Proof and the Art of Mathematics

Proof and the Art of Mathematics
Author: Joel David Hamkins
Publisher: MIT Press
Total Pages: 132
Release: 2021-02-23
Genre: Mathematics
ISBN: 0262362562

How to write mathematical proofs, shown in fully-worked out examples. This is a companion volume Joel Hamkins's Proof and the Art of Mathematics, providing fully worked-out solutions to all of the odd-numbered exercises as well as a few of the even-numbered exercises. In many cases, the solutions go beyond the exercise question itself to the natural extensions of the ideas, helping readers learn how to approach a mathematical investigation. As Hamkins asks, "Once you have solved a problem, why not push the ideas harder to see what further you can prove with them?" These solutions offer readers examples of how to write a mathematical proofs. The mathematical development of this text follows the main book, with the same chapter topics in the same order, and all theorem and exercise numbers in this text refer to the corresponding statements of the main text.

Puzzle and Proof

Puzzle and Proof
Author: Samuel Dittmer
Publisher: CRC Press
Total Pages: 132
Release: 2024-08-13
Genre: Mathematics
ISBN: 1040102050

Puzzle and Proof: A Decade of Problems from the Utah Math Olympiad is a compilation of the problems and solutions for the first 10 years of the Utah Math Olympiad. The problems are challenging but should be understandable at a high school level. Besides putting all problems in one place (70 in total), which have not previously appeared in print, the book provides additional inspiration for many of the problems and will contain the first published solutions for 10 problems that were originally published on the contest flyer. The book will be a fantastic resource for anyone who enjoys mathematical and/or logic puzzles or is interested in studying for mathematics competitions. Features 70 carefully designed, high-quality high-school level math proof problems, with full solutions Detailed pictures and diagrams throughout to aid understanding Suitable for anyone with high school-level mathematics skills with an interest in furthering their understanding, or just enjoying the puzzles Solutions in the back of the book, sorting the problems by difficulty and topic.

DiaLaw

DiaLaw
Author: Arno R. Lodder
Publisher: Springer Science & Business Media
Total Pages: 214
Release: 1999-07-31
Genre: Computers
ISBN: 9780792358305

In this work it is argued that legal justification can best be studied from a procedural, dialogical point of view: legal statements are justified if the audience is convinced in an argumentative dialog. The formalized and implemented model DiaLaw guards the procedure in which two players aim at justifying statements. DiaLaw shows the advances and problems linked to procedural models of legal justification. Moreover, an instructive discussion of the different models of procedural justification is provided. It is stressed that in legal justification not only logically compelling arguments should be considered, but also convincing arguments. Therefore DiaLaw also deals with the rhetorical, psychological aspects of argument. This book is relevant for scholars in legal theory, artificial intelligence, and argumentation, and can be used in graduate courses on AI and Law, and legal argumentation.

Proof Patterns

Proof Patterns
Author: Mark Joshi
Publisher: Springer
Total Pages: 189
Release: 2015-03-17
Genre: Mathematics
ISBN: 3319162500

This innovative textbook introduces a new pattern-based approach to learning proof methods in the mathematical sciences. Readers will discover techniques that will enable them to learn new proofs across different areas of pure mathematics with ease. The patterns in proofs from diverse fields such as algebra, analysis, topology and number theory are explored. Specific topics examined include game theory, combinatorics and Euclidean geometry, enabling a broad familiarity. The author, an experienced lecturer and researcher renowned for his innovative view and intuitive style, illuminates a wide range of techniques and examples from duplicating the cube to triangulating polygons to the infinitude of primes to the fundamental theorem of algebra. Intended as a companion for undergraduate students, this text is an essential addition to every aspiring mathematician’s toolkit.

Player Proof

Player Proof
Author: Derek Wellington
Publisher: CreateSpace
Total Pages: 212
Release: 2013-12-06
Genre: Family & Relationships
ISBN: 9781484046999

Are you tired of dating men and getting used, played and dumped? If so you're about to learn how to: Learn about the 13 different types of Players, the mental games they'll play on you and how to handle them. You will learn the three reasons why he doesn't call you after having sex. You will learn the 23 red flags to watch out for to know if you're dating a Player or a man with long term potential. You will learn how to quickly weed out the losers, posers, and men that will simply waste your time, and energy. You will learn how to find The ONE. Meaning the man that you're meant to spend the rest of your life with. You will learn how to quickly, and easily identify the kind of man you're dating, so you can decide how much time and energy to devote to the relationship. Imagine what your life will be like once you understand all the head games that men play? You learn how to quickly, and easily decide which men are trustworthy, and which men are not You will learn how to protect your heart, so that NO man ever breaks your heart again! You will learn what it takes for you to be with the man of your dreams. You will learn how to how to tell if the man has no intention of being in a relationship with you and only wants sex. You will learn how to how to keep a man once you get him. You will learn how to how to tell if a man will cheat on you.

