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Measures and integrals

Functional analysis. --- Geometry. --- Affine space. --- Axiom. --- C0. --- Combination. --- Commutative property. --- Complex number. --- Corollary. --- Countable set. --- Dimension (vector space). --- Dimension. --- Direct product. --- Discrete measure. --- Empty set. --- Euclidean space. --- Existential quantification. --- Finite set. --- Hilbert space. --- Infimum and supremum. --- Linear map. --- Linearity. --- Mutual exclusivity. --- Natural number. --- Ordinal number. --- Separable space. --- Sequence. --- Set (mathematics). --- Special case. --- Subset. --- Summation. --- Theorem. --- Theory. --- Transfinite induction. --- Transfinite. --- Unbounded operator. --- Variable (mathematics). --- Well-order. --- Well-ordering theorem.

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The description for this book, Convergence and Uniformity in Topology. (AM-2), Volume 2, will be forthcoming.

Topology. --- Absolute value. --- Abstract algebra. --- Algebraic topology. --- Axiom of choice. --- Binary relation. --- Cardinal number. --- Characteristic function (probability theory). --- Closed set. --- Closure operator. --- Combinatorial topology. --- Compact space. --- Complete lattice. --- Complete metric space. --- Continuous function (set theory). --- Continuous function. --- Countable set. --- Counterexample. --- Dimension theory (algebra). --- Dimension theory. --- Discrete space. --- Domain of a function. --- Empty set. --- Enumeration. --- Equivalence class. --- Equivalence relation. --- Existential quantification. --- Family of sets. --- Finite set. --- General topology. --- Geometry. --- Hahn–Banach theorem. --- Hausdorff space. --- Homeomorphism. --- Infimum and supremum. --- Integer. --- Interval (mathematics). --- Lebesgue constant (interpolation). --- Limit point. --- Linear space (geometry). --- Mathematician. --- Mathematics. --- Maximal element. --- Metric space. --- Monotonic function. --- Mutual exclusivity. --- Natural number. --- Negation. --- Normal space. --- Open set. --- Ordinal number. --- Real number. --- Regular space. --- Requirement. --- Scientific notation. --- Separation axiom. --- Set (mathematics). --- Set theory. --- Special case. --- Subsequence. --- Subset. --- Suggestion. --- Summation. --- Superspace. --- Theorem. --- Theory. --- Topological algebra. --- Total order. --- Transfinite induction. --- Transfinite number. --- Transfinite. --- Transitive relation. --- Tychonoff space. --- Ultrafilter. --- Uncountable set. --- Uniform continuity. --- Union (set theory). --- Upper and lower bounds. --- Zorn's lemma.

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The description for this book, Degrees of Unsolvability. (AM-55), Volume 55, will be forthcoming.

Recursive functions. --- Unsolvability (Mathematical logic) --- Addition. --- Aleph number. --- Algebraic topology. --- Approximation. --- Arithmetic function. --- Arithmetical set. --- Axiom of choice. --- Baire category theorem. --- Cardinality of the continuum. --- Cardinality. --- Cartesian product. --- Category theory. --- Commutative property. --- Conjecture. --- Continuum hypothesis. --- Contradiction. --- Corollary. --- Countable set. --- Disjoint union. --- Effective method. --- Empty set. --- Enumeration. --- Equation. --- Existence theorem. --- Existential quantification. --- Finite set. --- Fixed-point theorem. --- Fourier analysis. --- Fubini's theorem. --- Gödel numbering. --- Identity function. --- Inequality (mathematics). --- Infimum and supremum. --- Integer. --- Lebesgue measure. --- Limit of a sequence. --- Limit point. --- Mathematical induction. --- Mathematics. --- Mean of a function. --- Measure (mathematics). --- Metric space. --- Monotonic function. --- Mostowski. --- Mutual exclusivity. --- Natural number. --- Null set. --- Open set. --- Partial function. --- Partially ordered set. --- Predicate (mathematical logic). --- Product measure. --- Product topology. --- Real number. --- Recursion. --- Recursive set. --- Recursively enumerable set. --- Reductio ad absurdum. --- Regular space. --- Requirement. --- Scientific notation. --- Sequence. --- Set (mathematics). --- Simultaneous equations. --- Subset. --- Theorem. --- Topology. --- Transfinite induction. --- Tychonoff's theorem. --- Uncountable set. --- Union (set theory). --- Upper and lower bounds. --- Variable (mathematics). --- W0. --- Well-order. --- Without loss of generality. --- Zorn's lemma.

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This book is a spectacular introduction to the modern mathematical discipline known as the Theory of Games. Harold Kuhn first presented these lectures at Princeton University in 1952. They succinctly convey the essence of the theory, in part through the prism of the most exciting developments at its frontiers half a century ago. Kuhn devotes considerable space to topics that, while not strictly the subject matter of game theory, are firmly bound to it. These are taken mainly from the geometry of convex sets and the theory of probability distributions. The book opens by addressing "matrix games," a name first introduced in these lectures as an abbreviation for two-person, zero-sum games in normal form with a finite number of pure strategies. It continues with a treatment of games in extensive form, using a model introduced by the author in 1950 that quickly supplanted von Neumann and Morgenstern's cumbersome approach. A final section deals with games that have an infinite number of pure strategies for the two players. Throughout, the theory is generously illustrated with examples, and exercises test the reader's understanding. A historical note caps off each chapter. For readers familiar with the calculus and with elementary matrix theory or vector analysis, this book offers an indispensable store of vital insights on a subject whose importance has only grown with the years.

