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One of the world's great mathematicians shows why math is the ultimate timesaver--and how everyone can make their lives easier with a few simple shortcuts.
Hard work, we are often told, is the key to success. Putting in the effort, doing things the "right way," even if it's the long way. But according to Marcus du Sautoy, this common wisdom has it backwards. The key to success isn't hard work - it's shortcuts. We make the most progress when we find clever ways to do more with less. And there is no better way of finding shortcuts than math.
Journey to the Edge of Reason : The Life of Kurt Gödel by Stephen BudianskyThe first major biography written for a general audience of the logician and mathematician whose Incompleteness Theorems helped launch a modern scientific revolution. Nearly a hundred years after its publication, Kurt Gödel's famous proof that every mathematical system must contain propositions that are true--yet never provable--continues to unsettle mathematics, philosophy, and computer science. Yet unlike Einstein, with whom he formed a warm and abiding friendship, Gödel has long escaped all but the most casual scrutiny of his life. Stephen Budiansky's Journey to the Edge of Reason is the first biography to fully draw upon Gödel's voluminous letters and writings--including a never-before-transcribed shorthand diary of his most intimate thoughts--to explore Gödel's profound intellectual friendships, his moving relationship with his mother, his troubled yet devoted marriage, and the debilitating bouts of paranoia that ultimately took his life. It also offers an intimate portrait of the scientific and intellectual circles in prewar Vienna, a haunting account of Gödel's and Jewish intellectuals' flight from Austria and Germany at the start of the Second World War, and a vivid re-creation of the early days of the Institute for Advanced Study in Princeton, NJ, where Gödel and Einstein both worked. Eloquent and insightful, Journey to the Edge of Reason is a fully realized portrait of the odd, brilliant, and tormented man who has been called the greatest logician since Aristotle, and illuminates the far-reaching implications of Gödel's revolutionary ideas for philosophy, mathematics, artificial intelligence, and man's place in the cosmos.
Call Number: QA29.G58 B83 2021
In Pursuit of Zeta-3 : The World's Most Mysterious Unsolved Math Problem by Paul J. NahinAn engrossing look at the history and importance of a centuries-old but still unanswered math problem. For centuries, mathematicians the world over have tried, and failed, to solve the zeta-3 problem. Math genius Leonhard Euler attempted it in the 1700s and came up short. The straightforward puzzle considers if there exists a simple symbolic formula for the following: 1+(1/2)^3+(1/3)^3+(1/4)^3+. . . . But why is this issue--the sum of the reciprocals of the positive integers cubed--so important? With In Pursuit of Zeta-3, popular math writer Paul Nahin investigates the history and significance of this mathematical conundrum. Drawing on detailed examples, historical anecdotes, and even occasionally poetry, Nahin sheds light on the richness of the nature of zeta-3. He shows its intimate connections to the Riemann hypothesis, another mathematical mystery that has stumped mathematicians for nearly two centuries. He looks at its links with Euler's achievements and explores the modern research area of Euler sums, where zeta-3 occurs frequently. An exact solution to the zeta-3 question wouldn't simply satisfy pure mathematical interest: it would have critical ramifications for applications in physics and engineering, such as quantum electrodynamics. Challenge problems with detailed solutions and MATLAB code are included at the end of each of the book's sections. Detailing the trials and tribulations of mathematicians who have approached one of the field's great unsolved riddles, In Pursuit of Zeta-3 will tantalize curious math enthusiasts everywhere.
Call Number: QA351 .N34 2021
Explorations in Numerical Analysis by James V. Lambers; Amber C. Sumner; Vivian A. MontiforteThis textbook is intended to introduce advanced undergraduate and early-career graduate students to the field of numerical analysis. This field pertains to the design, analysis, and implementation of algorithms for the approximate solution of mathematical problems that arise in applications spanning science and engineering, and are not practical to solve using analytical techniques such as those taught in courses in calculus, linear algebra or differential equations. Topics covered include computer arithmetic, error analysis, solution of systems of linear equations, least squares problems, eigenvalue problems, nonlinear equations, optimization, polynomial interpolation and approximation, numerical differentiation and integration, ordinary differential equations, and partial differential equations. For each problem considered, the presentation includes the derivation of solution techniques, analysis of their efficiency, accuracy and robustness, and details of their implementation, illustrated through the Python programming language. This text is suitable for a year-long sequence in numerical analysis, and can also be used for a one-semester course in numerical linear algebra.
