Fast Track to Differential Equations
The second edition of this successful textbook includes a significantly extended chapter on Climate Change with an analysis of the CO2 budget. It also contains a completely new part on Epidemiology, treating the SEIR-model which describes the behavior and dynamics of epidemics. In particular, COVID-19 with actual data is discussed. This compact introduction to ordinary differential equations and their applications is aimed at anyone who in their studies is confronted voluntarily or involuntarily with this versatile subject. Numerous applications from physics, technology, biomathematics, cosmology, economy and optimization theory are given. Abstract proofs and unnecessary formalism are avoided as far as possible. The focus is on modelling ordinary differential equations of the first and second orders as well as their analytical and numerical solution methods, in which the theory is dealt with briefly before moving on to application examples. In addition, program codes show exemplarily how even more challenging questions can be tackled and represented meaningfully with the help of a computer algebra system. The first chapter deals with the necessary prior knowledge of integral and differential calculus. 103 motivating exercises together with their solutions round off the work. "I am happy to see such a book. It will serve as a support for many students, professors and faculty." Dr. Alessio Figalli, Professor at the ETH Z羹rich and Fields medalist 2018
A Million Nines
This is the sequel to A Million And One Random Digits. It contains 200 pages, each containing 50 lines that look like this: 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999.
Discovering Calculus
Learn Calculus, the easy way! This volume covers both differential and integral calculus, focusinging on conept, technique, and application: concept: a fresh perspective on the key concepts explained step-by-step in a way that students can understandtechnique: a few simple rules is all you need! A Calculus is a simple method for calculating, yet most other texts make it hopelessly confusing. It's actually meant to be easy. We state the key rules clearly and simply, do some examples, and carry on from there. application: this goes beyond any other text to prepare students for advanced courses in mathematics, science, and engineering. This book teaches the art of problem solving, covering a diverse range of interesting real-world applications.This text can be used as a two-semester applied calculus course for engineers, physicisits, and other students of the mathematical sciences. Be sure to check out our page Discovering Calculus on YouTube for free Calculus lectures and worked examples from the author. https: //bit.ly/3RfJ7QN
Stable Categories and Structured Ring Spectra
This comprehensive text focuses on the homotopical technology in use at the forefront of modern algebraic topology. Following on from a standard introductory algebraic topology sequence, it will provide students with a comprehensive background in spectra and structured ring spectra. Each chapter is an extended tutorial by a leader in the field, offering the first really accessible treatment of the modern construction of the stable category in terms of both model categories of point-set diagram spectra and infinity-categories. It is one of the only textbook sources for operadic algebras, structured ring spectra, and Bousfield localization, which are now basic techniques in the field, and the book provides a rare expository treatment of spectral algebraic geometry. Together the contributors -- Emily Riehl, Daniel Dugger, Clark Barwick, Michael A. Mandell, Birgit Richter, Tyler Lawson, and Charles Rezk -- offer a complete, authoritative source to learn the foundations of this vibrant area.
Advances in Discrete Applied Mathematics and Graph Theory
The present reprint contains twelve papers published in the Special Issue "Advances in Discrete Applied Mathematics and Graph Theory, 2021" of the MDPI Mathematics journal, which cover a wide range of topics connected to the theory and applications of Graph Theory and Discrete Applied Mathematics. The focus of the majority of papers is on recent advances in graph theory and applications in chemical graph theory. In particular, the topics studied include bipartite and multipartite Ramsey numbers, graph coloring and chromatic numbers, several varieties of domination (Double Roman, Quasi-Total Roman, Total 3-Roman) and two graph indices of interest in chemical graph theory (Sombor index, generalized ABC index), as well as hyperspaces of graphs and local inclusive distance vertex irregular graphs.
Seriously Fun Maths
In Seriously Fun Maths, Dr Laura Tuohilampi changes the narrative of mathematics education into something fascinating, intriguing and something that touches every human. Based on her cutting-edge research she challenges the outdated ways of motivating students around maths. This engaging book provides teachers with research, resources and activities to teach a lesson a month. The rich activities are accessible to young students and deep enough for secondary students. Even adults! This book will help mathematics educators reflect on their skills of orchestrating mathematical discussions and problem-solving. They will learn how to increase students' engagement in ways that reduce stress-inducing expectations around what a 'good' student in maths can and cannot do. Teachers will improve their grasp of what's important - making mathematics a meaningful experience.Everyone will have serious fun while learning maths!
