Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems.

Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.

"The binomial theorem is usually quite rightly considered as one of the most important theorems in the whole of analysis." Thus wrote Bernard Bolzano in 1816 in introducing the first correct proof of Newton's generalisation of a century and a half earlier of a result familiar to us all from elementary algebra. Bolzano's appraisal may surprise the modern reader familiar only with the finite algebraic version of the Binomial Theorem involving positive integral exponents, and may also appear incongruous to one familiar with Newton's series for rational exponents. Yet his statement was a sound judgment back in the day. Here the story of the Binomial Theorem is presented in all its glory, from the early days in India, the Moslem world, and China as an essential tool for root extraction, through Newton's generalisation and its central role in infinite series expansions in the 17th and 18th centuries, and to its rigorous foundation in the 19th. The exposition is well-organised and fairly complete with all the necessary details, yet still readable and understandable for those with a limited mathematical background, say at the Calculus level or just below that. The present book, with its many citations from the literature, will be of interest to anyone concerned with the history or foundations of mathematics.

Designed for first-year developmental math students who need support in beginning algebra, Elementary Algebra, 4/e, retains the hallmark features for which the Larson team is known: abundant, high-quality applications; the use of real data; the integration of visualization (figures and graphs) throughout; and extensive opportunities for self-assessment (mid-chapter quizzes, review exercises, tests, and cumulative tests). In developing supportive new features for the Fourth Edition, the authors' goal is for students to come away from the class with a firm understanding of algebra and how it functions as a modern modeling language.

The acclaimed author of A Tour of the Calculus and The Infinite Ascent offers an enlightening and enthralling tour of the basics of mathematics, and reveals a world of fascination in fundamental mathematical ideas. One, Two, Three is David Berlinski’s captivating exploration of the foundation of mathematics, its fundamental ideas, and why they matter. By unraveling the complex answers to these most elementary questions—What is a number? How do addition, subtraction, and other functions actually work? What are geometry and logic?—Berlinski reveals the intricacy behind their seemingly simple exteriors. Peppered with enlightening historical anecdotes and asides on some of history’s most fascinating mathematicians, One, Two, Three, revels in the beauty of numbers as Berlinski shows us how and why these often slippery concepts are as essential to the field of mathematics as to who we are.