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The new 6th edition of Applied Combinatorics builds on the previous editions with more in depth analysis of computer systems in order to help develop proficiency in basic discrete math problem solving.
As one of the most widely used book in combinatorial problems, this edition explains how to reason and model combinatorically while stressing the systematic analysis of different possibilities, exploration of the logical structure of a problem, and ingenuity. Although important uses of combinatorics in computer science, operations research, and finite probability are mentioned, these applications are often used solely for motivation. Numerical examples involving the same concepts use more interesting settings such as poker probabilities or logical games.
This book is designed for use by students with a wide range of ability and maturity (sophomores through beginning graduate students). The stronger the students, the harder the exercises that can be assigned. The book can be used for one-quarter, two-quarter, or one-semester course depending on how much material is used.
In addition to his ground-breaking research, Nobel Laureate Steven Weinberg is known for a series of highly praised texts on various aspects of physics, combining exceptional physical insight with his gift for clear exposition. Describing the foundations of modern physics in their historical context and with some new derivations, Weinberg introduces topics ranging from early applications of atomic theory through thermodynamics, statistical mechanics, transport theory, special relativity, quantum mechanics, nuclear physics, and quantum field theory. This volume provides the basis for advanced undergraduate and graduate physics courses as well as being a handy introduction to aspects of modern physics for working scientists.
Designed for a two-semester advanced undergraduate or graduate level course, this distinctive and modern textbook provides students with the physical intuition and mathematical skills to tackle even complex problems in quantum mechanics with ease and fluency. Beginning with a detailed introduction to quantum states and Dirac notation, the book then develops the overarching theoretical framework of quantum mechanics, before explaining physical quantum mechanical properties such as angular momentum and spin. Symmetries and groups in quantum mechanics, important components of current research, are covered at length. The second part of the text focuses on applications, and includes a detailed chapter on quantum entanglement, one of the most exciting modern applications of quantum mechanics, and of key importance in quantum information and computation. Numerous exercises are interspersed throughout the text, expanding upon key concepts and further developing students' understanding. A fully worked solutions manual and lecture slides are available for instructors.
Maths for Economics provides a comprehensive and solid foundation in core mathematical principles and methods used in economics, beginning with revisiting basic skills in arithmetic, algebra, equation solving, and slowly building to more advanced topics. Suitable for those with a range of prior school-level expereince or more generally for those who feel they need to go back to the very basics, students can learn with confidence. Drawing on his extensive experience of teaching in the area, the author appreciates that maths can be a daunting topic for many. As such the text is fully supports the reader by using a combination of engaging learning features including summary sections, examples to show how theory is used in practice and progress exercises, which encourage independent study. Each chapter ends with a conclusion check list to allow students to reflect on topics as they master them. Digital formats and resources The fifth edition is available for students and institutions to purchase in a variety of formats, and is supported by online resources. The e-book offers a mobile experience and convenient access along with functionality tools, navigation features, and links that offer extra learning support: www.oxfordtextbooks.co.uk/ebooks Online resources supporting the book include, For Students: - Ask the author forum - Excel tutorial - Maple tutorial - Further exercises - Answers to further questions - Expanded solutions to progress exercises For Lecturers: - Test exercises - Graphs from the book - Answers to test exercises
Economic theories can be expressed in words, numbers, graphs and symbols. The existing traditional economics textbooks cover all four methods, but the general focus is often more on writing about the theory and methods, with few practical examples. With an increasing number of universities having introduced mathematical economics at undergraduate level, Basic mathematics for economics students aims to fill this gap in the field. Basic mathematics for economics students begins with a comprehensive chapter on basic mathematical concepts and methods (suitable for self-study, revision or tutorial purposes) to ensure that students have the necessary foundation. The book is written in an accessible style and is extremely practical. Numerous mathematical economics examples and exercises are provided as well as fully worked solutions using numbers, graphs and symbols. Basic mathematics for economics students is aimed at all economics students. It focuses on quantitative aspects and especially complements the three highly popular theoretical economics textbooks, Understanding microeconomics, Understanding macroeconomics and Economics for South African students, all written by Philip Mohr and published by Van Schaik Publishers.