Mathematics: Its Historical Aspects, Wonders and Beyond
Whenever the topic of mathematics is mentioned, people tend to indicate their weakness in the subject as a result of not having enjoyed its instruction during their school experience. Many students unfortunately do not have very positive experiences when learning mathematics, which can result from teachers who have a tendency 'to teach to the test'. This is truly unfortunate for several reasons. First, basic algebra and geometry, which are taken by almost all students, are not difficult subjects, and all students should be able to master them with the proper motivational instruction. Second, we live in a technical age, and being comfortable with basic mathematics can certainly help you deal with life's daily challenges. Other, less tangible reasons, are the pleasure one can experience from understanding the many intricacies of mathematics and its relation to the real world, experiencing the satisfaction of solving a mathematical problem, and discovering the intrinsic beauty and historical development of many mathematical expressions and relationships. These are some of the experiences that this book is designed to deliver to the reader.The book offers 101 mathematical gems, some of which may require a modicum of high school mathematics and others, just a desire to carefully apply oneself to the ideas. Many folks have spent years encountering mathematical terms, symbols, relationships and other esoteric expressions. Their origins and their meanings may never have been revealed, such as the symbols +, -, =, π. ꝏ, √, ∑, and many others. This book provides a delightful insight into the origin of mathematical symbols and popular theorems such as the Pythagorean Theorem and the Fibonacci Sequence, common mathematical mistakes and curiosities, intriguing number relationships, and some of the different mathematical procedures in various countries. The book uses a historical and cultural approach to the topics, which enhances the subject matter and greatly adds to its appeal. The mathematical material can, therefore, be more fully appreciated and understood by anyone who has a curiosity and interest in mathematics, especially if in their past experience they were expected to simply accept ideas and concepts without a clear understanding of their origins and meaning. It is hoped that this will cast a new and positive picture of mathematics and provide a more favorable impression of this most important subject and be a different experience than what many may have previously encountered. It is also our wish that some of the fascination and beauty of mathematics shines through in these presentations.
Mathematics: Its Historical Aspects, Wonders and Beyond
Whenever the topic of mathematics is mentioned, people tend to indicate their weakness in the subject as a result of not having enjoyed its instruction during their school experience. Many students unfortunately do not have very positive experiences when learning mathematics, which can result from teachers who have a tendency 'to teach to the test'. This is truly unfortunate for several reasons. First, basic algebra and geometry, which are taken by almost all students, are not difficult subjects, and all students should be able to master them with the proper motivational instruction. Second, we live in a technical age, and being comfortable with basic mathematics can certainly help you deal with life's daily challenges. Other, less tangible reasons, are the pleasure one can experience from understanding the many intricacies of mathematics and its relation to the real world, experiencing the satisfaction of solving a mathematical problem, and discovering the intrinsic beauty and historical development of many mathematical expressions and relationships. These are some of the experiences that this book is designed to deliver to the reader.The book offers 101 mathematical gems, some of which may require a modicum of high school mathematics and others, just a desire to carefully apply oneself to the ideas. Many folks have spent years encountering mathematical terms, symbols, relationships and other esoteric expressions. Their origins and their meanings may never have been revealed, such as the symbols +, -, =, π. ꝏ, √, ∑, and many others. This book provides a delightful insight into the origin of mathematical symbols and popular theorems such as the Pythagorean Theorem and the Fibonacci Sequence, common mathematical mistakes and curiosities, intriguing number relationships, and some of the different mathematical procedures in various countries. The book uses a historical and cultural approach to the topics, which enhances the subject matter and greatly adds to its appeal. The mathematical material can, therefore, be more fully appreciated and understood by anyone who has a curiosity and interest in mathematics, especially if in their past experience they were expected to simply accept ideas and concepts without a clear understanding of their origins and meaning. It is hoped that this will cast a new and positive picture of mathematics and provide a more favorable impression of this most important subject and be a different experience than what many may have previously encountered. It is also our wish that some of the fascination and beauty of mathematics shines through in these presentations.
Homogeneous Ordered Graphs, Metrically Homogeneous Graphs, and Beyond
This is the second of two volumes by Professor Cherlin presenting the state of the art in the classification of homogeneous structures in binary languages and related problems in the intersection of model theory and combinatorics. Researchers and graduate students in the area will find in these volumes many far-reaching results and interesting new research directions to pursue. This volume continues the analysis of the first volume to 3-multi-graphs and 3-multi-tournaments, expansions of graphs and tournaments by the addition of a further binary relation. The opening chapter provides an overview of the volume, outlining the relevant results and conjectures. The author applies and extends the results of Volume I to obtain a detailed catalogue of such structures and a second classification conjecture. The book ends with an appendix exploring recent advances and open problems in the theory of homogeneous structures and related subjects.
Variational Convergence and Stochastic Homogenization of Nonlinear Reaction-Diffusion Problems
A substantial number of problems in physics, chemical physics, and biology, are modeled through reaction-diffusion equations to describe temperature distribution or chemical substance concentration. For problems arising from ecology, sociology, or population dynamics, they describe the density of some populations or species. In this book the state variable is a concentration, or a density according to the cases. The reaction function may be complex and include time delays terms that model various situations involving maturation periods, resource regeneration times, or incubation periods. The dynamics may occur in heterogeneous media and may depend upon a small or large parameter, as well as the reaction term. From a purely formal perspective, these parameters are indexed by n. Therefore, reaction-diffusion equations give rise to sequences of Cauchy problems.The first part of the book is devoted to the convergence of these sequences in a sense made precise in the book. The second part is dedicated to the specific case when the reaction-diffusion problems depend on a small parameter ∊ₙ intended to tend towards 0. This parameter accounts for the size of small spatial and randomly distributed heterogeneities. The convergence results obtained in the first part, with additionally some probabilistic tools, are applied to this specific situation. The limit problems are illustrated through biological invasion, food-limited or prey-predator models where the interplay between environment heterogeneities in the individual evolution of propagation species plays an essential role. They provide a description in terms of deterministic and homogeneous reaction-diffusion equations, for which numerical schemes are possible.
