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The Pleasures of Counting
What is the connection between the outbreak of cholera in Victorian Soho, the Battle of the Atlantic, African Eve and the design of anchors? One answer is that they are all examples chosen by Dr Tom Körner to show how a little mathematics can shed light on the world around us, and deepen our understanding of it. Dr Körner, an experienced author, describes a variety of topics which continue to interest professional mathematicians, like him. He does this using relatively simple terms and ideas, yet confronting difficulties (which are often the starting point for new discoveries) and avoiding condescension. If you have ever wondered what it is that mathematicians do, and how they go about it, then read on. If you are a mathematician wanting to explain to others how you spend your working days (and nights), then seek inspiration here.
A Companion to Analysis
This book not only provides a lot of solid information about real analysis, it also answers those questions which students want to ask but cannot figure how to formulate. To read this book is to spend time with one of the modern masters in the subject. --Steven G. Krantz, Washington University, St. Louis One of the major assets of the book is Korner's very personal writing style. By keeping his own engagement with the material continually in view, he invites the reader to a similarly high level of involvement. And the witty and erudite asides that are sprinkled throughout the book are a real pleasure. --Gerald Folland, University of Washingtion, Seattle Many students acquire knowledge of a l...
Fourier Analysis
Fourier analysis is a subject that was born in physics but grew up in mathematics. Now it is part of the standard repertoire for mathematicians, physicists and engineers. This diversity of interest is often overlooked, but in this much-loved book, Tom Körner provides a shop window for some of the ideas, techniques and elegant results of Fourier analysis, and for their applications. These range from number theory, numerical analysis, control theory and statistics, to earth science, astronomy and electrical engineering. The prerequisites are few (a reader with knowledge of second- or third-year undergraduate mathematics should have no difficulty following the text), and the style is lively and entertaining. This edition of Körner's 1989 text includes a foreword written by Professor Terence Tao introducing it to a new generation of fans.
Exercises in Fourier Analysis
Fourier analysis is an indispensable tool for physicists, engineers and mathematicians. A wide variety of the techniques and applications of fourier analysis are discussed in Dr. Körner's highly popular book, An Introduction to Fourier Analysis (1988). In this book, Dr. Körner has compiled a collection of exercises on Fourier analysis that will thoroughly test the reader's understanding of the subject. They are arranged chapter by chapter to correspond with An Introduction to Fourier Analysis, and for all who enjoyed that book, this companion volume will be an essential purchase.
Where Do Numbers Come From?
A clear, entertaining development of the number systems required in any course of modern mathematics.
Vectors, Pure and Applied
Explains both the how and the why of linear algebra to get students thinking like mathematicians.
Mountain Biodiversity
This book is the result of the first global conference on mountain biodiversity, and is a contribution to the International Year of Mountains, 2002. The Global Mountain Biodiversity Assessment program is a Special Target Area Region project of DIVERSITAS (UNESCO and UNEP). Biological diversity is essential for the integrity of mountain ecosystems and this dependency is likely to increase as environmental (climate) and social conditions change. Steep terrain and climate, and severe land-use pressure cause mountain ecosystems to rank among the world's most endangered landscapes. The 28 chapters in this book represent research on the biological riches in all major mountain ranges of the world, and synthesize existing knowledge on mountain biodiversity - from diversity of bacteria, plants and animals to human diversity. The book is divided into five sections: an introduction providing an overview of the issues; plant and animal diversity; climate change and mountain biodiversity; land use and conservation; and a synthesis.
Naive Decision Making
How should one choose the best restaurant to eat in? Can one really make money at gambling? Or predict the future? Naive Decision Making presents the mathematical basis for making decisions where the outcome may be uncertain or the interests of others have to taken into consideration. Professor Körner takes the reader on an enjoyable journey through many aspects of mathematical decision making, with pithy observations, anecdotes and quotations. Topics include probability, statistics, Arrow's theorem, Game Theory and Nash equilibrium. Readers will also gain a great deal of insight into mathematics in general and the role it can play within society. Intended for those with elementary calculus, this book is ideal as a supplementary text for undergraduate courses in probability, game theory and decision making. Engaging and intriguing, it will also appeal to all those of a mathematical mind. To aid understanding, many exercises are included, with solutions available online.
Information Theory
Information Theory: Coding Theorems for Discrete Memoryless Systems presents mathematical models that involve independent random variables with finite range. This three-chapter text specifically describes the characteristic phenomena of information theory. Chapter 1 deals with information measures in simple coding problems, with emphasis on some formal properties of Shannon's information and the non-block source coding. Chapter 2 describes the properties and practical aspects of the two-terminal systems. This chapter also examines the noisy channel coding problem, the computation of channel capacity, and the arbitrarily varying channels. Chapter 3 looks into the theory and practicality of multi-terminal systems. This book is intended primarily for graduate students and research workers in mathematics, electrical engineering, and computer science.
Calculus for the Ambitious
A short introduction perfect for any 16- to 18-year-old, about to begin studies in mathematics.
