I Want to Be a Mathematician: An Automathography
Author: Paul R. Halmos
Publisher: American Mathematical Soc.
Published: 2020-08-03
Total Pages: 421
ISBN-13: 1470459167
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Problems for Mathematicians, Young and Old
Author: Paul R. Halmos
Publisher: American Mathematical Soc.
Published: 1991-12-01
Total Pages: 318
ISBN-13: 1470457199
DOWNLOAD EBOOKA collection of math problems for people of varying skills from high school through professional level, organized into fourteen categories, such as matrices, space, probability, and puzzles, and including hints and solutions.
How to Write Mathematics
Author: Norman Earl Steenrod
Publisher: American Mathematical Soc.
Published: 1973-12-31
Total Pages: 76
ISBN-13: 9780821896785
DOWNLOAD EBOOKThis 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.
Mathematical Writing
Author: Donald E. Knuth
Publisher: Cambridge University Press
Published: 1989
Total Pages: 132
ISBN-13: 9780883850633
DOWNLOAD EBOOKThis book will help those wishing to teach a course in technical writing, or who wish to write themselves.
Reading, Writing, and Proving
Author: Ulrich Daepp
Publisher: Springer Science & Business Media
Published: 2006-04-18
Total Pages: 391
ISBN-13: 0387215603
DOWNLOAD EBOOKThis 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. Higham
Publisher: SIAM
Published: 1998-08-01
Total Pages: 304
ISBN-13: 0898714206
DOWNLOAD EBOOKNick Higham follows up his successful HWMS volume with this much-anticipated second edition.
What Is Mathematics, Really?
Author: Reuben Hersh
Publisher: Oxford University Press
Published: 1997-08-21
Total Pages: 368
ISBN-13: 0198027362
DOWNLOAD EBOOKMost 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.
Handbook of Analysis and Its Foundations
Author: Eric Schechter
Publisher: Academic Press
Published: 1996-10-24
Total Pages: 907
ISBN-13: 0080532993
DOWNLOAD EBOOKHandbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. Covers some hard-to-find results including: Bessagas and Meyers converses of the Contraction Fixed Point Theorem Redefinition of subnets by Aarnes and Andenaes Ghermans characterization of topological convergences Neumanns nonlinear Closed Graph Theorem van Maarens geometry-free version of Sperners Lemma Includes a few advanced topics in functional analysis Features all areas of the foundations of analysis except geometry Combines material usually found in many different sources, making this unified treatment more convenient for the user Has its own webpage: http://math.vanderbilt.edu/
Dr. Riemann's Zeros
Author: Karl Sabbagh
Publisher: Atlantic Books (UK)
Published: 2003
Total Pages: 306
ISBN-13:
DOWNLOAD EBOOKIn 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 Dieudonné
Publisher: Springer Science & Business Media
Published: 2009-09-01
Total Pages: 666
ISBN-13: 0817649077
DOWNLOAD EBOOKThis 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
