Sets for Mathematics
Cambridge University Press, Jan 27, 2003 - Mathematics - 261 pages
Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. For the first time, this book uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. Set theory as the algebra of mappings is introduced and developed as a unifying basis for advanced mathematical subjects such as algebra, geometry, analysis, and combinatorics. The formal study evolves from general axioms that express universal properties of sums, products, mapping sets, and natural number recursion.
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Amazon does have a Kindle version of this book; I'm looking at the sample chapter on my Android phone, trying both vertical and horizontal orientations; slightly jittery kerning but quite readable. The illustrations (a set is a wobbly bag of points! Mappings have arrows! Yay!) come through fine. Probably won't see any massive formulas in the first chapter.
Abstract Sets and Mappings
12 Listings Properties and Elements
13 Surjective and Injective Mappings
14 Associativity and Categories
15 Separators and the Empty Set
16 Generalized Elements
17 Mappings as Properties
18 Additional Exercises
62 Truth Values for TwoStage Variable Sets
63 Additional Exercises
Consequences and Uses of Exponentials
72 The Distributive Law
73 Cantors Diagonal Argument
74 Additional Exercises
More on Power Sets
82 The Covariant Power Set Functor
Sums Monomorphisms and Parts
22 Monomorphisms and Parts
23 Inclusion and Membership
24 Characteristic Functions
25 Inverse Image of a Part
26 Additional Exercises
Finite Inverse Limits
32 Isomorphism and Dedekind Finiteness
33 Cartesian Products and Graphs
36 Inverse Limits
37 Additional Exercises
Colimits Epimorphisms and the Axiom of Choice
42 Epimorphisms and Split Surjections
43 The Axiom of Choice
44 Partitions and Equivalence Relations
45 Split Images
46 The Axiom of Choice as the Distinguishing Property of ConstantRandom Sets
47 Additional Exercises
Mapping Sets and Exponentials
53 Functoriality of Function Spaces
54 Additional Exercises
Summary of the Axioms and an Example of Variable Sets
83 The Natural Map PX2˛ˣ
84 Measuring Averaging and Winning with VValued Quantities
85 Additional Exercises
Introduction to Variable Sets
93 Arithmetic of N
94 Additional Exercises
Models of Additional Variation
103 Reversible Graphs
104 Chaotic Graphs
105 Feedback and Control
106 To and from Idempotents
107 Additional Exercises
Logic as the Algebra of Parts
A1 Basic Operators and Their Rules of Inference
A2 Fields Nilpotents Idempotents
The Axiom of Choice and Maximal Principles
Definitions Symbols and the Greek Alphabet
C2 Mathematical Notations and Logical Symbols
C3 The Greek Alphabet
SETS FOR MATHEMATICS
SETS FOR MATHEMATICS. Advanced undergraduate or beginning graduate students need a unified ... Sets for mathematics / F. William Lawvere, Robert Rosebrugh. ...
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SETS FOR MATHEMATICS by F. WILLIAM LAWVERE AND ROBERT ROSEBRUGH
SETS FOR MATHEMATICS. F. William Lawvere Robert Rosebrugh. Published January 2003 by Cambridge University Press . ISBN: 0521010608 image of cover ...
www.mta.ca/ ~rrosebru/ setsformath/
SETS FOR MATHEMATICS
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