Topology Through Inquiry

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Topology Through Inquiry

Author : Michael Starbird
Publisher : American Mathematical Soc.
ISBN 13 : 1470462613
Total Pages : 313 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Topology Through Inquiry by : Michael Starbird

Download or read book Topology Through Inquiry written by Michael Starbird and published by American Mathematical Soc.. This book was released on 2020-09-10 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology Through Inquiry is a comprehensive introduction to point-set, algebraic, and geometric topology, designed to support inquiry-based learning (IBL) courses for upper-division undergraduate or beginning graduate students. The book presents an enormous amount of topology, allowing an instructor to choose which topics to treat. The point-set material contains many interesting topics well beyond the basic core, including continua and metrizability. Geometric and algebraic topology topics include the classification of 2-manifolds, the fundamental group, covering spaces, and homology (simplicial and singular). A unique feature of the introduction to homology is to convey a clear geometric motivation by starting with mod 2 coefficients. The authors are acknowledged masters of IBL-style teaching. This book gives students joy-filled, manageable challenges that incrementally develop their knowledge and skills. The exposition includes insightful framing of fruitful points of view as well as advice on effective thinking and learning. The text presumes only a modest level of mathematical maturity to begin, but students who work their way through this text will grow from mathematics students into mathematicians. Michael Starbird is a University of Texas Distinguished Teaching Professor of Mathematics. Among his works are two other co-authored books in the Mathematical Association of America's (MAA) Textbook series. Francis Su is the Benediktsson-Karwa Professor of Mathematics at Harvey Mudd College and a past president of the MAA. Both authors are award-winning teachers, including each having received the MAA's Haimo Award for distinguished teaching. Starbird and Su are, jointly and individually, on lifelong missions to make learning—of mathematics and beyond—joyful, effective, and available to everyone. This book invites topology students and teachers to join in the adventure.

Topology Through Inquiry

Author : Michael Starbird
Publisher : American Mathematical Soc.
ISBN 13 : 1470452766
Total Pages : 330 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Topology Through Inquiry by : Michael Starbird

Download or read book Topology Through Inquiry written by Michael Starbird and published by American Mathematical Soc.. This book was released on 2019-11-08 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology Through Inquiry is a comprehensive introduction to point-set, algebraic, and geometric topology, designed to support inquiry-based learning (IBL) courses for upper-division undergraduate or beginning graduate students. The book presents an enormous amount of topology, allowing an instructor to choose which topics to treat. The point-set material contains many interesting topics well beyond the basic core, including continua and metrizability. Geometric and algebraic topology topics include the classification of 2-manifolds, the fundamental group, covering spaces, and homology (simplicial and singular). A unique feature of the introduction to homology is to convey a clear geometric motivation by starting with mod 2 coefficients. The authors are acknowledged masters of IBL-style teaching. This book gives students joy-filled, manageable challenges that incrementally develop their knowledge and skills. The exposition includes insightful framing of fruitful points of view as well as advice on effective thinking and learning. The text presumes only a modest level of mathematical maturity to begin, but students who work their way through this text will grow from mathematics students into mathematicians. Michael Starbird is a University of Texas Distinguished Teaching Professor of Mathematics. Among his works are two other co-authored books in the Mathematical Association of America's (MAA) Textbook series. Francis Su is the Benediktsson-Karwa Professor of Mathematics at Harvey Mudd College and a past president of the MAA. Both authors are award-winning teachers, including each having received the MAA's Haimo Award for distinguished teaching. Starbird and Su are, jointly and individually, on lifelong missions to make learning—of mathematics and beyond—joyful, effective, and available to everyone. This book invites topology students and teachers to join in the adventure.

Number Theory Through Inquiry

Author : David C. Marshall
Publisher : American Mathematical Soc.
ISBN 13 : 1470461595
Total Pages : 140 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Number Theory Through Inquiry by : David C. Marshall

