Understanding Mathematics

Foundations of mathematics L. Brian Lawrence Department of Mathematics George Mason University Fairfax, VA 220304444 U.S.A. e air: blawrenc@mail.gmu.edu January 1, 2007 prolusion This set of notes is an outline of the concepts, structures, and theorems that serve as the vertex of vent for Mathematical Physics. The notes are intended to be utilise in conjunction with a companion volume authorize: Foundations riddle Set . Contents Introduction 3 I. logical system and Set Theory 1. muster in of the Language of Mathematics 4 2. Dynamic (Transformation) Viewpoint of the lead ideal 6 3. Stationary (Graph) Viewpoint of the Function Concept 9 4. transitive verb form Binary Relations 11 5. Cardinality 13 II. historical and heterogeneous Number Systems Algebra 1. Function Composition and refilling Groups 16 2. commutat ive Rings with Multiplicative Identity 18 3. handle 20 4. Fields of characteristic Zero 22 Structure of the Real Number System 5. fiated Fields 23 6. OrderComplete Ordered Fields 25 Structure of the interlocking Number System 7. Algebraically unlikeable Fields of Characteristic Zero 27 1 III. Convergence Concepts 1. Topological Spaces 28 2. metric function Spaces 32 3.

Operators on Topological Spaces 35 4. Alternative Characterizations of Topological Spaces 39 5. inciden tal Convergence 40 6. Compactness! 44 7. tie 46 8. Cauchy Completeness in Metric Spaces 47 IV. Mapping Concepts 1. nonstop Functions 49 2. Uniform Continuity 52 V. Analysis 1. section of simple-minded RealValued Functions of One Real uncertain 53 2. Limits and Continuity 58 3. Differentiation 59 4. desegregation 60 5. Theorems on Continuous Functions 62 6. Theorems on differentiable Functions 63 7. Retrospectus...If you want to get a full essay, entrap it on our website: OrderCustomPaper.com

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