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## Mathematics and Physical Reality

*Geoffrey Hellman*

### in Mathematics without Numbers: Towards a Modal-Structural Interpretation

- Published in print:
- 1993
- Published Online:
- November 2003
- ISBN:
- 9780198240341
- eISBN:
- 9780191597664
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198240341.003.0004
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Strategies for extending the modal‐structural approach to applications of mathematics are explored. The basic idea is to entertain what relationships would hold between a non‐mathematical system of ... More

## Mathematics in application

*Penelope Maddy*

### in Second Philosophy: A Naturalistic Method

- Published in print:
- 2007
- Published Online:
- January 2009
- ISBN:
- 9780199273669
- eISBN:
- 9780191706264
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199273669.003.0024
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Turning now to the role of mathematics in natural science, this chapter takes up a number of themes. First, the Quine/Putnam idea that the indispensability of mathematics for much of science confirms ... More

## Varying Interpretations

*Christopher Pincock*

### in Mathematics and Scientific Representation

- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780199757107
- eISBN:
- 9780199932313
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199757107.003.0004
- Subject:
- Philosophy, Philosophy of Science

Another kind of scientific representation is obtained when a scientist links representations using some shared mathematics. This sort of situation is quite different from the acausal representations ... More

## The Indispensability of Mathematics

*Mark Colyvan*

- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780195137545
- eISBN:
- 9780199833139
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/019513754X.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Looks at the Quine–Putnam indispensability argument in the philosophy of mathematics. This argument urges us to place mathematical entities on the same ontological footing as other theoretical ... More

## Applying Mathematics: Two Models

*Jody Azzouni*

### in Deflating Existential Consequence: A Case for Nominalism

- Published in print:
- 2004
- Published Online:
- January 2005
- ISBN:
- 9780195159882
- eISBN:
- 9780199834990
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195159888.003.0009
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Several applications of mathematics to empirical domains are described, including a small portion of Newtonian mechanics. The simplest case is one where a nonmathematical empirical description of the ... More

## Time Series Analysis

*Andrew J. Connolly, Jacob T. VanderPlas, Alexander Gray, Andrew J. Connolly, Jacob T. VanderPlas, and Alexander Gray*

### in Statistics, Data Mining, and Machine Learning in Astronomy: A Practical Python Guide for the Analysis of Survey Data

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691151687
- eISBN:
- 9781400848911
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691151687.003.0010
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter summarizes the fundamental concepts and tools for analyzing time series data. Time series analysis is a branch of applied mathematics developed mostly in the fields of signal processing ... More

## The Problem

*Penelope Maddy*

### in Defending the Axioms: On the Philosophical Foundations of Set Theory

- Published in print:
- 2011
- Published Online:
- May 2011
- ISBN:
- 9780199596188
- eISBN:
- 9780191725395
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199596188.003.0002
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

Proper understanding of contemporary set theory requires a clear sense of how it came to be what it is and the mathematical roles it is designed to play. This chapter traces the rise of pure ... More

## Quantum Chemistry qua Applied Mathematics: Approximation Methods and Crunching Numbers

*Kostas Gavroglu and Ana Simões*

### in Neither Physics nor Chemistry: A History of Quantum Chemistry

- Published in print:
- 2011
- Published Online:
- August 2013
- ISBN:
- 9780262016186
- eISBN:
- 9780262298759
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262016186.003.0004
- Subject:
- History, History of Science, Technology, and Medicine

In Britain, John Edward Lennard-Jones, Douglas Rayner Hartree, and Charles Alfred Coulson played important roles in expanding the domain of applied mathematics to include quantum chemistry. This ... More

## Academic Mathematics in France before 1699: The Administrative Turn at the Académie Royale des Sciences

*J.B. Shank*

### in Before Voltaire: The French Origins of "Newtonian" Mechanics, 1680-1715

- Published in print:
- 2018
- Published Online:
- May 2019
- ISBN:
- 9780226509297
- eISBN:
- 9780226509327
- Item type:
- chapter

- Publisher:
- University of Chicago Press
- DOI:
- 10.7208/chicago/9780226509327.003.0003
- Subject:
- History, History of Science, Technology, and Medicine

