“…With its accessible presentation and engaging style, A Sampling of Remarkable Groups is suitable for students in upper-level undergraduate or beginning graduate abstract algebra courses. It will also be of interest to researchers in mathematics, computer science, and related fields.…”
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“…It provides excellent preparation for courses in linear algebra, number theory, and modern/abstract algebra and for computer science courses in data structures, algorithms, programming languages, compilers, databases, and computation.* Covers all recommended topics in a self-contained, comprehensive, and understandable format for students and new professionals * Emphasizes problem-solving techniques, pattern recognition, conjecturing, induction, applications of varying nature, proof techniques, algorithm development and correctness, and numeric computations* Weaves numerous applications into the text* Helps students learn by doing with a wealth of examples and exercises: - 560 examples worked out in detail - More than 3,700 exercises - More than 150 computer assignments - More than 600 writing projects* Includes chapter summaries of important vocabulary, formulas, and properties, plus the chapter review exercises* Features interesting anecdotes and biographies of 60 mathematicians and computer scientists* Instructor''s Manual available for adopters* Student Solutions Manual available separately for purchase (ISBN: 0124211828)…”
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“…With their work the authors provide a solid background to module theory, accessible to anyone familiar with basic abstract algebra. The focus of the book is on direct sums of CS-modules and classes of modules related to CS-modules, such as relative (injective) ejective modules, (quasi) continuous modules, and lifting modules. …”
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“…Instructors and educators teaching problem-solving courses or organizing mathematics clubs, as well as motivated mathematics students from high school juniors to college seniors, will find Mathematical Bridges a useful resource in calculus, linear and abstract algebra, analysis and differential equations. …”
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“…This text-based on the author's popular courses at Pomona College-provides a readable, student-friendly, and somewhat sophisticated introduction to abstract algebra. It is aimed at sophomore or junior undergraduates who are seeing the material for the first time. …”
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“…It is suitable for use as a textbook in a course or self-study by advanced undergraduates or graduate students who possess a basic familiarity with abstract algebra. The text treats a variety of topics from elementary number theory including the distribution of primes, sums of squares, continued factions, the Legendre, Jacobi and Kronecker symbols, the class group and genera. …”
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“…I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. …”
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“…A transition course functions as a bridge between computational courses such as Calculus, and more theoretical courses such as linear algebra and abstract algebra. This text contains core topics that I believe any transition course should cover, as well as some optional material intended to give the instructor some flexibility in designing a course. …”
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“…From a logical point of view, the dynamical evaluation gives a constructive substitute for two highly nonconstructive tools of abstract algebra: the Law of Excluded Middle and Zorn's Lemma. …”
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“…Appendix A provides a brief review of the basic number theory and abstract algebra used in the text, as well as exercises related to this material. …”
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“…The book is intended as a textbook for a course on representation theory, which could immediately follow the standard graduate abstract algebra course, and for subsequent more advanced reading courses. …”
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“…Quadratic Number Theory is an introduction to algebraic number theory for readers with a moderate knowledge of elementary number theory and some familiarity with the terminology of abstract algebra. By restricting attention to questions about squares the author achieves the dual goals of making the presentation accessible to undergraduates and reflecting the historical roots of the subject. …”
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“…Knowledge of complex analysis, real analysis, and abstract algebra is required.…”
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“…Prerequisites include standard first-year graduate courses covering linear and abstract algebra, topology and geometry, and real and complex analysis.…”
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“…The members of the class have always come from a variety of departments and backgrounds, and con­ sequently have entered the class with levels of preparation ranging from first year calculus and a taste of transform theory on the one extreme to senior level real analysis and abstract algebra on the other.…”
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“…The objective of the course, and the book, is to give students enough experience in the algebraic theory of the integers and polynomials to appre­ ciate the basic concepts of abstract algebra. The main theoretical thread is to develop algebraic properties of the ring of integers: unique factorization into primes, congruences and congruence classes, Fermat's theorem, the Chinese remainder theorem; and then again for the ring of polynomials. …”
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“…This gradual introduction also makes a significant effort to teach students how to produce or discover a proof by presenting mathematics as an exploration, and at the same time, it provides the necessary mathematical underpinnings to investigate the practical and implementation side of elliptic curve cryptography (ECC). Elements of abstract algebra, number theory, and affine and projective geometry are introduced and developed, and their interplay is exploited. …”
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“…It makes the research literature on difference sets accessible to students who have studied linear algebra and abstract algebra, and it prepares them to do their own research. …”
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“…Topics in Commutative Ring Theory is a textbook for advanced undergraduate students as well as graduate students and mathematicians seeking an accessible introduction to this fascinating area of abstract algebra.Commutative ring theory arose more than a century ago to address questions in geometry and number theory. …”
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“…Assuming only a basic background in abstract algebra and number theory, the text uses Diophantine questions to motivate readers seeking an accessible pathway into arithmetic geometry.…”
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