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Introductory Graph Theory
by Gary ChartrandGraph theory is used today in the physical sciences, social sciences, computer science, and other areas. Introductory Graph Theory presents a nontechnical introduction to this exciting field in a clear, lively, and informative style. Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics. Ten major topics -- profusely illustrated -- include: Mathematical Models, Elementary Concepts of Graph Theory, Transportation Problems, Connection Problems, Party Problems, Digraphs and Mathematical Models, Games and Puzzles, Graphs and Social Psychology, Planar Graphs and Coloring Problems, and Graphs and Other Mathematics. A useful Appendix covers Sets, Relations, Functions, and Proofs, and a section devoted to exercises -- with answers, hints, and solutions -- is especially valuable to anyone encountering graph theory for the first time. Undergraduate mathematics students at every level, puzzlists, and mathematical hobbyists will find well-organized coverage of the fundamentals of graph theory in this highly readable and thoroughly enjoyable book.
An Introductory Guide to Computational Methods for the Solution of Physics Problems (Lecture Notes in Physics #955)
by George Rawitscher Victo dos Santos Filho Thiago Carvalho PeixotoThis monograph presents fundamental aspects of modern spectral and other computational methods, which are not generally taught in traditional courses. It emphasizes concepts as errors, convergence, stability, order and efficiency applied to the solution of physical problems. The spectral methods consist in expanding the function to be calculated into a set of appropriate basis functions (generally orthogonal polynomials) and the respective expansion coefficients are obtained via collocation equations. The main advantage of these methods is that they simultaneously take into account all available information, rather only the information available at a limited number of mesh points. They require more complicated matrix equations than those obtained in finite difference methods. However, the elegance, speed, and accuracy of the spectral methods more than compensates for any such drawbacks. During the course of the monograph, the authors examine the usually rapid convergence of the spectral expansions and the improved accuracy that results when nonequispaced support points are used, in contrast to the equispaced points used in finite difference methods. In particular, they demonstrate the enhanced accuracy obtained in the solution of integral equations.The monograph includes an informative introduction to old and new computational methods with numerous practical examples, while at the same time pointing out the errors that each of the available algorithms introduces into the specific solution. It is a valuable resource for undergraduate students as an introduction to the field and for graduate students wishing to compare the available computational methods. In addition, the work develops the criteria required for students to select the most suitable method to solve the particular scientific problem that they are confronting.
Introductory Lectures on Higher-Spin Theories (Lecture Notes in Physics #1028)
by Stefan FredenhagenThe book offers a pedagogical introduction to higher-spin gauge theories. These theories build upon fundamental gauge theories that are crucial for understanding core interactions. Electromagnetism and nuclear forces are associated with gauge fields of spin 1, while gravity can be conceptualized as a gauge theory of spin 2. This prompts the intriguing inquiry: do higher-spin gauge theories exist? Such theories would extend gravity, incorporating massless gauge fields of spins higher than two. They appear to bear connections to string theory and offer a captivating framework for exploring gravity and aspects of quantum gravity. The book initiates with a primer offering a comprehensive discussion on higher spins, delving into the challenges of establishing coherent interactions. It then explores methodologies to surmount these challenges within three-dimensional space-time. Furthermore, it investigates the emergence of asymptotic symmetry algebras, establishing links to a holographic dual conformal theory. The final chapter introduces Vasiliev’s approach to higher-spin gauge theory in four dimensions. Designed for advanced students and young researchers in theoretical physics and mathematical physics, the book aims to elucidate fundamental ideas, concepts, and tools underpinning higher-spin gauge theories. The inclusion of numerous exercises complements and illustrates the content, preparing readers for engagement with the subject's original literature and ongoing developments. To fully engage with the book's arguments, a prerequisite understanding of field theories and conventional gauge theories, including gravity, is assumed.
Introductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences (Ninth Edition)
by Ernest F. Haeussler Richard S. PaulThis ninth edition of Introductory Mathematical Analysis continues to provide a mathematical foundation for students in business, economics, and the life and social sciences. It begins with noncalculus topics such as equations, functions, matrix algebra, linear programming, mathematics of finance, and probability. Then it progresses through both single-variable and multivariable calculus, including continuous random variables.
