## Forbidden Areas and Anchor Points

*Rein Taagepera*

### in Making Social Sciences More Scientific: The Need for Predictive Models

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199534661
- eISBN:
- 9780191715921
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199534661.003.0008
- Subject:
- Political Science, Comparative Politics, Political Economy

The outcomes of sociopolitical processes often depend on the factor in shortest supply; this makes multiplication of factors superior to their addition. Naïve linear regression may not detect all ... More

## The rise and rise of the spreadsheet

*Martin Campbell-Kelly*

### in The History of Mathematical Tables: From Sumer to Spreadsheets

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198508410
- eISBN:
- 9780191708831
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508410.003.0013
- Subject:
- Mathematics, History of Mathematics

The mathematical table, as a paper-based artefact, is close to the end of its technological life. Tables had two main uses — as a calculating aid (such as a logarithm table) and as a data storage ... More

## Determinants

*Simon Scott*

### in Traces and Determinants of Pseudodifferential Operators

- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780198568360
- eISBN:
- 9780191594748
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568360.003.0003
- Subject:
- Mathematics, Analysis

Determinants as abstract invariants have received less study in the mathematical literature than traces, on which there is an extensive literature. However, determinants can be treated in a general ... More

## The making of logarithm tables

*Graham Jagger*

### in The History of Mathematical Tables: From Sumer to Spreadsheets

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198508410
- eISBN:
- 9780191708831
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508410.003.0003
- Subject:
- Mathematics, History of Mathematics

In 1614, the invention of logarithms burst upon the world with the publication of Napier's Mirifici logarithmorum canonis description, or A description of the admirable table of logarithms. By the ... More

## ELECTRICAL CONDUCTIVITY OF PARTIALLY IONIZED PLASMA

*V. E. Fortov, I. T. Iakubov, and A. G. Khrapak*

### in Physics of Strongly Coupled Plasma

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199299805
- eISBN:
- 9780191714948
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199299805.003.0006
- Subject:
- Physics, Nuclear and Plasma Physics

This chapter focuses on the electrical conductivity of partially ionized plasma. The case of ideal plasma is considered, and the Lorentz formula for weakly ionized plasma and Spitzer formula for ... More

## Some Extensions

*James Davidson*

### in Stochastic Limit Theory: An Introduction for Econometricians

- Published in print:
- 1994
- Published Online:
- November 2003
- ISBN:
- 9780198774037
- eISBN:
- 9780191596117
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198774036.003.0025
- Subject:
- Economics and Finance, Econometrics

Four extensions of the CLT are considered in this chapter. First, estimated normalization, using methods of heteroscedasticity and autocorrelation consistent variance estimation. Second, random ... More

## Material Structure and Calculating Machines

*Kurt Smith*

### in Matter Matters: Metaphysics and Methodology in the Early Modern Period

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199583652
- eISBN:
- 9780191723155
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199583652.003.0012
- Subject:
- Philosophy, History of Philosophy, Metaphysics/Epistemology

In this chapter it is shown how Leibniz and others in the period understood bodies to be mathematically informed (structured). This led to their designing and constructing calculating machines—the ... More

## Special Functions and Approximations

*Stefan Thurner, Rudolf Hanel, and Peter Klimekl*

### in Introduction to the Theory of Complex Systems

- Published in print:
- 2018
- Published Online:
- November 2018
- ISBN:
- 9780198821939
- eISBN:
- 9780191861062
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198821939.003.0008
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The chapter contains the most important mathematical forumas that are used throughout the book. This collection should make the book self-contained. The chapter also contains some useful ... More

## Mathematics Refresher

*Timothy E. Essington*

### in Introduction to Quantitative Ecology: Mathematical and Statistical Modelling for Beginners

- Published in print:
- 2021
- Published Online:
- November 2021
- ISBN:
- 9780192843470
- eISBN:
- 9780191926112
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780192843470.003.0011
- Subject:
- Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies

The chapter “Mathematics Refresher” provides a brief reminder of operations with logarithms, matrices, and calculus, for student reference. It starts off by reviewing the differences between regular ... More

## Renormalization Theory and Effective Field Theories

*Matthias Neubert*

### in Effective Field Theory in Particle Physics and Cosmology: Lecture Notes of the Les Houches Summer School: Volume 108, July 2017

- Published in print:
- 2020
- Published Online:
- August 2020
- ISBN:
- 9780198855743
- eISBN:
- 9780191889370
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198855743.003.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

Chapter 1 features lectures that review the formalism of renormalization in quantum field theories with special regard to effective quantum field theories. While renormalization theory is part of ... More

## Soft-Collinear Effective Theory

*Thomas Becher*

### in Effective Field Theory in Particle Physics and Cosmology: Lecture Notes of the Les Houches Summer School: Volume 108, July 2017

