Logic of Mathematics

Presents a uniquely balanced approach that bridges introductory and advanced topics in modern mathematics An accessible treatment of the fundamentals of modern mathematics, Principles of Mathematics: A Primer provides a unique approach to introductory andadvanced mathematical topics. The book features six main subjects, whichcan be studied independently or in conjunction with each other including: settheory; mathematical logic; proof theory; group theory; theory of functions; andlinear algebra. The author begins with comprehensive coverage of the necessary building blocks in mathematics and emphasizes the need to think abstractly and develop an appreciation for mathematical thinking. Maintaining a useful balance of introductory coverage and mathematical rigor, Principles of Mathematics: A Primer features: Detailed explanations of important theorems and their applications Hundreds of completely solved problems throughout each chapter Numerous exercises at the end of each chapter to encourage further exploration Discussions of interesting and provocative issues that spark readers’ curiosity and facilitate a better understanding and appreciation of the field of mathematics Principles of Mathematics: A Primer is an ideal textbook for upper-undergraduate courses in the foundations of mathematics and mathematical logic as well as for graduate-level courses related to physics, engineering, and computer science. The book is also a useful reference for readers interested in pursuing careers in mathematics and the sciences. Vladimir Lepetic, PhD, is Professor in the Department of Mathematical Sciences at DePaul University. His research interests include mathematical physics, set theory, foundations of mathematics, and the philosophy of mathematics.

Mathematics of Chance utilizes simple, real-world problems-some of which have only recently been solved-to explain fundamental probability theorems, methods, and statistical reasoning. Jiri Andel begins with a basic introduction to probability theory and its important points before moving on to more specific sections on vital aspects of probability, using both classic and modern problems. Each chapter begins with easy, realistic examples before covering the general formulations and mathematical treatments used. The reader will find ample use for a chapter devoted to matrix games and problem sets concerning waiting, probability calculations, expectation calculations, and statistical methods. A special chapter utilizes problems that relate to areas of mathematics outside of statistics and considers certain mathematical concepts from a probabilistic point of view. Sections and problems cover topics including: * Random walks * Principle of reflection * Probabilistic aspects of records * Geometric distribution * Optimization * The LAD method, and more Knowledge of the basic elements of calculus will be sufficient in understanding most of the material presented here, and little knowledge of pure statistics is required. Jiri Andel has produced a compact reference for applied statisticians working in industry and the social and technical sciences, and a book that suits the needs of students seeking a fundamental understanding of probability theory.

This new edition brings the fascinating and intriguing history of mathematics to life The Second Edition of this internationally acclaimed text has been thoroughly revised, updated, and reorganized to give readers a fresh perspective on the evolution of mathematics. Written by one of the world's leading experts on the history of mathematics, the book details the key historical developments in the field, providing an understanding and appreciation of how mathematics influences today's science, art, music, literature, and society. In the first edition, each chapter was devoted to a single culture. This Second Edition is organized by subject matter: a general survey of mathematics in many cultures, arithmetic, geometry, algebra, analysis, and mathematical inference. This new organization enables students to focus on one complete topic and, at the same time, compare how different cultures approached each topic. Many new photographs and diagrams have been added to this edition to enhance the presentation. The text is divided into seven parts: The World of Mathematics and the Mathematics of the World, including the origin and prehistory of mathematics, cultural surveys, and women mathematicians Numbers, including counting, calculation, ancient number theory, and numbers and number theory in modern mathematics Color Plates, illustrating the impact of mathematics on civilizations from Egypt to Japan to Mexico to modern Europe Space, including measurement, Euclidean geometry, post-Euclidean geometry, and modern geometrics Algebra, including problems leading to algebra, equations and methods, and modern algebra Analysis, including the calculus, real, and complex analysis Mathematical Inference, including probability and statistics, and logic and set theory As readers progress through the text, they learn about the evolution of each topic, how different cultures devised their own solutions, and how these solutions enabled the cultures to develop and progress. In addition, readers will meet some of the greatest mathematicians of the ages, who helped lay the groundwork for today's science and technology. The book's lively approach makes it appropriate for anyone interested in learning how the field of mathematics came to be what it is today. It can also serve as a textbook for undergraduate or graduate-level courses. An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.

