Author: Paul R. HalmosPublisher: American Mathematical Soc.
ISBN: 1470459167
Category : Mathematics
Languages : en
Pages : 421
Book Description
I Want to Be a Mathematician: An Automathography
Author: Paul R. HalmosPublisher: American Mathematical Soc.
ISBN: 1470459167
Category : Mathematics
Languages : en
Pages : 421
Book Description
How to Write Mathematics
Author: Norman Earl SteenrodPublisher: American Mathematical Soc.
ISBN: 9780821896785
Category : Mathematics
Languages : en
Pages : 76
Book Description
This classic guide contains four essays on writing mathematical books and papers at the research level and at the level of graduate texts. The authors are all well known for their writing skills, as well as their mathematical accomplishments. The first essay, by Steenrod, discusses writing books, either monographs or textbooks. He gives both general and specific advice, getting into such details as the need for a good introduction. The longest essay is by Halmos, and contains many of the pieces of his advice that are repeated even today: In order to say something well you must have something to say; write for someone; think about the alphabet. Halmos's advice is systematic and practical. Schiffer addresses the issue by examining four types of mathematical writing: research paper, monograph, survey, and textbook, and gives advice for each form of exposition. Dieudonne's contribution is mostly a commentary on the earlier essays, with clear statements of where he disagrees with his coauthors. The advice in this small book will be useful to mathematicians at all levels.
Lectures on Ergodic Theory
Author: Paul R. HalmosPublisher: Courier Dover Publications
ISBN: 0486814890
Category : Mathematics
Languages : en
Pages : 113
Book Description
This concise classic by Paul R. Halmos, a well-known master of mathematical exposition, has served as a basic introduction to aspects of ergodic theory since its first publication in 1956. "The book is written in the pleasant, relaxed, and clear style usually associated with the author," noted the Bulletin of the American Mathematical Society, adding, "The material is organized very well and painlessly presented." Suitable for advanced undergraduates and graduate students in mathematics, the treatment covers recurrence, mean and pointwise convergence, ergodic theorem, measure algebras, and automorphisms of compact groups. Additional topics include weak topology and approximation, uniform topology and approximation, invariant measures, unsolved problems, and other subjects.
Reading, Writing, and Proving
Author: Ulrich DaeppPublisher: Springer Science & Business Media
ISBN: 0387215603
Category : Mathematics
Languages : en
Pages : 391
Book Description
This book, based on Pólya's method of problem solving, aids students in their transition to higher-level mathematics. It begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematics and ends by providing projects for independent study. Students will follow Pólya's four step process: learn to understand the problem; devise a plan to solve the problem; carry out that plan; and look back and check what the results told them.
Handbook of Writing for the Mathematical Sciences
Author: Nicholas J. HighamPublisher: SIAM
ISBN: 0898714206
Category : Mathematics
Languages : en
Pages : 304
Book Description
Nick Higham follows up his successful HWMS volume with this much-anticipated second edition.
What Is Mathematics, Really?
Author: Reuben HershPublisher: Oxford University Press
ISBN: 0198027362
Category : Mathematics
Languages : en
Pages : 368
Book Description
Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.
Mathematical Writing
Author: Donald E. KnuthPublisher: Cambridge University Press
ISBN: 9780883850633
Category : Language Arts & Disciplines
Languages : en
Pages : 132
Book Description
This book will help those wishing to teach a course in technical writing, or who wish to write themselves.
Proofs and Refutations
Author: Imre LakatosPublisher: Cambridge University Press
ISBN: 9780521290388
Category : Mathematics
Languages : en
Pages : 190
Book Description
Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.
Dr. Riemann's Zeros
Author: Karl SabbaghPublisher: Atlantic Books (UK)
ISBN:
Category : Biography & Autobiography
Languages : en
Pages : 306
Book Description
In 1859 Bernhard Riemann, a shy German mathematician, gave an answer to a problem that had long puzzled mathematicians. Although he couldn't provide a proof, Riemann declared that his solution was 'very probably' true. For the next one hundred and fifty years, the world's mathematicians have longed to confirm the Riemann hypothesis. So great is the interest in its solution that in 2001, an American foundation offered a million-dollar prize to the first person to demonstrate that the hypothesis is correct. In this book, Karl Sabbagh makes accessible even the airiest peaks of maths and paints vivid portraits of the people racing to solve the problem. Dr. Riemann's Zeros is a gripping exploration of the mystery at the heart of our counting system.
A History of Algebraic and Differential Topology, 1900 - 1960
Author: Jean DieudonnéPublisher: Springer Science & Business Media
ISBN: 0817649077
Category : Mathematics
Languages : en
Pages : 666
Book Description
This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it! —MathSciNet