University of Toronto Mathematics Competition 2001 2015

Author: Edward J. Barbeau
Publisher: Springer
ISBN: 3319281062
Format: PDF, Kindle
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This text records the problems given for the first 15 annual undergraduate mathematics competitions, held in March each year since 2001 at the University of Toronto. Problems cover areas of single-variable differential and integral calculus, linear algebra, advanced algebra, analytic geometry, combinatorics, basic group theory, and number theory. The problems of the competitions are given in chronological order as presented to the students. The solutions appear in subsequent chapters according to subject matter. Appendices recall some background material and list the names of students who did well. The University of Toronto Undergraduate Competition was founded to provide additional competition experience for undergraduates preparing for the Putnam competition, and is particularly useful for the freshman or sophomore undergraduate. Lecturers, instructors, and coaches for mathematics competitions will find this presentation useful. Many of the problems are of intermediate difficulty and relate to the first two years of the undergraduate curriculum. The problems presented may be particularly useful for regular class assignments. Moreover, this text contains problems that lie outside the regular syllabus and may interest students who are eager to learn beyond the classroom.

Exploring Mathematics

Author: John Meier
Publisher: Cambridge University Press
ISBN: 1108509282
Format: PDF, ePub, Docs
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Exploring Mathematics gives students experience with doing mathematics - interrogating mathematical claims, exploring definitions, forming conjectures, attempting proofs, and presenting results - and engages them with examples, exercises, and projects that pique their interest. Written with a minimal number of pre-requisites, this text can be used by college students in their first and second years of study, and by independent readers who want an accessible introduction to theoretical mathematics. Core topics include proof techniques, sets, functions, relations, and cardinality, with selected additional topics that provide many possibilities for further exploration. With a problem-based approach to investigating the material, students develop interesting examples and theorems through numerous exercises and projects. In-text exercises, with complete solutions or robust hints included in an appendix, help students explore and master the topics being presented. The end-of-chapter exercises and projects provide students with opportunities to confirm their understanding of core material, learn new concepts, and develop mathematical creativity.

ARNOLD

Author: Boris A. Khesin
Publisher: American Mathematical Society
ISBN: 1470416999
Format: PDF, Kindle
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Vladimir Arnold, an eminent mathematician of our time, is known both for his mathematical results, which are many and prominent, and for his strong opinions, often expressed in an uncompromising and provoking manner. His dictum that "Mathematics is a part of physics where experiments are cheap" is well known. This book consists of two parts: selected articles by and an interview with Vladimir Arnold, and a collection of articles about him written by his friends, colleagues, and students. The book is generously illustrated by a large collection of photographs, some never before published. The book presents many a facet of this extraordinary mathematician and man, from his mathematical discoveries to his daredevil outdoor adventures.

Proof and Proving in Mathematics Education

Author: Gila Hanna
Publisher: Springer Science & Business Media
ISBN: 9400721293
Format: PDF, ePub
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One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.

Wandering Towards a Goal

Author: Anthony Aguirre
Publisher: Springer
ISBN: 3319757261
Format: PDF, ePub
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This collection of prize-winning essays addresses the controversial question of how meaning and goals can emerge in a physical world governed by mathematical laws. What are the prerequisites for a system to have goals? What makes a physical process into a signal? Does eliminating the homunculus solve the problem? The three first-prize winners, Larissa Albantakis, Carlo Rovelli and Jochen Szangolies tackle exactly these challenges, while many other aspects (agency, the role of the observer, causality versus teleology, ghosts in the machine etc.) feature in the other award winning contributions. All contributions are accessible to non-specialists. These seventeen stimulating and often entertaining essays are enhanced versions of the prize-winning entries to the FQXi essay competition in 2017.The Foundational Questions Institute, FQXi, catalyzes, supports, and disseminates research on questions at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality, but unlikely to be supported by conventional funding sources.

