The most comprehensive guide to the Spanish language takes you from beginner level through to conversational fluency! This complete Spanish language program is a special 2-in-1 book, containing the bestselling The Ultimate Spanish 101 plus a second-semester program, Spanish 201, based on The Ultimate Spanish Review and Practice. It covers everything required for basic conversational proficiency, from vocabulary and grammatical structures to audio exercises and drills to ensure proper pronunciation in speaking. Organized into 24 chapters (representing two semesters of study), The Complete Ultimate Spanish provides hundreds of short dialogues presenting new vocabulary and grammatical structures in context; grammar summaries providing explanations of how the Spanish language functions; and numerous exercises ensuring grammar and vocabulary are mastered through practical situations. Go from beginner to fluency with The Complete Ultimate Spanish, featuring: 2-books-in-1: The Ultimate Spanish 101, plus a second-semester program, Spanish 201, based on the authors' bestselling The Ultimate Spanish Review and Practice Program support from the McGraw-Hill Language Lab app, which includes extensive streaming audio recordings online (via web and app) Additional online support includes flashcards for all the vocabulary in the book, with audio for pronunciation help, audio exercises and drills, a digital glossary for quick reference, and diagnostic test to ensure the material has been mastered

This volume is the first of three in a series surveying the theory of theta functions. Based on lectures given by the author at the Tata Institute of Fundamental Research in Bombay, these volumes constitute a systematic exposition of theta functions, beginning with their historical roots as analytic functions in one variable (Volume I), touching on some of the beautiful ways they can be used to describe moduli spaces (Volume II), and culminating in a methodical comparison of theta functions in analysis, algebraic geometry, and representation theory (Volume III).

This ACM volume deals with tackling problems that can be represented by data structures which are essentially matrices with polynomial entries, mediated by the disciplines of commutative algebra and algebraic geometry. The discoveries stem from an interdisciplinary branch of research which has been growing steadily over the past decade. The author covers a wide range, from showing how to obtain deep heuristics in a computation of a ring, a module or a morphism, to developing means of solving nonlinear systems of equations - highlighting the use of advanced techniques to bring down the cost of computation. Although intended for advanced students and researchers with interests both in algebra and computation, many parts may be read by anyone with a basic abstract algebra course.

The second in a series of three volumes surveying the theory of theta functions, this volume gives emphasis to the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the Korteweg-de-Vries equations as well as other non-linear differential equations of mathematical physics. This book presents an explicit elementary construction of hyperelliptic Jacobian varieties and is a self-contained introduction to the theory of the Jacobians. It also ties together nineteenth-century discoveries due to Jacobi, Neumann, and Frobenius with recent discoveries of Gelfand, McKean, Moser, John Fay, and others. A definitive body of information and research on the subject of theta functions, this volume will be a useful addition to the individual and mathematics research libraries.