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Undergraduate Algebra is a text for the standard undergraduate algebra course. It concentrates on the basic structures and results of algebra, discussing groups, rings, modules, fields, polynomials, finite fields, Galois Theory, and other topics. The author has also included a chapter on groups of matrices which is unique in a book at this level. Throughout the book, the author strikes a balance between abstraction and concrete results, which enhance each other. Illustrative examples accompany the general theory. Numerous exercises range from the computational to the theoretical, complementing results from the main text. For the third edition, the author has included new material on product structure for matrices (e.g. the Iwasawa and polar decompositions), as well as a description of the conjugation representation of the diagonal group. He has also added material on polynomials, culminating in Noah Snyder’s proof of the Mason-Stothers polynomial abc theorem. About the First Edition: The exposition is down-to-earth and at the same time very smooth. The book can be covered easily in a one-year course and can be also used in a one-term course...the flavor of modern mathematics is sprinkled here and there. - Hideyuki Matsumura, Zentralblatt.

Algebra. --- Mathematics --- Mathematical analysis --- Field theory (Physics). --- Field Theory and Polynomials. --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics

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Mathematics --- Mathématiques --- #TELE:SISTA --- Math --- Science --- Mathematics. --- Mathématiques

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Complex analysis --- Algebraic geometry --- Number theory --- Elliptic functions --- 517.58 --- #WWIS:d.d. Prof. L. Bouckaert/ALTO --- Elliptic integrals --- Functions, Elliptic --- Integrals, Elliptic --- Transcendental functions --- Functions of complex variables --- Integrals, Hyperelliptic --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- 517.58 Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials --- Nombres, Théorie des --- Modular functions. --- Fonctions modulaires --- Number theory. --- Nombres, Théories des --- Geometrie algebrique --- Fonctions elliptiques --- Formes automorphes --- Varietes abeliennes

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Complex analysis --- 517.53 --- Functions of complex variables --- Mathematical analysis --- Advanced calculus --- Analysis (Mathematics) --- Algebra --- Complex variables --- Elliptic functions --- Functions of real variables --- Functions of a complex variable --- Functions of complex variables. --- Mathematical analysis. --- 517.1 Mathematical analysis --- 517.53 Functions of a complex variable --- 517.1. --- 517.1 --- Fonctions d'une variable complexe

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Number theory --- 511.5 --- Diophantine equations --- Diophantine analysis. --- Curves, Elliptic. --- 511.5 Diophantine equations --- Diophantine analysis --- Curves, Elliptic --- Analyse diophantienne --- Courbes elliptiques --- Approximation diophantienne