Some Modern Mathematics for Physicists and Other Outsiders: An Introduction to Algebra, Topology, and Functional Analysis.(2 Vo

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This is an outstanding book for learning functional analysis, especially if you are not a math major. Almost every other book is a distant second. Volume 1 contains two parts: (1) The Raw Materials of Mathematics (Sets, Maps), and (2) The Basic Structures of Mathematics (Algebraic Structures, Toplolgical Structures, Measure Structures). Obviously Part 2 is the bulk of Volume I. In Volume II, we have Part 3 of the book: Combination of Systems--Functional Analysis. The main chapters are Banach Spaces, Hilbert Spaces (falling under the heading Toplogical Linear Spaces) and Linear Functionals, Linear Operators, and Spectral Theory (falling under the heading Mappings of Toplogical Linear Spaces).












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