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This textbook, for an undergraduate course in modern algebraic geometry, recognizes that the typical undergraduate curriculum contains a great deal of analysis and, by contrast, little algebra. Because of this imbalance, it seems most natural to present algebraic geometry by highlighting the way it connects algebra and analysis; the average student will probably be more familiar and more comfortable with the analytic component. The book therefore focuses on Serre's GAGA theorem, which perhaps best encapsulates the link between algebra and analysis. GAGA provides the unifying theme of the book: we develop enough of the modern machinery of algebraic geometry to be able to give an essentially complete proof, at a level accessible to undergraduates throughout. The book is based on a course which the author has taught, twice, at the Australian National University.

Geometry, Algebraic --- Geometry, Analytic --- Géométrie algébrique --- Géométrie analytique --- Géométrie algébrique --- Géométrie analytique --- Geometry, Algebraic. --- Geometry, Analytic. --- Analytical geometry --- Algebra --- Conic sections --- Algebraic geometry --- Geometry --- Graphic methods

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In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic methods have also given rise to some exciting new applications of algebraic geometry. This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications of Gröbner bases and resultants. The book is written for nonspecialists and for readers with a diverse range of backgrounds. It assumes knowledge of the material covered in a standard undergraduate course in abstract algebra, and it would help to have some previous exposure to Gröbner bases. The book does not assume the reader is familiar with more advanced concepts such as modules. For the new edition, the authors have added a unified discussion of how matrices can be used to specify monomial orders; a revised presentation of the Mora normal form algorithm; two sections discussing the Gröbner fan of an ideal and the Gröbner Walk basis conversion algorithm; and a new chapter on the theory of order domains, associated codes, and the Berlekamp-Massey-Sakata decoding algorithm. They have also updated the references, improved some of the proofs, and corrected typographical errors. David Cox is Professor of Mathematics at Amherst College. John Little is Professor of Mathematics at College of the Holy Cross. Dona l O’Shea is the Elizabeth T. Kennan Professor of Mathematics and Dean of Faculty at Mt. Holyoke College. These authors also co-wrote the immensely successful book, Ideals, Varieties, and Algorithms.

Geometry, Algebraic. --- Géométrie algébrique --- Geometry, Algebraic --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- Géométrie algébrique --- EPUB-LIV-FT LIVMATHE SPRINGER-B --- Algebraic geometry --- Mathematics. --- Computer science --- Algebraic geometry. --- Algorithms. --- Algebraic Geometry. --- Symbolic and Algebraic Manipulation. --- Geometry, algebraic. --- Algebra --- Data processing. --- Algorism --- Arithmetic --- Foundations --- Computer science—Mathematics. --- Computer mathematics --- Electronic data processing

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D-module theory is essentially the algebraic study of systems of linear partial differential equations. This book, the first devoted specifically to holonomic D-modules, provides a unified treatment of both regular and irregular D-modules. The authors begin by recalling the main results of the theory of indsheaves and subanalytic sheaves, explaining in detail the operations on D-modules and their tempered holomorphic solutions. As an application, they obtain the Riemann-Hilbert correspondence for regular holonomic D-modules. In the second part of the book the authors do the same for the sheaf of enhanced tempered solutions of (not necessarily regular) holonomic D-modules. Originating from a series of lectures given at the Institut des Hautes Études Scientifiques in Paris, this book is addressed to graduate students and researchers familiar with the language of sheaves and D-modules, in the derived sense.

D-modules. --- Modules (Algebra) --- Sheaf theory. --- Geometry, Algebraic. --- Algebraic geometry --- Geometry --- Cohomology, Sheaf --- Sheaf cohomology --- Sheaves, Theory of --- Sheaves (Algebraic topology) --- Algebraic topology --- Finite number systems --- Modular systems (Algebra) --- Algebra --- Finite groups --- Rings (Algebra) --- D-modules, Théorie des. --- Modules (algèbre) --- Faisceaux, Théorie des. --- Géométrie algébrique.

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Not long ago, conducting child assessment was as simple as stating that "the child gets along with others" or "the child lags behind his peers." Today’s pediatric psychologists and allied professionals, by contrast, know the critical importance of using accurate measures with high predictive quality to identify pathologies early, form precise case conceptualizations, and provide relevant treatment options. Assessing Childhood Psychopathology and Developmental Disabilities provides a wide range of evidence-based methods in an immediately useful presentation from infancy through adolescence. Noted experts offer the most up-to-date findings in the most pressing areas, including: Emerging trends, new technologies, and implementation issues. Interviewing techniques and report writing guidelines. Intelligence testing, neuropsychological assessment, and scaling methods for measuring psychopathology. Assessment of major pathologies, including ADHD, conduct disorder, bipolar disorder, and depression. Developmental disabilities, such as academic problems, the autism spectrum and comorbid pathology, and self-injury. Behavioral medicine, including eating and feeding disorders as well as pain management. This comprehensive volume is an essential resource for the researcher’s library and the clinician’s desk as well as a dependable text for graduate and postgraduate courses in clinical child, developmental, and school psychology. (A companion volume, Treating Childhood Psychopathology and Developmental Disabilities, is also available to ensure greater continuity on the road from assessment to intervention to outcome.).

Child psychopathology. --- Children with mental disabilities -- Mental health. --- Developmentally disabled children -- Mental health. --- Geometry, Algebraic --- Mathematical Theory --- Pediatrics --- Geometry --- Medicine --- Mathematics --- Health & Biological Sciences --- Physical Sciences & Mathematics --- Congresses --- Children with mental disabilities --- Developmentally disabled children --- Child psychiatry. --- Mental health. --- Children --- Pediatric psychiatry --- Psychiatry, Child --- Children with developmental disabilities --- Mentally handicapped children --- Mentally retarded children --- Retarded children --- Mental illness in children --- Psychopathology, Child --- Psychopathology in children --- Mental disorders --- Dislocations in crystals. --- G-structures. --- Psychology. --- Psychiatry. --- Education. --- Child psychology. --- School psychology. --- Child and School Psychology. --- Education, general. --- 514.7 --- 514.7 Differential geometry. Algebraic and analytic methods in geometry --- Differential geometry. Algebraic and analytic methods in geometry --- 512 --- 512 Algebra --- Algebra --- Algebraic geometry --- Mathematical distribution theory --- Mathematical physics --- Differential geometry. Global analysis --- Mechanical properties of solids --- Child mental health services --- Pediatric neurology --- Psychiatry --- Child mental health --- Child psychology --- Child psychopathology --- Children with disabilities --- Child development deviations --- Youth with mental disabilities --- Psychology, Pathological --- Child psychiatry --- Congresses. --- Geometry, Differential. --- Géométrie algébrique --- Developmental psychology. --- Development (Psychology) --- Developmental psychobiology --- Psychology --- Life cycle, Human --- Medicine and psychology --- Mental health --- Education, Primitive --- Education of children --- Human resource development --- Instruction --- Pedagogy --- Schooling --- Students --- Youth --- Civilization --- Learning and scholarship --- Mental discipline --- Schools --- Teaching --- Training --- Psychology, School --- Psychology, Applied --- Behavior, Child --- Child behavior --- Child study --- Pediatric psychology --- Child development --- Developmental psychology --- Education --- Géometrie différentielle globale --- Mécanique --- Géométrie algébrique --- Géometrie différentielle globale --- Mécanique --- Micromecanique