Advanced Mathematics
This exploration of a selection of fundamental topics and general purpose tools provides a roadmap to undergraduate students who yearn for a deeper dive into many of the concepts and ideas they have been encountering in their classes whether their motivation is pure curiosity or preparation for graduate studies. The topics intersect a wide range of areas encompassing both pure and applied mathematics. The emphasis and style of the book are motivated by the goal of developing self-reliance and independent mathematical thought. Mathematics requires both intuition and common sense as well as rigorous, formal argumentation. This book attempts to showcase both, simultaneously encouraging readers to develop their own insights and understanding and the adoption of proof writing skills. The most satisfying proofs/arguments are fully rigorous and completely intuitive at the same time.
Homogeneous Ordered Graphs, Metrically Homogeneous Graphs, and Beyond
This is the first of two volumes by Professor Cherlin presenting the state of the art in the classification of homogeneous structures in binary languages and related problems in the intersection of model theory and combinatorics. Researchers and graduate students in the area will find in these volumes many far-reaching results and interesting new research directions to pursue. In this volume, Cherlin develops a complete classification of homogeneous ordered graphs and provides a full proof. He then proposes a new family of metrically homogeneous graphs, a weakening of the usual homogeneity condition. A general classification conjecture is presented, together with general structure theory and applications to a general classification conjecture for such graphs. It also includes introductory chapters giving an overview of the results and methods of both volumes, and an appendix surveying recent developments in the area. An extensive accompanying bibliography of related literature, organized by topic, is available online.
Mathematical Olympiad in China (2015-2016): Problems and Solutions
In China, lots of excellent maths students takes an active part in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results -- they have always been among the top 3, in fact in the first place most of the time.The authors of this book are coaches of the China national team. They are Xiong Bin, Yao Yijun, Qu Zhenhua, et al. The translator of this book is Chen Xiaomin.The materials of this book come from a series of two books (in Chinese) on Forward to IMO: A Collection of Mathematical Olympiad Problems (2015-2016). It is a collection of problems and solutions of the major mathematical competitions in China. It provides a glimpse of how the China national team is selected and formed.
The Art of Mathematics - Take Two
Lovers of mathematics, young and old, professional and amateur, will enjoy this book. It is mathematics with fun: a collection of attractive problems that will delight and test readers. Many of the problems are drawn from the large number that have entertained and challenged students, guests and colleagues over the years during afternoon tea. The problems have their roots in many areas of mathematics. They vary greatly in difficulty: some are very easy, but most are far from trivial, and quite a few rather hard. Many provide substantial and surprising results that form the tip of an iceberg, providing an introduction to an important topic. To enjoy and appreciate the problems, readers should browse the book choosing one that looks particularly enticing, and think about it on and off for a while before resorting to the hint or the solution. Follow threads for an enjoyable and enriching journey through mathematics.
Mathematical Olympiad in China (2015-2016): Problems and Solutions
In China, lots of excellent maths students takes an active part in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results -- they have always been among the top 3, in fact in the first place most of the time.The authors of this book are coaches of the China national team. They are Xiong Bin, Yao Yijun, Qu Zhenhua, et al. The translator of this book is Chen Xiaomin.The materials of this book come from a series of two books (in Chinese) on Forward to IMO: A Collection of Mathematical Olympiad Problems (2015-2016). It is a collection of problems and solutions of the major mathematical competitions in China. It provides a glimpse of how the China national team is selected and formed.
Retaining Women in Tech
For over 40 years, the tech industry has been working to attract more women. Yet, women continue to be underrepresented in technology jobs compared to other professions. Worse, once hired, women leave the field mid-career twice as often as men. In 2013, Karen Holtzblatt launched The Women in Tech Retention Project at WITops.org, dedicated to understanding what helps women in tech thrive. In 2014, Nicola Marsden joined the effort, bringing her extensive knowledge and research on gender and bias for women in tech. Together with worldwide volunteers, this research identified what helps women thrive and practical interventions to improve women's experience at work. In this book, we share women's stories, our research, relevant literature, and our perspective on making change to help retain women. All the research and solutions we share are based on deep research and user-centered ideation techniques. Part I describes the @Work Experience Framework and the six key factors that help women thrive: a dynamic valuing team; stimulating projects; the push into challenges with support; local role models; nonjudgmental flexibility to manage home/work balance; and developing personal power. Employees thinking of leaving their job have significantly lower scores on these factors showing their importance for retention. Part II describes tested interventions that redesign work practices to better support women, diverse teams, and all team members. We chose these interventions guided by data from over 1,000 people from multiple genders, ethnicities, family situations, and countries. Interventions target key processes in tech: onboarding new hires; group critique meetings; and Scrum. Interventions also address managing interpersonal dynamics to increase valuing and decrease devaluing behaviors and techniques for teams to define, monitor, and continuously improve their culture. We conclude by describing our principles for redesigning processes with an eye toward issues important to women and diverse teams.
Community College Mathematics
This book explores the rich history of community college math with a specific focus on gatekeeper math classes. Gatekeeper math classes include courses such as college algebra, introduction to statistics, and all developmental math classes. For community colleges, successful completion of these classes is imperative for student retention. This book presents a decade-by-decade analysis of the history of community college mathematics. The author employs a mix of conceptual, empirical, and quantitative research. The empirical research stems from interviews with 30 community college faculty members from seven community colleges.From the 1970s to the pandemic in the early 2020s, the book explores math curricula as well as trends, initiatives, teaching practices, and mandates that have impacted community college math. The positives and negatives of such trends, initiatives, and mandates are presented along with suggestions on how to apply such knowledge going forward.The author addresses the key questions: How can we build a future model for community college gatekeeper math classes that is both successful and sustainable? Additionally, how can we learn from the past and the present to build such a model?This book will be ideal for students in graduate programs focusing on community college leadership or developmental education leadership as well as all those hoping to improve success rates in community college mathematics programs.
Modeling Change and Uncertainty
This book offers a problem-solving approach. The authors introduce a problem to help motivate the learning of a particular mathematical modeling topic. The problem provides the issue or what is needed to solve using an appropriate modeling technique.
Paul Lorenzen -- Mathematician and Logician
This open access book examines the many contributions of Paul Lorenzen, an outstanding philosopher from the latter half of the 20th century. It features papers focused on integrating Lorenzen's original approach into the history of logic and mathematics. The papers also explore how practitioners can implement Lorenzen's systematical ideas in today's debates on proof-theoretic semantics, databank management, and stochastics. Coverage details key contributions of Lorenzen to constructive mathematics, Lorenzen's work on lattice-groups and divisibility theory, and modern set theory and Lorenzen's critique of actual infinity. The contributors also look at the main problem of Grundlagenforschung and Lorenzen's consistency proof and Hilbert's larger program. In addition, the papers offer a constructive examination of a Russell-style Ramified Type Theory and a way out of the circularity puzzle within the operative justification of logic and mathematics. Paul Lorenzen's name is associated with the Erlangen School of Methodical Constructivism, of which the approach in linguistic philosophy and philosophy of science determined philosophical discussions especially in Germany in the 1960s and 1970s. This volume features 10 papers from a meeting that took place at the University of Konstanz.
Surveys in Combinatorics 2022
This volume contains eight survey articles by the invited speakers of the 29th British Combinatorial Conference, held at Lancaster University in July 2022. Each article provides an overview of recent developments in a current hot research topic in combinatorics. These topics span graphs and hypergraphs, Latin squares, linear programming, finite fields, extremal combinatorics, Ramsey theory, graph minors and tropical geometry. The authors are among the world's foremost researchers on their respective topics but their surveys are aimed at nonspecialist readers: they are written clearly with little prior knowledge assumed and with pointers to the wider literature. Taken together these surveys give a snapshot of the research frontier in contemporary combinatorics, making the latest developments accessible to researchers and graduate students in mathematics and theoretical computer science with an interest in combinatorics and helping them to keep abreast of the field.
Felix Klein
About Felix Klein, the famous Greek mathematician Constantin Carath矇odory once said: "It is only by illuminating him from all angles that one can come to understand his significance." The author of this biography has done just this. A detailed study of original sources has made it possible to uncover new connections; to create a more precise representation of this important mathematician, scientific organizer, and educational reformer; and to identify misconceptions. Because of his edition of Julius Pl羹cker's work on line geometry and due to his own contributions to non-Euclidean geometry, Klein was already well known abroad before he received his first full professorship at the age of 23. By exchanging ideas with his most important cooperation partner, the Norwegian Sophus Lie, Klein formulated his Erlangen Program. Various other visionary programs followed, in which Klein involved mathematicians from Germany and abroad. Klein was the most active promoter of Riemann's geometric-physical approach to function theory, but he also integrated the analytical approaches of the Weierstrass school into his arsenal of methods. Klein was a citizen of the world who repeatedly travelled to France, Great Britain, Italy, the United States, and elsewhere. Despite what has often been claimed, it must be emphasized that Klein expressly opposed national chauvinism. He promoted mathematically gifted individuals regardless of their nationality, religion, or gender. Many of his works have been translated into English, French, Italian, Russian, and other languages; more than 300 supporters from around the world made it possible for his portrait to be painted by the prominent impressionist Max Liebermann. Inspired by international developments, Klein paved the way for women to work in the field of mathematics. He was instrumental in reforming mathematical education, and he endorsed an understanding of mathematics that affirmed its cultural importance as well as itsfundamental significance to scientific and technological progress.
Algebraic Groups
Algebraic groups play much the same role for algebraists as Lie groups play for analysts. This book is the first comprehensive introduction to the theory of algebraic group schemes over fields that includes the structure theory of semisimple algebraic groups, and is written in the language of modern algebraic geometry. The first eight chapters study general algebraic group schemes over a field and culminate in a proof of the Barsotti-Chevalley theorem, realizing every algebraic group as an extension of an abelian variety by an affine group. After a review of the Tannakian philosophy, the author provides short accounts of Lie algebras and finite group schemes. The later chapters treat reductive algebraic groups over arbitrary fields, including the Borel-Chevalley structure theory. Solvable algebraic groups are studied in detail. Prerequisites have also been kept to a minimum so that the book is accessible to non-specialists in algebraic geometry.
The Elements of Advanced Mathematics
This edition offers a more instructive Preface to assist instructors on developing the course they prefer. The prerequisites are more explicit and provide a roadmap for the course. Sample syllabi are included.
Real Homotopy of Configuration Spaces
- 1. Overview of the Volume. - 2. Configuration Spaces of Manifolds. - 3. Configuration Spaces of Closed Manifolds. - 4. Configuration Spaces of Manifolds with Boundary. - 5. Configuration Spaces and Operads.
Differential Equations and Their Applications
This textbook is a unique blend of the theory of differential equations and their exciting application to --real world" problems. First, and foremost, it is a rigorous study of ordinary differential equations and can be fully understood by anyone who has completed one year of calculus. However, in addition to the traditional applications, it also contains many exciting '-real life" problems. These applications are completely self contained. First, the problem to be solved is outlined clearly, and one or more differential equations are derived as a model for this problem. These equations are then solved, and the results are compared with real world data. The following applications are covered in this text. I. In Section 1.3 we prove that the beautiful painting --Disciples at Emmaus" which was bought by the Rembrandt Society of Belgium for $170,000 was a modern forgery. 2. In Section 1.5 we derive differential equations which govern the population growth of various species, and compare the results predicted by our models with the known values of the populations. 3. In Section 1.6 we try to determine whether tightly sealed drums filled with concentrated waste material will crack upon impact with the ocean floor. In this section we also describe several tricks for obtaining informa- tion about solutions of a differential equation that cannot be solved explicitly.
Non-Algorithmic Encryption
This report describe encryp-tion in a wider class of computation, as compared to ordinary clas-sic encryption algorithms. The security of the pro-posed systems are investig-ated, and it is shown, that the non-al-gorithmic ciphers have many advant-ageous properties. The theoretical foundation is presented with many con-venient refer-ences. The report also contain a discussion of the relev-ance, of the theory, in the real world. Practical issues, of cipher design, are discussed, and the Reader should easily be able to design a secure cipher; adopted to any local requirements or restrictions.
Modelling with Ordinary Differential Equations
Modelling with Ordinary Differential Equations: A Comprehensive Approach aims to provide a broad and self-contained introduction to the mathematical tools necessary to investigate and apply ODE models. The book starts by establishing the existence of solutions in various settings and analysing their stability properties. The next step is to illustrate modelling issues arising in the calculus of variation and optimal control theory that are of interest in many applications. This discussion is continued with an introduction to inverse problems governed by ODE models and to differential games.The book is completed with an illustration of stochastic differential equations and the development of neural networks to solve ODE systems. Many numerical methods are presented to solve the classes of problems discussed in this book.Features: Provides insight into rigorous mathematical issues concerning various topics, while discussing many different models of interest in different disciplines (biology, chemistry, economics, medicine, physics, social sciences, etc.) Suitable for undergraduate and graduate students and as an introduction for researchers in engineering and the sciences Accompanied by codes which allow the reader to apply the numerical methods discussed in this book in those cases where analytical solutions are not available
Structures of Domination in Graphs
This volume comprises 17 contributions that present advanced topics in graph domination, featuring open problems, modern techniques, and recent results. The book is divided into 3 parts. The first part focuses on several domination-related concepts: broadcast domination, alliances, domatic numbers, dominator colorings, irredundance in graphs, private neighbor concepts, game domination, varieties of Roman domination and spectral graph theory. The second part covers domination in hypergraphs, chessboards, and digraphs and tournaments. The third part focuses on the development of algorithms and complexity of signed, minus and majority domination, power domination, and alliances in graphs. The third part also includes a chapter on self-stabilizing algorithms. Of extra benefit to the reader, the first chapter includes a glossary of commonly used terms.The book is intended to provide a reference for established researchers in the fields of domination and graph theory and graduate students who wish to gain knowledge of the topics covered as well as an overview of the major accomplishments and proof techniques used in the field.
Analytical Groundwater Modeling
This book covers the theoretical aspects of mathematical groundwater models. It is aimed at advanced (under)graduate university students, as well as practicing hydrogeologists. The focus is on the fundamentals of the quantitative methods used to simulate, understand, and investigate groundwater systems.
