Topological Geometry

The Earlier Chapter Of This Self-contained Text Provide A Route From First Principles Through Standard Linear And Quadratic Algebra To Geometric Algebra, With Clifford's Geometric Algebras Taking Pride Of Place. In Parallel With This Is An Account, Also From First Principles, Of The Elementary Theory Of Topological Spaces And Of Continuous And Differentiable Maps That Leads Up To The Definitions Of Smooth Manifolds And Their Tangent Spaces And Of Lie Groups And Lie Algebras. The Calculus Is Presented As Far As Possible In Basis Free Form To Emphasize Its Geometrical Flavour And Its Linear Algebra Content. In This Second Edition Dr Porteous Has Taken The Opportunity To Add A Chapter On Triality Which Extends Earlier Work On The Spin Groups In The Chapter On Clifford Algebras. The Details Include A Number Of Important Transitive Group Actions And A Description Of One Of The Exceptional Lie Groups, The Group G2. A Number Of Corrections And Improvements Have Also Been Made. There Are Many Exercises Throughout The Book And Senior Undergraduates In Mathematics As Well As First-year Graduate Students Will Continue To Find It Stimulating And Rewarding. Ian R. Porteous. Includes Index. Bibliography: P. 463-466. FOREWORD CH 0 - GUIDE CH 1 - MAPS CH 2 - REAL AND COMPLEX NUMBERS CH 3 - LINEAR SPACES CH 4 - AFFINE SPACES CH 5 - QUOTIENT STRUCTURES CH 6 - FINITE-DIMENSIONAL SPACES CH 7 - DETERMINANTS CH 8 - DIRECT SUM CH 9 - ORTHOGONAL SPACES CH 10 - QuATERNIONS CH 11 - CORRELATIONS CH 12 - QUADRIC GRASSMANNIANS CH 13 - CLIFFORD ALGEBRAS CH 14 - THE CAYLEY ALGEBRA CH 15 - NORMED LINEAR SPACES CH 16 - TOPOLOGICAL SPACES CH 17 - TOPOLOGICAL GROUPS AND MANIFOLDS CH 18 - AFFINE APPROXIMATION CH 19 - THE INVERSE FUNCTION THEOREM CH 20 - SMOOTH MANIFOLDS CH 21 - TRIALITY BIBLIOGRAPHY LIST OF SYMBOLS INDEX Provides a route from first principles through standard linear and quadratic algebra to geometric algebra, with Clifford's geometric algebras taking pride of place.