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John Pell (1611-1685) and His Correspondence with Sir Charles Cavendish: The Mental World of an Early Modern Mathematician

Noel Malcolm and Jacqueline Stedall

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198564843
eISBN:
9780191713750
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198564843.001.0001
Subject:
Mathematics, History of Mathematics

The mathematician John Pell was a member of the Royal Society and one of the generation of scientists that included Boyle, Wren, and Hooke. Although he left a huge body of manuscript materials, he ... More


Using Perl to Do Calculations

Mark D. LeBlanc and Betsey Dexter Dyer

in Perl for Exploring DNA

Published in print:
2007
Published Online:
April 2010
ISBN:
9780195305890
eISBN:
9780199773862
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195305890.003.05
Subject:
Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies

This chapter elucidates some of the mysteries of calculating with Perl. Arithmetic in Perl is fairly intuitive in its use of symbols. There are all sorts of reasons for doing a little arithmetic on ... More


Pythagoras' Legacy: Mathematics in Ten Great Ideas

Marcel Danesi

Published in print:
2020
Published Online:
January 2020
ISBN:
9780198852247
eISBN:
9780191886959
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198852247.001.0001
Subject:
Mathematics, History of Mathematics, Educational Mathematics

The history of mathematics starts in earnest with one of Pythagoras’ most important proofs, the Pythagorean theorem. This proof was the first link in a chain of ground-breaking ideas, all ... More


Bayesianism—its Scope and Limits

Elliott Sober

in Bayes's Theorem

Published in print:
2005
Published Online:
January 2012
ISBN:
9780197263419
eISBN:
9780191734175
Item type:
chapter
Publisher:
British Academy
DOI:
10.5871/bacad/9780197263419.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter discusses the scope and limits of Bayesianism. The first topics discussed are the math and philosophy embedded in Bayesianism and the standard objection to Bayesianism. The concept of ... More


Epistemic Position and the First Meditation

David Cunning

in Argument and Persuasion in Descartes’ Meditations

Published in print:
2010
Published Online:
September 2010
ISBN:
9780195399608
eISBN:
9780199866502
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195399608.003.0002
Subject:
Philosophy, General

This chapter treats a number of interpretive issues including the ontological status of the simple natures that survive the painter analogy, the transparent truths and whether or not they are clearly ... More


The New Math: A Political History

Christopher J. Phillips

Published in print:
2014
Published Online:
May 2015
ISBN:
9780226184968
eISBN:
9780226185019
Item type:
book
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226185019.001.0001
Subject:
History, History of Science, Technology, and Medicine

The new math changed the way Americans think about mathematics. The mathematicians and teachers who designed the novel and controversial curriculum in the late 1950s--generously supported by the ... More


Lines of Thought: Central Concepts in Cognitive Psychology

Lance Rips

Published in print:
2011
Published Online:
January 2011
ISBN:
9780195183054
eISBN:
9780199865109
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195183054.001.0001
Subject:
Psychology, Cognitive Psychology

This book addresses how we are able to think about abstract possibilities: How can we think about math, despite the immateriality of numbers, sets, and other mathematical entities? How are we able to ... More


Numbers

Lance J. Rips

in Lines of Thought: Central Concepts in Cognitive Psychology

Published in print:
2011
Published Online:
January 2011
ISBN:
9780195183054
eISBN:
9780199865109
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195183054.003.0003
Subject:
Psychology, Cognitive Psychology

This chapter canvasses proposed connections between minds and numbers that might make knowledge of mathematics possible. The goal is to determine whether any promising leads are available in ... More


The Lone Star Challenge

Chester E. Finn and Andrew E. Scanlan

in Learning in the Fast Lane: The Past, Present, and Future of Advanced Placement

Published in print:
2019
Published Online:
May 2020
ISBN:
9780691178721
eISBN:
9780691185828
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691178721.003.0005
Subject:
Education, Higher and Further Education

This chapter focuses on the Advanced Placement (AP) program in Texas. No place in America offers a larger or more vivid example of AP's recent history, its widening mission, and the challenges of ... More


Make an educated guess, like Kepler with his Sphere-Packing Conjecture

Susan D'Agostino

in How to Free Your Inner Mathematician: Notes on Mathematics and Life

Published in print:
2020
Published Online:
April 2020
ISBN:
9780198843597
eISBN:
9780191879388
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198843597.003.0018
Subject:
Mathematics, Educational Mathematics, Applied Mathematics

“Make an educated guess, like Kepler with his Sphere-Packing Conjecture” provides an accessible discussion of the history and mathematics behind Johannes Kepler’s Sphere-Packing Conjecture—a ... More


The Trouble with Math

Ralph Abraham

in Educating the Whole Child for the Whole World: The Ross School Model and Education for the Global Era

Published in print:
2010
Published Online:
March 2016
ISBN:
9780814741405
eISBN:
9780814786550
Item type:
chapter
Publisher:
NYU Press
DOI:
10.18574/nyu/9780814741405.003.0010
Subject:
Education, Educational Policy and Politics

