MATHEMATICS / ALGEBRA This book is written for a very broad audience. There are no particular prerequisites for reading this book. We hope students of High Schools, Colleges, and Universities, as well as hobby mathematicians, will like and benefit from this book. The book is rigorous and self-contained. All results are proved (or the proofs are optional exercises) and stated as theorems. Important points are covered by examples and optional exercises. Additionally there are also two sections called More optional exercises (with answers). Modern technology uses complex numbers for just about everything. Actually, there is no way one can formulate quantum mechanics without resorting to complex numbers. Leonard Euler (1707-1786) considered it natural to introduce students to complex numbers much earlier than we do today. Even in his elementary algebra textbook he uses complex numbers throughout the book. Nils K. Oeijord is a science writer and a former assistant professor of mathematics at Tromsoe College, Norway. He is the author of The Very Basics of Tensors, and several other books in English and Norwegian. Nils K. Oeijord is the discoverer of the general genetic catastrophe (GGC).

This book presents detailed studies of the development of three kinds of number. In the first part the development of the natural numbers from Stone-Age times right up to the present day is examined not only from the point of view of pure history but also taking into account archaeological, anthropological and linguistic evidence. The dramatic change caused by the introduction of logical theories of number in the 19th century is also treated and this part ends with a non-technical account of the very latest developments in the area of G”del's theorem. The second part is concerned with the development of complex numbers and tries to answer the question as to why complex numbers were not introduced before the 16th century and then, by looking at the original materials, shows how they were introduced as a pragmatic device which was only subsequently shown to be theoretically justifiable. The third part concerns the real numbers and examines the distinction that the Greeks made between number and magnitude. It then traces the gradual development of a theory of real numbers up to the precise formulations in the nineteeth century. The importance of the Greek distinction between the number line and the geometric line is brought into sharp focus.This is an new edition of the book which first appeared privately published in 1980 and is now out of print. Substantial revisions have been made throughout the text, incorporating new material which has recently come to light and correcting a few relatively minor errors. The third part on real numbers has been very extensively revised and indeed the last chapter has been almost completely rewritten. Many revisions are the results of comments from earlier readers of the book.

This volume is, as may be readily apparent, the fruit of many years’ labor in archives and libraries, unearthing rare books, researching Nachlässe, and above all, systematic comparative analysis of fecund sources. The work not only demanded much time in preparation, but was also interrupted by other duties, such as time spent as a guest professor at universities abroad, which of course provided welcome opportunities to present and discuss the work, and in particular, the organizing of the 1994 International Graßmann Conference and the subsequent editing of its proceedings. If it is not possible to be precise about the amount of time spent on this work, it is possible to be precise about the date of its inception. In 1984, during research in the archive of the École polytechnique, my attention was drawn to the way in which the massive rupture that took place in 1811—precipitating the change back to the synthetic method and replacing the limit method by the method of the quantités infiniment petites—significantly altered the teaching of analysis at this first modern institution of higher education, an institution originally founded as a citadel of the analytic method.

This book is a detailed account of the Synthesizer Generator, a system for creat ing specialized editors that are customized for editing particular languages. The book is intended for those with an interest in software tools and in methods for building interactive systems. It is a must for people who are using the Syn thesizer Generator to build editors because it provides extensive discussions of how to write editor specifications. The book should also be valuable for people who are building specialized editors "by hand," without using an editor generating tool. The need to manage the development of large software systems is one of the most pressing problems faced by computer programmers. An important aspect of this problem is the design of new tools to aid interactive program develop ment. The Synthesizer Generator permits one to create specialized editors that are tailored for editing a particular language. In program editors built with the Synthesizer Generator, knowledge about the language is used to continuously assess whether a program contains errors and to determine where such errors occur. The information is then displayed on the terminal screen to provide feed back to the programmer as the program is developed and modified.

In the computerized world of today mathematics has had an impact on almost every aspect of our lives, yet most people believe they cannot hope to understand or enjoy the subject. This comprehensive survey sets out to show just how mistaken they are. Substantially revised and updated, this second edition takes into account recent dramatic developments and includes major new sections on Fermat's Last Theorem, knots and topology, and the mathematics of the physical universe. "Devlin's choice of material is excellent, and he is to be praised for the clarity and accuracy with which he presents it" - Martin Gardner in the New York Review of Books

Fully updated for the GMAT Focus! Developed for test-takers who need a math refresher, Manhattan Prep's GMAT Foundations of Math provides a user-friendly review of all of the fundamental math concepts crucial for success on the Quant and Data Insights sections of the GMAT. The ebook version is fully available for free, so check it out before you purchase! GMAT Foundations of Math provides: 500+ practice problems for realistic review Easy-to-follow explanations of fundamental math concepts Step-by-step application of concepts to example problems Full coverage of foundational quant topics tested on the GMAT, including arithmetic, algebra, story problems, number properties, fractions, percents, ratios, and more (for higher-level coverage of all GMAT topics, see the All the Quant and DI guide) Foundations of Math comes with access to the Atlas online learning platform. Your Atlas Foundations of Math syllabus includes: Hundreds of additional practice problems “Mid-term” and “final” exams to test your skills on the material you’re learning All lessons and practice problems were created by expert instructors with 99th-percentile scores on the GMAT. Publisher's Note: Products purchased from 3rd party sellers are not guaranteed by the publisher for quality, authenticity, or access to any online entities included with the product.

The first scientific entry in the acclaimed Art of Mentoring series from Basic Books, Letters to a Young Mathematician tells readers what Ian Stewart wishes he had known when he was a student and young faculty member. Subjects ranging from the philosophical to the practical -- what mathematics is and why it's worth doing, the relationship between logic and proof, the role of beauty in mathematical thinking, the future of mathematics, how to deal with the peculiarities of the mathematical community, and many others -- are dealt with in Stewart's much-admired style, which combines subtle, easygoing humor with a talent for cutting to the heart of the matter. In the tradition of G.H. Hardy's classic A Mathematician's Apology, this book is sure to be a perennial favorite with students at all levels, as well as with other readers who are curious about the frequently incomprehensible world of mathematics.

Livey's younger brother, Darby, a math genius, brings his imaginary friend to life through a mathematical proof. Bob is a creature of pure math, and he hates chaos and disorder. Now Livey, Darby, and some very unique allies must band together to find a way to stop Bob-before he fixes our disorderly world for good. Monster's Proof brings horror and math together in an unforgettable novel that will forever change the way you look at an equation.