Introductory Mathematical Analysis for Quantitative Finance (Chapman and Hall/CRC Financial Mathematics Series)
by Daniele Ritelli Giulia SpalettaIntroductory Mathematical Analysis for Quantitative Finance is a textbook designed to enable students with little knowledge of mathematical analysis to fully engage with modern quantitative finance. A basic understanding of dimensional Calculus and Linear Algebra is assumed. The exposition of the topics is as concise as possible, since the chapters are intended to represent a preliminary contact with the mathematical concepts used in Quantitative Finance. The aim is that this book can be used as a basis for an intensive one-semester course. Features: Written with applications in mind, and maintaining mathematical rigor. Suitable for undergraduate or master's level students with an Economics or Management background. Complemented with various solved examples and exercises, to support the understanding of the subject.
Introductory Mathematics: Concepts with Applications
by Charles P. McKeague"This textbook provides students with a solid foundation in basic mathematics, and an excellent preparation for algebra. The format, examples, and problems in this book have been refined through more than 20 years of classroom testing. As with all McKeague titles, his emphasis on study skills and his positive tone toward success are reflected in the presentation."
Introductory Mathematics
by McKeague Charles P. MckeagueThis textbook provides students with a solid foundation in basic mathematics, and an excellent preparation for algebra. The format, examples, and problems in this book have been refined through more than 20 years of classroom testing. As with all McKeague titles, his emphasis on study skills and his positive tone toward success are reflected in the presentation. Published by XYZ textbooks.
Introductory Mathematics for the Life Sciences (Modules In Life Science Ser.)
by David PhoenixIntroductory Mathematics for the Life Sciences offers a straightforward introduction to the mathematical principles needed for studies in the life sciences. Starting with the basics of numbers, fractions, ratios, and percentages, the author explains progressively more sophisticated concepts, from algebra, measurement, and scientific notation through the linear, power, exponential, and logarithmic functions to introductory statistics. Worked examples illustrate concepts, applications, and interpretations, and exercises at the end of each chapter help readers apply and practice the skills they develop. Answers to the exercises are posted at the end of the text.
Introductory Medical Statistics, 3rd edition
by Richard F. MouldIntroductory Medical Statistics, now in its third edition, is an introductory textbook on basic statistical techniques. It is written for physicians, surgeons, radiation oncologists, medical physicists, radiographers, hospital administrators, medical statisticians in training, biochemists, and other professionals allied to medicine. It is suitable
Introductory Modern Algebra
by Saul StahlPraise for the First Edition"Stahl offers the solvability of equations from the historical point of view...one of the best books available to support a one-semester introduction to abstract algebra."--CHOICEIntroductory Modern Algebra: A Historical Approach, Second Edition presents the evolution of algebra and provides readers with the opportunity to view modern algebra as a consistent movement from concrete problems to abstract principles. With a few pertinent excerpts from the writings of some of the greatest mathematicians, the Second Edition uniquely facilitates the understanding of pivotal algebraic ideas.The author provides a clear, precise, and accessible introduction to modern algebra and also helps to develop a more immediate and well-grounded understanding of how equations lead to permutation groups and what those groups can inform us about such diverse items as multivariate functions and the 15-puzzle. Featuring new sections on topics such as group homomorphisms, the RSA algorithm, complex conjugation, the factorization of real polynomials, and the fundamental theorem of algebra, the Second Edition also includes:An in-depth explanation of the principles and practices of modern algebra in terms of the historical development from the Renaissance solution of the cubic equation to Dedekind's idealsHistorical discussions integrated with the development of modern and abstract algebra in addition to many new explicit statements of theorems, definitions, and terminologyA new appendix on logic and proofs, sets, functions, and equivalence relationsOver 1,000 new examples and multi-level exercises at the end of each section and chapter as well as updated chapter summariesIntroductory Modern Algebra: A Historical Approach, Second Edition is an excellent textbook for upper-undergraduate courses in modern and abstract algebra.
Introductory Non-Euclidean Geometry (Dover Books on Mathematics)
by Henry Parker ManningThis fine and versatile introduction to non-Euclidean geometry is appropriate for both high-school and college classes. Its first two-thirds requires just a familiarity with plane and solid geometry and trigonometry, and calculus is employed only in the final part. It begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry. Major topics include hyperbolic geometry, single elliptic geometry, and analytic non-Euclidean geometry. 1901 edition.
