{"product_id":"algebraic-numbers-and-algebraic-functions-introductory-text","title":"Algebraic Numbers and Algebraic Functions - Introductory Text","description":"\u003cp\u003eIn this review of Algebraic Numbers and Algebraic Functions the bottom line is clear: this is a focused introductory text for readers who want a unified approach to algebraic number theory and function theory. Assuming only an undergraduate course in algebra and a little topology or complex function theory, the book's single biggest reason to buy is its coherent development using valuations, which presents both subjects with consistent methods and helps bridge to more advanced works. For a student or self-learner wanting conceptual clarity rather than encyclopedic coverage, this volume delivers.\u003c\/p\u003e\n\u003ch2\u003eKey Features\u003c\/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eUnified approach:\u003c\/strong\u003e The book develops both algebraic numbers and algebraic functions using the same valuation-based framework, making parallels between the two areas explicit.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eAccessible prerequisites:\u003c\/strong\u003e It requires only undergraduate algebra plus some topology and complex function theory, so motivated readers can follow the exposition without advanced background.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eNumber theory scope:\u003c\/strong\u003e The text treats central results such as the unit theorem and finiteness of the class number, giving a solid foundation in algebraic number theory.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eFunction theory aim:\u003c\/strong\u003e The treatment leads to the Abel-Jacobi theorem and an account of the divisor class group, useful for those interested in algebraic geometry connections.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eGeometrical asides:\u003c\/strong\u003e Occasional geometric comments aid intuition, helping readers see how abstract algebraic statements connect to geometry.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eWho It's For\u003c\/h2\u003e\n\u003cp\u003eThis book is best for advanced undergraduates, beginning graduate students, and self-directed learners who want a principled introduction to both algebraic number theory and algebraic function theory. It suits readers who appreciate a single coherent method - valuations - to link topics across number fields and function fields.\u003c\/p\u003e\n\u003cp\u003eThose seeking exhaustive reference tables, computational techniques, or a heavily example-driven primer may want a supplemental text focused on exercises and computations, since this work emphasizes conceptual development and theorems leading to further study in algebraic geometry or advanced number theory.\u003c\/p\u003e\n\u003ch2\u003ePros \u0026amp; Cons\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003ePros\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eClear unified method: valuations give a consistent viewpoint across two related subjects.\u003c\/li\u003e\n\u003cli\u003eConcise prerequisites: can be approached with standard undergraduate algebra and modest topology background.\u003c\/li\u003e\n\u003cli\u003eTargets key theorems: includes the unit theorem, finiteness of class number, and the Abel-Jacobi theorem for function theory.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eNot a problem-solution workbook: readers seeking many exercises or computational practice may need supplementary material.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eSpecifications\u003c\/h2\u003e\n\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003eTitle\u003c\/td\u003e\n\u003ctd\u003eAlgebraic Numbers and Algebraic Functions\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAuthor\u003c\/td\u003e\n\u003ctd\u003eP.M. Cohn\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSubject\u003c\/td\u003e\n\u003ctd\u003eAlgebraic number theory and algebraic function theory\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eApproach\u003c\/td\u003e\n\u003ctd\u003eValuations-based unified development\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePrerequisites\u003c\/td\u003e\n\u003ctd\u003eUndergraduate algebra; some topology and complex function theory\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eMain theorems\u003c\/td\u003e\n\u003ctd\u003eUnit theorem, finiteness of class number, Abel-Jacobi theorem\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n\u003ch2\u003eOur Verdict\u003c\/h2\u003e\n\u003cp\u003eAlgebraic Numbers and Algebraic Functions is a compact, principled introduction that pays off for readers who want conceptual unity and a clear path toward advanced texts in number theory or algebraic geometry. It represents strong value for students seeking a rigorous, valuation-centered treatment rather than a practice-heavy manual.\u003c\/p\u003e\n\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003eIs this suitable for self-study?\u003c\/strong\u003e\u003cbr\u003eThe book is suitable for self-study if you have undergraduate algebra and some familiarity with topology or complex functions; plan to use supplementary exercises if you need practice.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eDoes it cover class number theory?\u003c\/strong\u003e\u003cbr\u003eYes, the text develops number theory as far as the finiteness of the class number and includes the unit theorem.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eWill it help with algebraic geometry?\u003c\/strong\u003e\u003cbr\u003eYes, the treatment of algebraic functions and the Abel-Jacobi theorem, plus geometric asides, provides a foundation useful for later study in algebraic geometry.\u003c\/p\u003e","brand":"P.M. 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