Download or read book Number Theory Through Inquiry written by David C. Marshall and published by American Mathematical Soc.. This book was released on 2020-08-21 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number Theory Through Inquiry is an innovative textbook that leads students on a carefully guided discovery of introductory number theory. The book has two equally significant goals. One goal is to help students develop mathematical thinking skills, particularly, theorem-proving skills. The other goal is to help students understand some of the wonderfully rich ideas in the mathematical study of numbers. This book is appropriate for a proof transitions course, for an independent study experience, or for a course designed as an introduction to abstract mathematics. Math or related majors, future teachers, and students or adults interested in exploring mathematical ideas on their own will enjoy Number Theory Through Inquiry. Number theory is the perfect topic for an introduction-to-proofs course. Every college student is familiar with basic properties of numbers, and yet the exploration of those familiar numbers leads us to a rich landscape of ideas. Number Theory Through Inquiry contains a carefully arranged sequence of challenges that lead students to discover ideas about numbers and to discover methods of proof on their own. It is designed to be used with an instructional technique variously called guided discovery or Modified Moore Method or Inquiry Based Learning (IBL). Instructors' materials explain the instructional method. This style of instruction gives students a totally different experience compared to a standard lecture course. Here is the effect of this experience: Students learn to think independently: they learn to depend on their own reasoning to determine right from wrong; and they develop the central, important ideas of introductory number theory on their own. From that experience, they learn that they can personally create important ideas, and they develop an attitude of personal reliance and a sense that they can think effectively about difficult problems. These goals are fundamental to the educational enterprise within and beyond mathematics.

Mathematics for Human Flourishing

Author : Francis Su
Publisher : Yale University Press
ISBN 13 : 0300237138
Total Pages : 287 pages
Book Rating : 4.3/5 (2 download)

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Book Synopsis Mathematics for Human Flourishing by : Francis Su

Download or read book Mathematics for Human Flourishing written by Francis Su and published by Yale University Press. This book was released on 2020-01-07 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them."--Kevin Hartnett, Quanta Magazine" This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart."--James Tanton, Global Math Project For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires--such as for play, beauty, freedom, justice, and love--and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can--and must--be open to all.

Heidegger's Topology

Author : Jeff Malpas
Publisher : MIT Press
ISBN 13 : 0262250330
Total Pages : 425 pages
Book Rating : 4.2/5 (622 download)

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Book Synopsis Heidegger's Topology by : Jeff Malpas

Download or read book Heidegger's Topology written by Jeff Malpas and published by MIT Press. This book was released on 2008-08-29 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This groundbreaking inquiry into the centrality of place in Martin Heidegger's thinking offers not only an illuminating reading of Heidegger's thought but a detailed investigation into the way in which the concept of place relates to core philosophical issues. In Heidegger's Topology, Jeff Malpas argues that an engagement with place, explicit in Heidegger's later work, informs Heidegger's thought as a whole. What guides Heidegger's thinking, Malpas writes, is a conception of philosophy's starting point: our finding ourselves already "there," situated in the world, in "place". Heidegger's concepts of being and place, he argues, are inextricably bound together. Malpas follows the development of Heidegger's topology through three stages: the early period of the 1910s and 1920s, through Being and Time, centered on the "meaning of being"; the middle period of the 1930s into the 1940s, centered on the "truth of being"; and the late period from the mid-1940s on, when the "place of being" comes to the fore. (Malpas also challenges the widely repeated arguments that link Heidegger's notions of place and belonging to his entanglement with Nazism.) The significance of Heidegger as a thinker of place, Malpas claims, lies not only in Heidegger's own investigations but also in the way that spatial and topographic thinking has flowed from Heidegger's work into that of other key thinkers of the past 60 years.

Elementary Topology

Author : O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov
Publisher : American Mathematical Soc.
ISBN 13 : 9780821886250
Total Pages : 432 pages
Book Rating : 4.8/5 (862 download)

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Book Synopsis Elementary Topology by : O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov

Download or read book Elementary Topology written by O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov and published by American Mathematical Soc.. This book was released on with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment. Proofs of theorems are separated from their formulations and are gathered at the end of each chapter, making this book appear like a problem book and also giving it appeal to the expert as a handbook. The book includes about 1,000 exercises.

Topologies of the Flesh

Author : Steven M. Rosen
Publisher : Ohio University Press
ISBN 13 : 0821416766
Total Pages : 361 pages
Book Rating : 4.8/5 (214 download)

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Book Synopsis Topologies of the Flesh by : Steven M. Rosen

Download or read book Topologies of the Flesh written by Steven M. Rosen and published by Ohio University Press. This book was released on 2006 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an unprecedented marriage of topology (a branch of mathematics dealing with the properties of geometric figures that stay the same when the figures are distorted) and phenomenology. Through his unique application of qualitative mathematics, Rosen offers a detailed exploration of previously uncharted dimensions of human experience and the natural world.

