Математика
Различные книги в жанре МатематикаStatistics for Compensation. A Practical Guide to Compensation Analysis
An insightful, hands-on focus on the statistical methods used by compensation and human resources professionals in their everyday work Across various industries, compensation professionals work to organize and analyze aspects of employment that deal with elements of pay, such as deciding base salary, bonus, and commission provided by an employer to its employees for work performed. Acknowledging the numerous quantitative analyses of data that are a part of this everyday work, Statistics for Compensation provides a comprehensive guide to the key statistical tools and techniques needed to perform those analyses and to help organizations make fully informed compensation decisions. This self-contained book is the first of its kind to explore the use of various quantitative methods—from basic notions about percents to multiple linear regression—that are used in the management, design, and implementation of powerful compensation strategies. Drawing upon his extensive experience as a consultant, practitioner, and teacher of both statistics and compensation, the author focuses on the usefulness of the techniques and their immediate application to everyday compensation work, thoroughly explaining major areas such as: Frequency distributions and histograms Measures of location and variability Model building Linear models Exponential curve models Maturity curve models Power models Market models and salary survey analysis Linear and exponential integrated market models Job pricing market models Throughout the book, rigorous definitions and step-by-step procedures clearly explain and demonstrate how to apply the presented statistical techniques. Each chapter concludes with a set of exercises, and various case studies showcase the topic's real-world relevance. The book also features an extensive glossary of key statistical terms and an appendix with technical details. Data for the examples and practice problems are available in the book and on a related FTP site. Statistics for Compensation is an excellent reference for compensation professionals, human resources professionals, and other practitioners responsible for any aspect of base pay, incentive pay, sales compensation, and executive compensation in their organizations. It can also serve as a supplement for compensation courses at the upper-undergraduate and graduate levels.
Real Analysis. A Historical Approach
A provocative look at the tools and history of real analysis This new edition of Real Analysis: A Historical Approach continues to serve as an interesting read for students of analysis. Combining historical coverage with a superb introductory treatment, this book helps readers easily make the transition from concrete to abstract ideas. The book begins with an exciting sampling of classic and famous problems first posed by some of the greatest mathematicians of all time. Archimedes, Fermat, Newton, and Euler are each summoned in turn, illuminating the utility of infinite, power, and trigonometric series in both pure and applied mathematics. Next, Dr. Stahl develops the basic tools of advanced calculus, which introduce the various aspects of the completeness of the real number system as well as sequential continuity and differentiability and lead to the Intermediate and Mean Value Theorems. The Second Edition features: A chapter on the Riemann integral, including the subject of uniform continuity Explicit coverage of the epsilon-delta convergence A discussion of the modern preference for the viewpoint of sequences over that of series Throughout the book, numerous applications and examples reinforce concepts and demonstrate the validity of historical methods and results, while appended excerpts from original historical works shed light on the concerns of influential mathematicians in addition to the difficulties encountered in their work. Each chapter concludes with exercises ranging in level of complexity, and partial solutions are provided at the end of the book. Real Analysis: A Historical Approach, Second Edition is an ideal book for courses on real analysis and mathematical analysis at the undergraduate level. The book is also a valuable resource for secondary mathematics teachers and mathematicians.
The Ellipse. A Historical and Mathematical Journey
Explores the development of the ellipse and presents mathematical concepts within a rich, historical context The Ellipse features a unique, narrative approach when presenting the development of this mathematical fixture, revealing its parallels to mankind's advancement from the Counter-Reformation to the Enlightenment. Incorporating illuminating historical background and examples, the author brings together basic concepts from geometry, algebra, trigonometry, and calculus to uncover the ellipse as the shape of a planet's orbit around the sun. The book begins with a discussion that tells the story of man's pursuit of the ellipse, from Aristarchus to Newton's successful unveiling nearly two millenniums later. The narrative draws insightful similarities between mathematical developments and the advancement of the Greeks, Romans, Medieval Europe, and Renaissance Europe. The author begins each chapter by setting the historical backdrop that is pertinent to the mathematical material that is discussed, equipping readers with the knowledge to fully grasp the presented examples and derive the ellipse as the planetary pathway. All topics are presented in both historical and mathematical contexts, and additional mathematical excursions are clearly marked so that readers have a guidepost for the materials' relevance to the development of the ellipse. The Ellipse is an excellent book for courses on the history of mathematics at the undergraduate level. It is also a fascinating reference for mathematicians, engineers, or anyone with a general interest in historical mathematics.
