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Handbook of Analysis and Its Foundations
Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory a...
Classical and Nonclassical Logics
So-called classical logic--the logic developed in the early twentieth century by Gottlob Frege, Bertrand Russell, and others--is computationally the simplest of the major logics, and it is adequate for the needs of most mathematicians. But it is just one of the many kinds of reasoning in everyday thought. Consequently, when presented by itself--as in most introductory texts on logic--it seems arbitrary and unnatural to students new to the subject. In Classical and Nonclassical Logics, Eric Schechter introduces classical logic alongside constructive, relevant, comparative, and other nonclassical logics. Such logics have been investigated for decades in research journals and advanced books, bu...
Classical and Nonclassical Logics
Classical logic is traditionally introduced by itself, but that makes it seem arbitrary and unnatural. This text introduces classical alongside several nonclassical logics (relevant, constructive, quantative, paraconsistent).
777 Mathematical Conversation Starters
Illustrated book showing that there are few degrees of separation between mathematics and topics that provoke interesting conversations.
Tennessee Topology Conference
Contents:Endomorphism Properties of Algebraic Structures (M E Adams et al.)Alternate Methods for Generating Interaction Semigroups (G R Barnes et al.)Separate vs. Joint Continuity: A Tale of Four Topologies — A Summary (M Henriksen)Cardinal Functions on Continuous Images (I Juhász)A Survey of Topological Nearrings and Nearrings of Continuous Functions (K D Magill, Jr.)Ordered Quotients and the Semi-Lattice of Ordered Compactifications (D D Mooney & T A Richmond)Various Topologies on Trees (P J Nyikos)Backward Shifts on Banach Spaces C(X), II (M Rajagopalan & K Sundaresan)and other papers Readership: Mathematicians.
Semantics of the Probabilistic Typed Lambda Calculus
This book takes a foundational approach to the semantics of probabilistic programming. It elaborates a rigorous Markov chain semantics for the probabilistic typed lambda calculus, which is the typed lambda calculus with recursion plus probabilistic choice. The book starts with a recapitulation of the basic mathematical tools needed throughout the book, in particular Markov chains, graph theory and domain theory, and also explores the topic of inductive definitions. It then defines the syntax and establishes the Markov chain semantics of the probabilistic lambda calculus and, furthermore, both a graph and a tree semantics. Based on that, it investigates the termination behavior of probabilistic programs. It introduces the notions of termination degree, bounded termination and path stoppability and investigates their mutual relationships. Lastly, it defines a denotational semantics of the probabilistic lambda calculus, based on continuous functions over probability distributions as domains. The work mostly appeals to researchers in theoretical computer science focusing on probabilistic programming, randomized algorithms, or programming language theory.
Computable Foundations for Economics
Computable Foundations for Economics is a unified collection of essays, some of which are published here for the first time and all of which have been updated for this book, on an approach to economic theory from the point of view of algorithmic mathematics. By algorithmic mathematics the author means computability theory and constructive mathematics. This is in contrast to orthodox mathematical economics and game theory, which are formalised with the mathematics of real analysis, underpinned by what is called the ZFC formalism, i.e., set theory with the axiom of choice. This reliance on ordinary real analysis and the ZFC system makes economic theory in its current mathematical mode complete...
Lectures on the Curry-Howard Isomorphism
The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance,minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc.The isomorphism has many aspects, even at the syntactic level:formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to term reduction, etc.But there is more to the isomorphism than this. For instance,...
The Jigsaw Assassin
Selei City is the capital of the Imerialte and one of the most desired locales in all of the Skolian Empire. But its thin veneer of civilization is cracked when a series of brutal crimes implicates those in political power in a vast conspiracy. Three prominent scientists have lost their lives to a serial killer—and notes at the scenes of the crimes lead to a connection to the Royalist political party. Major Bhaajan, former military officer turned private detective, is called back to Selei City to solve the crime. Bhaaj and her crew of Undercity Dust Knights plunge into the Byzantine world of Imperial politics—a jigsaw world where none of the pieces seem to fit. As the assassination plot ...