A Mathematician's Apology
A Mathematician's Apology is the famous essay by British mathematician G. H. Hardy. It concerns the aesthetics of mathematics with some personal content and gives the layman an insight into the mind of a working mathematician. It is an attempt to justify and explain, pure mathematics. One of the main themes of the book is the beauty that mathematics possesses, which Hardy compares to painting and poetry.G. H. Hardy (7 Feb 1877 - 1 Dec 1947) was an eccentric British mathematician who worked extensively in mathematical analysis and analytical number theory alongside J.E Littlewood. He is perhaps even better known for his adoption and mentoring of the self-taught Indian mathematical genius, Srinivasa Ramanujan. Hardy wanted his work to be referred to as pure mathematics rather than applied mathematics. In his view, mathematics was not something to be used in social destruction and to fulfill political purposes.
On The Study and Difficulties of Mathematics
I. Introductory Remarks on the Nature and Objects of MathematicsII. On Arithmetical NotationIII. Elementary Rules of ArithmeticIV. Arithmetical FractionsV. Decimal FractionsVI. Algebraical Notation and PrinciplesVII. Elementary Rules of AlgebraVIII. Equations of the First DegreeIX. On the Negative Sign, etcX. Equations of the Second DegreeXI. On Roots in General, and LogarithmsXII. On the Study of AlgebraXIII. On the Definitions of GeometryXIV. On Geometrical ReasoningXV. On AxiomsXVI. On ProportionXVII. Application of Algebra to the Measurement of Lines, Angles, Proportion of Figures, and Surfaces
Spherical Trigonometry
I Great and Small CirclesII Spherical TrianglesIII Spherical GeometryIV Relations between the Trigonometrical Functions of the Sidesand the Angles of a Spherical TriangleV Solution of Right-angled TrianglesVI Solution of Oblique-Angled TrianglesVII Circumscribed and Inscribed CirclesVIII Area of a Spherical Triangle. Spherical ExcessIX On certain approximate Formul疆X Geodetical OperationsXI On small variations in the parts of a Spherical TriangleXII On the connexion of Formul疆 in Plane and Spherical Trigonometry.XIII PolyhedronsXIV Arcs drawn to fixed points on the Surface of a SphereXV Miscellaneous PropositionsXVI Numerical Solution of Spherical Triangles
Attractors for Semigroups and Evolution Equations
In this volume, Olga A. Ladyzhenskaya expands on her highly successful 1991 Accademia Nazionale dei Lincei lectures. The lectures were devoted to questions of the behaviour of trajectories for semigroups of nonlinear bounded continuous operators in a locally non-compact metric space and for solutions of abstract evolution equations. The latter contain many initial boundary value problems for dissipative partial differential equations. This work, for which Ladyzhenskaya was awarded the Russian Academy of Sciences' Kovalevskaya Prize, reflects the high calibre of her lectures; it is essential reading for anyone interested in her approach to partial differential equations and dynamical systems. This edition, reissued for her centenary, includes a new technical introduction, written by Gregory A. Seregin, Varga K. Kalantarov and Sergey V. Zelik, surveying Ladyzhenskaya's works in the field and subsequent developments influenced by her results.
Memcomputing
MemComputing is a new computing paradigm that employs time non-locality (memory) to both process and store information. This book, written by the originator of this paradigm, explains the main ideas behind MemComputing, explores its theoretical foundations, and shows its applicability to a wide variety of combinatorial optimization problems, machine learning, and quantum mechanics. The book is ideal for graduate students in Physics, Computer Science, Electrical Engineering, and Mathematics, as well as researchers in both academia and industry interested in unconventional computing. The author relies on extensive margin notes, important remarks, and many illustrations to better explain the main concepts and clarify jargon, making the book as self-contained as possible. The reader will be guided from the basic notions to the more advanced ones with an always clear and engaging writing style. Along the way, the reader will appreciate the advantages of this computing paradigm and the major differences that set it apart from the prevailing Turing model of computation, and even quantum computing.
Computability Theory and Foundations of Mathematics - Proceedings of the 9th International Conference on Computability Theory and Foundations of Mathematics
This volume features the latest scientific developments in the fields of computability theory and logical foundations of mathematics as well as applications. The scope involves the topics of Computability Theory, Reverse Mathematics, Nonstandard Analysis, Proof Theory, Set Theory, Philosophy of Mathematics, Constructive Mathematics, Theory of Randomness and Computational Complexity Theory.
Creating Autonomous Vehicle Systems, Second Edition
This book is one of the first technical overviews of autonomous vehicles written for a general computing and engineering audience. The authors share their practical experiences designing autonomous vehicle systems. These systems are complex, consisting of three major subsystems: (1) algorithms for localization, perception, and planning and control; (2) client systems, such as the robotics operating system and hardware platform; and (3) the cloud platform, which includes data storage, simulation, high-definition (HD) mapping, and deep learning model training. The algorithm subsystem extracts meaningful information from sensor raw data to understand its environment and make decisions as to its future actions. The client subsystem integrates these algorithms to meet real-time and reliability requirements. The cloud platform provides offline computing and storage capabilities for autonomous vehicles. Using the cloud platform, new algorithms can be tested so as to update the HD map--in addition to training better recognition, tracking, and decision models. Since the first edition of this book was released, many universities have adopted it in their autonomous driving classes, and the authors received many helpful comments and feedback from readers. Based on this, the second edition was improved by extending and rewriting multiple chapters and adding two commercial test case studies. In addition, a new section entitled "Teaching and Learning from this Book" was added to help instructors better utilize this book in their classes. The second edition captures the latest advances in autonomous driving and that it also presents usable real-world case studies to help readers better understand how to utilize their lessons in commercial autonomous driving projects. This book should be useful to students, researchers, and practitioners alike. Whether you are an undergraduate or a graduate student interested in autonomous driving, you will find herein a comprehensive overview of the whole autonomous vehicle technology stack. If you are an autonomous driving practitioner, the many practical techniques introduced in this book will be of interest to you. Researchers will also find extensive references for an effective, deeper exploration of the various technologies.