Calculus with Vectors grew out of a strong need for a beginning calculus textbook for undergraduates who intend to pursue careers in STEM fields. The approach introduces vector-valued functions from the start, emphasizing the connections between one-variable and multi-variable calculus. The text includes early vectors and early transcendentals and includes a rigorous but informal approach to vectors. Examples and focused applications are well presented along with an abundance of motivating exercises. The approaches taken to topics such as the derivation of the derivatives of sine and cosine, the approach to limits and the use of "tables" of integration have been modified from the standards seen in other textbooks in order to maximize the ease with which students may comprehend the material. Additionally, the material presented is intentionally non-specific to any software or hardware platform in order to accommodate the wide variety and rapid evolution of tools used. Technology is referenced in the text and is required for a good number of problems.
This book combines a comprehensive state-of-the-art analysis of bifurcations of discrete-time dynamical systems with concrete instruction on implementations (and example applications) in the free MATLAB (R) software MatContM developed by the authors. While self-contained and suitable for independent study, the book is also written with users in mind and is an invaluable reference for practitioners. Part I focuses on theory, providing a systematic presentation of bifurcations of fixed points and cycles of finite-dimensional maps, up to and including cases with two control parameters. Several complementary methods, including Lyapunov exponents, invariant manifolds and homoclinic structures, and parts of chaos theory, are presented. Part II introduces MatContM through step-by-step tutorials on how to use the general numerical methods described in Part I for simple dynamical models defined by one- and two-dimensional maps. Further examples in Part III show how MatContM can be used to analyze more complicated models from modern engineering, ecology, and economics.
The Standard Model of particle physics is an amazingly successful theory describing the fundamental particles and forces of nature. This text, written for a two-semester graduate course on the Standard Model, develops a practical understanding of the theoretical concepts it's built upon, to prepare students to enter research. The author takes a historical approach to demonstrate to students the process of discovery which is often overlooked in other textbooks, presenting quantum field theory and symmetries as the necessary tools for describing and understanding the Standard Model. He develops these tools using a basic understanding of quantum mechanics and classical field theory, such as Maxwell's electrodynamics, before discussing the important role that Noether's theorem and conserved charges play in the theory. Worked examples feature throughout the text, while homework exercises are included for the first five parts, with solutions available online for instructors. Inspired by the author's own teaching experience, suggestions for independent research topics have been provided for the second-half of the course, which students can then present to the rest of the class.
The book aims to expound the general theory of relativity with a mathematical point of view. Catering to the needs of postgraduate students and researchers in the field of astrophysics and mathematical physics, it offers the readers a comprehensive understanding of the advanced topics of the subject matter. It specifically discusses the mathematical foundation of tensor calculus, gives a background of geodesics, Einstein's field equations, linearised gravity, spacetime of spherically symmetric distribution of matter and black holes, and particle and photon orbits in spacetime. Apart from the formulation of general relativity, Lie derivatives and its applications, and causality of spacetime are also discussed in detail. Certain preliminary concepts of extrinsic curvature, Lagrangian formalism of general theory of relativity and 3 + 1 decomposition of space-time are covered and are provided in the book as appendices.
Quantum field theory (QFT), the language of particle physics, is crucial to a physicist's graduate education. Based on lecture notes for courses taught for many years at Radboud University in the Netherlands, this book presents an alternative approach to teaching QFT using Feynman diagrams. A diagrammatic approach to understanding QFT exposes young physicists to an orthogonal introduction to the theory, bringing new ways to understand challenges in the field. Diagrammatic techniques using Feynman diagrams are used didactically, starting from simple discussions in lower dimensions to more complex topics in the Standard Model. Worked examples and exercises, for which solutions are available online, help the reader develop a deep understanding and intuition that enhances their problem-solving skills and understanding of QFT. Classroom-tested, this accessible book is valuable resource for graduate students and researchers.
