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The updated new edition of the classic and comprehensive guide to the history of mathematics For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind’s relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat’s Last Theorem and the Poincar? Conjecture, in addition to recent advances in areas such as finite group theory and computer-aided proofs. Distills thousands of years of mathematics into a single, approachable volume Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present Includes up-to-date references and an extensive chronological table of mathematical and general historical developments. Whether you're interested in the age of Plato and Aristotle or Poincar? and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it.

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.

Presents an important and unique introduction to random walk theory Random walk is a stochastic process that has proven to be a useful model in understanding discrete-state discrete-time processes across a wide spectrum of scientific disciplines. Elements of Random Walk and Diffusion Processes provides an interdisciplinary approach by including numerous practical examples and exercises with real-world applications in operations research, economics, engineering, and physics. Featuring an introduction to powerful and general techniques that are used in the application of physical and dynamic processes, the book presents the connections between diffusion equations and random motion. Standard methods and applications of Brownian motion are addressed in addition to Levy motion, which has become popular in random searches in a variety of fields. The book also covers fractional calculus and introduces percolation theory and its relationship to diffusion processes. With a strong emphasis on the relationship between random walk theory and diffusion processes, Elements of Random Walk and Diffusion Processes features: Basic concepts in probability, an overview of stochastic and fractional processes, and elements of graph theory Numerous practical applications of random walk across various disciplines, including how to model stock prices and gambling, describe the statistical properties of genetic drift, and simplify the random movement of molecules in liquids and gases Examples of the real-world applicability of random walk such as node movement and node failure in wireless networking, the size of the Web in computer science, and polymers in physics Plentiful examples and exercises throughout that illustrate the solution of many practical problems Elements of Random Walk and Diffusion Processes is an ideal reference for researchers and professionals involved in operations research, economics, engineering, mathematics, and physics. The book is also an excellent textbook for upper-undergraduate and graduate level courses in probability and stochastic processes, stochastic models, random motion and Brownian theory, random walk theory, and diffusion process techniques.

Featuring key topics within finance, small business management, and entrepreneurship to develop and maintain prosperous business ventures With a comprehensive and organized approach to fundamental financial theories, tools, and management techniques, Entrepreneurial Finance: Fundamentals of Financial Planning and Management for Small Business equips readers with the necessary fundamental knowledge and advanced skills to succeed in small firm and business settings. With a unique combination of topics from finance, small business management, and entrepreneurship, the book prepares readers for the challenges of today’s economy. Entrepreneurial Finance: Fundamentals of Financial Planning and Management for Small Business begins with key concepts of small business management and entrepreneurship, including management tools and techniques needed to establish, run, and lead business ventures. The book then delves into how small businesses are operated, managed, and controlled. General finance skills and methods are integrated throughout, and the book also features: Numerous practical examples and scenarios that provide a real-world perspective on entrepreneurship and small business management A brief summary, list of key concepts, and ten discussion questions at the end of each chapter to prepare readers for the challenges of today's economy A practical guide to the complete life of a small business, from establishing a new venture to training and developing young entrepreneurs tasked with maintaining and developing a prosperous economy An in-depth discussion of the entire process of writing a successful business plan, including the rationale, significance, and requirements Techniques needed to solidify the free enterprise tradition, develop entrepreneurial strategies, and grow small businesses Entrepreneurial Finance: Fundamentals of Financial Planning and Management for Small Business is an ideal textbook for upper-undergraduate and first-year graduate courses in entrepreneurial finance within business, economics, management science, and public administration departments. The book is also useful for MBA-level courses as well as for business and management PhD majors as a resource in methodology. The book is also an idea reference for entrepreneurs, business managers, market analysts, and decision makers who require information about the theoretical and quantitative aspects of entrepreneurial finance.