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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.
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.
It's a sad truth that maths has the reputation of being "difficult." Part of the problem is that many of us simply don't speak the language. To a mathematician, an equation is a compact, efficient way to put across a relationship that would be far less comprehensible in words. But to many of us, the merest sign of an x, y, or symbol is an impenetrable mess that our eyes bounce off. This book provides an engaging overview of what maths is and what it can do, without having to solve simultaneous equations or prove geometric theorems, far more of us might get the point of it. It is divided into four chapters, each covering a major developmental route in the topic, from Arithmetic & Numbers to Geometry and from Algebra & Calculus to Applied Mathematics.
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.
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 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.
The Nelson Mathematics for Cambridge International AS & A Level series is tailored to the needs of A and AS level students of the latest 9709 syllabus. Developed by a team of experienced examiners and international authors, it provides comprehensive coverage for this syllabus and effective preparation for the Cambridge exams. The Nelson Mechanics 1 for Cambridge International A Level is for students taking the M1 exam paper. It provides introductions to topics and step-by-step worked examples to aid students in their understanding of the course material. Learning objectives are also included, letting students know exactly what they need to learn and understand in each topic. Plenty of examples throughout the text strengthen students' understanding. Students are well equipped to reach their full potential, with practice exam papers providing opportunities for effective exam preparation.
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.
The subject of this thesis is the Mu-calculus, which nowadays represents a very active research area in both theoretical and practical Computer Science. The Mu-calculus is a logic capable of expressing least and greatest solutions of fixpoint equations x=f(x), where f is a monotone function mapping some complete ordered set into itself. The thesis has two goals, one expository and one technical. The expository goal is to present some results and problems about the Mu-calculus. On the technical respect, this thesis addresses a specific expressiveness problem of the Mu-calculus, the alternation depth hierarchy problem.
Susanna Epp's DISCRETE MATHEMATICS WITH APPLICATIONS, 4e, International Edition provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography, and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. Overall, Epp's emphasis on reasoning provides students with a strong foundation for computer science and upper-level mathematics courses.
This modern text combines fundamental principles with advanced topics and recent techniques in a rigorous and self-contained treatment of quantum field theory.Beginning with a review of basic principles, starting with quantum mechanics and special relativity, students can refresh their knowledge of elementary aspects of quantum field theory and perturbative calculations in the Standard Model. Results and tools relevant to many applications are covered, including canonical quantization, path integrals, non-Abelian gauge theories, and the renormalization group. Advanced topics are explored, with detail given on effective field theories, quantum anomalies, stable extended field configurations, lattice field theory, and field theory at a finite temperature or in the strong field regime. Two chapters are dedicated to new methods for calculating scattering amplitudes (spinor-helicity, on-shell recursion, and generalized unitarity), equipping students with practical skills for research. Accessibly written, with numerous worked examples and end-of-chapter problems, this is an essential text for graduate students. The breadth of coverage makes it an equally excellent reference for researchers.
The Nelson Mathematics for Cambridge International AS & A Level series is tailored to the needs of A and AS Level students of the latest 9709 syllabus. Developed by a team of experienced examiners and international authors, it provides comprehensive coverage for this syllabus and effective preparation for the Cambridge exams. Nelson Mechanics 2 for Cambridge International A Level is for students taking the M2 exam paper. The text provides introductions to topics and step-by-step worked examples to aid students in their understanding of the course material. Other features include: learning objectives, letting students know what they need to learn in each topic; summaries of formulae and key information, helping students to revise; clear diagrams, helping to explain difficult concepts, and plenty of examples, strengthening students' understanding. In addition, practice exam papers provide students with opportunities for effective exam preparation and so help them reach their full potential.
This must-read textbook presents an essential introduction to Kolmogorov complexity (KC), a central theory and powerful tool in information science that deals with the quantity of information in individual objects. The text covers both the fundamental concepts and the most important practical applications, supported by a wealth of didactic features. This thoroughly revised and enhanced fourth edition includes new and updated material on, amongst other topics, the Miller-Yu theorem, the Gacs-Kucera theorem, the Day-Gacs theorem, increasing randomness, short lists computable from an input string containing the incomputable Kolmogorov complexity of the input, the Lovasz local lemma, sorting, the algorithmic full Slepian-Wolf theorem for individual strings, multiset normalized information distance and normalized web distance, and conditional universal distribution. Topics and features: describes the mathematical theory of KC, including the theories of algorithmic complexity and algorithmic probability; presents a general theory of inductive reasoning and its applications, and reviews the utility of the incompressibility method; covers the practical application of KC in great detail, including the normalized information distance (the similarity metric) and information diameter of multisets in phylogeny, language trees, music, heterogeneous files, and clustering; discusses the many applications of resource-bounded KC, and examines different physical theories from a KC point of view; includes numerous examples that elaborate the theory, and a range of exercises of varying difficulty (with solutions); offers explanatory asides on technical issues, and extensive historical sections; suggests structures for several one-semester courses in the preface. As the definitive textbook on Kolmogorov complexity, this comprehensive and self-contained work is an invaluable resource for advanced undergraduate students, graduate students, and researchers in all fields of science.