Call Number: QA297 .L335 2021
Combinatorial Convexity by Imre BaranyThis book is about the combinatorial properties of convex sets, families of convex sets in finite dimensional Euclidean spaces, and finite points sets related to convexity. This area is classic, with theorems of Helly, Caratheodory, and Radon that go back more than a hundred years. At the same time, it is a modern and active field of research with recent results like Tverberg's theorem, the colourful versions of Helly and Caratheodory, and the $(p, q)$ theorem of Alon and Kleitman. As the title indicates, the topic is convexity and geometry, and is close to discrete mathematics. The questions considered are frequently of a combinatorial nature, and the proofs use ideas from geometry and are often combined with graph and hypergraph theory. The book is intended for students (graduate and undergraduate alike), but postdocs and research mathematicians will also find it useful. It can be used as a textbook with short chapters, each suitable for a one- or two-hour lecture. Not much background is needed: basic linear algebra and elements of (hyper)graph theory as well as some mathematical maturity should suffice.
Call Number: QA640 .B37 2021
Augmented Humanity : Being and Remaining Agentic in a Digitalized World by Peter T. BryantThis open access book will examine the implications of digitalization for the understanding of humanity, conceived as a community of intelligent agency. It addresses important topics across a range of social and behavioral theories and identifies a range of novel mechanisms and their social behavioral effects. Across the book, the author highlights the expansion of intelligent processing capability brought about by digitalization and the challenges this exposes for integrating artificial and human capabilities. It includes the altered effects of bounded rationality in problem solving and decision making; related changes in the perception of rationality, plus novel myopias and biases. It also seeks to address cognitive intersubjectivity, learning from performance and agentic self-generation; and the novel methods and patterns of reasoned thought which emerge in a digitalized world; and how these mechanisms will combine in making and remaking the world of human experience and understanding. This book examines the problematics and prospects for digitally augmented humanity. In doing so, it maps the terrain for a future science of augmented agency. It will have cross-disciplinary appeal to students and scholars of applied psychology, cognitive and behavioral science, organizational psychology and management, business, finance, and digital cultures and humanities.
Call Number: QA7.9.H85 B79 2021
Introduction to Algebraic Geometry by Igor Kriz; Sophie KrizThe goal of this book is to provide an introduction to algebraic geometry accessible to students. Starting from solutions of polynomial equations, modern tools of the subject soon appear, motivated by how they improve our understanding of geometrical concepts. In many places, analogies and differences with related mathematical areas are explained. The text approaches foundations of algebraic geometry in a complete and self-contained way, also covering the underlying algebra. The last two chapters include a comprehensive treatment of cohomology and discuss some of its applications in algebraic geometry.
Call Number: QA564 .K75 2021
Lectures on the Geometry of Manifolds (Third Edition) by Liviu I. NicolaescuThe goal of this book is to introduce the reader to some of the main techniques, ideas and concepts frequently used in modern geometry. It starts from scratch and it covers basic topics such as differential and integral calculus on manifolds, connections on vector bundles and their curvatures, basic Riemannian geometry, calculus of variations, DeRham cohomology, integral geometry (tube and Crofton formulas), characteristic classes, elliptic equations on manifolds and Dirac operators. The new edition contains a new chapter on spectral geometry presenting recent results which appear here for the first time in printed form.
