Introduction1
Contemporary social science, even ethnographic work and archeology which are often thought of as the antithesis of cold, quantitative sociology and economics, is increasingly making use of tools which are mathematical in nature.
Students who opt out of the mathematical are effectively denying themselves a place at some important tables and seriously limiting their career options. This does not mean that everyone needs to become a statistician. Far from it. But competence and confidence and comfort with being able to learn new tools as necessary will allow one to pick research topics because of what is important to them rather than because of what methods they are comfortable with.
Here is a quick and dirty sketch of the range of mathematical tools currently used in the social sciences.
- Simple table construction.
- Percentaging, calculating densities and relative rates
- Basic statistical analysis of bivariate tables.
- Bivariate plotting
- Line fitting for bivariate and multivariate data.
- Basic game theory.
- Producing and interpreting charts.
- Graphing relationships and reading graphs
- Plotting and analyzing social networks
- Using probability to think about samples and significance
- Data reduction and extraction of latent dimensions
- Solving basic optimization and equilibrium problems
- Analyzing growth/evolution of populations/assets/etc. over time
And then there is the stuff that is what is happening today that students should want to be able to participate in.
- Computer simulation of social processes
- Statistical modeling
- Mapping and spatial analysis
- Data mining and analysis of very large datasets
- Advanced “rational choice” models
- Emergence, complexity, non-linear dynamics, adaptive systems
- Bayesian methods in social science
- Event history analysis
How about the skills? Here’s a modified list worked up by faculty. I think we might start putting some of these next to some of the social science doings up on the first list so that we could have a bit of a map in terms of what basic skills are associated with what social science tools.
Category 0
- Arithmetic operators, simple rules of order of precedence
- Associative, commutative, distributive properties.
- Fractions: find common denominators, the reciprocal of a fraction, arithmetic with fractions.
- Convert fractions to decimal/percent and vice versa.
- Arithmetic with negative numbers.
- Absolute value.
- Exponent notation and idea of powers
- Basic logic of sets : and/intersection, or/union, not/complement
- Algebraic use of variables in equations
Category 1
- Exponent identities
- An understanding of the idea of proportionality, and of the difference between a percentage and percentage points.
- Calculate the area of a rectangle or of a right triangle if they are told its base and height.
- Read/interpret/draw simple two dimensional charts of data
- Read (and draw) graphs of simple functions (e.g. linear or quadratic equations in two variables).
- The knowledge that a line can be represented by an equation, and the ability to graph the line, and find its slope and its y-intercept.
- The ability to express a linear equation in two variables in terms of either of the two variables, i.e. to express x as a function of y, and to express y as a function of x.
- The ability to recognize the equation of a line when it is not in slope-intercept form, and to convert it into that form.
- Category 2
- The ability to solve very simple systems of linear equations in several variables.
- Basic probability: proportions, joint probability, conditional, calculating permutations.
- Enough of an understanding of exponents that they be able to calculate compound interest or the present discounted value of a simple financial asset.
- To recognize that a curve doesn’t have a single slope, but that the slope of a tangent line to the curve approximates “the slope” in the point of tangency.