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In the same way the subject evolved historically, Ronald Solomon lets the abstract concepts emerge gradually from less abstract problems about geometry, polynomials, numbers, and more. Solomon also strongly emphasizes the connections between algebra and other areas of mathematics --analysis (the infinitesimal calculus) and geometry. Students will see that the various areas of mathematics are not hermetically sealed off from each other and that most of the truly important achievements in mathematics have been the product of a fruitful interaction of different areas. Using this text, students will gain a true understanding of the subject while being creative mathematically as opposed to simply imitating template problems.
About the Author
Ronald Solomon earned his Ph.D. at Yale University. Now teaching at The Ohio State University, Solomon's research area is the theory of finite groups, especially the classification and structure theory of the finite sample groups. Other interests include representation theory of finite groups and finite-dimensional algebras and in the geometries associated with groups. Outside of work, Dr. Solomon's interests include classical music, theater, his children, and the social needs of the underprivileged.
In the same way the subject evolved historically, Ronald Solomon lets the abstract concepts emerge gradually from less abstract problems about geometry, polynomials, numbers, and more. Solomon also strongly emphasizes the connections between algebra and other areas of mathematics --analysis (the infinitesimal calculus) and geometry. Students will see that the various areas of mathematics are not hermetically sealed off from each other and that most of the truly important achievements in mathematics have been the product of a fruitful interaction of different areas. Using this text, students will gain a true understanding of the subject while being creative mathematically as opposed to simply imitating template problems.
About the Author
Ronald Solomon earned his Ph.D. at Yale University. Now teaching at The Ohio State University, Solomon's research area is the theory of finite groups, especially the classification and structure theory of the finite sample groups. Other interests include representation theory of finite groups and finite-dimensional algebras and in the geometries associated with groups. Outside of work, Dr. Solomon's interests include classical music, theater, his children, and the social needs of the underprivileged.
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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unique factorization theorem, four squares theorem, nonidentity rotation, same minimum polynomial, constructible numbers, finite skew field, casus irreducibilis, splitting field, degree vector, elementary symmetric polynomials, cyclotomic polynomial, little theorem Key Phrases - Capitalized Phrases (CAPs): (learn more)
Lagrange's Theorem, Division Algorithm, Euclid's Lemma, Cancellation Law, Factor Theorem, Euclidean Algorithm, Fundamental Theorem of Algebra, Fermat's Last Theorem, Cauchy's Theorem, Commutative Law, Fermat's Little Theorem, Exercises Let, Euler's Theorem, Well-Ordering Principle, Binomial Theorem, Gaussian Prime, Associative Law, More Exercises, Chinese Remainder Theorem, Fermat's Theorem, Cauchy's Formula, Pythagorean Equation, Galois Correspondence, Main Theorem, Erlanger Programm Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
unique factorization theorem, four squares theorem, nonidentity rotation, same minimum polynomial, constructible numbers, finite skew field, casus irreducibilis, splitting field, degree vector, elementary symmetric polynomials, cyclotomic polynomial, little theorem Key Phrases - Capitalized Phrases (CAPs): (learn more)
Lagrange's Theorem, Division Algorithm, Euclid's Lemma, Cancellation Law, Factor Theorem, Euclidean Algorithm, Fundamental Theorem of Algebra, Fermat's Last Theorem, Cauchy's Theorem, Commutative Law, Fermat's Little Theorem, Exercises Let, Euler's Theorem, Well-Ordering Principle, Binomial Theorem, Gaussian Prime, Associative Law, More Exercises, Chinese Remainder Theorem, Fermat's Theorem, Cauchy's Formula, Pythagorean Equation, Galois Correspondence, Main Theorem, Erlanger Programm Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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