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This text aims to differentiate itself from other business statistics texts in two important ways. It seeks: to present the material in a non-technical manner to make it easier for a student with limited mathematical background to grasp the subject matter; and to develop an intuitive understanding of the techniques by framing them in the context of a management question, giving layman-type explanations of methods, using illustrative business examples and focusing on the management interpretations of the statistical findings. This further edition continues the theme of using Excel as a computational tool to perform statistical analysis. While all statistical functions have been adjusted to the Excel (2013) format, the statistical output remains unchanged. Using Excel to perform the statistical analysis in this text allows a student: To examine more realistic business problems with larger datasets; To focus more on the statistical interpretation of the statistical findings; and to transfer this skill of performing statistical analysis more easily to the work environment. Its overall purpose is to develop a management student's statistical reasoning and statistical decision-making skills to give him or her a competitive advantage in the workplace.
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.
This popular, world-wide selling textbook teaches engineering mathematics in a step-by-step fashion and uniquely through engineering examples and exercises which apply the techniques right from their introduction. This contextual use of mathematics is highly motivating, as with every topic and each new page students see the importance and relevance of mathematics in engineering. The examples are taken from mechanics, aerodynamics, electronics, engineering, fluid dynamics and other areas. While being general and accessible for all students, they also highlight how mathematics works in any individual's engineering discipline. The material is often praised for its careful pace, and the author pauses to ask questions to keep students reflecting. Proof of mathematical results is kept to a minimum. Instead the book develops learning by investigating results, observing patterns, visualizing graphs and answering questions using technology. This textbook is ideal for first year undergraduates and those on pre-degree courses in Engineering (all disciplines) and Science.
The best-selling introductory mathematics textbook for students on science and engineering degree and pre-degree courses. Sales stand at more than half a million copies world-wide. Its unique programmed approach takes students through the mathematics they need in a step-by-step fashion with a wealth of examples and exercises. The text demands that students engage with it by asking them to complete steps that they should be able to manage from previous examples or knowledge they have acquired, while carefully introducing new steps. By working with the authors through the examples, students become proficient as they go. By the time they come to trying examples on their own, confidence is high. Aimed at undergraduates on Foundation and First Year degree programmes in all Engineering disciplines and Science. The Foundation section covers mathematics from GCSE onwards to allow for revision and gap-filling, and so means the book can be used for a range of abilities and all levels of access.
Now in its eighth edition, Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams. John Bird's approach is based on worked examples and interactive problems. Mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in order to ensure that readers can relate theory to practice. The extensive and thorough topic coverage makes this an ideal text for a range of Level 2 and 3 engineering courses. This title is supported by a companion website with resources for both students and lecturers, including lists of essential formulae and multiple choice tests.
Discover a simple, direct approach that highlights the basics you need within A FIRST COURSE IN THE FINITE ELEMENT METHOD, 6E. This unique book is written so both undergraduate and graduate students can easily comprehend the content without the usual prerequisites, such as structural analysis. The book is written primarily as a basic learning tool for students, like you, in civil and mechanical engineering who are primarily interested in stress analysis and heat transfer. The text offers ideal preparation for utilizing the finite element method as a tool to solve practical physical problems.
In their bestselling MATHEMATICAL STATISTICS WITH APPLICATIONS, premiere authors Dennis Wackerly, William Mendenhall, and Richard L. Scheaffer present a solid foundation in statistical theory while conveying the relevance and importance of the theory in solving practical problems in the real world. The authors' use of practical applications and excellent exercises helps you discover the nature of statistics and understand its essential role in scientific research.
Active student engagement is key to this classroom-tested combinatorics text, boasting 1200+ carefully designed problems, ten mini-projects, section warm-up problems, and chapter opening problems. The author - an award-winning teacher - writes in a conversational style, keeping the reader in mind on every page. Students will stay motivated through glimpses into current research trends and open problems as well as the history and global origins of the subject. All essential topics are covered, including Ramsey theory, enumerative combinatorics including Stirling numbers, partitions of integers, the inclusion-exclusion principle, generating functions, introductory graph theory, and partially ordered sets. Some significant results are presented as sets of guided problems, leading readers to discover them on their own. More than 140 problems have complete solutions and over 250 have hints in the back, making this book ideal for self-study. Ideal for a one semester upper undergraduate course, prerequisites include the calculus sequence and familiarity with proofs.
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.
Engineering is mathematics in action. But engineering students do not always see the link between what they learn in mathematics and how this applies to engineering problems.
From relatively simple questions, like determining the maximum weight a beam can support to complex projects like mapping out the most efficient electrical flow for a city’s traffic lights, mathematics is essential.
Presenting innovative modelling approaches to the analysis of fiscal policy and government debt, this book moves beyond previous models that have relied upon the assumption that various age-specific rates and policy variables remain unchanged when it comes to generating government expenditures and tax revenues. As a result of population ageing, current policy settings in many countries are projected to lead to unsustainable levels of public debt; Tax Policy and Uncertainty explores models that allow for feedbacks and uncertainty to combat this. Applicable to any country, the models in the book explore the optimal timing and extent of tax changes in the face of anticipated high future debt. Chapters produce stochastic debt projections, including probability distribution of debt ratios at each point in time. It also offers important analysis of fiscal policy trade-offs as well as providing advice on when and by how much tax rates should be increased. Economics scholars focusing on fiscal policy will appreciate the improved models in this book that allow both for uncertainty and feedback effects arising from responses to increased debt. It will also be helpful to economic policy advisors and economists in government departments.