Chapter 3 completes Part I's assessment of the culture of French academic mathematics begun in Chapter 2. It focuses on the institutional and social developments that turned the Académie Royale des ... More

## Why Empirically Indispensable Mathematical Doctrine and (Some) Scientific Law Must Be Taken as True: Preliminary Considerations

*Jody Azzouni*

### in Deflating Existential Consequence: A Case for Nominalism

- Published in print:
- 2004
- Published Online:
- January 2005
- ISBN:
- 9780195159882
- eISBN:
- 9780199834990
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195159888.003.0002
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

A version of the indispensability of the truth of applied mathematical doctrine and empirical scientific law is established in this and the next chapter. This chapter begins the argument with a ... More

## The Game Theory Phenomenon

*Paul Erickson*

### in The World the Game theorists Made

- Published in print:
- 2015
- Published Online:
- May 2016
- ISBN:
- 9780226097039
- eISBN:
- 9780226097206
- Item type:
- chapter

- Publisher:
- University of Chicago Press
- DOI:
- 10.7208/chicago/9780226097206.003.0001
- Subject:
- History, History of Science, Technology, and Medicine

Writing about game theory’s past presents several historiographical challenges. At least prior to its prominent appearances in economics since the 1980s, game theory does not correlate neatly with ... More

## A Second Pilgrim’s Progress

*Mark Wilson*

### in Physics Avoidance: and other essays in conceptual strategy

- Published in print:
- 2017
- Published Online:
- December 2017
- ISBN:
- 9780198803478
- eISBN:
- 9780191841651
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198803478.003.0009
- Subject:
- Philosophy, Philosophy of Science, Philosophy of Language

Influenced by Quine, self-styled naturalist projects within the philosophy of mathematics rest upon simplistic conceptions of linguistic reference and how the inferential tools of applied mathematics ... More

## Rays, Waves, and Scattering: Topics in Classical Mathematical Physics

*John A. Adam*

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691148373
- eISBN:
- 9781400885404
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691148373.001.0001
- Subject:
- Mathematics, Applied Mathematics

This book presents many of the mathematical concepts, structures, and techniques used in the study of rays, waves, and scattering. It includes discussions of how ocean waves are refracted around ... More

## Kitcher against the Platonists

*Gideon Rosen*

### in The Philosophy of Philip Kitcher

- Published in print:
- 2016
- Published Online:
- June 2016
- ISBN:
- 9780199381357
- eISBN:
- 9780199381371
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199381357.003.0002
- Subject:
- Philosophy, General, Philosophy of Science

Gideon Rosen discusses Kitcher’s recent critique of platonism and defense of formalism. Kitcher argues that any view that attributes a subject matter to mathematics, including platonism, has no good ... More

## Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

*G. F. Roach, I. G. Stratis, and A. N. Yannacopoulos*

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691142173
- eISBN:
- 9781400842650
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691142173.001.0001
- Subject:
- Mathematics, Applied Mathematics

Electromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. Because of their wide range of important ... More

## Eli’s Impact: A Case Study

*Charles Fefferman*

*Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, Stephen Wainger, Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, and Stephen Wainger (eds)*

### in Advances in Analysis: The Legacy of Elias M. Stein

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691159416
- eISBN:
- 9781400848935
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159416.003.0002
- Subject:
- Mathematics, Numerical Analysis

This chapter illustrates the continuing powerful influence of Eli Stein's ideas. It starts by recalling his ideas on Littlewood–Paley theory, as well as several major developments in pure and applied ... More

## Scientific Method

*Marjorie Senechal*

### in I Died for Beauty: A Biography of Dorothy Wrinch

- Published in print:
- 2012
- Published Online:
- March 2015
- ISBN:
- 9780199732593
- eISBN:
- 9780190254353
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:osobl/9780199732593.003.0008
- Subject:
- History, History of Science, Technology, and Medicine

This chapter describes Dot's work with Harold Jeffreys. Like Dot, Harold was drawn to applied mathematics, first to astronomy, then to geophysics, the earth. Like Dot, he was drawn to the philosophy ... More

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