Paperback ISBN: 9780521295147
Paperback publication date: 31 March 1981
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Approximation Theory and Methods
Online ISBN: 9781139171502
Online publication date:
28 May 2018
- Textbook
Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematics at Cambridge University, sufficient attention is given to theory to make it highly suitable as a mathematical textbook at undergraduate or postgraduate level.
Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematics at Cambridge University, sufficient attention is given to theory to make it highly suitable as a mathematical textbook at undergraduate or postgraduate level.
An Introduction to General Relativity
, King's College London, , University of Oxford
Online ISBN: 9781139171977
Online publication date:
28 May 2018
Paperback ISBN: 9780521339438
Paperback publication date: 25 January 1991
This textbook provides an introduction to general relativity for mathematics undergraduates or graduate physicists. After a review of Cartesian tensor notation and special relativity the concepts of Riemannian differential geometry are introducted. More emphasis is placed on an intuitive grasp of the subject and a calculational facility than on a rigorous mathematical exposition. General relativity is then presented as a relativistic theory of gravity reducing in the appropriate limits to Newtonian gravity or special relativity. The Schwarzchild solution is derived and the gravitational red-shift, time dilation and classic tests of general relativity are discussed. There is a brief account of gravitational collapse and black holes based on the extended Schwarzchild solution. Other vacuum solutions are described, motivated by their counterparts in linearised general relativity. The book ends with chapters on cosmological solutions to the field equations. There are exercises attached to each chapter, some of which extend the development given in the text.
This textbook provides an introduction to general relativity for mathematics undergraduates or graduate physicists. After a review of Cartesian tensor notation and special relativity the concepts of Riemannian differential geometry are introducted. More emphasis is placed on an intuitive grasp of the subject and a calculational facility than on a rigorous mathematical exposition. General relativity is then presented as a relativistic theory of gravity reducing in the appropriate limits to Newtonian gravity or special relativity. The Schwarzchild solution is derived and the gravitational red-shift, time dilation and classic tests of general relativity are discussed. There is a brief account of gravitational collapse and black holes based on the extended Schwarzchild solution. Other vacuum solutions are described, motivated by their counterparts in linearised general relativity. The book ends with chapters on cosmological solutions to the field equations. There are exercises attached to each chapter, some of which extend the development given in the text.
An Introduction to Mathematical Reasoning
Numbers, Sets and Functions
, University of Manchester
Online ISBN: 9780511801136
Online publication date:
05 June 2012
Hardback ISBN: 9780521592697
Hardback publication date: 13 January 1998
Paperback ISBN: 9780521597180
Paperback publication date: 28 January 1998
- Textbook
The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. This is achieved by exploring set theory, combinatorics and number theory, topics which include many fundamental ideas which are part of the tool kit of any mathematician. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. Over 250 problems include questions to interest and challenge the most able student as well as plenty of routine exercises to help familiarize the reader with the basic ideas.
The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. This is achieved by exploring set theory, combinatorics and number theory, topics which include many fundamental ideas which are part of the tool kit of any mathematician. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. Over 250 problems include questions to interest and challenge the most able student as well as plenty of routine exercises to help familiarize the reader with the basic ideas.
Linear Algebra for Everyone
, Massachusetts Institute of Technology
- Textbook
Linear algebra has become the subject to know for people in quantitative disciplines of all kinds. No longer the exclusive domain of mathematicians and engineers, it is now used everywhere there is data and everybody who works with data needs to know more. This new book from Professor Gilbert Strang, author of the acclaimed Introduction to Linear Algebra, now in its fifth edition, makes linear algebra accessible to everybody, not just those with a strong background in mathematics. It takes a more active start, beginning by finding independent columns of small matrices, leading to the key concepts of linear combinations and rank and column space. From there it passes on to the classical topics of solving linear equations, orthogonality, linear transformations and subspaces, all clearly explained with many examples and exercises. The last major topics are eigenvalues and the important singular value decomposition, illustrated with applications to differential equations and image compression. A final optional chapter explores the ideas behind deep learning.
Linear algebra has become the subject to know for people in quantitative disciplines of all kinds. No longer the exclusive domain of mathematicians and engineers, it is now used everywhere there is data and everybody who works with data needs to know more. This new book from Professor Gilbert Strang, author of the acclaimed Introduction to Linear Algebra, now in its fifth edition, makes linear algebra accessible to everybody, not just those with a strong background in mathematics. It takes a more active start, beginning by finding independent columns of small matrices, leading to the key concepts of linear combinations and rank and column space. From there it passes on to the classical topics of solving linear equations, orthogonality, linear transformations and subspaces, all clearly explained with many examples and exercises. The last major topics are eigenvalues and the important singular value decomposition, illustrated with applications to differential equations and image compression. A final optional chapter explores the ideas behind deep learning.
General Topology for Beginners
, Sardar Patel University
Coming soon
Online ISBN: 9781009505871
Expected online publication date:
December 2025
Paperback ISBN: 9781009505888
Expected Paperback publication date: 31 December 2025
This textbook focuses on general topology. Meant for graduate and senior undergraduate mathematics students, it introduces topology thoroughly from scratch and assumes minimal basic knowledge of real analysis and metric spaces. It begins with thought-provoking questions to encourage students to learn about topology and how it is related to, yet different from, geometry. Using concepts from real analysis and metric spaces, the definition of topology is introduced along with its motivation and importance. The text covers all the topics of topology, including homeomorphism, subspace topology, weak topology, product topology, quotient topology, coproduct topology, order topology, metric topology, and topological properties such as countability axioms, separation axioms, compactness, and connectedness. It also helps to understand the significance of various topological properties in classifying topological spaces.
This textbook focuses on general topology. Meant for graduate and senior undergraduate mathematics students, it introduces topology thoroughly from scratch and assumes minimal basic knowledge of real analysis and metric spaces. It begins with thought-provoking questions to encourage students to learn about topology and how it is related to, yet different from, geometry. Using concepts from real analysis and metric spaces, the definition of topology is introduced along with its motivation and importance. The text covers all the topics of topology, including homeomorphism, subspace topology, weak topology, product topology, quotient topology, coproduct topology, order topology, metric topology, and topological properties such as countability axioms, separation axioms, compactness, and connectedness. It also helps to understand the significance of various topological properties in classifying topological spaces.
Financial Data Science
, Politecnico di Torino, Italy, and VinUniversity, Hanoi, , VinUniversity, Vietnam, , Politecnico di Torino, , University of California, Berkeley
Online ISBN: 9781009432283
Online publication date:
17 December 2025
Hardback ISBN: 9781009432245
Hardback publication date: 17 July 2025
- Textbook
Confidently analyze, interpret and act on financial data with this practical introduction to the fundamentals of financial data science. Master the fundamentals with step-by-step introductions to core topics will equip you with a solid foundation for applying data science techniques to real-world complex financial problems. Extract meaningful insights as you learn how to use data to lead informed, data-driven decisions, with over 50 examples and case studies and hands-on Matlab and Python code. Explore cutting-edge techniques and tools in machine learning for financial data analysis, including deep learning and natural language processing. Accessible to readers without a specialized background in finance or machine learning, and including coverage of data representation and visualization, data models and estimation, principal component analysis, clustering methods, optimization tools, mean/variance portfolio optimization and financial networks, this is the ideal introduction for financial services professionals, and graduate students in finance and data science.
Confidently analyze, interpret and act on financial data with this practical introduction to the fundamentals of financial data science. Master the fundamentals with step-by-step introductions to core topics will equip you with a solid foundation for applying data science techniques to real-world complex financial problems. Extract meaningful insights as you learn how to use data to lead informed, data-driven decisions, with over 50 examples and case studies and hands-on Matlab and Python code. Explore cutting-edge techniques and tools in machine learning for financial data analysis, including deep learning and natural language processing. Accessible to readers without a specialized background in finance or machine learning, and including coverage of data representation and visualization, data models and estimation, principal component analysis, clustering methods, optimization tools, mean/variance portfolio optimization and financial networks, this is the ideal introduction for financial services professionals, and graduate students in finance and data science.
Introductory Ring Theory
, Shaheed Rajguru College of Applied Sciences for Women, University of Delhi, , Bharati College, University of Delhi
Coming soon
Online ISBN: 9781009633529
Expected online publication date:
December 2025
Paperback ISBN: 9781009633536
Expected Paperback publication date: 31 January 2026
- Textbook
This book provides a clear and accessible introduction to ring theory for undergraduate students. Aligned with standard curricula, it simplifies abstract concepts through structured explanations, practical examples, and real-world applications. Ideal for both students and instructors, it serves as a valuable resource for mastering fundamental concepts in ring theory with ease. The text begins with an introduction to rings and goes on to cover subrings, integral domains, ideals, and factor rings. It also discusses ring homomorphisms and polynomial rings. The book concludes with topics such as polynomial factorization and divisibility in integral domains. Each chapter is supplemented with solved examples to foster a deeper understanding of the subject. A set of practice questions is also provided to sharpen problem-solving skills.
This book provides a clear and accessible introduction to ring theory for undergraduate students. Aligned with standard curricula, it simplifies abstract concepts through structured explanations, practical examples, and real-world applications. Ideal for both students and instructors, it serves as a valuable resource for mastering fundamental concepts in ring theory with ease. The text begins with an introduction to rings and goes on to cover subrings, integral domains, ideals, and factor rings. It also discusses ring homomorphisms and polynomial rings. The book concludes with topics such as polynomial factorization and divisibility in integral domains. Each chapter is supplemented with solved examples to foster a deeper understanding of the subject. A set of practice questions is also provided to sharpen problem-solving skills.
Foundations and Applications of Engineering Mechanics
, Kamla Nehru Institute of Technology, , Kamla Nehru Institute of Technology
Online ISBN: 9781316182567
Online publication date:
26 June 2025
Paperback ISBN: 9781107499836
Paperback publication date: 16 March 2015
- Textbook
Engineering mechanics is the branch of engineering that applies the laws of mechanics in design, and is at the core of every machine that is designed. This book offers a comprehensive discussion of the fundamental theories and principles of engineering mechanics. It begins by explaining the laws and idealization of mechanics, and then establishes the equation of equilibrium for a rigid body and free body diagram (FBD), along with their applications. Chapters on method of virtual work and mechanical vibration discuss in detail important topics such as principle of virtual work, potential energy and equilibrium and free vibration. The book also introduces the elastic spring method for finding deflection in beams and uses a simple integration method to calculate centroid and moment of inertia. This volume will serve as a useful textbook for undergraduates and engineering students studying engineering mechanics.
Engineering mechanics is the branch of engineering that applies the laws of mechanics in design, and is at the core of every machine that is designed. This book offers a comprehensive discussion of the fundamental theories and principles of engineering mechanics. It begins by explaining the laws and idealization of mechanics, and then establishes the equation of equilibrium for a rigid body and free body diagram (FBD), along with their applications. Chapters on method of virtual work and mechanical vibration discuss in detail important topics such as principle of virtual work, potential energy and equilibrium and free vibration. The book also introduces the elastic spring method for finding deflection in beams and uses a simple integration method to calculate centroid and moment of inertia. This volume will serve as a useful textbook for undergraduates and engineering students studying engineering mechanics.
Fundamentals of Transport Processes with Applications
, Indian Institute of Science, Bangalore
Online ISBN: 9781009036658
Online publication date:
28 February 2025
Paperback ISBN: 9781009005333
Paperback publication date: 13 April 2023
- Textbook
The study of transport phenomena is an essential part of chemical engineering, as well as other disciplines concerned with material transformations such as biomedical engineering, microfluidics, reactor design and metallurgy. Material transformations require the motion of constituents relative to each other, the transfer of heat across materials and fluid flow. This lucid textbook introduces the student to the fundamentals and applications of transport phenomena in a single volume and explains how the outcomes of transformation processes depend on fluid flow and heat/mass transfer. It demonstrates the progression from physical concepts to the mathematical formulation, followed by the solution techniques for predicting outcomes in industrial applications. The ordering of the topics, gradual build-up of complexity and easy to read language make it a vital resource for anyone looking for an introduction to the domain. It also provides a foundation for advanced courses in fluid mechanics, multiphase flows and turbulence.
The study of transport phenomena is an essential part of chemical engineering, as well as other disciplines concerned with material transformations such as biomedical engineering, microfluidics, reactor design and metallurgy. Material transformations require the motion of constituents relative to each other, the transfer of heat across materials and fluid flow. This lucid textbook introduces the student to the fundamentals and applications of transport phenomena in a single volume and explains how the outcomes of transformation processes depend on fluid flow and heat/mass transfer. It demonstrates the progression from physical concepts to the mathematical formulation, followed by the solution techniques for predicting outcomes in industrial applications. The ordering of the topics, gradual build-up of complexity and easy to read language make it a vital resource for anyone looking for an introduction to the domain. It also provides a foundation for advanced courses in fluid mechanics, multiphase flows and turbulence.
Introduction to Marine Dynamics
, University of Michigan, Ann Arbor
Online ISBN: 9781009418065
Online publication date:
31 October 2024
Hardback ISBN: 9781009418096
Hardback publication date: 08 August 2024
Master the fundamentals of complex marine systems with this introduction to marine dynamics, vibrations, hydrodynamics, and stochastic processes. It connects key theoretical concepts, including as the velocity potential, impulsive force and L'Hôpital's Rule, to real-world marine engineering applications such as such as marine platform dynamics, extreme motions and exceedance probabilities, and includes over 60 multi-part end-of-chapter problems, building from simplified questions to advanced exercises, enabling students to grow in confidence towards solving complex questions. Students will gain a deep understanding effective design and safe operation of offshore systems and ocean resources; and is supported by downloadable Matlab code, and online solutions for instructors. Including over 300 full-colour illustrations and worked examples, drawing on the author's 45 years of teaching experience in marine dynamics, this textbook provides the ideal introduction to marine dynamics for senior undergraduate and graduate students in marine engineering, and is a comprehensive reference for practitioners in industry.
Master the fundamentals of complex marine systems with this introduction to marine dynamics, vibrations, hydrodynamics, and stochastic processes. It connects key theoretical concepts, including as the velocity potential, impulsive force and L'Hôpital's Rule, to real-world marine engineering applications such as such as marine platform dynamics, extreme motions and exceedance probabilities, and includes over 60 multi-part end-of-chapter problems, building from simplified questions to advanced exercises, enabling students to grow in confidence towards solving complex questions. Students will gain a deep understanding effective design and safe operation of offshore systems and ocean resources; and is supported by downloadable Matlab code, and online solutions for instructors. Including over 300 full-colour illustrations and worked examples, drawing on the author's 45 years of teaching experience in marine dynamics, this textbook provides the ideal introduction to marine dynamics for senior undergraduate and graduate students in marine engineering, and is a comprehensive reference for practitioners in industry.
The Atmospheric General Circulation
, University of Washington, , University of Washington, , Colorado State University, , University of Washington
Online ISBN: 9781108563857
Online publication date:
26 May 2023
Hardback ISBN: 9781108474245
Hardback publication date: 20 April 2023
An engaging, comprehensive, richly illustrated textbook about the atmospheric general circulation, written by leading researchers in the field. The book elucidates the pervasive role of atmospheric dynamics in the Earth System, interprets the structure and evolution of atmospheric motions across a range of space and time scales in terms of fundamental theoretical principles, and includes relevant historical background and tutorials on research methodology. The book includes over 300 exercises and is accompanied by extensive online resources, including solutions manuals, an animations library, and an introduction to online visualization and analysis tools. This textbook is suitable as a textbook for advanced undergraduate and graduate level courses in atmospheric sciences and geosciences curricula and as a reference textbook for researchers.
An engaging, comprehensive, richly illustrated textbook about the atmospheric general circulation, written by leading researchers in the field. The book elucidates the pervasive role of atmospheric dynamics in the Earth System, interprets the structure and evolution of atmospheric motions across a range of space and time scales in terms of fundamental theoretical principles, and includes relevant historical background and tutorials on research methodology. The book includes over 300 exercises and is accompanied by extensive online resources, including solutions manuals, an animations library, and an introduction to online visualization and analysis tools. This textbook is suitable as a textbook for advanced undergraduate and graduate level courses in atmospheric sciences and geosciences curricula and as a reference textbook for researchers.
Actions of Groups
A Second Course in Algebra
, Vassar College, New York
Online ISBN: 9781009158107
Online publication date:
03 May 2023
Hardback ISBN: 9781009158121
Hardback publication date: 05 January 2023
Paperback ISBN: 9781009158114
Paperback publication date: 05 January 2023
Using the unifying notion of group actions, this second course in modern algebra introduces the deeper algebraic tools needed to get into topics only hinted at in a first course, like the successful classification of finite simple groups and how groups play a role in the solutions of polynomial equations. Because groups may act as permutations of a set, as linear transformations on a vector space, or as automorphisms of a field, the deeper structure of a group may emerge from these viewpoints, two different groups can be distinguished, or a polynomial equation can be shown to be solvable by radicals. By developing the properties of these group actions, readers encounter essential algebra topics like the Sylow theorems and their applications, Galois theory, and representation theory. Warmup chapters that review and build on the first course and active learning modules help students transition to a deeper understanding of ideas.
Using the unifying notion of group actions, this second course in modern algebra introduces the deeper algebraic tools needed to get into topics only hinted at in a first course, like the successful classification of finite simple groups and how groups play a role in the solutions of polynomial equations. Because groups may act as permutations of a set, as linear transformations on a vector space, or as automorphisms of a field, the deeper structure of a group may emerge from these viewpoints, two different groups can be distinguished, or a polynomial equation can be shown to be solvable by radicals. By developing the properties of these group actions, readers encounter essential algebra topics like the Sylow theorems and their applications, Galois theory, and representation theory. Warmup chapters that review and build on the first course and active learning modules help students transition to a deeper understanding of ideas.
Stochastic Finance
An Introduction with Examples
, University of Leeds, , Lancaster University
Online ISBN: 9781009049672
Online publication date:
16 February 2023
Hardback ISBN: 9781316511251
Hardback publication date: 06 April 2023
Paperback ISBN: 9781009048941
Paperback publication date: 06 April 2023
- Textbook
Stochastic Finance provides an introduction to mathematical finance that is unparalleled in its accessibility. Through classroom testing, the authors have identified common pain points for students, and their approach takes great care to help the reader to overcome these difficulties and to foster understanding where comparable texts often do not. Written for advanced undergraduate students, and making use of numerous detailed examples to illustrate key concepts, this text provides all the mathematical foundations necessary to model transactions in the world of finance. A first course in probability is the only necessary background. The book begins with the discrete binomial model and the finite market model, followed by the continuous Black–Scholes model. It studies the pricing of European options by combining financial concepts such as arbitrage and self-financing trading strategies with probabilistic tools such as sigma algebras, martingales and stochastic integration. All these concepts are introduced in a relaxed and user-friendly fashion.
Stochastic Finance provides an introduction to mathematical finance that is unparalleled in its accessibility. Through classroom testing, the authors have identified common pain points for students, and their approach takes great care to help the reader to overcome these difficulties and to foster understanding where comparable texts often do not. Written for advanced undergraduate students, and making use of numerous detailed examples to illustrate key concepts, this text provides all the mathematical foundations necessary to model transactions in the world of finance. A first course in probability is the only necessary background. The book begins with the discrete binomial model and the finite market model, followed by the continuous Black–Scholes model. It studies the pricing of European options by combining financial concepts such as arbitrage and self-financing trading strategies with probabilistic tools such as sigma algebras, martingales and stochastic integration. All these concepts are introduced in a relaxed and user-friendly fashion.
Finite Element and Finite Volume Methods for Heat Transfer and Fluid Dynamics
, Texas A & M University, , Texas A & M University, , Lawrence Livermore National Laboratory, California
Online ISBN: 9781009275453
Online publication date:
27 January 2023
Hardback ISBN: 9781009275484
Hardback publication date: 26 January 2023
- Textbook
Introduces the two most common numerical methods for heat transfer and fluid dynamics equations, using clear and accessible language. This unique approach covers all necessary mathematical preliminaries at the beginning of the book for the reader to sail smoothly through the chapters. Students will work step-by-step through the most common benchmark heat transfer and fluid dynamics problems, firmly grounding themselves in how the governing equations are discretized, how boundary conditions are imposed, and how the resulting algebraic equations are solved. Providing a detailed discussion of the discretization steps and time approximations, and clearly presenting concepts of explicit and implicit formulations, this graduate textbook has everything an instructor needs to prepare students for their exams and future careers. Each illustrative example shows students how to draw comparisons between the results obtained using the two numerical methods, and at the end of each chapter they can test and extend their understanding by working through the problems provided. A solutions manual is also available for instructors.
Introduces the two most common numerical methods for heat transfer and fluid dynamics equations, using clear and accessible language. This unique approach covers all necessary mathematical preliminaries at the beginning of the book for the reader to sail smoothly through the chapters. Students will work step-by-step through the most common benchmark heat transfer and fluid dynamics problems, firmly grounding themselves in how the governing equations are discretized, how boundary conditions are imposed, and how the resulting algebraic equations are solved. Providing a detailed discussion of the discretization steps and time approximations, and clearly presenting concepts of explicit and implicit formulations, this graduate textbook has everything an instructor needs to prepare students for their exams and future careers. Each illustrative example shows students how to draw comparisons between the results obtained using the two numerical methods, and at the end of each chapter they can test and extend their understanding by working through the problems provided. A solutions manual is also available for instructors.
An Elementary Course on Partial Differential Equations
, Aligarh Muslim University, India, , Aligarh Muslim University, India
Online ISBN: 9781009201469
Online publication date:
15 September 2022
Paperback ISBN: 9781009201445
Paperback publication date: 23 February 2023
- Textbook
Partial differential equations are a vital part of any course in pure or applied mathematics. This book will be invaluable to anyone looking for a lucid but comprehensive introduction to PDEs. Designed to strike a balance between theory and practical problems, it covers all major methods as well as their historical backgrounds, theoretical rigour, and geometric significance. The book is divided into three parts. It starts with basic topics like ordinary differential equations, multivariable calculus, and geometry. This is followed by important techniques to solve certain types of partial differential equations. The last part is devoted to first, second, and higher-order PDEs. The chapters have been arranged to help students develop their knowledge gradually and systematically. Each method is discussed through theoretical descriptions in the form of theorems followed by illustrative problems to help the readers. Finally, numerous solved examples and practice problems helps the student learn to apply this knowledge.
Partial differential equations are a vital part of any course in pure or applied mathematics. This book will be invaluable to anyone looking for a lucid but comprehensive introduction to PDEs. Designed to strike a balance between theory and practical problems, it covers all major methods as well as their historical backgrounds, theoretical rigour, and geometric significance. The book is divided into three parts. It starts with basic topics like ordinary differential equations, multivariable calculus, and geometry. This is followed by important techniques to solve certain types of partial differential equations. The last part is devoted to first, second, and higher-order PDEs. The chapters have been arranged to help students develop their knowledge gradually and systematically. Each method is discussed through theoretical descriptions in the form of theorems followed by illustrative problems to help the readers. Finally, numerous solved examples and practice problems helps the student learn to apply this knowledge.
Game Theory Basics
, London School of Economics and Political Science
Online ISBN: 9781108910118
Online publication date:
22 October 2021
Hardback ISBN: 9781108843300
Hardback publication date: 04 November 2021
Paperback ISBN: 9781108824231
Paperback publication date: 04 November 2021
Game theory is the science of interaction. This textbook, derived from courses taught by the author and developed over several years, is a comprehensive, straightforward introduction to the mathematics of non-cooperative games. It teaches what every game theorist should know: the important ideas and results on strategies, game trees, utility theory, imperfect information, and Nash equilibrium. The proofs of these results, in particular existence of an equilibrium via fixed points, and an elegant direct proof of the minimax theorem for zero-sum games, are presented in a self-contained, accessible way. This is complemented by chapters on combinatorial games like Go; and, it has introductions to algorithmic game theory, traffic games, and the geometry of two-player games. This detailed and lively text requires minimal mathematical background and includes many examples, exercises, and pictures. It is suitable for self-study or introductory courses in mathematics, computer science, or economics departments.
