Description This books does not presuppose any previous background in number theory or algebra, but it quickly moves into material beyond the usual courses in math departments because of the emphasis on algorithms and computation. The chapter titles give an idea of the unusual flavor of this book, which has a number of topics that would be suitable for a senior level “advanced topics” course following a more traditional algebra or number theory course. The author writes that the book could “be used as a textbook in a graduate or upper-division undergraduate course on (computational) number theory and algebra, perhaps geared towards computer science students.”
Description The book is quite new but has already been used by a number of other faculty at other institutions who say that they recommend the book and would use it again. This book originated as lecture notes for the undergraduate analysis course at the University of Illinois in 2009, and so it follows the syllabus for that course based on the text of Bartle and Sherbert.
Description From an instructor who recently used this book: “I found it mathematically sound, well organized and very instructive for a good upper division undergraduate class. In particular, the exercise sets are well thought out and both the proofs and the narrative speak well to that level of student without sacrificing any rigor.”
Description This text was originally published by Prentice Hall in 2001. The second (and current) edition published in 2008 is essentially the same with misprints and other errors corrected. For a discussion of this text and the graduate analysis text by the same authors see the review by James Caragal in the UMAP Journal.
Description This text grew out of the lecture notes from the author at the University of Windsor and was originally copyrighted in 1975. It is now published by the Trillia Group, a publishing company started by his son-in-law, Bradley Lucier, a professor of mathematics and computer science at Purdue. The level of the book is appropriate for a rigorous analysis course. The author writes in the introduction that “we try to simplify the modern Bourbaki approach to make it accessible to sufficiently advanced undergraduates.”
Description This text for a semester course portrays real analysis in the context of its historical development. It is written in a direct style aimed at students and not instructors. A student using the book is guided to understand and prove much of the actual mathematical content through the more than 200 problems that are embedded within the narrative and not placed at the end of sections as in most textbooks. For a course taught in the inquiry based learning mode this book should work better than standard texts. On the other hand, with the instructor offering more guidance it should also work well with a more traditional classroom style.
Description This text grew out of the lecture notes of a single semester undergraduate course taught at Binghamton University (SUNY) and San Francisco State University, and it has benefited from the comments and suggestions from other instructors who have used the book. From the introduction: 'For many of our students, complex analysis is their first rigorous analysis (if not mathematics) class they take, and these notes reflect this very much. We tried to rely on as few concepts from real analysis as possible. In particular, series and sequences are treated “from scratch.”'
Description Geometry with an Introduction to Cosmic Topology offers an introduction to non-Euclidean geometry through the lens of questions that have ignited the imagination of stargazers since antiquity. What is the shape of the universe? Does the universe have an edge? Is it infinitely big?This text is intended for undergraduate mathematics and physics majors who have completed a multivariable calculus course and are ready for a course that practices the habits of thought needed in advanced courses of the undergraduate mathematics curriculum. The text is also particularly suited to independent study, with essays and other discussions complementing the mathematical content in several sections.
Description This book of about 500 pages has become a classic because of its engaging style, interesting examples, historical notes, pedagogical use of computer simulations, and more than 600 exercises. Thanks to the American Mathematical Society the book is freely available, although many readers will want to buy the hardcover edition from the AMS.
Description As the authors write in the preface, “Data is messy, and statistical tools are imperfect. But, when you understand the strengths and weaknesses of these tools, you can use them to learn about the real world.” This book is full of examples and exercises on topics of current interest pulled from the popular media and published research.
Description This is a highly engaging “textbook” that makes extensive use of the capability for interactive instruction with current software, computers, and the Internet. Although it requires an internet connection, the students need only an up-to-date browser (Firefox recommended) and so there is no need to buy or install any other software. The author has been developing the course material for more than 15 years, and it is both stable and reliable. It resides on a server in the Statistics Department at UC Berkeley and will be there for the foreseeable future.
Description This book is written for upper division mathematics students with the aim of getting to and understanding the incompleteness theorems in a single semester. The authors outline two paths to this goal as described in the preface to the second edition: 'This has allowed us to chart two paths to the incompleteness theorems, splitting after the material in Chapter 4. Readers of the first edition will find that the exposition in Chapters 5 and 6 follows a familiar route, although the material there has been pretty thoroughly reworked. It is also possible, if you choose, to move directly from Chapter 4 to Chapter 7 and see a development of computability theory that covers the Entschei- dungsproblem, Hilbert’s 10th Problem, and Gödel’s First Incompleteness Theorem.'
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