General Video Game Artificial Intelligence
Research on general video game playing aims at designing agents or content generators that can perform well in multiple video games, possibly without knowing the game in advance and with little to no specific domain knowledge. The general video game AI framework and competition propose a challenge in which researchers can test their favorite AI methods with a potentially infinite number of games created using the Video Game Description Language. The open-source framework has been used since 2014 for running a challenge. Competitors around the globe submit their best approaches that aim to generalize well across games. Additionally, the framework has been used in AI modules by many higher-education institutions as assignments, or as proposed projects for final year (undergraduate and Master's) students and Ph.D. candidates. The present book, written by the developers and organizers of the framework, presents the most interesting highlights of the research performed by the authors duringthese years in this domain. It showcases work on methods to play the games, generators of content, and video game optimization. It also outlines potential further work in an area that offers multiple research directions for the future.
On the Study of Human Cooperation via Computer Simulation
Cooperation is pervasive throughout nature, but its origin remains an open question. For decades, social scientists, business leaders, and economists have struggled with an important question: why is cooperation so ubiquitous among unrelated humans? The answers would have profound effects because anything that promotes cooperation leads to more productive work environments and benefits society at large. Game theory provides an ideal framework for studying social dilemmas, or those situations in which people decide whether to cooperate with others (benefitting the group) or defect by prioritizing their self-interest (benefitting only the individual). The social dilemma is formulated as a mathematical game and then programmed into a computer model. Simulating the game allows researchers to investigate potential theories to explain how cooperation emerges and what promotes its persistence. Over the past 25 years, countless papers on social dilemma games have been published, yet arguably little progress has been made. The problem is the social dilemma game models are unrealistic in the sense they contain artificial constructs that deviate from the way humans act. This book describes the shortcomings in current social dilemma game modeling techniques and provides guidance on designing more effective models. A basic introduction to game theory is provided with an emphasis on the prisoner's dilemma, the most widely studied social dilemma game. Individual chapters are provided detailing the shortcomings of weak selection, spatial games, and the Moran process. Computer model validation is also discussed at length. The recommendations found in this book should help design more realistic social dilemma game models likely to produce a better understanding of human cooperation.
Blockchain Platforms
This book introduces all the technical features that make up blockchain technology today. It starts with a thorough explanation of all technological concepts necessary to understand any discussions related to distributed ledgers and a short history of earlier implementations. It then discusses in detail how the Bitcoin network looks and what changes are coming in the near future, together with a range of altcoins that were created on the same base code. To get an even better idea, the book shortly explores how Bitcoin might be forked before going into detail on the Ethereum network and cryptocurrencies running on top of the network, smart contracts, and more. The book introduces the Hyperledger foundation and the tools offered to create private blockchain solutions. For those willing, it investigates directed acyclic graphs (DAGs) and several of its implementations, which could solve several of the problems other blockchain networks are still dealing with to this day. In Chapter 4, readers can find an overview of blockchain networks that can be used to build solutions of their own and the tools that can help them in the process.
Sound Synthesis, Propagation, and Rendering
This book gives a broad overview of research on sound simulation driven by a variety of applications. Vibrating objects produce sound, which then propagates through a medium such as air or water before finally being heard by a listener. As a crucial sensory channel, sound plays a vital role in many applications. There is a well-established research community in acoustics that has studied the problems related to sound simulation for six decades. Some of the earliest work was motivated by the design of concert halls, theaters, or lecture rooms with good acoustic characteristics. These problems also have been investigated in other applications, including noise control and sound design for urban planning, building construction, and automotive applications. Moreover, plausible or realistic sound effects can improve the sense of presence in a virtual environment or a game. In these applications, sound can provide important clues such as source directionality and spatial size. The book first surveys various sound synthesis methods, including harmonic synthesis, texture synthesis, spectral analysis, and physics-based synthesis. Next, it provides an overview of sound propagation techniques, including wave-based methods, geometric-based methods, and hybrid methods. The book also summarizes various techniques for sound rendering. Finally, it surveys some recent trends, including the use of machine learning methods to accelerate sound simulation and the use of sound simulation techniques for other applications such as speech recognition, source localization, and computer-aided design.