Game theory is the science of interaction. This textbook, derived from courses taught by the author and developed over several years, is a comprehensive, straightforward introduction to the mathematics of non-cooperative games. It teaches what every game theorist should know: the important ideas and results on strategies, game trees, utility theory, imperfect information, and Nash equilibrium. The proofs of these results, in particular existence of an equilibrium via fixed points, and an elegant direct proof of the minimax theorem for zero-sum games, are presented in a self-contained, accessible way. This is complemented by chapters on combinatorial games like Go; and, it has introductions to algorithmic game theory, traffic games, and the geometry of two-player games. This detailed and lively text requires minimal mathematical background and includes many examples, exercises, and pictures. It is suitable for self-study or introductory courses in mathematics, computer science, or economics departments.
A First Course in Quantitative Finance
, Ernst-Moritz-Arndt-Universität Greifswald, Germany
Online ISBN: 9781108303606
Online publication date:
06 August 2018
Paperback ISBN: 9781108411431
Paperback publication date: 22 March 2018
Hardback ISBN: 9781108419574
Hardback publication date: 25 April 2018
This new and exciting book offers a fresh approach to quantitative finance and utilises novel features, including stereoscopic images which permit 3D visualisation of complex subjects without the need for additional tools. Offering an integrated approach to the subject, A First Course in Quantitative Finance introduces students to the architecture of complete financial markets before exploring the concepts and models of modern portfolio theory, derivative pricing and fixed income products in both complete and incomplete market settings. Subjects are organised throughout in a way that encourages a gradual and parallel learning process of both the economic concepts and their mathematical descriptions, framed by additional perspectives from classical utility theory, financial economics and behavioural finance. Suitable for postgraduate students studying courses in quantitative finance, financial engineering and financial econometrics as part of an economics, finance, econometric or mathematics program, this book contains all necessary theoretical and mathematical concepts and numerical methods, as well as the necessary programming code for porting algorithms onto a computer.
This new and exciting book offers a fresh approach to quantitative finance and utilises novel features, including stereoscopic images which permit 3D visualisation of complex subjects without the need for additional tools. Offering an integrated approach to the subject, A First Course in Quantitative Finance introduces students to the architecture of complete financial markets before exploring the concepts and models of modern portfolio theory, derivative pricing and fixed income products in both complete and incomplete market settings. Subjects are organised throughout in a way that encourages a gradual and parallel learning process of both the economic concepts and their mathematical descriptions, framed by additional perspectives from classical utility theory, financial economics and behavioural finance. Suitable for postgraduate students studying courses in quantitative finance, financial engineering and financial econometrics as part of an economics, finance, econometric or mathematics program, this book contains all necessary theoretical and mathematical concepts and numerical methods, as well as the necessary programming code for porting algorithms onto a computer.
Computability
An Introduction to Recursive Function Theory
, University of York
Online ISBN: 9781139171496
Online publication date:
28 May 2018
Paperback ISBN: 9780521294652
Paperback publication date: 30 June 1980
- Textbook
What can computers do in principle? What are their inherent theoretical limitations? These are questions to which computer scientists must address themselves. The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function: intuitively a function whose values can be calculated in an effective or automatic way. This book is an introduction to computability theory (or recursion theory as it is traditionally known to mathematicians). Dr Cutland begins with a mathematical characterisation of computable functions using a simple idealised computer (a register machine); after some comparison with other characterisations, he develops the mathematical theory, including a full discussion of non-computability and undecidability, and the theory of recursive and recursively enumerable sets. The later chapters provide an introduction to more advanced topics such as Gödel's incompleteness theorem, degrees of unsolvability, the Recursion theorems and the theory of complexity of computation. Computability is thus a branch of mathematics which is of relevance also to computer scientists and philosophers. Mathematics students with no prior knowledge of the subject and computer science students who wish to supplement their practical expertise with some theoretical background will find this book of use and interest.
