Gill J. Essential Mathematics for Political and Social Research

Cambridge: Cambridge University Press, 2006. — 476 р. — (Analytical Methods for Social Research). — ISBN 978-0-521-83426-1.Essential Mathematics for Political and Social Research addresses an educational deficiency in the social and behavioral sciences. This is the first book of its kind to specifically address the comprehensive introduction to the mathematical principles needed by modern social scientists. The material introduces basic mathematical principles necessary to do analytical work in the social sciences, starting from first principles, but without unnecessary complexity. The core purpose is to present fundamental notions in standard notation and standard language with a clear, unified framework throughout. Through examples and exercises, this book is intended to not only motivate specific mathematical principles and practices, but also introduce the way that social science researchers use these tools. The intended emphasis is on conceptual understanding of key principles and their subsequent application.The Basics
Objectives
Essential Arithmetic Principles
Notation, Notation, Notation
Basic Terms
Functions and Equations
Polynomial Functions
Logarithms and Exponents
New Terminology
Chapter Appendix: It’s All Greek to Me
Analytic Geometry
Objectives (the Width of a Circle)
Radian Measurement and Polar Coordinates
What Is Trigonometry?
New Terminology
Linear Algebra: Vectors, Matrices, and Operations
Objectives
Working with Vectors
So What Is the Matrix?
Controlling the Matrix
Matrix Transposition
Advanced Topics
New Terminology
Linear Algebra Continued: Matrix Structure
Objectives
Space and Time
The Trace and Determinant of a Matrix
Matrix Rank
Matrix Norms
Matrix Inversion
Linear Systems of Equations
Eigen-Analysis of Matrices
Quadratic Forms and Descriptions
New Terminology
Elementary Scalar Calculus
Objectives
Limits and Lines
Understanding Rates, Changes, and Derivatives
Derivative Rules for Common Functions
Understanding Areas, Slices, and Integrals
The Fundamental Theorem of Calculus
Additional Topics: Calculus of Trigonometric Functions
New Terminology
Additional Topics in Scalar and Vector Calculus
Objectives
Partial Derivatives
Derivatives and Partial Derivatives of Higher Order
MAXIMA, Minima, and Root Finding
Multidimensional Integrals
Finite and Infinite Series
The Calculus of Vector and Matrix Forms
Constrained Optimization
New Terminology
Probability Theory
Objectives
Counting Rules and Permutations
Sets and Operations on Sets
The Probability Function
Calculations with Probabilities
Conditional Probability and Bayes Law
Independence
Odds
New Terminology
Random Variables
Objectives
Levels of Measurement
Distribution Functions
Measures of Central Tendency: Mean, Median, and Mode
Measures of Dispersion: Variance, Standard Deviation, and MAD
Correlation and Covariance
Expected Value
Some Handy Properties and Rules
Inequalities Based on Expected Values
Moments of a Distribution
New Terminology
Markov Chains
Objectives
Defining Stochastic Processes and Markov Chains
Properties of Markov Chains
New Terminology