E-Book Overview
Recent advances in computing and algorithms make it easier to do many classical problems in algebra. Suitable for graduate students, this book brings advanced algebra to life with many examples. The first three chapters provide an introduction to commutative algebra and connections to geometry. The remainder of the book focuses on three active areas of contemporary algebra: homological algebra; algebraic combinatorics and algebraic topology; and algebraic geometry.
E-Book Content
COMPUTATIONAL ALGEBRAIC GEOMETRY LONDON MATHEMATICAL SOCIETY STUDENT TEXTS Managing editor: Professor J.W. Bruce, Department of Mathematics, University of Liverpool, UK 3 4 5 7 8 9 11 12 13 15 17 18 19 20 21 22 23 24 25 26 27 28 29 31 32 33 34 35 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 Local fields, J.W.S. CASSELS An introduction to twistor theory: Second edition, S.A. HUGGETT & K.P. TOD Introduction to general relativity, L.P. HUGHSTON & K.P. TOD The theory of evolution and dynamical systems, J. HOFBAUER & K. SIGMUND Summing and nuclear norms in Banach space theory, G.J.O. JAMESON Automorphisms of surfaces after Nielsen and Thurston, A. CASSON & S. BLEILER Spacetime and singularities, G. NABER Undergraduate algebraic geometry, MILES REID An introduction to Hankel operators, J.R. PARTINGTON Presentations of groups: Second edition, D.L. JOHNSON Aspects of quantum field theory in curved spacetime, S.A. FULLING Braids and coverings: Selected topics, VAGN LUNDSGAARD HANSEN Steps in commutative algebra, R.Y. SHARP Communication theory, C.M. GOLDIE & R.G.E. PINCH Representations of finite groups of Lie type, FRANC¸OIS DIGNE & JEAN MICHEL Designs, graphs, codes, and their links, P.J. CAMERON & J.H. VAN LINT Complex algebraic curves, FRANCES KIRWAN Lectures on elliptic curves, J.W.S. CASSELS Hyperbolic geometry, BIRGER IVERSEN An introduction to the theory of L-functions and