Topology
Topology

Author: Marco Manetti

Publisher: Springer

Published: 2015-06-19

Total Pages: 315

ISBN-13: 3319169580

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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.

Borges and Mathematics
Borges and Mathematics

Author: Guillermo Martínez

Publisher:

Published: 2012

Total Pages: 140

ISBN-13: 9781612492520

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Borges and Mathematics is a short book of essays that explores the scientific thinking of the Argentine writer Jorge Luis Borges (1899-1986). Around half of the book consists of two "lectures" focused on mathematics. The rest of the book reflects on the relationship between literature, artistic creation, physics, and mathematics more generally. Written in a way that will be accessible even to those "who can only count to ten," the book presents a bravura demonstration of the intricate links between the worlds of sciences and arts, and it is a thought-provoking call to dialog for readers from both traditions. The author, Guillermo Mart nez, is both a recognized writer, whose murder mystery The Oxford Murders has been translated into thirty-five languages, and a PhD in mathematics. Contents: Borges and Mathematics: First Lecture; Borges and Mathematics: Second Lecture; The Golem and Artificial Intelligence; The Short Story as Logical System; A Margin Too Narrow; Euclid, or the Aesthetics of Mathematical Reasoning; Solutions and Disillusions; The Pythagorean Twins; The Music of Chance (Interview with Gregory Chaikin); Literature and Rationality; Who's Afraid of the Big Bad One?; A Small, Small God; God's Sinkhole. This book was originally published in Spanish as Borges y la matem tica (2003). It has been translated with generous support from the Latino Cultural Center at Purdue University.

Peano
Peano

Author: H. Kennedy

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 238

ISBN-13: 9400989849

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All students of mathematics know of Peano's postulates for the natural numbers and his famous space-filling curve, yet their knowledge often stops there. Part of the reason is that there has not until now been a full-scale study of his life and works. This must surely be surprising, when one realizes the length of his academic career (over 50 years) and the extent of his publica tions (over 200) in a wide variety of fields, many of which had immediate and long-term effects on the development of modern mathematics. A study of his life seems long overdue. It appeared to me that the most likely person to write a biography of Peano would be his devoted disciple Ugo Cassina, with whom I studied at the University of Milan in 1957-58. I wrote to Professor Cassina on 29 October, 1963, inquiring if he planned to write the biography, and I offered him my assistance, since I hoped to return to Italy for a year. He replied on 28 November, 1963, suggesting that we collaborate, meaning by this that I would write the biography, in English, using his material and advice. I gladly agreed to this suggestion, but work on the project had hardly begun when Professor Cassina died unexpectedly on 5 October, 1964. I then decided to continue the project on my own. I spent the academic year 1966-67 in Turin; completion of the book took ten years.

Author:

Publisher: Bib. Orton IICA / CATIE

Published:

Total Pages: 130

ISBN-13:

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Teaching the Content Areas to English Language Learners in Secondary Schools
Teaching the Content Areas to English Language Learners in Secondary Schools

Author: Luciana C. de Oliveira

Publisher: Springer

Published: 2019-01-17

Total Pages: 334

ISBN-13: 3030022455

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This practitioner-based book provides different approaches for reaching an increasing population in today’s schools - English language learners (ELLs). The recent development and adoption of the Common Core State Standards for English Language Arts and Literacy in History/Social Studies, Science, and Technical Subjects (CCSS-ELA/Literacy), the Common Core State Standards for Mathematics, the C3 Framework, and the Next Generation Science Standards (NGSS) highlight the role that teachers have in developing discipline-specific competencies. This requires new and innovative approaches for teaching the content areas to all students. The book begins with an introduction that contextualizes the chapters in which the editors highlight transdisciplinary theories and approaches that cut across content areas. In addition, the editors include a table that provides a matrix of how strategies and theories map across the chapters. The four sections of the book represent the following content areas: English language arts, mathematics, science, and social studies. This book offers practical guidance that is grounded in relevant theory and research and offers teachers suggestions on how to use the approaches described.

Maths for Social Sciences
Maths for Social Sciences

Author: Lorenzo Peccati

Publisher: Springer

Published: 2018-12-28

Total Pages: 353

ISBN-13: 3030023362

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This book is aimed at students in social sciences programs that include some course in quantitative methods. Stats for social sciences is frequently the subject of textbooks, while maths for social sciences is often neglected: monographs on specific themes (like, for instance, social choice systems or game theory applications) are available, but they do not adequately cover the topic in general. This textbook stems from the Bocconi University’s new "Bachelor in Government", which was launched in 2015, and is intended for undergraduate students who do not exclude maths from their toolbox. It discusses various concrete applications in political economics, political science, sociology, and demography and explores topics like Grexit, Macron’s success, immigration effects and the Arab Spring.