Call Number: QA649 .N53 2021
What's the Use? : How Mathematics Shapes Everyday Life by Ian StewartSee the world in a completely new way as an esteemed mathematician shows how math powers the world--from technology to health care and beyond. Almost all of us have sat in a math class, wondering when we'd ever need to know how to find the roots of a polynomial or graph imaginary numbers. And in one sense, we were right: if we needed to, we'd use a computer. But as Ian Stewart argues in What's the Use?, math isn't just about boring computations. Rather, it offers us new and profound insights into our world, allowing us to accomplish feats as significant as space exploration and organ donation. From the trigonometry that keeps a satellite in orbit to the prime numbers used by the world's most advanced security systems to the imaginary numbers that enable augmented reality, math isn't just relevant to our lives. It is the very fabric of our existence.
Call Number: QA93 .S744 2021
What Are the Chances of That? : How to Think about Uncertainty by Andrew C. A. ElliottChance fills every day of our lives and affects every decision we make. Yet, for something woven so closely into the fabric of our being, we are not very good at thinking about uncertainty and risk. In this lively and engaging book, Andrew C. A. Elliott asks why this is so. He picks at the threads and, in showing how our world is built on probability rather than certainty, he identifies five obstacles to thinking about uncertainty that confuse us time after time. Elliott takes us into the casino, but this is not an invitation to gamble. He looks at financial markets, but this is not a guide to investment. There's discussion of health, but this is not a medical book. He touches on genetics and evolution, and music-making, and writing, because chance is at work there too. Entering many different fields, What are the Chances of That? is always following the trail of chance and randomness. One purpose of the book is to go cross-country, to show that there are connected ways of thinking that disrespect boundaries and cut across the domains of finance, and gambling, and genetics, and public health, and creativity. Through it, one visits the vantage points that give a broad view of the landscape and sees how these different areas of life and knowledge are connected - through chance. What are the Chances of That? discusses chance and the importance of understanding how it affects our lives. It goes beyond a mathematical approach to the subject, showing how our thinking about chance and uncertainty has been shaped by history and culture, and only relatively recently by the mathematical theory of probability. In considering how we think about uncertainty, Elliott proposes five "dualities" that encapsulate many of the ambiguities that arise.
Call Number: QA273.18 .E55 2021
ISBN: 0198869029
Elementary Modular Iwasawa Theory by Haruzo HidaThe only book available that exposes the Iwasawa theoretic aspects of modular forms and Galois deformation theory. The results found in the book are at the cutting edge of the present research. The first few chapters provide the fundamentals while the latter chapters cater to first or second-year graduate students. Contains numerous open research problems for young researchers.
Call Number: QA247.3 .H53 2022
Modern Data Science with R by Benjamin Baumer; Daniel Kaplan; Nicholas J. HortonModern Data Science with R is a comprehensive data science textbook for undergraduates that incorporates statistical and computational thinking to solve real-world data problems. Rather than focus exclusively on case studies or programming syntax, this book illustrates how statistical programming in the state-of-the-art R/RStudio computing environment can be leveraged to extract meaningful information from a variety of data in the service of addressing compelling questions. The second edition is updated to reflect the growing influence of the tidyverse set of packages. All code in the book has been revised and styled to be more readable and easier to understand. New functionality from packages like sf, purrr, tidymodels, and tidytext is now integrated into the text. All chapters have been revised, and several have been split, re-organized, or re-imagined to meet the shifting landscape of best practice.
Illustrating Mathematics by Diana DavisThis book is for anyone who wishes to illustrate their mathematical ideas, which in our experience means everyone. It is organized by material, rather than by subject area, and purposefully emphasizes the process of creating things, including discussions of failures that occurred along the way. As a result, the reader can learn from the experiences of those who came before, and will be inspired to create their own illustrations. Topics illustrated within include prime numbers, fractals, the Klein bottle, Borromean rings, tilings, space-filling curves, knot theory, billiards, complex dynamics, algebraic surfaces, groups and prime ideals, the Riemann zeta function, quadratic fields, hyperbolic space, and hyperbolic 3-manifolds. Everyone who opens this book should find a type of mathematics with which they identify. Each contributor explains the mathematics behind their illustration at an accessible level, so that all readers can appreciate the beauty of both the object itself and the mathematics behind it.