Praise for the Second Edition «An amazing assemblage of worldwide contributions in mathematics and, in addition to use as a course book, a valuable resource . . . essential.» —CHOICE This Third Edition of The History of Mathematics examines the elementary arithmetic, geometry, and algebra of numerous cultures, tracing their usage from Mesopotamia, Egypt, Greece, India, China, and Japan all the way to Europe during the Medieval and Renaissance periods where calculus was developed. Aimed primarily at undergraduate students studying the history of mathematics for science, engineering, and secondary education, the book focuses on three main ideas: the facts of who, what, when, and where major advances in mathematics took place; the type of mathematics involved at the time; and the integration of this information into a coherent picture of the development of mathematics. In addition, the book features carefully designed problems that guide readers to a fuller understanding of the relevant mathematics and its social and historical context. Chapter-end exercises, numerous photographs, and a listing of related websites are also included for readers who wish to pursue a specialized topic in more depth. Additional features of The History of Mathematics, Third Edition include: Material arranged in a chronological and cultural context Specific parts of the history of mathematics presented as individual lessons New and revised exercises ranging between technical, factual, and integrative Individual PowerPoint presentations for each chapter and a bank of homework and test questions (in addition to the exercises in the book) An emphasis on geography, culture, and mathematics In addition to being an ideal coursebook for undergraduate students, the book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the history of mathematics.

Image processing problems are often not well defined because real images are contaminated with noise and other uncertain factors. In Mathematics of Shape Description, the authors take a mathematical approach to address these problems using the morphological and set-theoretic approach to image processing and computer graphics by presenting a simple shape model using two basic shape operators called Minkowski addition and decomposition. This book is ideal for professional researchers and engineers in Information Processing, Image Measurement, Shape Description, Shape Representation and Computer Graphics. Post-graduate and advanced undergraduate students in pure and applied mathematics, computer sciences, robotics and engineering will also benefit from this book. Key Features Explains the fundamental and advanced relationships between algebraic system and shape description through the set-theoretic approach Promotes interaction of image processing geochronology and mathematics in the field of algebraic geometry Provides a shape description scheme that is a notational system for the shape of objects Offers a thorough and detailed discussion on the mathematical characteristics and significance of the Minkowski operators

Forget the jargon. Forget the anxiety. Just remember the math. In this age of cheap calculators and powerful spreadsheets, who needs to know math? The answer is: everyone. Math is all around us. We confront it shopping in the supermarket, paying our bills, checking the sports stats, and working at our jobs. It is also one of the most fascinating-and useful-subjects. Mastering math can make a difference in your career, your studies, and your daily life. If you are among the millions of people who would love to understand math but are turned away by fear of its complexity, here is your salvation. The A to Z of Mathematics makes math simple without making it simplistic. Both easy to use and easy to read, the book covers all the topics in basic mathematics. You'll learn the definitions of such terms as «proportion»and «hexomino,» and grasp the concepts behind algebra, statistics, and other processes. The book's alphabetical arrangement helps you quickly home in on any topic, and its text is rich with stimulating examples, diagrams, and other illustrations that make the discussion crystal clear to every reader. Everyone will find something of interest in this wide-ranging guide to mathematics. The perfect antidote to math anxiety, this is an invaluable resource for parents and students, home schoolers, teachers, and anyone else who wants to improve his or her math skills and discover the amazing relevance of mathematics to the world around us.