Distilling Ideas

Author : Brian P. Katz
Publisher : MAA
ISBN 13 : 1939512034
Total Pages : 189 pages
Book Rating : 4.9/5 (395 download)

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Book Synopsis Distilling Ideas by : Brian P. Katz

Download or read book Distilling Ideas written by Brian P. Katz and published by MAA. This book was released on 2013 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction -- Graphs -- Groups -- Calculus -- Conclusion.

Topology

Author : Tai-Danae Bradley
Publisher : MIT Press
ISBN 13 : 0262359626
Total Pages : 167 pages
Book Rating : 4.2/5 (623 download)

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Book Synopsis Topology by : Tai-Danae Bradley

Download or read book Topology written by Tai-Danae Bradley and published by MIT Press. This book was released on 2020-08-18 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-level textbook that presents basic topology from the perspective of category theory. This graduate-level textbook on topology takes a unique approach: it reintroduces basic, point-set topology from a more modern, categorical perspective. Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them. Teaching the subject using category theory--a contemporary branch of mathematics that provides a way to represent abstract concepts--both deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.

Dimensions of Apeiron

Author : Steven M. Rosen
Publisher : BRILL
ISBN 13 : 9401210217
Total Pages : 262 pages
Book Rating : 4.4/5 (12 download)

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Book Synopsis Dimensions of Apeiron by : Steven M. Rosen

Download or read book Dimensions of Apeiron written by Steven M. Rosen and published by BRILL. This book was released on 2004-01-01 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the evolution of space and time from the apeiron —the spaceless, timeless chaos of primordial nature. Rosen examines Western culture’s effort to deny apeiron, and the critical need now to lift the repression on apeiron for the sake of human individuation.

Calculus I: A Guided Inquiry

Author : Andrei Straumanis
Publisher : Wiley
ISBN 13 : 9781118877487
Total Pages : 0 pages
Book Rating : 4.8/5 (774 download)

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Book Synopsis Calculus I: A Guided Inquiry by : Andrei Straumanis

Download or read book Calculus I: A Guided Inquiry written by Andrei Straumanis and published by Wiley. This book was released on 2014-07-21 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students learn when they are activity engaged and thinking in class. The activities in this book are the primary classroom materials for teaching Calculus 1, using the POGIL method. Each activity leads students to discovery of the key concepts by having them analyze data and make inferences. The result is an I can do this attitude, increased retention, and a feeling of ownership over the material.

Topology of Violence

Author : Byung-Chul Han
Publisher : MIT Press
ISBN 13 : 0262534959
Total Pages : 167 pages
Book Rating : 4.2/5 (625 download)

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Book Synopsis Topology of Violence by : Byung-Chul Han

Download or read book Topology of Violence written by Byung-Chul Han and published by MIT Press. This book was released on 2018-04-20 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of today's most widely read philosophers considers the shift in violence from visible to invisible, from negativity to excess of positivity. Some things never disappear—violence, for example. Violence is ubiquitous and incessant but protean, varying its outward form according to the social constellation at hand. In Topology of Violence, the philosopher Byung-Chul Han considers the shift in violence from the visible to the invisible, from the frontal to the viral to the self-inflicted, from brute force to mediated force, from the real to the virtual. Violence, Han tells us, has gone from the negative—explosive, massive, and martial—to the positive, wielded without enmity or domination. This, he says, creates the false impression that violence has disappeared. Anonymized, desubjectified, systemic, violence conceals itself because it has become one with society. Han first investigates the macro-physical manifestations of violence, which take the form of negativity—developing from the tension between self and other, interior and exterior, friend and enemy. These manifestations include the archaic violence of sacrifice and blood, the mythical violence of jealous and vengeful gods, the deadly violence of the sovereign, the merciless violence of torture, the bloodless violence of the gas chamber, the viral violence of terrorism, and the verbal violence of hurtful language. He then examines the violence of positivity—the expression of an excess of positivity—which manifests itself as over-achievement, over-production, over-communication, hyper-attention, and hyperactivity. The violence of positivity, Han warns, could be even more disastrous than that of negativity. Infection, invasion, and infiltration have given way to infarction.

