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1. Números reales 2. Números complejos 3. Funciones 4. Funciones elementales más comunes 5. Límites 6. Derivadas 7. Integración 8. Álgebra. Matrices y determinantes 9. Introducción al espacio vectorial Rn y la geometría analítica. Bibliografía. Índice alfabético.
The book aims at showing the state-of-the-art in the field of modeling and applications in mathematics education. This is the first volume to do this. The book deals with the question of how key competencies of applications and modeling at the heart of mathematical literacy may be developed; with the roles that applications and modeling may play in mathematics teaching, making mathematics more relevant for students.
This volume examines how the history of mathematics can find application in the teaching of mathematics itself.
The aim of the book is to present a precise and comprehensive introduction to the basic theory of derived functors, with an emphasis on sheaf cohomology and spectral sequences. It keeps the treatment as simple as possible, aiming at the same time to provide a number of examples, mainly from sheaf theory, and also from algebra.The first part of the book provides the foundational material: Chapter 1 deals with category theory and homological algebra. Chapter 2 is devoted to the development of the theory of derived functors, based on the notion of injective object. In particular, the universal properties of derived functors are stressed, with a view to make the proofs in the following chapters as simple and natural as possible. Chapter 3 provides a rather thorough introduction to sheaves, in a general topological setting. Chapter 4 introduces sheaf cohomology as a derived functor, and, after also defining Čech cohomology, develops a careful comparison between the two cohomologies which is a detailed analysis not easily available in the literature. This comparison is made using general, universal properties of derived functors. This chapter also establishes the relations with the de Rham and Dolbeault cohomologies. Chapter 5 offers a friendly approach to the rather intricate theory of spectral sequences by means of the theory of derived triangles, which is precise and relatively easy to grasp. It also includes several examples of specific spectral sequences. Readers will find exercises throughout the text, with additional exercises included at the end of each chapter.
The book provides detailed descriptions, including more than 550 mathematical formulas, for more than 150 trading strategies across a host of asset classes and trading styles. These include stocks, options, fixed income, futures, ETFs, indexes, commodities, foreign exchange, convertibles, structured assets, volatility, real estate, distressed assets, cash, cryptocurrencies, weather, energy, inflation, global macro, infrastructure, and tax arbitrage. Some strategies are based on machine learning algorithms such as artificial neural networks, Bayes, and k-nearest neighbors. The book also includes source code for illustrating out-of-sample backtesting, around 2,000 bibliographic references, and more than 900 glossary, acronym and math definitions. The presentation is intended to be descriptive and pedagogical and of particular interest to finance practitioners, traders, researchers, academics, and business school and finance program students.
Ratio and Proportion—Research and Teaching in Mathematics Teachers’ Education offers its readers an intellectual adventure where they can acquire invaluable tools to turn teaching ratio and proportion to professionals and school children into an enjoyable experience. Based on in-depth research, it presents a deep, comprehensive view of the topic, focusing on both the mathematical and psychological-didactical aspects of teaching it. The unique teaching model incorporates both theoretical and practical knowledge, allowing instructors to custom-design teacher courses according to their speci?c needs. The book reports on hands-on experience in the college classes plus teachers’ experience in the actual classroom setting. An important feature is the extensive variety of interesting, meaningful authentic activities. While these activities are on a level that will engage pre- and in-service mathematics teachers in training, most can also be utilized in upper elementary and middle school classes. Accompanying the majority of these activities are detailed remarks, explanations, and solutions, along with creative ideas on how to conduct and expand the learning adventure. While primarily written for educators of mathematics teachers, this book can be an invaluable source of information for mathematics teachers of elementary and middle school classes, pre-service teachers, and mathematics education researchers.
A Deleuzian reading of Whitehead and a Whiteheadian reading of Deleuze open the possibility of a critical aesthetics of contemporary culture. In Without Criteria, Steven Shaviro proposes and explores a philosophical fantasy: imagine a world in which Alfred North Whitehead takes the place of Martin Heidegger. What if Whitehead, instead of Heidegger, had set the agenda for postmodern thought? Heidegger asks, “Why is there something, rather than nothing?” Whitehead asks, “How is it that there is always something new?” In a world where everything from popular music to DNA is being sampled and recombined, argues Shaviro, Whitehead's question is the truly urgent one. Without Criteria is Shaviro's experiment in rethinking postmodern theory, especially the theory of aesthetics, from a point of view that hearkens back to Whitehead rather than Heidegger. In working through the ideas of Whitehead and Deleuze, Shaviro also appeals to Kant, arguing that certain aspects of Kant's thought pave the way for the philosophical “constructivism” embraced by both Whitehead and Deleuze. Kant, Whitehead, and Deleuze are not commonly grouped together, but the juxtaposition of them in Without Criteria helps to shed light on a variety of issues that are of concern to contemporary art and media practices.