Call Number: QA93 .I425 2020
The Wonder Book of Geometry : A Mathematical Story by David AchesonHow can we be sure that Pythagoras's theorem is really true? Why is the "angle in a semicircle" always 90 degrees? And how can tangents help determine the speed of a bullet? David Acheson takes the reader on a highly illustrated tour through the history of geometry, from ancient Greece to the present day. He emphasizes throughout elegant deduction and practical applications, and argues that geometry can offer the quickest route to the whole spirit of mathematics at its best. Along the way, we encounter the quirky and the unexpected, meet the great personalities involved, and uncover some of the loveliest surprises in mathematics.
Call Number: QA445 .A24 2020
Games for Your Mind : The History and Future of Logic Puzzles by Jason RosenhouseA lively and engaging look at logic puzzles and their role in recreation, mathematics, and philosophy. Logic puzzles were first introduced to the public by Lewis Carroll in the late nineteenth century and have been popular ever since. Games like Sudoku and Mastermind are fun and engrossing recreational activities, but they also share deep foundations in mathematical logic and are worthy of serious intellectual inquiry. Games for Your Mind explores the history and future of logic puzzles while enabling you to test your skill against a variety of puzzles yourself. In this informative and entertaining book, Jason Rosenhouse begins by introducing readers to logic and logic puzzles and goes on to reveal the rich history of these puzzles. He shows how Carroll's puzzles presented Aristotelian logic as a game for children, yet also informed his scholarly work on logic. He reveals how another pioneer of logic puzzles, Raymond Smullyan, drew on classic puzzles about liars and truthtellers to illustrate Kurt Gödel's theorems and illuminate profound questions in mathematical logic. Rosenhouse then presents a new vision for the future of logic puzzles based on nonclassical logic, which is used today in computer science and automated reasoning to manipulate large and sometimes contradictory sets of data. Featuring a wealth of sample puzzles ranging from simple to extremely challenging, this lively and engaging book brings together many of the most ingenious puzzles ever devised, including the "Hardest Logic Puzzle Ever," metapuzzles, paradoxes, and the logic puzzles in detective stories.
Call Number: GV1493 .R67 2020
Mathematics and Its Logics : Philosophical Essays by Geoffrey HellmanIn these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appear to be contradictions between different systems, and positing different frameworks serving different legitimate purposes. The essays refine and extend Hellman's modal-structuralist account of mathematics, developing a height-potentialist view of higher set theory which recognizes indefinite extendability of models and stages at which sets occur. In the first of three new essays written for this volume, Hellman shows how extendability can be deployed to derive the axiom of Infinity and that of Replacement, improving on earlier accounts; he also shows how extendability leads to attractive, novel resolutions of the set-theoretic paradoxes. Other essays explore advantages and limitations of restrictive systems - nominalist, predicativist, and constructivist. Also included are two essays, with Solomon Feferman, on predicative foundations of arithmetic.
Call Number: QA9.2 .H45 2021
Abstract Algebra : A Comprehensive Introduction by John Lawrence; Frank ZorzittoThrough this book, upper undergraduate mathematics majors will master a challenging yet rewarding subject, and approach advanced studies in algebra, number theory and geometry with confidence. Groups, rings and fields are covered in depth with a strong emphasis on irreducible polynomials, a fresh approach to modules and linear algebra, a fresh take on Gröbner theory, and a group theoretic treatment of Rejewski's deciphering of the Enigma machine. It includes a detailed treatment of the basics on finite groups, including Sylow theory and the structure of finite abelian groups. Galois theory and its applications to polynomial equations and geometric constructions are treated in depth. Those interested in computations will appreciate the novel treatment of division algorithms. This rigorous text 'gets to the point', focusing on concisely demonstrating the concept at hand, taking a 'definitions first, examples next' approach. Exercises reinforce the main ideas of the text and encourage students' creativity.