This authoritative volume by a renowned Russian scientist offers
advanced students a thorough background in theoretical physics. The
treatment's review of basic methods takes an approach that's as
rigorous and systematic as it is practical.
Practical, readable volume offers advanced undergraduates and beginning graduate students the essential mathematical tools required for thorough comprehension of their disciplines. Topics cover elementary vector calculus, special functions of mathematical physics, calculus of variations, curve fitting and numerical approximation methods, and much more. Rather than aiming at complete mastery of these complicated subjects, the text focuses on the fundamental applied mathematics needed by students to deal with physics and engineering problems. An excellent self-contained study resource. 1968 ed.
This second book on Unity Root Matrix Theory extends its original three-dimensional formulation, as given in the first book, to an arbitrary number of higher dimensions. Unity Root Matrix Theory is formulated with strong adherence to concepts in mathematical physics and it is thought it may provide a discrete formulation of physical phenomena at the Planck level and upward. Consequently, it is essential that the theory incorporates the geometric dimensionality present in established physical theories. In particular, it must naturally embody the four-dimensional spacetime of Special Relativity, the five dimensions of Kaluza-Klein theory, and the eleven or more dimensions of Grand Unified Theories such as String Theory. Not only has an n-dimensional extension of Unity Root Matrix Theory successfully been achieved, whilst retaining all the three-dimensional mathematical and physical properties detailed in the first book, but a complete n-dimensional solution has been obtained which exhibits the geometric property of compactification, or dimensional reduction. This solution shows that dimensional shrinkage of higher dimensions may occur over long evolutionary timescales. The emergence of compactification and other physical phenomena gives further confidence that n-dimensional Unity Root Matrix Theory may, indeed, offer a discrete formulation of Physics starting at its most elemental level.
Developed on surprisingly simple but fundamental concepts, it provides a rich mathematical and physical structure, justifying it as a subject to be studied in its own right by physicists and mathematicians alike. Ultimately, it is thought that unity root matrix theory may provide an alternative reformulation of some fundamental concepts in physics and an integer-based escape from the current, unification impasse.
Designed specifically for business, economics, or life/social sciences majors, CALCULUS: AN APPLIED APPROACH, BRIEF, 10E, INTERNATIONAL METRIC EDITION motivates your study while fostering understanding and mastery. The book emphasizes integrated and engaging applications that show you the real-world relevance of topics and concepts. Applied problems drawn from government sources, industry, current events, and other disciplines provide well-rounded examples and appeal to diverse interests. The Tenth Edition builds upon its applications emphasis through updated exercises and relevant examples. Throughout the text, features such as algebra review and study tips,- provide you with extra guidance and practice. Stepped-out solution videos with instruction are available at CalcView.com for selected exercises throughout the text. Additionally, the companion website, LarsonAppliedCalculus.com, offers free access to multiple tools and resources. CalcChat.com offers free step-by-step solutions to the odd-numbered exercises in the text.
Some people fear and mistrust numbers. Others want to use them for everything. After a long career as a statistician, Paul Goodwin has learned the hard way that the ones who want to use them for everything are a very good reason for the rest of us to fear and mistrust them. Something Doesn't Add Up is a fieldguide to the numbers that rule our world, even though they don't make sense. Wry, witty and humane, Goodwin explains mathematical subtleties so painlessly that you hardly need to think about numbers at all. He demonstrates how statistics that are meant to make life simpler often make it simpler than it actually is, but also reveals some of the ways we really can use maths to make better decisions. Enter the world of fitness tracking, the history of IQ testing, China's social credit system, Effective Altruism, and learn how someone should have noticed that Harold Shipman was killing his patients years before they actually did. In the right hands, maths is a useful tool. It's just a pity there are so many of the wrong hands about.