Edusemiotics A Handbook

Author: Inna Semetsky
Publisher: Springer
ISBN: 9811014957
Format: PDF, ePub, Mobi
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Edusemiotics is a pioneering area of study that connects semiotics – the science of signs – with educational theory and the philosophy of education. This volume reflects cutting-edge research by scholars in education and in semiotics worldwide, bridging the two discourses to present the state of the art in this new transdisciplinary field. The book’s emphasis is on educational theory as based on semiotic philosophy: as such, it challenges the current conception of semiotics in education as merely a sub-branch of applied semiotics. It presents edusemiotics as a novel unified conceptual framework at the interface of theoretical semiotics and educational philosophy, based on both theoretical and empirical studies from around the world. The chapters in this handbook also bring to the fore the intellectual legacy of Charles S. Peirce, John Dewey, Gilles Deleuze, Umberto Eco, Julia Kristeva, Mikhail Bakhtin, Paul Ricoeur, Martin Heidegger and other thinkers, pointing out the implications of edusemiotics for meaningful pedagogy and experiential learning in diverse contexts.

Social Theory

Author: Roberta Garner
Publisher: University of Toronto Press
ISBN: 1442606487
Format: PDF, Mobi
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The organization of this popular social theory reader, which pairs classical articles with contemporary theoretical and empirical studies, highlights the historical flow of social theory and demonstrates how disagreements and confrontations shape theory over time. Written in clear, down-to-earth language, the introductions to each selection link theorists to one another, illustrating how theoretical traditions are not rigidly separate but are always in conversation, addressing and challenging each other. The third edition incorporates significant changes: more readings reflecting a wide diversity of theorists, a completely revamped chapter on gender, new chapters on race and culture, and unique material on the "transitional giants" who have helped to transform classical theory into contemporary theory. As well, new contextual and biographical materials surround each reading and each chapter includes a study guide with key terms and innovative discussion questions and classroom exercises. The result is a fresh take on social theory that foregrounds a plurality of perspectives and reflects contemporary trends in the field, while still managing to be a teachable and affordable text.

Social Theory Volume I

Author: Roberta Garner
Publisher: University of Toronto Press
ISBN: 1442607351
Format: PDF, ePub
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The third edition of this popular reader reflects considerable changes. The framework for understanding theory as a set of conversations over time is maintained and deepened, pairing classical with contemporary readings to illustrate the ways in which theory continues to be reinterpreted over time. Volume I has been completely reorganized, with new contextual and biographical materials surrounding the primary readings, and end-of-chapter study guides that include key terms, discussion questions, and innovative classroom exercises. The result is a fresh and expansive take on social theory that foregrounds a plurality of perspectives and reflects contemporary trends in the field, while being an accessible and manageable teaching tool.

Second Order Elliptic Equations and Elliptic Systems

Author: Abba B. Gumel
Publisher: American Mathematical Soc.
ISBN: 0821898620
Format: PDF
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This volume contains the proceedings of the AMS Special Session on Nonstandard Finite-Difference Discretizations and Nonlinear Oscillations, in honor of Ronald Mickens's 70th birthday, held January 9-10, 2013, in San Diego, CA. Included are papers on design and analysis of discrete-time and continuous-time dynamical systems arising in the natural and engineering sciences, in particular, the design of robust nonstandard finite-difference methods for solving continuous-time ordinary and partial differential equation models, the analytical and numerical study of models that undergo nonlinear oscillations, as well as the design of deterministic and stochastic models for epidemiological and ecological processes. Some of the specific topics covered in the book include the analysis of deterministic and stochastic SIR-type models, the assessment of cost-effectiveness of vaccination problems, finite-difference methods for oscillatory dynamical systems (including the Schrödinger equation and Brusselator system), the design of exact and elementary stable finite-difference methods, the study of a two-patch model with Allee effects and disease-modified fitness, the study of the delay differential equation model with application to circadian rhythm and the application of some special functions in the solutions of some problems arising in the natural and engineering sciences. A notable feature of the book is the collection of some relevant open problems, intended to help guide the direction of future research in the area.