An Introduction to Mathematical Modeling. A Course in Mechanics
A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equations Electromagnetic Field Theory and Quantum Mechanics contains a brief account of electromagnetic wave theory and Maxwell's equations as well as an introductory account of quantum mechanics with related topics including ab initio methods and Spin and Pauli's principles Statistical Mechanics presents an introduction to statistical mechanics of systems in thermodynamic equilibrium as well as continuum mechanics, quantum mechanics, and molecular dynamics Each part of the book concludes with exercise sets that allow readers to test their understanding of the presented material. Key theorems and fundamental equations are highlighted throughout, and an extensive bibliography outlines resources for further study. Extensively class-tested to ensure an accessible presentation, An Introduction to Mathematical Modeling is an excellent book for courses on introductory mathematical modeling and statistical mechanics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for professionals working in the areas of modeling and simulation, physics, and computational engineering.
Fibonacci and Catalan Numbers. An Introduction
Discover the properties and real-world applications of the Fibonacci and the Catalan numbers With clear explanations and easy-to-follow examples, Fibonacci and Catalan Numbers: An Introduction offers a fascinating overview of these topics that is accessible to a broad range of readers. Beginning with a historical development of each topic, the book guides readers through the essential properties of the Fibonacci numbers, offering many introductory-level examples. The author explains the relationship of the Fibonacci numbers to compositions and palindromes, tilings, graph theory, and the Lucas numbers. The book proceeds to explore the Catalan numbers, with the author drawing from their history to provide a solid foundation of the underlying properties. The relationship of the Catalan numbers to various concepts is then presented in examples dealing with partial orders, total orders, topological sorting, graph theory, rooted-ordered binary trees, pattern avoidance, and the Narayana numbers. The book features various aids and insights that allow readers to develop a complete understanding of the presented topics, including: Real-world examples that demonstrate the application of the Fibonacci and the Catalan numbers to such fields as sports, botany, chemistry, physics, and computer science More than 300 exercises that enable readers to explore many of the presented examples in greater depth Illustrations that clarify and simplify the concepts Fibonacci and Catalan Numbers is an excellent book for courses on discrete mathematics, combinatorics, and number theory, especially at the undergraduate level. Undergraduates will find the book to be an excellent source for independent study, as well as a source of topics for research. Further, a great deal of the material can also be used for enrichment in high school courses.
Engineering Optimization. An Introduction with Metaheuristic Applications
An accessible introduction to metaheuristics and optimization, featuring powerful and modern algorithms for application across engineering and the sciences From engineering and computer science to economics and management science, optimization is a core component for problem solving. Highlighting the latest developments that have evolved in recent years, Engineering Optimization: An Introduction with Metaheuristic Applications outlines popular metaheuristic algorithms and equips readers with the skills needed to apply these techniques to their own optimization problems. With insightful examples from various fields of study, the author highlights key concepts and techniques for the successful application of commonly-used metaheuristc algorithms, including simulated annealing, particle swarm optimization, harmony search, and genetic algorithms. The author introduces all major metaheuristic algorithms and their applications in optimization through a presentation that is organized into three succinct parts: Foundations of Optimization and Algorithms provides a brief introduction to the underlying nature of optimization and the common approaches to optimization problems, random number generation, the Monte Carlo method, and the Markov chain Monte Carlo method Metaheuristic Algorithms presents common metaheuristic algorithms in detail, including genetic algorithms, simulated annealing, ant algorithms, bee algorithms, particle swarm optimization, firefly algorithms, and harmony search Applications outlines a wide range of applications that use metaheuristic algorithms to solve challenging optimization problems with detailed implementation while also introducing various modifications used for multi-objective optimization Throughout the book, the author presents worked-out examples and real-world applications that illustrate the modern relevance of the topic. A detailed appendix features important and popular algorithms using MATLAB® and Octave software packages, and a related FTP site houses MATLAB code and programs for easy implementation of the discussed techniques. In addition, references to the current literature enable readers to investigate individual algorithms and methods in greater detail. Engineering Optimization: An Introduction with Metaheuristic Applications is an excellent book for courses on optimization and computer simulation at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners working in the fields of mathematics, engineering, computer science, operations research, and management science who use metaheuristic algorithms to solve problems in their everyday work.