Introductory Numerical Analysis
by Anthony J. PettofrezzoGeared toward undergraduate mathematics majors, engineering students, and future high school mathematics teachers, this text offers an understanding of the principles involved in numerical analysis. Its main theme is interpolation from the standpoint of finite differences, least squares theory, and harmonic analysis. Additional considerations include the numerical solutions of ordinary differential equations and approximations through Fourier series. Discussions of the relationships between the calculus of finite differences and the calculus of infinitesimals will prove especially important to future teachers of mathematics.More than seventy worked-out illustrative examples are featured; some include solutions by different methods, showing the relative merits of a variety of approaches. Over 280 multipart exercises range from drill problems to those requiring some degree of ingenuity on the part of the student. Answers are provided to problems with numerical solutions. The only prerequisites are a grasp of differential and integral calculus and some familiarity with determinants. An appendix containing definitions and several theorems from elementary determinant theory is included.
An Introductory Path to Quantum Theory: Using Mathematics to Understand the Ideas of Physics
by Stephen Bruce SontzSince the 17th century, physical theories have been expressed in the language of mathematical equations. This introduction to quantum theory uses that language to enable the reader to comprehend the notoriously non-intuitive ideas of quantum physics. The mathematical knowledge needed for using this book comes from standard undergraduate mathematics courses and is described in detail in the section Prerequisites. This text is especially aimed at advanced undergraduate and graduate students of mathematics, computer science, engineering and chemistry among other disciplines, provided they have the math background even though lacking preparation in physics. In fact, no previous formal study of physics is assumed.
Introductory Physics: Summaries, Examples, and Practice Problems
by Michael AntoshPhysics describes how motion works in everyday life. Clothes washers and rolling pins are undergoing rotational motion. A flying bird uses forces. Tossing a set of keys involves equations that describe motion (kinematics). Two people bumping into each other while cooking in a kitchen involves linear momentum. This textbook covers topics related to units, kinematics, forces, energy, momentum, circular and rotational motion, Newton’s general equation for gravity, and simple harmonic motion (things that go back and forth). A math review is also included, with a focus on algebra and trigonometry. The goal of this textbook is to present a clear introduction to these topics, in small pieces, with examples that readers can relate to. Each topic comes with a short summary, a fully solved example, and practice problems. Full solutions are included for over 400 problems. This book is a very useful study guide for students in introductory physics courses, including high school and college students in an algebra-based introductory physics course and even students in an introductory calculus-level course. It can also be used as a standalone textbook in courses where derivations are not emphasized.
Introductory Physics for the Life Sciences (Undergraduate Texts in Physics)
by Simon Mochrie Claudia De GrandiThis classroom-tested textbook is an innovative, comprehensive, and forward-looking introductory undergraduate physics course. While it clearly explains physical principles and equips the student with a full range of quantitative tools and methods, the material is firmly grounded in biological relevance and is brought to life with plenty of biological examples throughout.It is designed to be a self-contained text for a two-semester sequence of introductory physics for biology and premedical students, covering kinematics and Newton’s laws, energy, probability, diffusion, rates of change, statistical mechanics, fluids, vibrations, waves, electromagnetism, and optics. Each chapter begins with learning goals, and concludes with a summary of core competencies, allowing for seamless incorporation into the classroom. In addition, each chapter is replete with a wide selection of creative and often surprising examples, activities, computational tasks, and exercises, many of which are inspired by current research topics, making cutting-edge biological physics accessible to the student.
Introductory Real Analysis
by Richard A. Silverman S. V. Fomin A. N. KolmogorovThis volume in Richard Silverman's exceptional series of translations of Russian works in the mathematical science is a comprehensive, elementary introduction to real and functional analysis by two faculty members from Moscow University. It is self-contained, evenly paced, eminently readable, and readily accessible to those with adequate preparation in advanced calculus.The first four chapters present basic concepts and introductory principles in set theory, metric spaces, topological spaces, and linear spaces. The next two chapters consider linear functionals and linear operators, with detailed discussions of continuous linear functionals, the conjugate space, the weak topology and weak convergence, generalized functions, basic concepts of linear operators, inverse and adjoint operators, and completely continuous operators. The final four chapters cover measure, integration, differentiation, and more on integration. Special attention is here given to the Lebesque integral, Fubini's theorem, and the Stieltjes integral. Each individual section -- there are 37 in all -- is equipped with a problem set, making a total of some 350 problems, all carefully selected and matched.With these problems and the clear exposition, this book is useful for self-study or for the classroom -- it is basic one-year course in real analysis. Dr. Silverman is a former member of the Institute of Mathematical Sciences of New York University and the Lincoln Library of M.I.T. Along with his translation, he has revised the text with numerous pedagogical and mathematical improvements and restyled the language so that it is even more readable.
