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This volume explores A.P. Morse's (1911-1984) development of a formal language for writing mathematics, his application of that language in set theory and mathematical analysis, and his unique perspective on mathematics. The editor brings together a variety of Morse's works in this compilation, including Morse's book A Theory of Sets, Second Edition (1986), in addition to material from another of Morse's publications, Web Derivatives, and notes for a course on analysis from the early 1950's. Because Morse provided very little in the way of explanation in his written works, the editor's commentary serves to outline Morse's goals, give informal explanations of Morse's formal language, and compare Morse's often unique approaches to more traditional approaches. Minor corrections to Morse's previously published works have also been incorporated into the text, including some updated axioms, theorems, and definitions. The editor's introduction thoroughly details the corrections and changes made and provides readers with valuable insight on Morse's methods. A.P. Morse's Set Theory and Analysis will appeal to graduate students and researchers interested in set theory and analysis who also have an interest in logic. Readers with a particular interest in Morse's unique perspective and in the history of mathematics will also find this book to be of interest.
Mathematical logic --- Functional analysis --- Differential equations --- Mathematical analysis --- Mathematics --- Measuring methods in physics --- Mathematical physics --- History --- differentiaalvergelijkingen --- analyse (wiskunde) --- geschiedenis --- mathematische modellen --- meettechniek --- wiskunde --- logica --- Set theory. --- Logic, Symbolic and mathematical. --- Measure theory. --- Anàlisi matemàtica --- Teoria de conjunts
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Anàlisi matemàtica --- Teoria de conjunts --- Agregats (Matemàtica) --- Classes (Matemàtica) --- Conjunts (Matemàtica) --- Matemàtica --- Àlgebra de Boole --- Aritmètica --- Conjunts analítics --- Conjunts convexos --- Conjunts ordenats --- Espais mètrics --- Forcing (Teoria de models) --- Funcions --- Morfismes (Matemàtica) --- Nombres ordinals --- Teoria axiomàtica de conjunts --- Teoria combinatòria de conjunts --- Teoria dels reticles --- Teoria descriptiva de conjunts --- Topologia --- Lògica matemàtica --- Àlgebra lineal --- Anàlisi combinatòria --- Anàlisi de Fourier --- Anàlisi estocàstica --- Anàlisi matemàtica no-estàndard --- Anàlisi numèrica --- Matemàtica per a enginyers --- Sèries infinites --- Teoria del potencial (Matemàtica) --- Teories no lineals --- Rutes aleatòries (Matemàtica) --- Àlgebra --- Càlcul --- Set theory. --- Logic, Symbolic and mathematical. --- Measure theory. --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical
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