What can computers do in principle? What are their inherent theoretical limitations? These are questions to which computer scientists must address themselves. The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function: intuitively a function whose values can be calculated in an effective or automatic way. This book is an introduction to computability theory (or recursion theory as it is traditionally known to mathematicians). Dr Cutland begins with a mathematical characterisation of computable functions using a simple idealised computer (a register machine); after some comparison with other characterisations, he develops the mathematical theory, including a full discussion of non-computability and undecidability, and the theory of recursive and recursively enumerable sets. The later chapters provide an introduction to more advanced topics such as Gödel's incompleteness theorem, degrees of unsolvability, the Recursion theorems and the theory of complexity of computation. Computability is thus a branch of mathematics which is of relevance also to computer scientists and philosophers. Mathematics students with no prior knowledge of the subject and computer science students who wish to supplement their practical expertise with some theoretical background will find this book of use and interest.
Communication Theory
, University of Sussex,
Online ISBN: 9781139172448
Online publication date:
28 May 2018
Paperback ISBN: 9780521406062
Paperback publication date: 29 November 1991
This book is an introduction, for mathematics students, to the theories of information and codes. They are usually treated separately but, as both address the problem of communication through noisy channels (albeit from different directions), the authors have been able to exploit the connection to give a reasonably self-contained treatment, relating the probabilistic and algebraic viewpoints. The style is discursive and, as befits the subject, plenty of examples and exercises are provided. Some examples and exercises are provided. Some examples of computer codes are given to provide concrete illustrations of abstract ideas.
This book is an introduction, for mathematics students, to the theories of information and codes. They are usually treated separately but, as both address the problem of communication through noisy channels (albeit from different directions), the authors have been able to exploit the connection to give a reasonably self-contained treatment, relating the probabilistic and algebraic viewpoints. The style is discursive and, as befits the subject, plenty of examples and exercises are provided. Some examples and exercises are provided. Some examples of computer codes are given to provide concrete illustrations of abstract ideas.
A Course on Cooperative Game Theory
, Indian Statistical Institute, Kolkata, , Indian Statistical Institute, Kolkata, , Indian Statistical Institute, Kolkata
Online ISBN: 9781107415997
Online publication date:
28 May 2018
Hardback ISBN: 9781107058798
Hardback publication date: 09 February 2015
Paperback ISBN: 9781107691322
Paperback publication date: 17 October 2014
Cooperative game theory deals with situations where objectives of participants of the game are partially cooperative and partially conflicting. It is in the interest of participants to cooperate in the sense of making binding agreements to achieve the maximum possible benefit. When it comes to distribution of benefit/payoffs, participants have conflicting interests. Such situations are usually modelled as cooperative games. While the book mainly discusses transferable utility games, there is also a brief analysis of non-transferable utility games. Alternative solution concepts to cooperative game theoretic problems are presented in chapters 1-9 and the next four chapters present issues related to computations of solutions discussed in the earlier chapters. The proofs of all results presented in the book are quite explicit. Additionally the mathematical techniques employed in demonstrating the results will be helpful to those who wish to learn application of mathematics for solving problems in game theory.
Cooperative game theory deals with situations where objectives of participants of the game are partially cooperative and partially conflicting. It is in the interest of participants to cooperate in the sense of making binding agreements to achieve the maximum possible benefit. When it comes to distribution of benefit/payoffs, participants have conflicting interests. Such situations are usually modelled as cooperative games. While the book mainly discusses transferable utility games, there is also a brief analysis of non-transferable utility games. Alternative solution concepts to cooperative game theoretic problems are presented in chapters 1-9 and the next four chapters present issues related to computations of solutions discussed in the earlier chapters. The proofs of all results presented in the book are quite explicit. Additionally the mathematical techniques employed in demonstrating the results will be helpful to those who wish to learn application of mathematics for solving problems in game theory.