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Through this book, upper undergraduate mathematics majors will master a challenging yet rewarding subject, and approach advanced studies in algebra, number theory and geometry with confidence. Groups, rings and fields are covered in depth with a strong emphasis on irreducible polynomials, a fresh approach to modules and linear algebra, a fresh take on Gröbner theory, and a group theoretic treatment of Rejewski's deciphering of the Enigma machine. It includes a detailed treatment of the basics on finite groups, including Sylow…
Balances accessibility with rigor, allowing motivated students to gain mastery of advanced topics
Takes a 'definitions first, examples next' approach, striking the right balance between abstract material and its motivation
Prepares students for advanced studies in mathematics by offering a uniquely wide base of knowledge in key topics
Coverage includes: finite abelian groups, Sylow theory, semi-direct products, solvable groups, unique factorization, irreducibility of polynomials, Galois theory and solvability by radicals, ruler and compass constructions, module theory over principal ideal domains, and a novel approach to Gröbner bases
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Authors
John W. Lawrence,University of Waterloo, Ontario
John W. Lawrence is Professor Emeritus at the University of Waterloo. He was born in Ottawa, Canada, and received degrees from Carleton University and McGill University. After a year of postdoctoral work at the University of Chicago, he joined the Pure Mathematics Department of the University of Waterloo. He now lives with his wife Louise, in Thornhill Canada, where he continues his research in mathematics and probability.
Frank A. Zorzitto,University of Waterloo, Ontario
Frank A. Zorzitto is Professor Emeritus at the University of Waterloo. After receiving his doctorate at Queen's University in Kingston, Canada, he served for forty years as a researcher in algebra and a professor in the Pure Mathematics Department at the University of Waterloo, and served as Department Chair for twelve years. In recognition of his commitment to the education of students, he received the University's Distinguished Teaching Award. Upon his retirement he was made an Honorary Member of the University. Currently he offers an online course to high school math teachers, based on his e-book A Taste of Number Theory. He continues to teach and to write in his retirement.