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Making Mathematics Come to Life

Making Mathematics Come to Life

Author: Oleg A. Ivanov

Publisher: American Mathematical Soc.

ISBN: 9780821848081

Category: Mathematics

Page: 337

View: 138

``It is difficult to define the genre of the book. It is not a problem book, nor a textbook, nor a `book for reading about mathematics'. It is most of all reminiscent of a good lecture course, from which a thoughtful student comes away with more than was actually spoken about in the lectures.'' --from the Preface by A. S. Merkurjev If you are acquainted with mathematics at least to the extent of a standard high school curriculum and like it enough to want to learn more, and if, in addition, you are prepared to do some serious work, then you should start studying this book. An understanding of the material of the book requires neither a developed ability to reason abstractly nor skill in using the refined techniques of mathematical analysis. In each chapter elementary problems are considered, accompanied by theoretical material directly related to them. There are over 300 problems in the book, most of which are intended to be solved by the reader. In those places in the book where it is natural to introduce concepts outside the high school syllabus, the corresponding definitions are given with examples. And in order to bring out the meaning of such concepts clearly, appropriate (but not too many) theorems are proved concerning them. Unfortunately, what is sometimes studied at school under the name ``mathematics'' resembles real mathematics not any closer than a plucked flower gathering dust in a herbarium or pressed between the pages of a book resembles that same flower in the meadow besprinkled with dewdrops sparkling in the light of the rising sun.
Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being
Language: en
Pages: 492

Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being

Authors: George Lakoff, Rafael E. Nunez
Categories: Mathematics
Type: BOOK - Published: 2000-11-02 - Publisher:

Provides an in-depth analysis of the cognitive science of mathematical ideas that argues that conceptual metaphor plays a definitive role in mathematical ideas, exploring such concepts as arithmetic, algebra, sets, logic, and infinity. 20,000 first printing.
Mathematics Under the Microscope
Language: en
Pages: 317

Mathematics Under the Microscope

Authors: Alexandre Borovik
Categories: Mathematics
Type: BOOK - Published: 2010 - Publisher: American Mathematical Soc.

The author's goal is to start a dialogue between mathematicians and cognitive scientists. He discusses, from a working mathematician's point of view, the mystery of mathematical intuition: why are certain mathematical concepts more intuitive than others? To what extent does the ``small scale'' structure of mathematical concepts and algorithms reflect
Curriculum 21
Language: en
Pages: 254

Curriculum 21

Authors: Heidi Hayes Jacobs
Categories: Education
Type: BOOK - Published: 2010-01-05 - Publisher: ASCD

“What year are you preparing your students for? 1973? 1995? Can you honestly say that your school’s curriculum and the program you use are preparing your students for 2015 or 2020? Are you even preparing them for today?” With those provocative questions, author and educator Heidi Hayes Jacobs launches a
Sociology, Science, and the End of Philosophy
Language: en
Pages: 370

Sociology, Science, and the End of Philosophy

Authors: Sal Restivo
Categories: Social Science
Type: BOOK - Published: 2017-07-06 - Publisher: Springer

This book offers a unique analysis of how ideas about science and technology in the public and scientific imaginations (in particular about maths, logic, the gene, the brain, god, and robots) perpetuate the false reality that values and politics are separate from scientific knowledge and its applications. These ideas are
Foundations of Geometric Cognition
Language: en
Pages: 188

Foundations of Geometric Cognition

Authors: Mateusz Hohol
Categories: Psychology
Type: BOOK - Published: 2019-09-12 - Publisher: Routledge

The cognitive foundations of geometry have puzzled academics for a long time, and even today are mostly unknown to many scholars, including mathematical cognition researchers. Foundations of Geometric Cognition shows that basic geometric skills are deeply hardwired in the visuospatial cognitive capacities of our brains, namely spatial navigation and object

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