Individuals and groups reading the Scriptures for their own enrichment can find appropriate guides for Genesis and Exodus. Numbers is another matter. The complexities of ritual laws, holy days, moral codes, and conflicts experienced by Moses and the people during their forty years in the wilderness form a daunting maze. Average readers, especially Christians, are often unsure of the inner logic of the regulations or of how to apply the sound theology found therein. This compact study starts with Numbers, following the story from exodus to the wilderness. The format is Socratic, asking as many step-by-step questions as seems reasonable and providing the answers at the back to encourage note taking and discussion beforehand. The forty years of strife depict the deep spiritual stresses experienced by the Chosen People (and by God), and can serve our own understanding for surviving challenges as a people called by God. Another lesson is the significant role of ancient Jewish laypeople within their system of ritual and prayer. They did much more than simply watch priests handle altar sacrifices and incense. A better understanding of that ancient teamwork in worship can aid our own modern worship customs.

This text is a comprehensive pedagogical presentation of the theory of representation of finite and compact Lie groups. It considers both the general theory and representation of specific groups. Representation theory is discussed on the following types of groups: finite groups of rotations, permutation groups, and classical compact semisimple Lie groups. Along the way, the structure theory of the compact semisimple Lie groups is exposed. This is aimed at research mathematicians and graduate students studying group theory.

Beginners scanning Leviticus will find much detail about rituals and sinful situations, but little enlightening context or rationale. This study explores how scholars imagine that these rituals and moral laws made sense to those living back then, even though many of these early rituals and customs have been discontinued or replaced by consensus with alternative forms of worship. The authors seem to be unquestioningly devout, and quite realistic about life at the same time. Everyone shared in rituals of faith at home, at shrines, or in Jerusalem; everyone honored the proper food and eligibility regulations, and everyone was called to the common code of justice. Likewise, most everyone knew at least the temptation to shirk religious duties; they understood the lure of trying to contact other gods, ones more lenient or at least easier to understand; and they could be inclined to look the other way at improper romances, or quick but dishonest chances to get a bigger slice of the pie. The Covenant was not a deal made by saints. It was a cry for help from sinners, a cry for help for which they had not earned the right. The same is true for us believers even now.

This book is about all kinds of numbers, from rationals to octonians, reals to infinitesimals. It is a story about a major thread of mathematics over thousands of years, and it answers everything from why Hamilton was obsessed with quaternions to what the prospect was for quaternionic analysis in the 19th century. It glimpses the mystery surrounding imaginary numbers in the 17th century and views some major developments of the 20th century.

Geared toward undergraduate and beginning graduate students, this study explores natural numbers, integers, rational numbers, real numbers, and complex numbers. Numerous exercises and appendixes supplement the text. 1973 edition.

The Conference on "Mathematics and the 21st Century" was held in Cairo, Egypt during the period 15-20 January 2000. The conference's sessions consisted of plenary lectures and topical sessions. Some of the plenary lectures covered general fields such as: rewriting the history of mathematics; education of mathematics; relation between mathematics and sciences; and mathematical aspects of transportation.

The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of e to mathematics and illuminates a golden era in the age of science.

In the American Mathematical Society's first-ever book for kids (and kids at heart), mathematician and author Richard Evan Schwartz leads math lovers of all ages on an innovative and strikingly illustrated journey through the infinite number system. By means of engaging, imaginative visuals and endearing narration, Schwartz manages the monumental task of presenting the complex concept of Big Numbers in fresh and relatable ways. The book begins with small, easily observable numbers before building up to truly gigantic ones, like a nonillion, a tredecillion, a googol, and even ones too huge for names! Any person, regardless of age, can benefit from reading this book. Readers will find themselves returning to its pages for a very long time, perpetually learning from and growing with the narrative as their knowledge deepens. Really Big Numbers is a wonderful enrichment for any math education program and is enthusiastically recommended to every teacher, parent and grandparent, student, child, or other individual interested in exploring the vast universe of numbers.

Presents an accessible, in-depth look at the history of numbers and their applications in life and science, from math's surreal presence in the virtual world to the debates about the role of math in science.

This book is a revised and greatly expanded version of our book Elements of Number Theory published in 1972. As with the first book the primary audience we envisage consists of upper level undergraduate mathematics majors and graduate students. We have assumed some familiarity with the material in a standard undergraduate course in abstract algebra. A large portion of Chapters 1-11 can be read even without such background with the aid of a small amount of supplementary reading. The later chapters assume some knowledge of Galois theory, and in Chapters 16 and 18 an acquaintance with the theory of complex variables is necessary. Number theory is an ancient subject and its content is vast. Any intro ductory book must, of necessity, make a very limited selection from the fascinat ing array of possible topics. Our focus is on topics which point in the direction of algebraic number theory and arithmetic algebraic geometry. By a careful selection of subject matter we have found it possible to exposit some rather advanced material without requiring very much in the way oftechnical background. Most of this material is classical in the sense that is was dis covered during the nineteenth century and earlier, but it is also modern because it is intimately related to important research going on at the present time.