{"product_id":"advanced-algebra-9780817645229","title":"Advanced Algebra","description":"\u003cp\u003e • Author(s): Anthony W. Knapp\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Birkhauser\u003cbr\u003e • BISAC: Algebra - General\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom the Back Cover\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003cem\u003eBasic Algebra\u003c\/em\u003e and \u003cem\u003eAdvanced Algebra\u003c\/em\u003e systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole.\u003c\/p\u003e \u003cp\u003eKey topics and features of \u003cem\u003eAdvanced Algebra\u003c\/em\u003e: \u003c\/p\u003e \u003cp\u003e*Topics build upon the linear algebra, group theory, factorization of ideals, structure of fields, Galois theory, and elementary theory of modules as developed in \u003cem\u003eBasic Algebra\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e*Chapters treat various topics in commutative and noncommutative algebra, providing introductions to the theory of associative algebras, homological algebra, algebraic number theory, and algebraic geometry\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e*Sections in two chapters relate the theory to the subject of Gröbner bases, the foundation for handling systems of polynomial equations in computer applications\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e*Text emphasizes connections between algebra and other branches of mathematics, particularly topology and complex analysis\u003c\/p\u003e \u003cp\u003e*Book carries on two prominent themes recurring in \u003cem\u003eBasic Algebra\u003c\/em\u003e: the analogy between integers and polynomials in one variable over a field, and the relationship between number theory and geometry\u003c\/p\u003e \u003cp\u003e*Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems\u003c\/p\u003e \u003cp\u003e*The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them; it includes blocks of problems that illuminate aspects of the text and introduce additional topics\u003c\/p\u003e \u003cp\u003e\u003cem\u003eAdvanced Algebra\u003c\/em\u003e presents its subject matter in a forward-looking way that takes into account the historical development of the subject. It is suitable as a text for the more advanced parts of a two-semester first-year graduate sequence in algebra. It requires of the reader only a familiarity with the topics developed in \u003cem\u003eBasic Algebra\u003c\/em\u003e.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Hardcover","offer_id":45274019004567,"sku":"9780817645229","price":9460.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780817645229.webp?v=1769238451","url":"https:\/\/atlanticbooks.com\/products\/advanced-algebra-9780817645229","provider":"Atlantic Books","version":"1.0","type":"link"}