter 2, Meyer's results on relevant arithmetic are set out, and his view that they have a bearing on G8del's incompleteness theorems is discussed. Model theory for nonclassical logics is also set out so as to be able to show that the inconsistency of inconsistent theories can be controlled or limited, but in this book model theory is kept in the background as much as possible. This is then used to study the functional properties of various equational number theories.
Author: C.E. Mortensen
Publisher: Springer Science & Business Media
Category: American literature
The prime numbers appear to be distributed in a very irregular way amongst the integers, but the prime number theorem provides a simple formula that tells us (in an approximate but well-defined sense) how many primes we can expect to find that are less than any integer we might choose. This is indisputably one of the the great classical theorems of mathematics. Suitable for advanced undergraduates and beginning graduates, this textbook demonstrates how the tools of analysis can be used in number theory to attack a famous problem.
Author: G. J. O. Jameson
Publisher: Cambridge University Press
This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.
Author: Eric Lehman,F. Thomson Leighton,Albert R. Meyer
In recent years, a number of works have appeared with important implications for the age-old question of the existence of a god. These writings, many of which are not by theologians, strengthen the rational case for the existence of a god, even as this god may not be exactly the Christian God of history. This book brings together for the first time such recent diverse contributions from fields such as physics, the philosophy of human consciousness, evolutionary biology, mathematics, the history of religion, and theology. Based on such new materials as well as older ones from the twentieth century, it develops five rational arguments that point strongly to the (very probable) existence of a god. They do not make use of the scientific method, which is inapplicable to the question of a god. Rather, they are in an older tradition of rational argument dating back at least to the ancient Greeks. For those who are already believers, the book will offer additional rational reasons that may strengthen their belief. Those who do not believe in the existence of a god at present will encounter new rational arguments that may cause them to reconsider their opinion.
Five Rational Ways to Think about the Question of a God
Author: Robert H. Nelson
Publisher: Wipf and Stock Publishers
After rave reviews for last year's issue of What's Happening, volume 2 has been eagerly awaited. Very well written, '' said one reader of volume 1. The writing is brilliant, positively brilliant.'' A terrific publication, '' said another. This is a wonderful tool for showing people what mathematics is about and what mathematicians can do.'' One reader called it a must for all mathematics department reading and coffee lounges.'' Volume 2 of What's Happening features the same lively writing and all new topics. Here you can read about a new class of solitons, the contributions wavelets are making to solving scientific problems, how mathematics is improving medical imaging, and Andrew Wiles's acclaimed work on Fermat's Last Theorem. What's Happening is great for mathematics undergraduates, graduate students, and mathematics clubs---not to mention mathematics faculty, who will enjoy reading about recent developments in fields other than their own. Highlighting the excitement and wonder of mathematics, What's Happening is in a class by itself.
Author: Barry Cipra
Publisher: American Mathematical Soc.
This book, updated and improved, introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills--the skills needed to solve complex problems, to evaluate horrendous-looking sums, to solve complex recurrence relations, and to discover subtle patterns in data. It is an indispensable text and reference, not only for computer scientists but for all technical professionals in virtually every discipline.
A Foundation for Computer Science
Author: Ronald L. Graham,Donald Ervin Knuth,Oren Patashnik
Publisher: Addison-Wesley Professional
Emphasizes a Problem Solving Approach A first course in combinatorics Completely revised, How to Count: An Introduction to Combinatorics, Second Edition shows how to solve numerous classic and other interesting combinatorial problems. The authors take an easily accessible approach that introduces problems before leading into the theory involved. Although the authors present most of the topics through concrete problems, they also emphasize the importance of proofs in mathematics. New to the Second Edition This second edition incorporates 50 percent more material. It includes seven new chapters that cover occupancy problems, Stirling and Catalan numbers, graph theory, trees, Dirichlet’s pigeonhole principle, Ramsey theory, and rook polynomials. This edition also contains more than 450 exercises. Ideal for both classroom teaching and self-study, this text requires only a modest amount of mathematical background. In an engaging way, it covers many combinatorial tools, such as the inclusion-exclusion principle, generating functions, recurrence relations, and Pólya’s counting theorem.
An Introduction to Combinatorics, Second Edition
Author: R.B.J.T. Allenby,Alan Slomson
Publisher: CRC Press
Providing a general overview of fundamental theoretical and methodological topics, with coverage in greater depth of selected issues, the text covers various issues in basic network concepts, data collection and network analytical methodology.
Author: David Knoke,Song Yang
Category: Social Science