Call Number: QA162 .L39 2021
Introduction to Linear Regression Analysis by Douglas C. Montgomery; Elizabeth A. Peck; G Geoffrey ViningIntroduction to Linear Regression Analysis is the most comprehensive, fulsome, and current examination of the foundations of linear regression analysis. Fully updated in this new sixth edition, the distinguished authors have included new material on generalized regression techniques and new examples to help the reader understand retain the concepts taught in the book. The new edition focuses on four key areas of improvement over the fifth edition: New exercises and data sets New material on generalized regression techniques The inclusion of JMP software in key areas Carefully condensing the text where possible Introduction to Linear Regression Analysis skillfully blends theory and application in both the conventional and less common uses of regression analysis in today's cutting-edge scientific research. The text equips readers to understand the basic principles needed to apply regression model-building techniques in various fields of study, including engineering, management, and the health sciences.
Thinking Better : The Art of the Shortcut in Math and Life by 
Journey to the Edge of Reason : The Life of Kurt Gödel by The first major biography written for a general audience of the logician and mathematician whose Incompleteness Theorems helped launch a modern scientific revolution. Nearly a hundred years after its publication, Kurt Gödel's famous proof that every mathematical system must contain propositions that are true--yet never provable--continues to unsettle mathematics, philosophy, and computer science. Yet unlike Einstein, with whom he formed a warm and abiding friendship, Gödel has long escaped all but the most casual scrutiny of his life. Stephen Budiansky's Journey to the Edge of Reason is the first biography to fully draw upon Gödel's voluminous letters and writings--including a never-before-transcribed shorthand diary of his most intimate thoughts--to explore Gödel's profound intellectual friendships, his moving relationship with his mother, his troubled yet devoted marriage, and the debilitating bouts of paranoia that ultimately took his life. It also offers an intimate portrait of the scientific and intellectual circles in prewar Vienna, a haunting account of Gödel's and Jewish intellectuals' flight from Austria and Germany at the start of the Second World War, and a vivid re-creation of the early days of the Institute for Advanced Study in Princeton, NJ, where Gödel and Einstein both worked. Eloquent and insightful, Journey to the Edge of Reason is a fully realized portrait of the odd, brilliant, and tormented man who has been called the greatest logician since Aristotle, and illuminates the far-reaching implications of Gödel's revolutionary ideas for philosophy, mathematics, artificial intelligence, and man's place in the cosmos.
In Pursuit of Zeta-3 : The World's Most Mysterious Unsolved Math Problem by An engrossing look at the history and importance of a centuries-old but still unanswered math problem. For centuries, mathematicians the world over have tried, and failed, to solve the zeta-3 problem. Math genius Leonhard Euler attempted it in the 1700s and came up short. The straightforward puzzle considers if there exists a simple symbolic formula for the following: 1+(1/2)^3+(1/3)^3+(1/4)^3+. . . . But why is this issue--the sum of the reciprocals of the positive integers cubed--so important? With In Pursuit of Zeta-3, popular math writer Paul Nahin investigates the history and significance of this mathematical conundrum. Drawing on detailed examples, historical anecdotes, and even occasionally poetry, Nahin sheds light on the richness of the nature of zeta-3. He shows its intimate connections to the Riemann hypothesis, another mathematical mystery that has stumped mathematicians for nearly two centuries. He looks at its links with Euler's achievements and explores the modern research area of Euler sums, where zeta-3 occurs frequently. An exact solution to the zeta-3 question wouldn't simply satisfy pure mathematical interest: it would have critical ramifications for applications in physics and engineering, such as quantum electrodynamics. Challenge problems with detailed solutions and MATLAB code are included at the end of each of the book's sections. Detailing the trials and tribulations of mathematicians who have approached one of the field's great unsolved riddles, In Pursuit of Zeta-3 will tantalize curious math enthusiasts everywhere.