Introductory Regression Analysis: with Computer Application for Business and Economics
by Allen WebsterRegression analysis is arguably the single most powerful and widely applicable tool in any effective examination of common business issues. Every day, decision-makers face problems that require constructive actions with significant consequences, and regression procedures can prove a meaningful and valuable asset in the decision-making process. This text is designed to help students achieve a full understanding of regression and the many ways it can be used. Taking into consideration current statistical technology, Introductory Regression Analysis focuses on the use and interpretation of software, while also demonstrating the logic, reasoning, and calculations that lie behind any statistical analysis. Furthermore, the text emphasizes the application of regression tools to real-life business concerns. This multilayered, yet pragmatic approach fully equips students to derive the benefit and meaning of a regression analysis. This text is designed to serve in a second undergraduate course in statistics, focusing on regression and its component features. The material presented in this text will build from a foundation of the principles of data analysis. Although previous exposure to statistical concepts would prove helpful, all the material needed for an examination of regression analysis is presented here in a clear and complete form.
Introductory Relational Database Design for Business, with Microsoft Access
by Jonathan Eckstein Bonnie R. SchultzA hands-on beginner’s guide to designing relational databases and managing data using Microsoft Access Relational databases represent one of the most enduring and pervasive forms of information technology. Yet most texts covering relational database design assume an extensive, sophisticated computer science background. There are texts on relational database software tools like Microsoft Access that assume less background, but they focus primarily on details of the user interface, with inadequate coverage of the underlying design issues of how to structure databases. Growing out of Professor Jonathan Eckstein’s twenty years’ experience teaching courses on management information systems (MIS) at Rutgers Business School, this book fills this gap in the literature by providing a rigorous introduction to relational databases for readers without prior computer science or programming experience. Relational Database Design for Business, with Microsoft Access helps readers to quickly develop a thorough, practical understanding of relational database design. It takes a step-by-step, real-world approach, using application examples from business and finance every step the way. As a result, readers learn to think concretely about database design and how to address issues that commonly arise when developing and manipulating relational databases. By the time they finish the final chapter, students will have the knowledge and skills needed to build relational databases with dozens of tables. They will also be able to build complete Microsoft Access applications around such databases. This text: Takes a hands-on approach using numerous real-world examples drawn from the worlds of business, finance, and more Gets readers up and running, fast, with the skills they need to use and develop relational databases with Microsoft Access Moves swiftly from conceptual fundamentals to advanced design techniques Leads readers step-by-step through data management and design, relational database theory, multiple tables and the possible relationships between them, Microsoft Access features such as forms and navigation, formulating queries in SQL, and normalization Introductory Relational Database Design for Business, with Microsoft Access is the definitive guide for undergraduate and graduate students in business, finance, and data analysis without prior experience in database design. While Microsoft Access is its primary “hands-on” learning vehicle, most of the skills in this text are transferrable to other relational database software such as MySQL.
Introductory Special Relativity
by W G RosserA comprehensive introduction to special relativity for undergraduate study. Based on the highly regarded textbook Relativity and High Energy Physics. Includes numerous worked examples. Now thoroughly revised and expanded. Fully meets the needs of first year physics undergraduates.