During the last three decades geosciences and geo-engineering were influenced by two essential scenarios: First, the technological progress has changed completely the observational and measurement techniques. Modern high speed computers and satellite based techniques are entering more and more all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, its environment and about an expected shortage of natural resources. Obviously, both aspects, viz. efficient strategies of protection against threats of a changing Earth and the exceptional situation of getting terrestrial, airborne as well as space borne data of better and better quality explain the strong need of new mathematical structures, tools and methods. Mathematics concerned with geoscientific problems, i.e., Geomathematics, is becoming increasingly important. The 'Handbook of Geomathematics' deals with the qualitative and quantitative properties for the current and possible structures of the system Earth. As a central reference work it comprises the following geoscientific fields: (I) observational and measurement key technologies (II) modelling of the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, biosphere) (III) analytic, algebraic and operator-theoretic methods (IV) statistical and stochastic methods (V) computational and numerical analysis methods (VI) historical background and future perspectives.
This textbook provides a rigorous mathematical perspective on error-correcting codes, starting with the basics and progressing through to the state-of-the-art. Algebraic, combinatorial, and geometric approaches to coding theory are adopted with the aim of highlighting how coding can have an important real-world impact. Because it carefully balances both theory and applications, this book will be an indispensable resource for readers seeking a timely treatment of error-correcting codes. Early chapters cover fundamental concepts, introducing Shannon's theorem, asymptotically good codes and linear codes. The book then goes on to cover other types of codes including chapters on cyclic codes, maximum distance separable codes, LDPC codes, p-adic codes, amongst others. Those undertaking independent study will appreciate the helpful exercises with selected solutions. A Course in Algebraic Error-Correcting Codes suits an interdisciplinary audience at the Masters level, including students of mathematics, engineering, physics, and computer science. Advanced undergraduates will find this a useful resource as well. An understanding of linear algebra is assumed.
Two-part treatment begins with a self-contained introduction to the subject, followed by applications to stochastic analysis and mathematical physics. "A welcome addition." -- "Bulletin of the American Mathematical Society." 1986 edition.
Derived from a course in fluid mechanics, this text for advanced
undergraduates and beginning graduate students employs symmetry
arguments to demonstrate the principles of dimensional analysis.
The examples provided illustrate the effectiveness of symmetry
arguments in obtaining the mathematical form of the functions
yielded by dimensional analysis. Students will find these methods
applicable to a wide field of interests.
Geometry, of all the branches of mathematics, is the one that is most easily visualized by making something. However, it is all too easy to reduce it to reams of formulas to memorize and proofs to replicate. This book aims to take geometry back to its practical roots with 3D printed models and puzzles as well as demonstrations with household objects like flashlights and paper towel tubes. This is not a traditional geometry textbook, but rather builds up understanding of geometry concepts while also bringing in elements of concepts normally learned much later. Some of the models are counterintuitive, and figuring out how and why they work will both entertain and give insights. Two final chapters suggesting open-ended projects in astronomy and physics, and art and architecture, allow for deeper understanding and integration of the learning in the rest of the book.
Noncommutative geometry combines themes from algebra, analysis and geometry and has significant applications to physics. This book focuses on cyclic theory, and is based upon the lecture courses by Daniel G. Quillen at the University of Oxford from 1988-92, which developed his own approach to the subject. The basic definitions, examples and exercises provided here allow non-specialists and students with a background in elementary functional analysis, commutative algebra and differential geometry to get to grips with the subject. Quillen's development of cyclic theory emphasizes analogies between commutative and noncommutative theories, in which he reinterpreted classical results of Hamiltonian mechanics, operator algebras and differential graded algebras into a new formalism. In this book, cyclic theory is developed from motivating examples and background towards general results. Themes covered are relevant to current research, including homomorphisms modulo powers of ideals, traces on noncommutative differential forms, quasi-free algebras and Chern characters on connections.
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