Explorations in Numerical Analysis by This textbook is intended to introduce advanced undergraduate and early-career graduate students to the field of numerical analysis. This field pertains to the design, analysis, and implementation of algorithms for the approximate solution of mathematical problems that arise in applications spanning science and engineering, and are not practical to solve using analytical techniques such as those taught in courses in calculus, linear algebra or differential equations. Topics covered include computer arithmetic, error analysis, solution of systems of linear equations, least squares problems, eigenvalue problems, nonlinear equations, optimization, polynomial interpolation and approximation, numerical differentiation and integration, ordinary differential equations, and partial differential equations. For each problem considered, the presentation includes the derivation of solution techniques, analysis of their efficiency, accuracy and robustness, and details of their implementation, illustrated through the Python programming language. This text is suitable for a year-long sequence in numerical analysis, and can also be used for a one-semester course in numerical linear algebra.
Combinatorial Convexity by This book is about the combinatorial properties of convex sets, families of convex sets in finite dimensional Euclidean spaces, and finite points sets related to convexity. This area is classic, with theorems of Helly, Caratheodory, and Radon that go back more than a hundred years. At the same time, it is a modern and active field of research with recent results like Tverberg's theorem, the colourful versions of Helly and Caratheodory, and the $(p, q)$ theorem of Alon and Kleitman. As the title indicates, the topic is convexity and geometry, and is close to discrete mathematics. The questions considered are frequently of a combinatorial nature, and the proofs use ideas from geometry and are often combined with graph and hypergraph theory. The book is intended for students (graduate and undergraduate alike), but postdocs and research mathematicians will also find it useful. It can be used as a textbook with short chapters, each suitable for a one- or two-hour lecture. Not much background is needed: basic linear algebra and elements of (hyper)graph theory as well as some mathematical maturity should suffice.
Augmented Humanity : Being and Remaining Agentic in a Digitalized World by This open access book will examine the implications of digitalization for the understanding of humanity, conceived as a community of intelligent agency. It addresses important topics across a range of social and behavioral theories and identifies a range of novel mechanisms and their social behavioral effects. Across the book, the author highlights the expansion of intelligent processing capability brought about by digitalization and the challenges this exposes for integrating artificial and human capabilities. It includes the altered effects of bounded rationality in problem solving and decision making; related changes in the perception of rationality, plus novel myopias and biases. It also seeks to address cognitive intersubjectivity, learning from performance and agentic self-generation; and the novel methods and patterns of reasoned thought which emerge in a digitalized world; and how these mechanisms will combine in making and remaking the world of human experience and understanding. This book examines the problematics and prospects for digitally augmented humanity. In doing so, it maps the terrain for a future science of augmented agency. It will have cross-disciplinary appeal to students and scholars of applied psychology, cognitive and behavioral science, organizational psychology and management, business, finance, and digital cultures and humanities.
Introduction to Algebraic Geometry by The goal of this book is to provide an introduction to algebraic geometry accessible to students. Starting from solutions of polynomial equations, modern tools of the subject soon appear, motivated by how they improve our understanding of geometrical concepts. In many places, analogies and differences with related mathematical areas are explained. The text approaches foundations of algebraic geometry in a complete and self-contained way, also covering the underlying algebra. The last two chapters include a comprehensive treatment of cohomology and discuss some of its applications in algebraic geometry.
Lectures on the Geometry of Manifolds (Third Edition) by The goal of this book is to introduce the reader to some of the main techniques, ideas and concepts frequently used in modern geometry. It starts from scratch and it covers basic topics such as differential and integral calculus on manifolds, connections on vector bundles and their curvatures, basic Riemannian geometry, calculus of variations, DeRham cohomology, integral geometry (tube and Crofton formulas), characteristic classes, elliptic equations on manifolds and Dirac operators. The new edition contains a new chapter on spectral geometry presenting recent results which appear here for the first time in printed form.