Introductory Statistical Inference with the Likelihood Function
by Charles A. RohdeThis textbook covers the fundamentals of statistical inference and statistical theory including Bayesian and frequentist approaches and methodology possible without excessive emphasis on the underlying mathematics. This book is about some of the basic principles of statistics that are necessary to understand and evaluate methods for analyzing complex data sets. The likelihood function is used for pure likelihood inference throughout the book. There is also coverage of severity and finite population sampling. The material was developed from an introductory statistical theory course taught by the author at the Johns Hopkins University's Department of Biostatistics. Students and instructors in public health programs will benefit from the likelihood modeling approach that is used throughout the text. This will also appeal to epidemiologists and psychometricians. After a brief introduction, there are chapters on estimation, hypothesis testing, and maximum likelihood modeling. The book concludes with sections on Bayesian computation and inference. An appendix contains unique coverage of the interpretation of probability, and coverage of probability and mathematical concepts.
Introductory Statistics: Exploring the World through Data
by Robert Gould Rebecca Wong Colleen RyanFor courses in Introductory Statistics. Data analysis for everyone Data in the real world are dynamic and sometimes messy. This complexity can intimidate students who are new to math and statistics ― but it’s also what makes statistics so interesting! Embracing these characteristics, Introductory Statistics teaches students how to explore and analyze real data to answer real-world problems. Crafted by authors who are active in the classroom and in the statistics education community, the 3rd Edition pairs a clear, conversational writing style with new and frequent opportunities to apply statistical thinking. Its tone and learning aids are designed to equip any student to analyze, interpret, and tell a story about modern data, regardless of the student’s mathematical proficiency.
Introductory Statistics
by Barbara Illowsky Susan DeanIntroductory Statistics is designed for the one-semester, introduction to statistics course and is geared toward students majoring in fields other than math or engineering. This text assumes students have been exposed to intermediate algebra, and it focuses on the applications of statistical knowledge rather than the theory behind it. The foundation of this textbook is Collaborative Statistics, by Barbara Illowsky and Susan Dean.
Introductory Statistics: Lecture Guide And Student Notebook
by KokoskaThis text helps students develop the fundamental lifelong skill of solving problems and interpreting solutions in real-world terms. One of our goals was to make this problem-solving approach accessible and easy to apply in many situations. We certainly want students to appreciate the beauty of statistics and connections to so many other disciplines. However, it is even more important for students to be able to apply problem-solving skills to a wide range of academic and career pursuits, including business, science and technology, and education. Third Edition, presents long-term, universal skills for students taking a one- or two-semester introductory-level statistics course. Examples include guided, explanatory solutions that emphasize problem-solving techniques. Example solutions are presented in a numbered, step-by-step format. The generous collection and variety of exercises provide ample opportunity for practice and review in a variety of contexts. Concepts, examples, and exercises are presented from a practical, realistic perspective. Real and realistic data sets are current and relevant. The text uses mathematically correct notation and symbols and precise definitions to clearly illustrate statistical procedures and proper communication. This text is designed to help students fully understand the steps in basic statistical arguments, emphasizing the importance of assumptions in order to follow valid arguments or identify inaccurate conclusions. Most importantly, students will understand the process of statistical inference. A four-step process (Claim, Experiment, Likelihood, Conclusion) is used throughout the text to present the smaller pieces of introductory statistics upon which the large, essential statistical inference puzzle is built.
Introductory Statistics
by Stephen KokoskaStephen Kokoska's Introductory Statistics: A Problem-Solving Approach demonstrated that when presented in a precise step-by-step manner, with an understanding of what makes the material difficult, statistics can be made accessible, meaningful, and useful, even to the most skeptical students. In this thoroughly updated new edition, Kokoska again combines a traditional, classic approach to teaching statistics with contemporary examples and pedagogical features, blending solid mathematics with lucid, often humorous writing and a distinctive stepped "Solution Trail" problem-solving approach to help students understand the processes behind basic statistical arguments, statistical inference, and data-based decision making.
Introductory Statistics
by OpenStaxIntroductory Statistics is intended for the one-semester introduction to statistics course for students who are not mathematics or engineering majors. It focuses on the interpretation of statistical results, especially in real world settings, and assumes that students have an understanding of intermediate algebra. In addition to end of section practice and homework sets, examples of each topic are explained step-by-step throughout the text and followed by a Try It problem that is designed as extra practice for students. This book also includes collaborative exercises and statistics labs designed to give students the opportunity to work together and explore key concepts. To support today's student in understanding technology, this book features TI 83, 83+, 84, or 84+ calculator instructions at strategic points throughout. While the book has been built so that each chapter builds on the previous, it can be rearranged to accommodate any instructor's particular needs.