Discovering Dynamical Systems Through Experiment and Inquiry

Author : Thomas Lofaro
Publisher : CRC Press
ISBN 13 : 9780367713768
Total Pages : 0 pages
Book Rating : 4.7/5 (137 download)

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Book Synopsis Discovering Dynamical Systems Through Experiment and Inquiry by : Thomas Lofaro

Download or read book Discovering Dynamical Systems Through Experiment and Inquiry written by Thomas Lofaro and published by CRC Press. This book was released on 2024-08-26 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book differs from most texts on the topic by blending the use of computer simulations with inquiry-based learning (IBL). Students can discover examples and counterexamples through manipulations built into the software though a link to the website.

An Inquiry Into Modes of Existence

Author : Bruno Latour
Publisher : Harvard University Press
ISBN 13 : 0674728556
Total Pages : 519 pages
Book Rating : 4.6/5 (747 download)

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Book Synopsis An Inquiry Into Modes of Existence by : Bruno Latour

Download or read book An Inquiry Into Modes of Existence written by Bruno Latour and published by Harvard University Press. This book was released on 2013-08-19 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a new approach to philosophical anthropology, Bruno Latour offers answers to questions raised in We Have Never Been Modern: If not modern, what have we been, and what values should we inherit? An Inquiry into Modes of Existence offers a new basis for diplomatic encounters with other societies at a time of ecological crisis.

The Joy of X

Author : Steven Henry Strogatz
Publisher : Houghton Mifflin Harcourt
ISBN 13 : 0547517653
Total Pages : 333 pages
Book Rating : 4.5/5 (475 download)

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Book Synopsis The Joy of X by : Steven Henry Strogatz

Download or read book The Joy of X written by Steven Henry Strogatz and published by Houghton Mifflin Harcourt. This book was released on 2012 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: A delightful tour of the greatest ideas of math, showing how math intersects with philosophy, science, art, business, current events, and everyday life, by an acclaimed science communicator and regular contributor to the "New York Times."

A Mathematical Gift, III

Author : Koji Shiga
Publisher : American Mathematical Society
ISBN 13 : 9780821832844
Total Pages : 148 pages
Book Rating : 4.8/5 (328 download)

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Book Synopsis A Mathematical Gift, III by : Koji Shiga

Download or read book A Mathematical Gift, III written by Koji Shiga and published by American Mathematical Society. This book was released on 2005-07-18 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings the beauty and fun of mathematics to the classroom. It offers serious mathematics in a lively, reader-friendly style. Included are exercises and many figures illustrating the main concepts. The first chapter talks about the theory of manifolds. It includes discussion of smoothness, differentiability, and analyticity, the idea of local coordinates and coordinate transformation, and a detailed explanation of the Whitney imbedding theorem (both in weak and in strong form).The second chapter discusses the notion of the area of a figure on the plane and the volume of a solid body in space. It includes the proof of the Bolyai-Gerwien theorem about scissors-congruent polynomials and Dehn's solution of the Third Hilbert Problem. This is the third volume originating from a series of lectures given at Kyoto University (Japan). It is suitable for classroom use for high school mathematics teachers and for undergraduate mathematics courses in the sciences and liberal arts. The first and second volumes are available as Volume 19 and Volume 20 in the AMS series, ""Mathematical World"".

Tools of the Trade

Author : Paul J. Sally (Jr.)
Publisher : American Mathematical Soc.
ISBN 13 : 0821846345
Total Pages : 210 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Tools of the Trade by : Paul J. Sally (Jr.)

Download or read book Tools of the Trade written by Paul J. Sally (Jr.) and published by American Mathematical Soc.. This book was released on 2008 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book provides a transition from the formula-full aspects of the beginning study of college level mathematics to the rich and creative world of more advanced topics. It is designed to assist the student in mastering the techniques of analysis and proof that are required to do mathematics." "Along with the standard material such as linear algebra, construction of the real numbers via Cauchy sequences, metric spaces and complete metric spaces, there are three projects at the end of each chapter that form an integral part of the text. These projects include a detailed discussion of topics such as group theory, convergence of infinite series, decimal expansions of real numbers, point set topology and topological groups. They are carefully designed to guide the student through the subject matter. Together with numerous exercises included in the book, these projects may be used as part of the regular classroom presentation, as self-study projects for students, or for Inquiry Based Learning activities presented by the students."--BOOK JACKET.