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The Mathematical Expanse

Author: Jason Vanbilliard

Publisher: CreateSpace

Published: 2014-08-15

Total Pages: 334

ISBN-13: 9781499795011

Transforms your perspective of mathematics!Extend your understanding of geometric topics by investigating dimensions, fractals, topological equivalence, and other geometries. Develop your reasoning skills through identifying deception in statistics, discriminating between cause and correlation, evaluating various voting methods, and exploring chaos theory. Refine your understanding of numbers and systems through studying prime, figurate, vampire, narcissistic, powerful, abundant, and transcendental numbers.[**Note: there are two versions of this book. Read below for more details.]After studying each mathematical topic, we will consider how the topic informs our answers to questions like: Who are we? What is the nature of reality? How do we know if something is true? What is good? What is beautiful? These questions and their related sub-questions have been part of the human experience from the dawn of human history. Considering how mathematics helps to inform these questions provides for a deeper, more meaningful understanding of mathematics. This book is ideal for:- Anyone interested in extending his or her own understanding of the scope and depth of mathematics- An undergraduate “Mathematics for Liberal Arts” course- A half-year high school senior mathematics elective for studentsEach section features:- Introductory exercises that prompt the reader to recall relevant information or skills- Concept development sections that explain the mathematics for even the math-phobic student- Content sections that connect the mathematics to literature, art, music, science, and other subjects- A “Something to Consider” section that asks the reader to think about related enduring questions- “Covering the Reading” questions that help to process the text- “Problems” that require the reader to research and consider the topic more thoroughly[**You may wish to consider the parallel book titled "Mathematical Explorations for the Christian Thinker." That book addresses the same enduring questions in mathematics but from an explicitly Christian perspective]

The Math You Need

Author: Thomas Mack

Publisher: MIT Press

Published: 2023-10-31

Total Pages: 497

ISBN-13: 0262375745

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A comprehensive survey of undergraduate mathematics, compressing four years of study into one robust overview. In The Math You Need, Thomas Mack provides a singular, comprehensive survey of undergraduate mathematics, compressing four years of math curricula into one volume. Without sacrificing rigor, this book provides a go-to resource for the essentials that any academic or professional needs. Each chapter is followed by numerous exercises to provide the reader an opportunity to practice what they learned. The Math You Need is distinguished in its use of the Bourbaki style—the gold standard for concision and an approach that mathematicians will find of particular interest. As ambitious as it is compact, this text embraces mathematical abstraction throughout, avoiding ad hoc computations in favor of general results. Covering nine areas—group theory, commutative algebra, linear algebra, topology, real analysis, complex analysis, number theory, probability, and statistics—this thorough and highly effective overview of the undergraduate curriculum will prove to be invaluable to students and instructors alike.

Mathematics for Machine Learning

Author: Marc Peter Deisenroth

Publisher: Cambridge University Press

Published: 2020-04-23

Total Pages: 392

ISBN-13: 1108569323

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The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.

Mathematical Excursions to the World's Great Buildings

Author: Alexander J. Hahn

Publisher: Princeton University Press

Published: 2012-07-22

Total Pages: 336

ISBN-13: 1400841992

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How mathematics helped build the world's most important buildings from early Egypt to the present From the pyramids and the Parthenon to the Sydney Opera House and the Bilbao Guggenheim, this book takes readers on an eye-opening tour of the mathematics behind some of the world's most spectacular buildings. Beautifully illustrated, the book explores the milestones in elementary mathematics that enliven the understanding of these buildings and combines this with an in-depth look at their aesthetics, history, and structure. Whether using trigonometry and vectors to explain why Gothic arches are structurally superior to Roman arches, or showing how simple ruler and compass constructions can produce sophisticated architectural details, Alexander Hahn describes the points at which elementary mathematics and architecture intersect. Beginning in prehistoric times, Hahn proceeds to guide readers through the Greek, Roman, Islamic, Romanesque, Gothic, Renaissance, and modern styles. He explores the unique features of the Pantheon, the Hagia Sophia, the Great Mosque of Cordoba, the Duomo in Florence, Palladio's villas, and Saint Peter's Basilica, as well as the U.S. Capitol Building. Hahn celebrates the forms and structures of architecture made possible by mathematical achievements from Greek geometry, the Hindu-Arabic number system, two- and three-dimensional coordinate geometry, and calculus. Along the way, Hahn introduces groundbreaking architects, including Brunelleschi, Alberti, da Vinci, Bramante, Michelangelo, della Porta, Wren, Gaudí, Saarinen, Utzon, and Gehry. Rich in detail, this book takes readers on an expedition around the globe, providing a deeper understanding of the mathematical forces at play in the world's most elegant buildings.