This chapter disagrees with how math is being taught today, addresses the development of a now pervasive “math anxiety,” and aims to devise an approach to teaching math that seeks to avoid it. ... More


How to Free Your Inner Mathematician: Notes on Mathematics and Life

Susan D'Agostino

Published in print:
2020
Published Online:
April 2020
ISBN:
9780198843597
eISBN:
9780191879388
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198843597.001.0001
Subject:
Mathematics, Educational Mathematics, Applied Mathematics

How to Free Your Inner Mathematician: Notes on Mathematics and Life offers readers guidance in managing the fear, freedom, frustration, and joy that often accompany calls to think mathematically. ... More


Look all around, as Archimedes did in life

Susan D'Agostino

in How to Free Your Inner Mathematician: Notes on Mathematics and Life

Published in print:
2020
Published Online:
April 2020
ISBN:
9780198843597
eISBN:
9780191879388
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198843597.003.0010
Subject:
Mathematics, Educational Mathematics, Applied Mathematics

“Look all around, as Archimedes did in life” offers a range of tales about Archimedes doing mathematics in unusual places, including in the bathtub, under starry skies, and at the beach. Out in the ... More


Untangle problems, with knot theory

Susan D'Agostino

in How to Free Your Inner Mathematician: Notes on Mathematics and Life

Published in print:
2020
Published Online:
April 2020
ISBN:
9780198843597
eISBN:
9780191879388
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198843597.003.0012
Subject:
Mathematics, Educational Mathematics, Applied Mathematics

“Untangle problems, with knot theory” offers a basic introduction to the mathematical subfield of knot theory, including the classification of knots by crossing numbers. A mathematical knot is a ... More


Consider all options, as the shortest path between two points is not always straight

Susan D'Agostino

in How to Free Your Inner Mathematician: Notes on Mathematics and Life

Published in print:
2020
Published Online:
April 2020
ISBN:
9780198843597
eISBN:
9780191879388
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198843597.003.0013
Subject:
Mathematics, Educational Mathematics, Applied Mathematics

“Consider all options, as the shortest path between two points is not always straight” explains how to find the shortest path between two points on the globe by way of a “great circle”—an ... More


Look for beauty, because of Fibonacci numbers

Susan D'Agostino

in How to Free Your Inner Mathematician: Notes on Mathematics and Life

Published in print:
2020
Published Online:
April 2020
ISBN:
9780198843597
eISBN:
9780191879388
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198843597.003.0014
Subject:
Mathematics, Educational Mathematics, Applied Mathematics

“Look for beauty, because of Fibonacci numbers” explains how to use addition to construct an ordered list of numbers known as the Fibonacci numbers. The chapter explores several unexpected and lovely ... More


Embrace change, considering non-Euclidean geometry

Susan D'Agostino

in How to Free Your Inner Mathematician: Notes on Mathematics and Life

Published in print:
2020
Published Online:
April 2020
ISBN:
9780198843597
eISBN:
9780191879388
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198843597.003.0016
Subject:
Mathematics, Educational Mathematics, Applied Mathematics

“Embrace change, considering non-Euclidean geometry” offers a basic introduction to the geometry of curved surfaces in which the sum of the degrees of a triangle may equal more or less than 180°. The ... More


Pursue an easier approach, considering the Pigeonhole Principle

Susan D'Agostino

in How to Free Your Inner Mathematician: Notes on Mathematics and Life

Published in print:
2020
Published Online:
April 2020
ISBN:
9780198843597
eISBN:
9780191879388
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198843597.003.0017
Subject:
Mathematics, Educational Mathematics, Applied Mathematics

“Pursue an easier approach, considering the Pigeonhole Principle” offers an introduction to a mathematical principle by way of answering a version of a popular mathematics question: “are there are ... More


Proceed at your own pace, because of terminal velocity

Susan D'Agostino

in How to Free Your Inner Mathematician: Notes on Mathematics and Life

Published in print:
2020
Published Online:
April 2020
ISBN:
9780198843597
eISBN:
9780191879388
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198843597.003.0019
Subject:
Mathematics, Educational Mathematics, Applied Mathematics

“Proceed at your own pace, because of terminal velocity” offers a short introduction to the mathematics behind terminal velocity—the speed at which the force of air resistance equals the force of ... More


Pay attention to details, as Earth is an oblate spheroid

Susan D'Agostino

in How to Free Your Inner Mathematician: Notes on Mathematics and Life

Published in print:
2020
Published Online:
April 2020
ISBN:
9780198843597
eISBN:
9780191879388
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198843597.003.0020
Subject:
Mathematics, Educational Mathematics, Applied Mathematics

“Pay attention to details, as Earth is an oblate spheroid” explains that, due to gravitational and rotational forces, all planets in the solar system could more accurately be described as oblate ... More


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