Game Theory

Game Theory
Author: Nikolai N. Vorob'ev
Publisher: Springer Science & Business Media
Total Pages: 189
Release: 2012-12-06
Genre: Science
ISBN: 1461263417

The basis for this book is a number of lectures given frequently by the author to third year students of the Department of Economics at Leningrad State University who specialize in economical cybernetics. The main purpose of this book is to provide the student with a relatively simple and easy-to-understand manual containing the basic mathematical machinery utilized in the theory of games. Practical examples (including those from the field of economics) serve mainly as an interpretation of the mathematical foundations of this theory rather than as indications of their actual or potential applicability. The present volume is significantly different from other books on the theory of games. The difference is both in the choice of mathematical problems as well as in the nature of the exposition. The realm of the problems is somewhat limited but the author has tried to achieve the greatest possible systematization in his exposition. Whenever possible the author has attempted to provide a game-theoretical argument with the necessary mathematical rigor and reasonable generality. Formal mathematical prerequisites for this book are quite modest. Only the elementary tools of linear algebra and mathematical analysis are used.

Conjecture and Proof

Conjecture and Proof
Author: Miklós Laczkovich
Publisher: American Mathematical Society
Total Pages: 130
Release: 2022-08-11
Genre: Mathematics
ISBN: 1470472414

The Budapest semesters in mathematics were initiated with the aim of offering undergraduate courses that convey the tradition of Hungarian mathematics to English-speaking students. This book is an elaborate version of the course on Conjecture and Proof. It gives miniature introductions to various areas of mathematics by presenting some interesting and important, but easily accessible results and methods. The text contains complete proofs of deep results such as the transcendence of $e$, the Banach-Tarski paradox and the existence of Borel sets of arbitrary (finite) class. One of the purposes is to demonstrate how far one can get from the first principles in just a couple of steps. Prerequisites are kept to a minimum, and any introductory calculus course provides the necessary background for understanding the book. Exercises are included for the benefit of students. However, this book should prove fascinating for any mathematically literate reader.

Algorithmic Game Theory

Algorithmic Game Theory
Author: Spyros Kontogiannis
Publisher: Springer Science & Business Media
Total Pages: 370
Release: 2010-10-06
Genre: Computers
ISBN: 3642161693

Thepresentvolumewasdevotedto thethirdeditionofthe InternationalSym- sium on Algorithmic Game Theory (SAGT), an interdisciplinary scienti?c event intended to provide a forum for researchers as well as practitioners to exchange innovative ideas and to be aware of each other's e?orts and results. SAGT 2010 took place in Athens, on October 18–20, 2010. The present volume contains all contributed papers presented at SAGT 2010 together with the distinguished invited lectures of Amos Fiat (Tel-Aviv University, Israel), and Paul Goldberg (University of Liverpool, UK). The two invited papers are presented at the - ginning of the proceedings, while the regular papers follow in alphabetical order (by the authors' names). In response to the call for papers, the Program Committee (PC) received 61 submissions.Amongthesubmissionswerefour paperswith atleastonecoauthor that was also a PC member of SAGT 2010. For these PC-coauthored papers, anindependent subcommittee (EliasKoutsoupias,PaulG. Spirakis,andXiaotie Deng) made the judgment, and eventually two of these papers were proposedfor inclusion in the Scienti?c Program. For the remaining 57 (non-PC-coauthored) papers, the PC of SAGT 2010 conducted a thorough evaluation (at least 3, and on average 3.9 reviews per paper) and electronic discussion, and eventually selected 26 papers for inclusion in the Scienti?c Program. An additional tutorial, “Games Played in Physics”, was also provided in SAGT 2010, courtesy of the academic research network Algogames (A??o?a????o) of the University of Patras.

Algorithmic Learning Theory

Algorithmic Learning Theory
Author: Ricard Gavaldà
Publisher: Springer Science & Business Media
Total Pages: 410
Release: 2009-09-21
Genre: Computers
ISBN: 3642044131

This book constitutes the refereed proceedings of the 20th International Conference on Algorithmic Learning Theory, ALT 2009, held in Porto, Portugal, in October 2009, co-located with the 12th International Conference on Discovery Science, DS 2009. The 26 revised full papers presented together with the abstracts of 5 invited talks were carefully reviewed and selected from 60 submissions. The papers are divided into topical sections of papers on online learning, learning graphs, active learning and query learning, statistical learning, inductive inference, and semisupervised and unsupervised learning. The volume also contains abstracts of the invited talks: Sanjoy Dasgupta, The Two Faces of Active Learning; Hector Geffner, Inference and Learning in Planning; Jiawei Han, Mining Heterogeneous; Information Networks By Exploring the Power of Links, Yishay Mansour, Learning and Domain Adaptation; Fernando C.N. Pereira, Learning on the Web.

Computability and Complexity

Computability and Complexity
Author: Hubie Chen
Publisher: MIT Press
Total Pages: 413
Release: 2023-08-29
Genre: Computers
ISBN: 0262048620

A clear, comprehensive, and rigorous introduction to the theory of computation. What is computable? What leads to efficiency in computation? Computability and Complexity offers a clear, comprehensive, and rigorous introduction to the mathematical study of the capabilities and limitations of computation. Hubie Chen covers the core notions, techniques, methods, and questions of the theory of computation before turning to several advanced topics. Emphasizing intuitive learning and conceptual discussion, this textbook’s accessible approach offers a robust foundation for understanding both the reach and restrictions of algorithms and computers. Extensive exercises and diagrams enhance streamlined, student-friendly presentation of mathematically rigorous material Includes thorough treatment of automata theory, computability theory, and complexity theory—including the P versus NP question and the theory of NP-completeness Suitable for undergraduate and graduate students, researchers, and professionals