# Mathematics for Social Scientists

- Jonathan Kropko - University of Virginia, USA

**Mathematics for Social Scientists**offers a non-intimidating approach to learning or reviewing math skills essential in quantitative research methods. The text is designed to build 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.

**Available with**

**Perusall****—an eBook that makes it easier to prepare for class**

*Perusall*is an award-winning eBook platform featuring social annotation tools that allow students and instructors to collaboratively mark up and discuss their SAGE textbook. Backed by research and supported by technological innovations developed at Harvard University, this process of learning through collaborative annotation keeps your students engaged and makes teaching easier and more effective. Learn more.

Numbers |

Fractions |

Exponents |

Roots |

Logarithms |

Summations and Products |

Solving Equations and Inequalities |

Set Notation |

Intervals |

Venn Diagrams |

Functions |

Polynomials |

Events and Sample Spaces |

Properties and Probability Functions |

Counting Theory |

Sampling Problems |

Conditional Probability |

Bayes' Rule |

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 Rule |

Terminology |

Finding Maxima and Minima |

The Newton-Raphson Method |

Informal Definitions of an Integral |

Riemann Sums |

Integral Notation |

Solving Integrals |

Advanced Techniques for Solving Integrals |

Probability Density Functions |

Moments |

Multivariate Functions |

Multivariate Limits |

Partial Derivatives |

Multiple Integrals |

Matrix Notation |

Types of Matrices |

Matrix Arithmetic |

Matrix Multiplication |

Geometric Representation of Vectors and Transformation Matrices |

Elementary Row and Column Operations |

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 Dependency |

Nonsingular Coefficient Matrices |

Singular Coefficient Matrices |

Homogeneous Systems |

Eigenvalues and Eigenvectors |

Statistical Measurement Models |

### Supplements

**Use the Student Study Site to get the most out of your course!**

The companion website includes solutions to the practice problems in the book.

“Students in the social and behavioral sciences increasingly need a solid foundation of mathematical knowledge to be able to contribute to the research literature and be able to keep themselves current on new methodology. Unfortunately, math department classes really are not tailored to their needs. **Mathematics for Social Scientists**, on the other hand, is clearly aimed at what students need to be able to advance in subsequent methodology courses and in their future careers. It is written in an inviting and clear manner, without ever sacrificing rigor.”

**The City University of New York**

“Many students entering higher-level statistics classes have somehow forgotten their basic statistics or were never properly exposed to more than a cookbook explanation. More often than not, a student will leave the course without an understanding of probability, random variables, basic distribution theory and concepts etc. Without some background, it proves difficult for students to catch up with these ideas when they are introduced (or assumed to be known) in more advanced courses. This gap is especially pronounced between those students who were exposed to basic probability in a previous course and those who were not. **Mathematics for Social Scientists **will be a great resource for an instructor wishing to add this content to a basic statistics course as well as for the motivated self-learner.”

**University of Texas at Austin**

This is a required texbook for understanding advanced univariate and multivariate statistics. I use this book as complementary book in my courses.

**Educational Psychology , University Of Saskatchewan**