This text develops the theory of systems of stochastic differential
equations and presents applications in probability, partial
differential equations, and stochastic control problems. Originally
published in 2 volumes, it combines a book of basic theory with a
book of applications. Familiarity with elementary probability is
the sole prerequisite. 1975 edition.
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.
Reflecting the latest technology and tools of the trade, MATHEMATICS FOR MACHINE TECHNOLOGY, 7e provides the mathematical skills and practice that students and apprentices will use on the job in the machine trades and manufacturing fields. This comprehensive book combines math concepts with relevant machine applications through industry-specific examples, realistic illustrations, and actual machine applications. Problems and examples progress from simpler to more complex, from general math to trigonometry and solid geometry, and relate directly to how the math is used in machine trades and manufacturing fields. The new Seventh Edition also includes all-new units on electronic calipers, height gages, and electronic micrometers, as well as thorough coverage of measuring in both metric and customary systems.
The possibility that we live in a higher-dimensional world with spatial dimensions greater than three started with the early work of Kaluza and Klein. However, in addressing experimental constraints, early model-builders were forced to compactify these extra dimensions to very tiny scales. With the development of brane-world scenarios it became possible to consider novel compactifications which allow the extra dimensions to be large or to provide observable effects of these dimensions at experimentally accessible energy scales. This book provides a comprehensive account of these recent developments, keeping the high-energy physics implications in focus. After an historical survey of the idea of extra dimensions, the book deals in detail with models of large extra dimensions, warped extra dimensions and other models such as universal extra dimensions. The theoretical and phenomenological implications are discussed in a pedagogical manner for both researchers and graduate students.
The full measure of Wolfgang Doeblin's mathematical stature became apparent only in 2000 when the sealed envelope containing his construction of diffusion processes in terms of a time change of Brownian motion was finally opened, 60 years after it was sent to the Academy of Sciences in Paris.
This film documents scientific and human aspects of this amazing discovery and throws new light on the startling circumstances of his death at the age of 25.
For courses in Actuarial Mathematics, Introduction to Insurance, and Personal/Business Finance. This text presents the basic core of information needed to understand the impact of interest rates on the world of investments, real estate, corporate planning, insurance, and securities transactions. The authors presuppose a working knowledge of basic algebra, arithmetic, and percents for the core of the book: their goal is for students to understand well those few underlying principles that play out in nearly every finance and interest problem. There are several sections that utilize calculus and one chapter that requires statistics. Using time line diagrams as important tools in analyzing money and interest exercises, the text contains a great deal of practical financial applications of interest theory as well as its foundational definitions and theorems. It relies on the use of calculator and computer technology instead of tables; this approach frees students to understand challenging topics without wilting under labor-intensive details.
Exam board: OCR Level: A-level Subject: Mathematics First teaching: September 2017 First exams: Summer 2018 Target success in OCR (A) A Level Mathematics with this proven formula for effective, structured revision; key content coverage and plentiful worked examples are combined with exam-style and multiple choice questions to create a revision guide that students can rely on to review, strengthen and test their knowledge. - Help develop the key skills needed for success with skills-focused questions around problem-solving, proof, modelling and the use of ICT (spreadsheets, graphing software and graphing calculators). - Strategically target revision with diagnostic questions to establish which areas need focus. - Get assessment-ready with exam-style questions and advice on common examination pitfalls. - Embed knowledge and identify weaknesses with hundreds of multiple choice 'Test Yourself' questions, all carefully written to elicit misconceptions; full worked solutions online offer detailed, instructive explanations for all choices (whether they are correct or incorrect) - Consolidate revision with summaries for each topic that focus on what to concentrate on in the build-up to exams, with special focus on common pitfalls such as how to show correct workings. -Access answers at the back of the book, with detailed step-by-step worked solutions for ALL questions available for free online. Includes all Year 1 and Year 2 A-level Maths content.
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