God and the Mathematics of Infinity

Author: H Chris Ransford

Publisher: BoD – Books on Demand

Published: 2017-03-30

Total Pages: 154

ISBN-13: 3838210190

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Drawing on incontrovertible results from the science and mathematics of Infinity, H. Chris Ransford analyzes the traditional concept of Godhood and reaches astonishing conclusions. He addresses humankind's abiding core debate on the meaning of spirituality and God. Using mathematics to explore key questions within this debate, the author is led to counter-intuitive conclusions, including some that had long baffled humanity: For instance, why does evil exist if there is a God? The book fastidiously does not take sides nor proffers opinions, it only follows allowable mathematics wherever it leads. By doing so, it makes a major contribution to an understanding of the nature of reality.

The Mathematics Playbook

Author: John Almarode

Publisher: Corwin Press

Published: 2024-03-05

Total Pages: 193

ISBN-13: 1071907662

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Your Guide to Engaging and Effective Math Instruction With the latest research on what works best in teaching and learning, The Mathematics Playbook is your comprehensive guide to enhancing mathematics teaching and learning. With a focus on fostering equity and maximizing student learning, the authors provide practical modules that integrate the latest research on effective teaching practices, and answer four critical questions: How do we foster, nurture, and sustain mathematics learning? How do we ensure all learners have equity of access and opportunity? What are the non-negotiables in a high-quality mathematics task? How do we know if learners really "get it"? Through real-life examples and an emphasis on self-assessment and reflection, this playbook empowers you to create engaging and impactful learning experiences in mathematics.

Chronergy Nexus

Author: Aditya Singh

Publisher: Aditya Singh

Published: 2023-08-13

Total Pages: 89

ISBN-13:

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In the vast expanse of cosmic exploration, a profound reimagining of the universe's origins and evolution beckons our intellectual curiosity. Within these pages unfolds a quest that transcends conventional boundaries, delving into the intricate interplay of time and energy that influences the very essence of existence. Anchored in Einstein's groundbreaking theory of relativity, this journey reveals a tapestry of revelations woven by the symphonic dynamics of fundamental forces. Central to this exploration is "The Trifold Temporal Paradigm," intricately weaving Forward Time, Backward Time, and Cyclic Time into a symphony of distinct patterns. Beyond theoretical discourse, this expedition illuminates the enigmatic genesis of the universe, its complex evolution, and the harmonious rhythm that echoes throughout cosmic epochs.

Mathematical Learning and Understanding in Education

Author: Kristie Newton

Publisher: Routledge

Published: 2018-05-16

Total Pages: 112

ISBN-13: 113498345X

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Mathematics holds an essential, ubiquitous presence in the education sector, as do ongoing explorations of its effective teaching and learning. Written by leading experts on mathematics and mathematics education, this book situates issues of student thinking and learning about mathematics within the broader context of educational psychology research and theory and brings them to a wider audience. With chapters on knowing and understanding mathematics, mathematical habits, early mathematical thinking, and learning mathematics, this concise volume is designed for any educational psychology, mathematics education, or general education course that includes student learning in the curriculum. It will be indispensable for student researchers and both pre- and in-service teachers alike.

Great Feuds in Mathematics

Author: Hal Hellman

Publisher: Turner Publishing Company

Published: 2010-12-17

Total Pages: 292

ISBN-13: 1118040112

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Praise for Hal Hellman Great Feuds in Mathematics "Those who think that mathematicians are cold, mechanical proving machines will do well to read Hellman's book on conflicts in mathematics. The main characters are as excitable and touchy as the next man. But Hellman's stories also show how scientific fights bring out sharper formulations and better arguments." -Professor Dirk van Dalen, Philosophy Department, Utrecht University Great Feuds in Technology "There's nothing like a good feud to grab your attention. And when it comes to describing the battle, Hal Hellman is a master." -New Scientist Great Feuds in Science "Unusual insight into the development of science . . . I was excited by this book and enthusiastically recommend it to general as well as scientific audiences." -American Scientist "Hellman has assembled a series of entertaining tales . . . many fine examples of heady invective without parallel in our time." -Nature Great Feuds in Medicine "This engaging book documents [the] reactions in ten of the most heated controversies and rivalries in medical history. . . . The disputes detailed are . . . fascinating. . . . It is delicious stuff here." -The New York Times "Stimulating." -Journal of the American Medical Association