Puzzle and Proof

Puzzle and Proof

Author: Samuel Dittmer

Publisher: CRC Press

Published: 2024-08-13

Total Pages: 132

ISBN-13: 1040102050

DOWNLOAD EBOOK

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.


Book Synopsis Puzzle and Proof by : Samuel Dittmer

Download or read book Puzzle and Proof written by Samuel Dittmer and published by CRC Press. This book was released on 2024-08-13 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Proof and the Art of Mathematics

Proof and the Art of Mathematics

Author: Joel David Hamkins

Publisher: MIT Press

Published: 2021-02-23

Total Pages: 132

ISBN-13: 026254220X

DOWNLOAD EBOOK

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.


Book Synopsis Proof and the Art of Mathematics by : Joel David Hamkins

Download or read book Proof and the Art of Mathematics written by Joel David Hamkins and published by MIT Press. This book was released on 2021-02-23 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Conjecture and Proof

Conjecture and Proof

Author: Miklós Laczkovich

Publisher: American Mathematical Society

Published: 2022-08-11

Total Pages: 130

ISBN-13: 1470472414

DOWNLOAD EBOOK

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.


Book Synopsis Conjecture and Proof by : Miklós Laczkovich

Download or read book Conjecture and Proof written by Miklós Laczkovich and published by American Mathematical Society. This book was released on 2022-08-11 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Proof Patterns

Proof Patterns

Author: Mark Joshi

Publisher: Springer

Published: 2015-03-17

Total Pages: 190

ISBN-13: 3319162500

DOWNLOAD EBOOK

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.


Book Synopsis Proof Patterns by : Mark Joshi

Download or read book Proof Patterns written by Mark Joshi and published by Springer. This book was released on 2015-03-17 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Energy Modelling and Fairness for Efficient Mobile Communication

Energy Modelling and Fairness for Efficient Mobile Communication

Author: Ekhiotz Jon Vergara Alonso

Publisher: Linköping University Electronic Press

Published: 2016-03-01

Total Pages: 241

ISBN-13: 9176858227

DOWNLOAD EBOOK

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.


Book Synopsis Energy Modelling and Fairness for Efficient Mobile Communication by : Ekhiotz Jon Vergara Alonso

Download or read book Energy Modelling and Fairness for Efficient Mobile Communication written by Ekhiotz Jon Vergara Alonso and published by Linköping University Electronic Press. This book was released on 2016-03-01 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Bootlegger’s 200 Proof Blackjack

Bootlegger’s 200 Proof Blackjack

Author: Mike "Bootlegger" Turner

Publisher: Square One Publishers, Inc.

Published: 2014-01-08

Total Pages: 241

ISBN-13: 0757050484

DOWNLOAD EBOOK

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.


Book Synopsis Bootlegger’s 200 Proof Blackjack by : Mike "Bootlegger" Turner

Download or read book Bootlegger’s 200 Proof Blackjack written by Mike "Bootlegger" Turner and published by Square One Publishers, Inc.. This book was released on 2014-01-08 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


A Digest of Decisions in Criminal Cases

A Digest of Decisions in Criminal Cases

Author: Thomas Whitney Waterman

Publisher:

Published: 1877

Total Pages: 872

ISBN-13:

DOWNLOAD EBOOK


Book Synopsis A Digest of Decisions in Criminal Cases by : Thomas Whitney Waterman

Download or read book A Digest of Decisions in Criminal Cases written by Thomas Whitney Waterman and published by . This book was released on 1877 with total page 872 pages. Available in PDF, EPUB and Kindle. Book excerpt:


The Geometry of Efficient Fair Division

The Geometry of Efficient Fair Division

Author: Julius B. Barbanel

Publisher: Cambridge University Press

Published: 2005-01-24

Total Pages: 480

ISBN-13: 9781139444392

DOWNLOAD EBOOK

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.


Book Synopsis The Geometry of Efficient Fair Division by : Julius B. Barbanel

Download or read book The Geometry of Efficient Fair Division written by Julius B. Barbanel and published by Cambridge University Press. This book was released on 2005-01-24 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Game Theory

Game Theory

Author: Michael Maschler

Publisher: Cambridge University Press

Published: 2013-03-21

Total Pages: 1008

ISBN-13: 1107310741

DOWNLOAD EBOOK

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.


Book Synopsis Game Theory by : Michael Maschler

Download or read book Game Theory written by Michael Maschler and published by Cambridge University Press. This book was released on 2013-03-21 with total page 1008 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


From Zeno to Arbitrage

From Zeno to Arbitrage

Author: Brian Skyrms

Publisher: Oxford University Press (UK)

Published: 2012-11-29

Total Pages: 264

ISBN-13: 0199652813

DOWNLOAD EBOOK

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.


Book Synopsis From Zeno to Arbitrage by : Brian Skyrms

Download or read book From Zeno to Arbitrage written by Brian Skyrms and published by Oxford University Press (UK). This book was released on 2012-11-29 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.