What's the Use? : How Mathematics Shapes Everyday Life by See the world in a completely new way as an esteemed mathematician shows how math powers the world--from technology to health care and beyond. Almost all of us have sat in a math class, wondering when we'd ever need to know how to find the roots of a polynomial or graph imaginary numbers. And in one sense, we were right: if we needed to, we'd use a computer. But as Ian Stewart argues in What's the Use?, math isn't just about boring computations. Rather, it offers us new and profound insights into our world, allowing us to accomplish feats as significant as space exploration and organ donation. From the trigonometry that keeps a satellite in orbit to the prime numbers used by the world's most advanced security systems to the imaginary numbers that enable augmented reality, math isn't just relevant to our lives. It is the very fabric of our existence.
What Are the Chances of That? : How to Think about Uncertainty by Chance fills every day of our lives and affects every decision we make. Yet, for something woven so closely into the fabric of our being, we are not very good at thinking about uncertainty and risk. In this lively and engaging book, Andrew C. A. Elliott asks why this is so. He picks at the threads and, in showing how our world is built on probability rather than certainty, he identifies five obstacles to thinking about uncertainty that confuse us time after time. Elliott takes us into the casino, but this is not an invitation to gamble. He looks at financial markets, but this is not a guide to investment. There's discussion of health, but this is not a medical book. He touches on genetics and evolution, and music-making, and writing, because chance is at work there too. Entering many different fields, What are the Chances of That? is always following the trail of chance and randomness. One purpose of the book is to go cross-country, to show that there are connected ways of thinking that disrespect boundaries and cut across the domains of finance, and gambling, and genetics, and public health, and creativity. Through it, one visits the vantage points that give a broad view of the landscape and sees how these different areas of life and knowledge are connected - through chance. What are the Chances of That? discusses chance and the importance of understanding how it affects our lives. It goes beyond a mathematical approach to the subject, showing how our thinking about chance and uncertainty has been shaped by history and culture, and only relatively recently by the mathematical theory of probability. In considering how we think about uncertainty, Elliott proposes five "dualities" that encapsulate many of the ambiguities that arise.
Elementary Modular Iwasawa Theory by The only book available that exposes the Iwasawa theoretic aspects of modular forms and Galois deformation theory. The results found in the book are at the cutting edge of the present research. The first few chapters provide the fundamentals while the latter chapters cater to first or second-year graduate students. Contains numerous open research problems for young researchers.
Modern Data Science with R by Modern Data Science with R is a comprehensive data science textbook for undergraduates that incorporates statistical and computational thinking to solve real-world data problems. Rather than focus exclusively on case studies or programming syntax, this book illustrates how statistical programming in the state-of-the-art R/RStudio computing environment can be leveraged to extract meaningful information from a variety of data in the service of addressing compelling questions. The second edition is updated to reflect the growing influence of the tidyverse set of packages. All code in the book has been revised and styled to be more readable and easier to understand. New functionality from packages like sf, purrr, tidymodels, and tidytext is now integrated into the text. All chapters have been revised, and several have been split, re-organized, or re-imagined to meet the shifting landscape of best practice.
Illustrating Mathematics by This book is for anyone who wishes to illustrate their mathematical ideas, which in our experience means everyone. It is organized by material, rather than by subject area, and purposefully emphasizes the process of creating things, including discussions of failures that occurred along the way. As a result, the reader can learn from the experiences of those who came before, and will be inspired to create their own illustrations. Topics illustrated within include prime numbers, fractals, the Klein bottle, Borromean rings, tilings, space-filling curves, knot theory, billiards, complex dynamics, algebraic surfaces, groups and prime ideals, the Riemann zeta function, quadratic fields, hyperbolic space, and hyperbolic 3-manifolds. Everyone who opens this book should find a type of mathematics with which they identify. Each contributor explains the mathematics behind their illustration at an accessible level, so that all readers can appreciate the beauty of both the object itself and the mathematics behind it.
The Wonder Book of Geometry : A Mathematical Story by How can we be sure that Pythagoras's theorem is really true? Why is the "angle in a semicircle" always 90 degrees? And how can tangents help determine the speed of a bullet? David Acheson takes the reader on a highly illustrated tour through the history of geometry, from ancient Greece to the present day. He emphasizes throughout elegant deduction and practical applications, and argues that geometry can offer the quickest route to the whole spirit of mathematics at its best. Along the way, we encounter the quirky and the unexpected, meet the great personalities involved, and uncover some of the loveliest surprises in mathematics.