Introduction to Statistics Through Resampling Methods and R
A highly accessible alternative approach to basic statistics Praise for the First Edition: «Certainly one of the most impressive little paperback 200-page introductory statistics books that I will ever see . . . it would make a good nightstand book for every statistician.»—Technometrics Written in a highly accessible style, Introduction to Statistics through Resampling Methods and R, Second Edition guides students in the understanding of descriptive statistics, estimation, hypothesis testing, and model building. The book emphasizes the discovery method, enabling readers to ascertain solutions on their own rather than simply copy answers or apply a formula by rote. The Second Edition utilizes the R programming language to simplify tedious computations, illustrate new concepts, and assist readers in completing exercises. The text facilitates quick learning through the use of: More than 250 exercises—with selected «hints»—scattered throughout to stimulate readers' thinking and to actively engage them in applying their newfound skills An increased focus on why a method is introduced Multiple explanations of basic concepts Real-life applications in a variety of disciplines Dozens of thought-provoking, problem-solving questions in the final chapter to assist readers in applying statistics to real-life applications Introduction to Statistics through Resampling Methods and R, Second Edition is an excellent resource for students and practitioners in the fields of agriculture, astrophysics, bacteriology, biology, botany, business, climatology, clinical trials, economics, education, epidemiology, genetics, geology, growth processes, hospital administration, law, manufacturing, marketing, medicine, mycology, physics, political science, psychology, social welfare, sports, and toxicology who want to master and learn to apply statistical methods.
Revolutions of Geometry
Guides readers through the development of geometry and basic proof writing using a historical approach to the topic In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfully equipped with the necessary logic to develop a full understanding of geometric theorems. Following a presentation of the geometry of ancient Egypt, Babylon, and China, the author addresses mathematical philosophy and logic within the context of works by Thales, Plato, and Aristotle. Next, the mathematics of the classical Greeks is discussed, incorporating the teachings of Pythagoras and his followers along with an overview of lower-level geometry using Euclid's Elements. Subsequent chapters explore the work of Archimedes, Viete's revolutionary contributions to algebra, Descartes' merging of algebra and geometry to solve the Pappus problem, and Desargues' development of projective geometry. The author also supplies an excursion into non-Euclidean geometry, including the three hypotheses of Saccheri and Lambert and the near simultaneous discoveries of Lobachevski and Bolyai. Finally, modern geometry is addressed within the study of manifolds and elliptic geometry inspired by Riemann's work, Poncelet's return to projective geometry, and Klein's use of group theory to characterize different geometries. The book promotes the belief that in order to learn how to write proofs, one needs to read finished proofs, studying both their logic and grammar. Each chapter features a concise introduction to the presented topic, and chapter sections conclude with exercises that are designed to reinforce the material and provide readers with ample practice in writing proofs. In addition, the overall presentation of topics in the book is in chronological order, helping readers appreciate the relevance of geometry within the historical development of mathematics. Well organized and clearly written, Revolutions of Geometry is a valuable book for courses on modern geometry and the history of mathematics at the upper-undergraduate level. It is also a valuable reference for educators in the field of mathematics.
Analysis of Ordinal Categorical Data
Statistical science’s first coordinated manual of methods for analyzing ordered categorical data, now fully revised and updated, continues to present applications and case studies in fields as diverse as sociology, public health, ecology, marketing, and pharmacy. Analysis of Ordinal Categorical Data, Second Edition provides an introduction to basic descriptive and inferential methods for categorical data, giving thorough coverage of new developments and recent methods. Special emphasis is placed on interpretation and application of methods including an integrated comparison of the available strategies for analyzing ordinal data. Practitioners of statistics in government, industry (particularly pharmaceutical), and academia will want this new edition.
Introduction to Digital Systems. Modeling, Synthesis, and Simulation Using VHDL
A unique guide to using both modeling and simulation in digital systems design Digital systems design requires rigorous modeling and simulation analysis that eliminates design risks and potential harm to users. Introduction to Digital Systems: Modeling, Synthesis, and Simulation Using VHDL introduces the application of modeling and synthesis in the effective design of digital systems and explains applicable analytical and computational methods. Through step-by-step explanations and numerous examples, the author equips readers with the tools needed to model, synthesize, and simulate digital principles using Very High Speed Integrated Circuit Hardware Description Language (VHDL) programming. Extensively classroom-tested to ensure a fluid presentation, this book provides a comprehensive overview of the topic by integrating theoretical principles, discrete mathematical models, computer simulations, and basic methods of analysis. Topical coverage includes: Digital systems modeling and simulation Integrated logic Boolean algebra and logic Logic function optimization Number systems Combinational logic VHDL design concepts Sequential and synchronous sequential logic Each chapter begins with learning objectives that outline key concepts that follow, and all discussions conclude with problem sets that allow readers to test their comprehension of the presented material. Throughout the book, VHDL sample codes are used to illustrate circuit design, providing guidance not only on how to learn and master VHDL programming, but also how to model and simulate digital circuits. Introduction to Digital Systems is an excellent book for courses in modeling and simulation, operations research, engineering, and computer science at the upper-undergraduate and graduate levels. The book also serves as a valuable resource for researchers and practitioners in the fields of operations research, mathematical modeling, simulation, electrical engineering, and computer science.