Mathematics for social scientists

著者

    • Kropko, Jonathan

書誌事項

Mathematics for social scientists

Jonathan Kropko

Sage, c2016

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注記

Includes index

内容説明・目次

内容説明

The text builds students' confidence by presenting material in a conversational tone and using a wealth of clear and applied examples. Author Jonathan Kropko argues that mastering these concepts will break students' reliance on using basic models in statistical software, allowing them to engage with research data beyond simple software calculations.

目次

Part I: ALGEBRA, PRECALCULUS, AND PROBABILITY1. Algebra Review Numbers Fractions Exponents Roots Logarithms Summations and Products Solving Equations and Inequalities2. Sets and Functions Set Notation Intervals Venn Diagrams Functions Polynomials3. Probability Events and Sample Spaces Properties and Probability Functions Counting Theory Sampling Problems Conditional Probability Bayes' RulePART II: CALCULUS4. Limits and Derivatives What is a Limit? Continuity and Asymptotes Solving Limits The Number e Point Estimates and Comparative Statics Definitions of the Derivative Notation Shortcuts for Finding Derivatives The Chain Rule5. Optimization Terminology Finding Maxima and Minima The Newton-Raphson Method6. Integration Informal Definitions of an Integral Riemann Sums Integral Notation Solving Integrals Advanced Techniques for Solving Integrals Probability Density Functions Moments7. Multivariate Calculus Multivariate Functions Multivariate Limits Partial Derivatives Multiple IntegralsPART III: LINEAR ALGEBRA8. Matrix Notation and Arithmetic Matrix Notation Types of Matrices Matrix Arithmetic Matrix Multiplication Geometric Representation of Vectors and Transformation Matrices Elementary Row and Column Operations9. Matrix Inverses, Singularity, and Rank Inverse of a (2 x 2) Matrix Inverse of a Larger Square Matrix Multiple Regression and the Ordinary Least Squares Estimator Singularity, Rank, and Linear Dependency10. Linear Systems of Equations and Eigenvalues Nonsingular Coefficient Matrices Singular Coefficient Matrices Homogeneous Systems Eigenvalues and Eigenvectors Statistical Measurement Models

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