- Published in print:
- 2020
- Published Online:
- August 2020
- ISBN:
- 9780198855743
- eISBN:
- 9780191889370
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198855743.003.0005
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

The lectures that appear within this chapter provide an introduction to soft-collinear effective theory (SCET). It begins by discussing resummation for soft-photon effects in QED, including soft ... More

## Mathematics

*Patrick Magee and Mark Tooley*

### in The Physics, Clinical Measurement and Equipment of Anaesthetic Practice for the FRCA

- Published in print:
- 2011
- Published Online:
- November 2020
- ISBN:
- 9780199595150
- eISBN:
- 9780191918032
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199595150.003.0005
- Subject:
- Clinical Medicine and Allied Health, Anesthesiology

Graphs are used to represent pictorially or clarify a relationship between two variables, say x and y, or t and function (t). If x and y are related by the linear equation y = mx + c, then the ... More

## Essential Mathematics

*Christopher O. Oriakhi*

### in Chemistry in Quantitative Language: Fundamentals of General Chemistry Calculations

- Published in print:
- 2009
- Published Online:
- November 2020
- ISBN:
- 9780195367997
- eISBN:
- 9780197562635
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195367997.003.0005
- Subject:
- Chemistry, Analytical Chemistry

Significant figures are the number of digits in a measured or calculated value that are statistically significant or offer reasonable and reliable information. Significant figures in any ... More

## Making Regression More Flexible

### in Introductory Econometrics: Intuition, Proof, and Practice

- Published in print:
- 2011
- Published Online:
- June 2013
- ISBN:
- 9780804772624
- eISBN:
- 9780804777209
- Item type:
- chapter

- Publisher:
- Stanford University Press
- DOI:
- 10.11126/stanford/9780804772624.003.0013
- Subject:
- Economics and Finance, Econometrics

This chapter shows that explanatory variables can appear in discrete and nonlinear form. These forms give us the opportunity to represent a wide and varied range of possible relationships between the ... More

## The Modern Approach: Right-Angled Triangles

*Glen Van Brummelen*

### in Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175997
- eISBN:
- 9781400844807
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175997.003.0005
- Subject:
- Mathematics, History of Mathematics

This chapter discusses the modern approach to solving right-angled triangles. After a brief background on John Napier's trigonometric work, in which he referred mostly to right-angled spherical ... More

## Other Worlds

*Laura Kolb*

### in Fictions of Credit in the Age of Shakespeare

- Published in print:
- 2021
- Published Online:
- February 2021
- ISBN:
- 9780198859697
- eISBN:
- 9780191892066
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198859697.003.0005
- Subject:
- Literature, 16th-century and Renaissance Literature, Shakespeare Studies

Chapter 4 turns from social fictions to fictive renderings of the wide and variegated world of trade. Early modern merchandise mirrored—and fueled—the poetic imagination. In turn, poets conjured ... More

## A Quick Introduction to Benfordʼs Law

*Steven J. Miller*

### in Benford's Law: Theory and Applications

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691147611
- eISBN:
- 9781400866595
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691147611.003.0001
- Subject:
- Mathematics, Probability / Statistics

This chapter provides a brief overview of Benford's law. It states Benford's law of digit bias and describes its history. The chapter then discusses the origins of Benford's law and gives numerous ... More

## Cryptographic Primitives

*Andreas Bolfing*

### in Cryptographic Primitives in Blockchain Technology: A mathematical introduction

- Published in print:
- 2020
- Published Online:
- October 2020
- ISBN:
- 9780198862840
- eISBN:
- 9780191895463
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198862840.003.0003
- Subject:
- Mathematics, Computational Mathematics / Optimization, Logic / Computer Science / Mathematical Philosophy

This chapter provides a very detailed introduction to cryptography. It first explains the cryptographic basics and introduces the concept of public-key encryption which is based on one-way and ... More

## Exponents: Notation and discovery

*Marcel Danesi*

### in Pythagoras' Legacy: Mathematics in Ten Great Ideas

- Published in print:
- 2020
- Published Online:
- January 2020
- ISBN:
- 9780198852247
- eISBN:
- 9780191886959
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198852247.003.0005
- Subject:
- Mathematics, History of Mathematics, Educational Mathematics

Mathematicians have devised notations and symbols to compress information and to explore mathematics via the symbols themselves. In the 1500s the invention of exponential notation, which was devised ... More

## Descriptive statistics

*Andrew Gelman and Deborah Nolan*

### in Teaching Statistics: A Bag of Tricks

- Published in print:
- 2017
- Published Online:
- September 2017
- ISBN:
- 9780198785699
- eISBN:
- 9780191827518
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198785699.003.0003
- Subject:
- Mathematics, Educational Mathematics

Descriptive statistics is the typical starting point for a statistics course, and it can be tricky to teach because the material is more difficult than it first appears. The activities in this ... More