Throughout banking, mathematical techniques are used. Some of these are within software products or models; mathematicians use others to analyse data. The current literature on the subject is either very basic or very advanced. The Mathematics of Banking offers an intermediate guide to the various techniques used in the industry, and a consideration of how each one should be approached. Written in a practical style, it will enable readers to quickly appreciate the purpose of the techniques and, through illustrations, see how they can be applied in practice. Coverage is extensive and includes techniques such as VaR analysis, Monte Carlo simulation, extreme value theory, variance and many others. A practical review of mathematical techniques needed in banking which does not expect a high level of mathematical competence from the reader

This new edition features the latest tools for modeling, characterizing, and solving partial differential equations The Third Edition of this classic text offers a comprehensive guide to modeling, characterizing, and solving partial differential equations (PDEs). The author provides all the theory and tools necessary to solve problems via exact, approximate, and numerical methods. The Third Edition retains all the hallmarks of its previous editions, including an emphasis on practical applications, clear writing style and logical organization, and extensive use of real-world examples. Among the new and revised material, the book features: * A new section at the end of each original chapter, exhibiting the use of specially constructed Maple procedures that solve PDEs via many of the methods presented in the chapters. The results can be evaluated numerically or displayed graphically. * Two new chapters that present finite difference and finite element methods for the solution of PDEs. Newly constructed Maple procedures are provided and used to carry out each of these methods. All the numerical results can be displayed graphically. * A related FTP site that includes all the Maple code used in the text. * New exercises in each chapter, and answers to many of the exercises are provided via the FTP site. A supplementary Instructor's Solutions Manual is available. The book begins with a demonstration of how the three basic types of equations-parabolic, hyperbolic, and elliptic-can be derived from random walk models. It then covers an exceptionally broad range of topics, including questions of stability, analysis of singularities, transform methods, Green's functions, and perturbation and asymptotic treatments. Approximation methods for simplifying complicated problems and solutions are described, and linear and nonlinear problems not easily solved by standard methods are examined in depth. Examples from the fields of engineering and physical sciences are used liberally throughout the text to help illustrate how theory and techniques are applied to actual problems. With its extensive use of examples and exercises, this text is recommended for advanced undergraduates and graduate students in engineering, science, and applied mathematics, as well as professionals in any of these fields. It is possible to use the text, as in the past, without use of the new Maple material.

This book is for students who did not follow mathematics through to the end of their school careers, and graduates and professionals who are looking for a refresher course. This new edition contains many new problems and also has associated spreadsheets designed to improve students' understanding. These spreadsheets can also be used to solve many of the problems students are likely to encounter during the remainder of their geological careers. The book aims to teach simple mathematics using geological examples to illustrate mathematical ideas. This approach emphasizes the relevance of mathematics to geology, helps to motivate the reader and gives examples of mathematical concepts in a context familiar to the reader. With an increasing use of computers and quantitative methods in all aspects of geology it is vital that geologists be seen as numerate as their colleagues in other physical sciences. The book begins by discussing basic tools such as the use of symbols to represent geological quantities and the use of scientific notation for expressing very large and very small numbers. Simple functional relationships between geological variables are then covered (for example, straight lines, polynomials, logarithms) followed by chapters on algebraic manipulations. The mid-part of the book is devoted to trigonometry (including an introduction to vectors) and statistics. The last two chapters give an introduction to differential and integral calculus. The book is prepared with a large number of worked examples and problems for the students to attempt themselves. Answers to all the questions are given at the end of the book.

By focusing on the cellular mechanisms that underlie ontogeny, phylogeny and regeneration of complex physiologic traits, Evolution, the Logic of Biology demonstrates the use of homeostasis, the fundamental principle of physiology and medicine, as the unifying mechanism for evolution as all of biology. The homeostasis principle can be used to understand how environmental stressors have affected physiologic mechanisms to generate condition-specific novelty through cellular mechanisms. Evolution, the Logic of Biology allows the reader to understand the vertebrate life-cycle as an intergenerational continuum in support of effective, on-going environmental adaptation. By understanding the principles of physiology from their fundamental unicellular origins, culminating in modern-day metazoans, the reader as student, researcher or practitioner will be encouraged to think in terms of the prevention of disease, rather than in the treatment of disease as the eradication of symptoms. By tracing the ontogeny and phylogeny of this and other phenotypic homologies, one can perceive and understand how complex physiologic traits have mechanistically evolved from their simpler ancestral and developmental origins as cellular structures and functions, providing a logic of biology for the first time. Evolution, the Logic of Biology will be an invaluable resource for graduate students and researchers studying evolutionary development, medicine and biology, anthropology, comparative and developmental biology, genetics and genomics, and physiology.