Games for Your Mind : The History and Future of Logic Puzzles by A lively and engaging look at logic puzzles and their role in recreation, mathematics, and philosophy. Logic puzzles were first introduced to the public by Lewis Carroll in the late nineteenth century and have been popular ever since. Games like Sudoku and Mastermind are fun and engrossing recreational activities, but they also share deep foundations in mathematical logic and are worthy of serious intellectual inquiry. Games for Your Mind explores the history and future of logic puzzles while enabling you to test your skill against a variety of puzzles yourself. In this informative and entertaining book, Jason Rosenhouse begins by introducing readers to logic and logic puzzles and goes on to reveal the rich history of these puzzles. He shows how Carroll's puzzles presented Aristotelian logic as a game for children, yet also informed his scholarly work on logic. He reveals how another pioneer of logic puzzles, Raymond Smullyan, drew on classic puzzles about liars and truthtellers to illustrate Kurt Gödel's theorems and illuminate profound questions in mathematical logic. Rosenhouse then presents a new vision for the future of logic puzzles based on nonclassical logic, which is used today in computer science and automated reasoning to manipulate large and sometimes contradictory sets of data. Featuring a wealth of sample puzzles ranging from simple to extremely challenging, this lively and engaging book brings together many of the most ingenious puzzles ever devised, including the "Hardest Logic Puzzle Ever," metapuzzles, paradoxes, and the logic puzzles in detective stories.
Mathematics and Its Logics : Philosophical Essays by In these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appear to be contradictions between different systems, and positing different frameworks serving different legitimate purposes. The essays refine and extend Hellman's modal-structuralist account of mathematics, developing a height-potentialist view of higher set theory which recognizes indefinite extendability of models and stages at which sets occur. In the first of three new essays written for this volume, Hellman shows how extendability can be deployed to derive the axiom of Infinity and that of Replacement, improving on earlier accounts; he also shows how extendability leads to attractive, novel resolutions of the set-theoretic paradoxes. Other essays explore advantages and limitations of restrictive systems - nominalist, predicativist, and constructivist. Also included are two essays, with Solomon Feferman, on predicative foundations of arithmetic.
Abstract Algebra : A Comprehensive Introduction by Through this book, upper undergraduate mathematics majors will master a challenging yet rewarding subject, and approach advanced studies in algebra, number theory and geometry with confidence. Groups, rings and fields are covered in depth with a strong emphasis on irreducible polynomials, a fresh approach to modules and linear algebra, a fresh take on Gröbner theory, and a group theoretic treatment of Rejewski's deciphering of the Enigma machine. It includes a detailed treatment of the basics on finite groups, including Sylow theory and the structure of finite abelian groups. Galois theory and its applications to polynomial equations and geometric constructions are treated in depth. Those interested in computations will appreciate the novel treatment of division algorithms. This rigorous text 'gets to the point', focusing on concisely demonstrating the concept at hand, taking a 'definitions first, examples next' approach. Exercises reinforce the main ideas of the text and encourage students' creativity.
Introduction to Linear Regression Analysis by Introduction to Linear Regression Analysis is the most comprehensive, fulsome, and current examination of the foundations of linear regression analysis. Fully updated in this new sixth edition, the distinguished authors have included new material on generalized regression techniques and new examples to help the reader understand retain the concepts taught in the book. The new edition focuses on four key areas of improvement over the fifth edition: New exercises and data sets New material on generalized regression techniques The inclusion of JMP software in key areas Carefully condensing the text where possible Introduction to Linear Regression Analysis skillfully blends theory and application in both the conventional and less common uses of regression analysis in today's cutting-edge scientific research. The text equips readers to understand the basic principles needed to apply regression model-building techniques in various fields of study, including engineering, management, and the health sciences.