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This textbook covers topics of undergraduate mathematics in abstract algebra, geometry, topology and analysis with the purpose of connecting the underpinning key ideas. It guides STEM students towards developing knowledge and skills to enrich their scientific education. In doing so it avoids the common mechanical approach to problem-solving based on the repetitive application of dry formulas. The presentation preserves the mathematical rigour throughout and still stays accessible to undergraduates. The didactical focus is threaded through the assortment of subjects and reflects in the book's structure. Part 1 introduces the mathematical language and its rules together with the basic building blocks. Part 2 discusses the number systems of common practice, while the backgrounds needed to solve equations and inequalities are developed in Part 3. Part 4 breaks down the traditional, outdated barriers between areas, exploring in particular the interplay between algebra and geometry. Two appendices form Part 5: the Greek etymology of frequent terms and a list of mathematicians mentioned in the book. Abundant examples and exercises are disseminated along the text to boost the learning process and allow for independent work. Students will find invaluable material to shepherd them through the first years of an undergraduate course, or to complement previously learnt subject matters. Teachers may pick'n'mix the contents for planning lecture courses or supplementing their classes.

Mathematical logic --- Algebra --- Topology --- Geometry --- Discrete mathematics --- algebra --- lineaire algebra --- discrete wiskunde --- wiskunde --- logica --- geometrie --- topologie

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Simulating the behavior of a human heart, predicting tomorrow's weather, optimizing the aerodynamics of a sailboat, finding the ideal cooking time for a hamburger: to solve these problems, cardiologists, meteorologists, sportsmen, and engineers can count on math help. This book will lead you to the discovery of a magical world, made up of equations, in which a huge variety of important problems for our life can find useful answers.

Computer science. --- Models matemàtics --- Algorismes --- Informatics --- Science --- Algorisme d'Euclides --- Algoritmes --- Àlgebra --- Algorismes computacionals --- Algorismes genètics --- Anàlisi numèrica --- Funcions recursives --- Programació (Matemàtica) --- Programació (Ordinadors) --- Teoria de màquines --- Traducció automàtica --- Models (Matemàtica) --- Models experimentals --- Models teòrics --- Mètodes de simulació --- Anàlisi de sistemes --- Mètode de Montecarlo --- Modelització multiescala --- Models economètrics --- Models lineals (Estadística) --- Models multinivell (Estadística) --- Models no lineals (Estadística) --- Simulació per ordinador --- Models biològics --- Mathematical models. --- Algorithms. --- Mathematics --- Numerical analysis. --- Epidemiology. --- Mathematical Modeling and Industrial Mathematics. --- Computational Science and Engineering. --- Numerical Analysis. --- Computational Mathematics and Numerical Analysis. --- Data processing. --- Diseases --- Public health --- Mathematical analysis --- Algorism --- Algebra --- Arithmetic --- Models, Mathematical --- Simulation methods --- Foundations

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In this book we describe the magic world of mathematical models: starting from real-life problems, we formulate them in terms of equations, transform equations into algorithms and algorithms into programs to be executed on computers. A broad variety of examples and exercises illustrate that properly designed models can, e.g.: predict the way the number of dolphins in the Aeolian Sea will change as food availability and fishing activity vary; describe the blood flow in a capillary network; calculate the PageRank of websites. This book also includes a chapter with an elementary introduction to Octave, an open-source programming language widely used in the scientific community. Octave functions and scripts for dealing with the problems presented in the text can be downloaded from https://paola-gervasio.unibs.it/quarteroni-gervasio This book is addressed to any student interested in learning how to construct and apply mathematical models.

Mathematical analysis. --- Analysis (Mathematics). --- Applied mathematics. --- Engineering mathematics. --- Mathematical models. --- Analysis. --- Applications of Mathematics. --- Mathematical Modeling and Industrial Mathematics. --- Models, Mathematical --- Simulation methods --- Engineering --- Engineering analysis --- Mathematical analysis --- 517.1 Mathematical analysis --- Mathematics

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The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.

Mathematics. --- Algebraic geometry. --- Topological groups. --- Lie groups. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Differential geometry. --- Topological Groups, Lie Groups. --- Differential Geometry. --- Global Analysis and Analysis on Manifolds. --- Algebraic Geometry. --- Geometry, Differential. --- Differential geometry --- Topological Groups. --- Global differential geometry. --- Global analysis. --- Geometry, algebraic. --- Algebraic geometry --- Geometry --- Geometry, Differential --- Groups, Topological --- Continuous groups --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups