An Introduction To C*Algebras And Noncommutative Geometry (Birkhuser Advanced Texts Basler Lehrbcher)

This Is The First Textbook On C*-Algebra Theory With A View Toward Noncommutative Geometry. Moreover, It Fills A Gap In The Literature, Providing A Clear And Accessible Account Of The Geometric Picture Of K-Theory And Its Relation To The C*-Algebraic Picture. The Text Can Be Used As The Basis For A Graduate Level Or A Capstone Course With The Goal Being To Bring A Relative Novice Up To Speed On The Basic Ideas While Offering A Glimpse At Some Of The More Advanced Topics Of The Subject. Coverage Includes C*-Algebra Theory, K-Theory, K-Homology, Index Theory And Connes Noncommuntative Riemannian Geometry.Aimed At Graduate Level Students, The Book Is Also A Valuable Resource For Mathematicians Who Wish To Deepen Their Understanding Of Noncommutative Geometry And Algebraic K-Theory. A Wide Range Of Important Examples Are Introduced At The Beginning Of The Book. There Are Lots Of Excellent Exercises And Any Student Working Through These Will Benefit Significantly. Prerequisites Include A Basic Knowledge Of Algebra, Analysis, And A Bit Of Functional Analysis. As The Book Progresses, A Little More Mathematical Maturity Is Required As The Text Discusses Smooth Manifolds, Some Differential Geometry And Elliptic Operator Theory, And K-Theory. The Text Is Largely Self-Contained Though Occasionally The Reader May Opt To Consult More Specialized Material To Further Deepen Their Understanding Of Certain Details.