Author: Joel David Hamkins Publisher: MIT Press ISBN: 026254220X Category : Mathematics Languages : en Pages : 132
Book Description
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.
Author: Miklós Laczkovich Publisher: American Mathematical Society ISBN: 1470472414 Category : Mathematics Languages : en Pages : 130
Book Description
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.
Author: Mark Joshi Publisher: Springer ISBN: 3319162500 Category : Mathematics Languages : en Pages : 190
Book Description
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.
Author: Eric Gossett Publisher: John Wiley & Sons ISBN: 0470457937 Category : Mathematics Languages : en Pages : 932
Book Description
A Trusted Guide to Discrete Mathematics with Proof?Now in a Newly Revised Edition Discrete mathematics has become increasingly popular in recent years due to its growing applications in the field of computer science. Discrete Mathematics with Proof, Second Edition continues to facilitate an up-to-date understanding of this important topic, exposing readers to a wide range of modern and technological applications. The book begins with an introductory chapter that provides an accessible explanation of discrete mathematics. Subsequent chapters explore additional related topics including counting, finite probability theory, recursion, formal models in computer science, graph theory, trees, the concepts of functions, and relations. Additional features of the Second Edition include: An intense focus on the formal settings of proofs and their techniques, such as constructive proofs, proof by contradiction, and combinatorial proofs New sections on applications of elementary number theory, multidimensional induction, counting tulips, and the binomial distribution Important examples from the field of computer science presented as applications including the Halting problem, Shannon's mathematical model of information, regular expressions, XML, and Normal Forms in relational databases Numerous examples that are not often found in books on discrete mathematics including the deferred acceptance algorithm, the Boyer-Moore algorithm for pattern matching, Sierpinski curves, adaptive quadrature, the Josephus problem, and the five-color theorem Extensive appendices that outline supplemental material on analyzing claims and writing mathematics, along with solutions to selected chapter exercises Combinatorics receives a full chapter treatment that extends beyond the combinations and permutations material by delving into non-standard topics such as Latin squares, finite projective planes, balanced incomplete block designs, coding theory, partitions, occupancy problems, Stirling numbers, Ramsey numbers, and systems of distinct representatives. A related Web site features animations and visualizations of combinatorial proofs that assist readers with comprehension. In addition, approximately 500 examples and over 2,800 exercises are presented throughout the book to motivate ideas and illustrate the proofs and conclusions of theorems. Assuming only a basic background in calculus, Discrete Mathematics with Proof, Second Edition is an excellent book for mathematics and computer science courses at the undergraduate level. It is also a valuable resource for professionals in various technical fields who would like an introduction to discrete mathematics.
Author: Ekhiotz Jon Vergara Alonso Publisher: Linköping University Electronic Press ISBN: 9176858227 Category : Languages : en Pages : 241
Book Description
Energy consumption and its management have been clearly identified as a challenge in computing and communication system design, where energy economy is obviously of paramount importance for battery powered devices. This thesis addresses the energy efficiency of mobile communication at the user end in the context of cellular networks. We argue that energy efficiency starts by energy awareness and propose EnergyBox, a parametrised tool that enables accurate and repeatable energy quantification at the user end using real data traffic traces as input. EnergyBox offers an abstraction of the underlying states for operation of the wireless interfaces and allows to estimate the energy consumption for different operator settings and device characteristics. The tool is used throughout the thesis to quantify and reveal inefficient data communication patterns of widely used mobile applications. We consider two different perspectives in the search of energy-efficient solutions. From the application perspective, we show that systematically quantifying the energy consumption of design choices (e.g., communication patterns, protocols, and data formats) contributes to a significantly smaller energy footprint. From the system perspective, we devise a cross-layer solution that schedules packet transmissions based on the knowledge of the network parameters that impact the energy consumption of the handset. These attempts show that application level decisions require a better understanding of possible energy apportionment policies at system level. Finally, we study the generic problem of determining the contribution of an entity (e.g., application) to the total energy consumption of a given system (e.g., mobile device). We compare the state-of-the-art policies in terms of fairness leveraging cooperative game theory and analyse their required information and computational complexity. We show that providing incentives to reduce the total energy consumption of the system (as part of fairness) is tightly coupled to the policy selection. Our study provides guidelines to select an appropriate policy depending on the characteristics of the system.
Author: Mike "Bootlegger" Turner Publisher: Square One Publishers, Inc. ISBN: 0757050484 Category : Games & Activities Languages : en Pages : 241
Book Description
For most people, the game of blackjack provides excitement and entertainment—and somewhat erratic results. Although we may know the basic rules and even a few strategies, most of us still manage to lose our stakes time and again. Now, gambling columnist and blackjack expert Mike “Bootlegger” Turner has written the perfect guide to help the average player turn the tables. Bootlegger’s 200 Proof Blackjack begins by explaining the basics of blackjack. It then analyzes the most effective strategies for increasing your odds of winning. Included are discussions of money management for strategic and advantage play, tips for avoiding common pitfalls, a unique section on using the casinos’ promotional money to play, and simple instructions on the best card-counting system for novice counters. Easy-to-follow tables and card hands illustrate strategies. And each book includes a pocket-sized “Quick-Reference Guide” that you can use at the tables.
Author: Julius B. Barbanel Publisher: Cambridge University Press ISBN: 9781139444392 Category : Mathematics Languages : en Pages : 480
Book Description
What is the best way to divide a 'cake' and allocate the pieces among some finite collection of players? In this book, the cake is a measure space, and each player uses a countably additive, non-atomic probability measure to evaluate the size of the pieces of cake, with different players generally using different measures. The author investigates efficiency properties (is there another partition that would make everyone at least as happy, and would make at least one player happier, than the present partition?) and fairness properties (do all players think that their piece is at least as large as every other player's piece?). He focuses exclusively on abstract existence results rather than algorithms, and on the geometric objects that arise naturally in this context. By examining the shape of these objects and the relationship between them, he demonstrates results concerning the existence of efficient and fair partitions.
Author: Michael Maschler Publisher: Cambridge University Press ISBN: 1107310741 Category : Business & Economics Languages : en Pages : 1008
Book Description
Covering both noncooperative and cooperative games, this comprehensive introduction to game theory also includes some advanced chapters on auctions, games with incomplete information, games with vector payoffs, stable matchings and the bargaining set. Mathematically oriented, the book presents every theorem alongside a proof. The material is presented clearly and every concept is illustrated with concrete examples from a broad range of disciplines. With numerous exercises the book is a thorough and extensive guide to game theory from undergraduate through graduate courses in economics, mathematics, computer science, engineering and life sciences to being an authoritative reference for researchers.
Author: Brian Skyrms Publisher: Oxford University Press (UK) ISBN: 0199652813 Category : Philosophy Languages : en Pages : 264
Book Description
Brian Skyrms presents a set of influential essays which deploy formal methods to address epistemological and metaphysical questions. The first part of the book focuses on quantity; the second on degrees of belief, belief revision, and coherence; the third on aspects of inductive reasoning.
Author: Joel David Hamkins
Author: Miklós Laczkovich
Author: Mark Joshi
Author: Eric Gossett
Author: Ekhiotz Jon Vergara Alonso
Author: Mike "Bootlegger" Turner
Author: Thomas Whitney Waterman
Author: Julius B. Barbanel
Author: Michael Maschler
Author: Brian Skyrms