Algebraic number theory introduces students to new algebraic notions as well as related concepts: groups, rings, fields, ideals, quotient rings, and... quotient fields. This text covers the basics, from divisibility theory in principal ideal domains to the unit theorem, finiteness of the class number, and Hilbert ramification theory. 1970 edition.

This book introduces the important ideas of algebraic topology by emphasizing the relation of these ideas with other areas of mathematics. Rather than... choosing one point of view of modern topology (homotropy theory, axiomatic homology, or differential topology, say) the author concentrates on concrete problems in spaces with a few dimensions, introducing only as much algebraic machinery as necessary for the problems encountered. This makes it possible to see a wider variety of important features in the subject than is common in introductory texts; it is also in harmony with the historical development of the subject. The book is aimed at students who do not necessarily intend on specializing in algebraic topology.

In most major universities one of the three or four basic first-year graduate mathematics courses is algebraic topology. This introductory text is... suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. The four main chapters present the basics: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature is the inclusion of many optional topics not usually part of a first course due to time constraints: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and Steenrod squares and powers.

Moreshet Sepharad: The Sephardi Legacy sets out to summarize the monumental legacy of a Jewish community that resided within the historical boundaries... of Spain for some fifteen hundred years. Many chapters evaluate the contribution of Sephardi Jewry to the renaissance of Hebrew Language and science. These as well as many issues in Jewish communal life, have been analyzed and evaluated both in the context of Spain prior to the Expulsion and in the various settings where the exiles settled and formed new social patterns. The thirty-eight chapters which make up the work provide guidelines which the student or interested reader may utilize to gain a deeper understanding of the essence of Sephardi Jewry in the basis of its glorious past and heritage.

In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential... manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples. Topics covered include Mayer-Vietoris exact sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This book will be suitable for graduate students taking courses in algebraic topology and in differential topology. Mathematicians studying relativity and mathematical physics will find this an invaluable introduction to the techniques of differential geometry.

SparkChartsTM—created by Harvard students for students everywhere—serve as study companions and reference tools that cover a wide range of college... and graduate school subjects, including Business, Computer Programming, Medicine, Law, Foreign Language, Humanities, and Science. Titles like How to Study, Microsoft Word for Windows, Microsoft PowerPoint for Windows, and HTML give you what it takes to find success in school and beyond. Outlines and summaries cover key points, while diagrams and tables make difficult concepts easier to digest.  This four-page chart reviews:Polynomial basicsFactoring polynomialsQuadratic equations in one variableDivision of polynomialsInequalities in two variablesGraphing absolute valueLogarithms definition and lawsSequences and seriesFactorials, combinations, permutations, and Pascal's triangleProbabilityComplex numbersConic sections types and table

600 Algebra II Study Cards. These 600 cards will help you master Algebra II with definitions, graphs, word problems, matrices, and more. Perfect study... aid for the SAT. Review key formulas and concepts. Study alone or with friends.

This text offers a special account of Indian work in diophantine equations during the 6th through 12th centuries and Italian work on solutions of cubic... and biquadratic equations from the 11th through 16th centuries. The volume traces the historical development of algebra and the theory of equations from ancient times to the beginning of modern algebra, outlining some modern themes such as the fundamental theorem of algebra, Clifford algebras, and quarternions. It is geared toward undergraduates who have no background in calculus.

As in previous editions, the focus in ALGEBRA: INTRODUCTORY & INTERMEDIATE remains on the Aufmann Interactive Method (AIM). Students are encouraged... to be active participants in the classroom and in their own studies as they work through the How To examples and the paired Examples and You Try It problems. The role of "active participant" is crucial to success. Presenting students with worked examples, and then providing them with the opportunity to immediately work similar problems, helps them build their confidence and eventually master the concepts. To this point, simplicity plays a key factor in the organization of this edition, as in all other editions. All lessons, exercise sets, tests, and supplements are organized around a carefully-constructed hierarchy of objectives. This "objective-based" approach not only serves the needs of students, in terms of helping them to clearly organize their thoughts around the content, but instructors as well, as they work to design syllabi, lesson plans, and other administrative documents. The Eighth Edition features a new design, enhancing the Aufmann Interactive Method and the organization of the text around objectives, making the pages easier for both students and instructors to follow.

SparkCharts™—created by Harvard students for students everywhere—serve as study companions and reference tools that cover a wide range of college... and graduate school subjects, including Business, Computer Programming, Medicine, Law, Foreign Language, Humanities, and Science. Titles like How to Study, Microsoft Word for Windows, Microsoft PowerPoint for Windows, and HTML give you what it takes to find success in school and beyond. Outlines and summaries cover key points, while diagrams and tables make difficult concepts easier to digest.  This four-page chart reviews:Definitions of number systems and setsProperties of arithmetic operationsLinear equations in one variableSolving absolute value equationsGraphing equations on the number lineThe Cartesian planeGraphing linear equationsSolving simultaneous linear equationsExponents and powersRoots and radicalsPolynomialsWord problems