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.
The study of complex variables is beautiful from a purely mathematical point of view, and very useful for solving a wide array of problems arising in applications. This introduction to complex variables, suitable as a text for a one-semester course, has been written for undergraduate students in applied mathematics, science, and engineering. Based on the authors' extensive teaching experience, it covers topics of keen interest to these students, including ordinary differential equations, as well as Fourier and Laplace transform methods for solving partial differential equations arising in physical applications. Many worked examples, applications, and exercises are included. With this foundation, students can progress beyond the standard course and explore a range of additional topics, including generalized Cauchy theorem, Painleve equations, computational methods, and conformal mapping with circular arcs. Advanced topics are labeled with an asterisk and can be included in the syllabus or form the basis for challenging student projects.
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.
Now in its second edition, this popular textbook on game theory is unrivalled in the breadth of its coverage, the thoroughness of technical explanations and the number of worked examples included. Covering non-cooperative and cooperative games, this introduction to game theory includes advanced chapters on auctions, games with incomplete information, games with vector payoffs, stable matchings and the bargaining set. This edition contains new material on stochastic games, rationalizability, and the continuity of the set of equilibrium points with respect to the data of the game. The material is presented clearly and every concept is illustrated with concrete examples from a range of disciplines. With numerous exercises, and the addition of a solution manual with this edition, the book is an extensive guide to game theory for undergraduate through graduate courses in economics, mathematics, computer science, engineering and life sciences, and will also serve as useful reference for researchers.
This advanced level engineering mathematics text builds upon the skills that students would have developed in earlier courses. It adheres to the philosophy that students learn by doing, providing a wealth of engineering examples and problems to help students develop their mathematical ability.
Mathematics plays a key part in every quantitative and theoretical subject, and is taught to all science and engineering students. Foundations of Science Mathematics bridges the gap between school and university, and spans a large range of topics, from basic arithmetic and algebra to calculus, Fourier transforms, and elementary data analysis. Problems and worked solutions are presented in an informal and readable tutorial style, making the text accessible to the novice, while its concise nature ensures that it is a useful reference for the experienced professional. The first edition primer and its companion 'Worked Problems' workbook are combined in this new edition, and a new chapter on data analysis has been added to ensure the book remains as comprehensive and useful to students as possible.
"A lucid representation of the fundamental concepts and methods of the whole field of mathematics. It is an easily understandable introduction for the layman and helps to give the mathematical student a general view of the basic principles and methods."--Albert Einstein (on the first edition)
For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but not to real understanding or greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.
Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics?, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts. Brought up to date with a new chapter by Ian Stewart, What is Mathematics, Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.
Formal mathematics is like spelling and grammar: a matter of the correct application of local rules. Meaningful mathematics is like journalism: it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature: it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is a marvelously literate story: it opens a window onto the world of mathematics for anyone interested to view.
Discover the subject of optimization in a new light with this modern and unique treatment. Includes a thorough exposition of applications and algorithms in sufficient detail for practical use, while providing you with all the necessary background in a self-contained manner. Features a deeper consideration of optimal control, global optimization, optimization under uncertainty, multiobjective optimization, mixed-integer programming and model predictive control. Presents a complete coverage of formulations and instances in modelling where optimization can be applied for quantitative decision-making. As a thorough grounding to the subject, covering everything from basic to advanced concepts and addressing real-life problems faced by modern industry, this is a perfect tool for advanced undergraduate and graduate courses in chemical and biochemical engineering.
From Backlund to Darboux, this monograph presents a comprehensive journey through the transformation theory of constrained Willmore surfaces, a topic of great importance in modern differential geometry and, in particular, in the field of integrable systems in Riemannian geometry. The first book on this topic, it discusses in detail a spectral deformation, Backlund transformations and Darboux transformations, and proves that all these transformations preserve the existence of a conserved quantity, defining, in particular, transformations within the class of constant mean curvature surfaces in 3-dimensional space-forms, with, furthermore, preservation of both the space-form and the mean curvature, and bridging the gap between different approaches to the subject, classical and modern. Clearly written with extensive references, chapter introductions and self-contained accounts of the core topics, it is suitable for newcomers to the theory of constrained Wilmore surfaces. Many detailed computations and new results unavailable elsewhere in the literature make it also an appealing reference for experts.
Probability theory has diverse applications in a plethora of fields, including physics, engineering, computer science, chemistry, biology and economics. This book will familiarize students with various applications of probability theory, stochastic modeling and random processes, using examples from all these disciplines and more. The reader learns via case studies and begins to recognize the sort of problems that are best tackled probabilistically. The emphasis is on conceptual understanding, the development of intuition and gaining insight, keeping technicalities to a minimum. Nevertheless, a glimpse into the depth of the topics is provided, preparing students for more specialized texts while assuming only an undergraduate-level background in mathematics. The wide range of areas covered - never before discussed together in a unified fashion - includes Markov processes and random walks, Langevin and Fokker-Planck equations, noise, generalized central limit theorem and extreme values statistics, random matrix theory and percolation theory.
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