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Real Mathematical Analysis
Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.
Invariant Manifolds
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A First Course in Real Analysis
The first course in analysis which follows elementary calculus is a critical one for students who are seriously interested in mathematics. Traditional advanced calculus was precisely what its name indicates-a course with topics in calculus emphasizing problem solving rather than theory. As a result students were often given a misleading impression of what mathematics is all about; on the other hand the current approach, with its emphasis on theory, gives the student insight in the fundamentals of analysis. In A First Course in Real Analysis we present a theoretical basis of analysis which is suitable for students who have just completed a course in elementary calculus. Since the sixteen chap...
Autonomy, Rationality, and Contemporary Bioethics
Personal autonomy is often lauded as a key value in contemporary Western bioethics, and the claim that there is an important relationship between autonomy and rationality is often treated as an uncontroversial claim in this sphere. Yet, there is also considerable disagreement about how we should cash out the relationship between rationality and autonomy. In particular, it is unclear whether a rationalist view of autonomy can be compatible with legal judgments that enshrine a patient's right to refuse medical treatment, regardless of whether ". . . the reasons for making the choice are rational, irrational, unknown or even non-existent". In this book, I bring recent philosophical work on the ...
Anthropocene Islands
'A must read … a new analytical agenda for the Anthropocene, coherently drawing out the power of thinking with islands.' – Elena Burgos Martinez, Leiden University ‘This is an essential book. [The] analytics they propose … offer both a critical agenda for island studies and compass points through which to navigate the haunting past, troubling present, and precarious future.’ – Craig Santos Perez, University of Hawai’i, Manoa ‘All academic books should be like this: hard to put down. Informative, careful, sometimes devasting, yet absolutely necessary - if you read one book about the Anthropocene let it be this. You will never think of islands in the same way again.’ – Kimb...
Mathematical Analysis I
This work by Zorich on Mathematical Analysis constitutes a thorough first course in real analysis, leading from the most elementary facts about real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, Fourier, Laplace, and Legendre transforms, and elliptic functions.
Basic Elements of Real Analysis
From the author of the highly-acclaimed "A First Course in Real Analysis" comes a volume designed specifically for a short one-semester course in real analysis. Many students of mathematics and the physical and computer sciences need a text that presents the most important material in a brief and elementary fashion. The author meets this need with such elementary topics as the real number system, the theory at the basis of elementary calculus, the topology of metric spaces and infinite series. There are proofs of the basic theorems on limits at a pace that is deliberate and detailed, backed by illustrative examples throughout and no less than 45 figures.
Understanding Analysis
This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions.
The Tumbleweed Society
This book examines how we navigate questions of commitment and flexibility at work and at home in a world where insecurity has become the norm. How do people today, especially parents, think and talk about what we owe each other on the job and in intimate relationships-with partners, children, and others-when so much is perpetually up in the air?
Speak for Britain!
Appearing at a critical juncture in the history of the Labour Party, Martin Pugh provides an original and challenging interpretation of Labour's evolution from its sectional trade union origins through to governing the entire nation.