Operational research. Game theory --- Game theory --- 519.83 --- Theory of games --- 519.83 Theory of games --- Game theory. --- Games, Theory of --- Mathematical models --- Mathematics --- Abstract algebra. --- Addition. --- Algorithm. --- Almost surely. --- Analytic geometry. --- Axiom. --- Basic solution (linear programming). --- Big O notation. --- Bijection. --- Binary relation. --- Boundary (topology). --- Bounded set (topological vector space). --- Branch point. --- Calculation. --- Cardinality of the continuum. --- Cardinality. --- Cartesian coordinate system. --- Characteristic function (probability theory). --- Combination. --- Computation. --- Connectivity (graph theory). --- Constructive proof. --- Convex combination. --- Convex function. --- Convex hull. --- Convex set. --- Coordinate system. --- David Gale. --- Diagram (category theory). --- Differential equation. --- Dimension (vector space). --- Dimensional analysis. --- Disjoint sets. --- Distribution function. --- Embedding. --- Empty set. --- Enumeration. --- Equation. --- Equilibrium point. --- Equivalence relation. --- Estimation. --- Euclidean space. --- Existential quantification. --- Expected loss. --- Extreme point. --- Formal scheme. --- Fundamental theorem. --- Galois theory. --- Geometry. --- Hyperplane. --- Inequality (mathematics). --- Infimum and supremum. --- Integer. --- Iterative method. --- Line segment. --- Linear equation. --- Linear inequality. --- Matching Pennies. --- Mathematical induction. --- Mathematical optimization. --- Mathematical theory. --- Mathematician. --- Mathematics. --- Matrix (mathematics). --- Measure (mathematics). --- Min-max theorem. --- Minimum distance. --- Mutual exclusivity. --- Prediction. --- Probability distribution. --- Probability interpretations. --- Probability measure. --- Probability theory. --- Probability. --- Proof by contradiction. --- Quantity. --- Rank (linear algebra). --- Rational number. --- Real number. --- Requirement. --- Scientific notation. --- Sign (mathematics). --- Solution set. --- Special case. --- Statistics. --- Strategist. --- Strategy (game theory). --- Subset. --- Theorem. --- Theory of Games and Economic Behavior. --- Theory. --- Three-dimensional space (mathematics). --- Total order. --- Two-dimensional space. --- Union (set theory). --- Unit interval. --- Unit square. --- Vector Analysis. --- Vector calculus. --- Vector space.

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At the heart of human intelligence rests a fundamental puzzle: How are we incredibly smart and stupid at the same time? No existing machine can match the power and flexibility of human perception, language, and reasoning. Yet, we routinely commit errors that reveal the failures of our thought processes. 'What Makes Us Smart' makes sense of this paradox by arguing that our cognitive errors are not haphazard. Rather, they are the inevitable consequences of a brain optimized for efficient inference and decision making within the constraints of time, energy, and memory - in other words, data and resource limitations. Framing human intelligence in terms of these constraints, Samuel Gershman shows how a deeper computational logic underpins the 'stupid' errors of human cognition.

Cognition --- Cognitive psychology. --- Age factors. --- Psychology, Cognitive --- Cognitive science --- Psychology --- Age factors in cognition --- Ability, Influence of age on --- Cognition. --- Intellect. --- Human intelligence --- Intelligence --- Mind --- Ability --- Thought and thinking --- Accuracy and precision. --- Action potential. --- Ad hoc hypothesis. --- Ad hominem. --- Adaptive bias. --- Almost surely. --- Alternative hypothesis. --- Altruism. --- Ambiguity. --- Analogy. --- Anecdote. --- Approximation. --- Attractiveness. --- Bayes' theorem. --- Bayesian inference. --- Bayesian probability. --- Bayesian. --- Behavior. --- Circular reasoning. --- Cognitive flexibility. --- Cognitive style. --- Commitment device. --- Confidence. --- Confirmation bias. --- Conspiracy theory. --- Controllability. --- Counterintuitive. --- Credibility. --- Decision-making. --- Effectiveness. --- Efficacy. --- Efficiency. --- Efficient coding hypothesis. --- Efficient frontier. --- Estimation. --- Expected value. --- Explanation. --- Fair coin. --- Fair market value. --- Gimmick. --- Guessing. --- Heuristic. --- Hot Hand. --- Human intelligence. --- Hypothesis. --- Illusion of control. --- Inductive bias. --- Inference. --- Intelligent design. --- Learnability. --- Lightness (philosophy). --- Likelihood function. --- Logical extreme. --- Logical reasoning. --- Moral hazard. --- Motivated reasoning. --- Mutual exclusivity. --- Natural approach. --- Normative. --- Observation. --- Observational learning. --- Of Miracles. --- Opportunity cost. --- Optimism bias. --- Optimism. --- Our Choice. --- Pairwise comparison. --- Perfect rationality. --- Physical attractiveness. --- Point estimation. --- Politeness. --- Positive feedback. --- Predictability. --- Prediction. --- Predictive coding. --- Predictive power. --- Principle of rationality. --- Prior probability. --- Probability. --- Prosocial behavior. --- Quantity. --- Rational agent. --- Rational choice theory. --- Rationality. --- Reason. --- Reinforcement learning. --- Result. --- Self-control. --- Sophistication. --- Spontaneous recovery. --- Strong inference. --- Suggestion. --- Theory. --- Thought. --- Truth value. --- Uncertainty. --- Utility. --- Value of information. --- With high probability. --- PSYCHOLOGY / Cognitive Psychology & Cognition --- COMPUTERS / Logic Design