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This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises. The covered topics include: set theory and cardinal arithmetic; axiom of choice and Zorn's lemma; topological spaces and continuous functions; connectedness and compactness; Alexandrov compactification; quotient topologies; countability and separation axioms; prebasis and Alexander's theorem; the Tychonoff theorem and paracompactness; complete metric spaces and function spaces; Baire spaces; homotopy of maps; the fundamental group; the van Kampen theorem; covering spaces; Brouwer and Borsuk's theorems; free groups and free product of groups; and basic category theory. While it is very concrete at the beginning, abstract concepts are gradually introduced. It is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications.

Mathematics. --- Algebraic Topology. --- Mathematics, general. --- Algebraic topology. --- Mathématiques --- Topologie algébrique --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- Topology --- Math --- Science

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"This is a text that covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity. The goal is to slowly develop students' problem-solving and writing skills"--Provided by publisher.

Mathematics --- Computer science --- Informatique --- MATHEMATICS / General. --- Mathematics. --- Mathématiques --- Math --- Science --- Computer mathematics --- Electronic data processing --- Informatics

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Since 2001 the Scuola Normale Superiore di Pisa has organized the "Colloquio De Giorgi", a series of colloquium talks named after Ennio De Giorgi. The Colloquio is addressed to a general mathematical audience, and especially meant to attract graduate students and advanced undergraduate students. The lectures are intended to be not too technical, in fields of wide interest. They must provide an overview of the general topic, possibly in a historical perspective, together with a description of more recent progress. The idea of collecting the materials from these lectures and publishing them in annual volumes came out recently, as a recognition of their intrinsic mathematical interest, and also with the aim of preserving memory of these events.

Mathematics. --- Mathematics, general. --- Mathématiques --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Algebraic functions. --- Galois theory. --- Functions, Algebraic --- Equations, Theory of --- Group theory --- Number theory --- Functions --- Math --- Science

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The Whole Truth About Whole Numbers is an introduction to the field of Number Theory for students in non-math and non-science majors who have studied at least two years of high school algebra. Rather than giving brief introductions to a wide variety of topics, this book provides an in-depth introduction to the field of Number Theory. The topics covered are many of those included in an introductory Number Theory course for mathematics majors, but the presentation is carefully tailored to meet the needs of elementary education, liberal arts, and other non-mathematical majors. The text covers logic and proofs, as well as major concepts in Number Theory, and contains an abundance of worked examples and exercises to both clearly illustrate concepts and evaluate the students’ mastery of the material.

Mathematics. --- Number Theory. --- Numerical Analysis. --- Mathematics, general. --- Numerical analysis. --- Number theory. --- Mathématiques --- Analyse numérique --- Théorie des nombres --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Number study --- Numbers, Theory of --- Mathematical analysis --- Math --- Science

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This book gathers a selection of invited and contributed lectures from the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) held in Lausanne, Switzerland, August 26-30, 2013. It provides an overview of recent developments in numerical analysis, computational mathematics and applications from leading experts in the field. New results on finite element methods, multiscale methods, numerical linear algebra and discretization techniques for fluid mechanics and optics are presented. As such, the book offers a valuable resource for a wide range of readers looking for a state-of-the-art overview of advanced techniques, algorithms and results in numerical mathematics and scientific computing.

Mathematics. --- Computational Science and Engineering. --- Mathematical Modeling and Industrial Mathematics. --- Mathematical Software. --- Computer science. --- Computer software. --- Mathématiques --- Informatique --- Logiciels --- MATHEMATICS -- Numerical Analysis. --- Numerical analysis -- Congresses. --- Mathematics --- Physical Sciences & Mathematics --- Mathematics - General --- Numerical analysis --- Conferences - Meetings --- Computer science --- Computer mathematics. --- Mathematical models. --- Models, Mathematical --- Simulation methods --- Software, Computer --- Computer systems --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Math --- Science --- Informatics