Introduction to Logic, Third Edition
This book is a gentle but rigorous introduction to Formal Logic. It is intended primarily for use at the college level. However, it can also be used for advanced secondary school students, and it can be used at the start of graduate school for those who have not yet seen the material.The approach to teaching logic used here emerged from more than 20 years of teaching logic to students at Stanford University and from teaching logic to tens of thousands of others via online courses on the World Wide Web. The approach differs from that taken by other books in logic in two essential ways, one having to do with content, the other with form.Like many other books on logic, this one covers logical syntax and semantics and proof theory plus induction. However, unlike other books, this book begins with Herbrand semantics rather than the more traditional Tarskian semantics. This approach makes the material considerably easier for students to understand and leaves them with a deeper understanding of what logic is all about.In addition to this text, there are online exercises (with automated grading), online logic tools and applications, online videos of lectures, and an online forum for discussion. They are available at http: //intrologic.stanford.edu/
Virtual Crowds
There are many applications of computer animation and simulation where it is necessary to model virtual crowds of autonomous agents. Some of these applications include site planning, education, entertainment, training, and human factors analysis for building evacuation. Other applications include simulations of scenarios where masses of people gather, flow, and disperse, such as transportation centers, sporting events, and concerts. Most crowd simulations include only basic locomotive behaviors possibly coupled with a few stochastic actions. Our goal in this survey is to establish a baseline of techniques and requirements for simulating large-scale virtual human populations. Sometimes, these populations might be mutually engaged in a common activity such as evacuation from a building or area; other times they may be going about their individual and personal agenda of work, play, leisure, travel, or spectator. Computational methods to model one set of requirements may not mesh well withgood approaches to another. By including both crowd and individual goals and constraints into a comprehensive computational model, we expect to simulate the visual texture and contextual behaviors of groups of seemingly sentient beings. Table of Contents: Introduction / Crowd Simulation Methodology Survey / Individual Differences in Crowds / Framework (HiDAC + MACES + CAROSA) / HiDAC: Local Motion / MACES: Wayfinding with Communication and Roles / CAROSA: Functional Crowds / Initializing a Scenario / Evaluating Crowds
Analytical Performance Modeling for Computer Systems, Third Edition
This book is an introduction to analytical performance modeling for computer systems, i.e., writing equations to describe their performance behavior. It is accessible to readers who have taken college-level courses in calculus and probability, networking, and operating systems. This is not a training manual for becoming an expert performance analyst. Rather, the objective is to help the reader construct simple models for analyzing and understanding the systems that they are interested in. Describing a complicated system abstractly with mathematical equations requires a careful choice of assumptions and approximations. They make the model tractable, but they must not remove essential characteristics of the system, nor introduce spurious properties. To help the reader understand the choices and their implications, this book discusses the analytical models for 40 research papers. These papers cover a broad range of topics: GPUs and disks, routers and crawling, databases and multimedia, worms and wireless, multicore and cloud, security and energy, etc. An appendix provides many questions for readers to exercise their understanding of the models in these papers.
Fast Start Differential Calculus
This book reviews the algebraic prerequisites of calculus, including solving equations, lines, quadratics, functions, logarithms, and trig functions. It introduces the derivative using the limit-based definition and covers the standard function library and the product, quotient, and chain rules. It explores the applications of the derivative to curve sketching and optimization and concludes with the formal definition of the limit, the squeeze theorem, and the mean value theorem.
Fast Start Integral Calculus
This book introduces integrals, the fundamental theorem of calculus, initial value problems, and Riemann sums. It introduces properties of polynomials, including roots and multiplicity, and uses them as a framework for introducing additional calculus concepts including Newton's method, L'H繫pital's Rule, and Rolle's theorem. Both the differential and integral calculus of parametric, polar, and vector functions are introduced. The book concludes with a survey of methods of integration, including u-substitution, integration by parts, special trigonometric integrals, trigonometric substitution, and partial fractions.
Digital Heritage Reconstruction Using Super-Resolution and Inpainting
Heritage sites across the world have witnessed a number of natural calamities, sabotage and damage from visitors, resulting in their present ruined condition. Many sites are now restricted to reduce the risk of further damage. Yet these masterpieces are significant cultural icons and critical markers of past civilizations that future generations need to see. A digitally reconstructed heritage site could diminish further harm by using immersive navigation or walkthrough systems for virtual environments. An exciting key element for the viewer is observing fine details of the historic work and viewing monuments in their undamaged form. This book presents image super-resolution methods and techniques for automatically detecting and inpainting damaged regions in heritage monuments, in order to provide an enhanced visual experience. The book presents techniques to obtain higher resolution photographs of the digitally reconstructed monuments, and the resulting images can serve as input to immersive walkthrough systems. It begins with the discussion of two novel techniques for image super-resolution and an approach for inpainting a user-supplied region in the given image, followed by a technique to simultaneously perform super-resolution and inpainting of given missing regions. It then introduces a method for automatically detecting and repairing the damage to dominant facial regions in statues, followed by a few approaches for automatic crack repair in images of heritage scenes. This book is a giant step toward ensuring that the iconic sites of our past are always available, and will never be truly lost.
