The overarching goal of Quantitative Analysis (QA) courses is that students learn to understand, communicate, and interpret quantitative information and mathematical ideas. Though they will vary in emphasis, all should develop skills in the recognition of patterns, generalization, abstraction to a formal system, and application of the system to specific situations.
QA courses further include learning outcomes from one or more of the following categories:
- Data Analysis and Statistical Inference
Students are better able to evaluate information, both quantitative and qualitative, gathered to assess the plausibility, or validity, of an open question of interest. This may include the construction of graphical and numerical summaries, applications of probability to properly assess the uncertainty surrounding any estimates, or discussions of how to design a study/experiment so that the desired questions are adequately addressed, all in order to make sound decisions based on the gathered data.
- Formal symbolic systems
Students can abstract from a concrete situation to a representation in a formal symbolic system whose primary units are not words, and apply this formal system to other specific examples. Some examples of the formal system are symbolic logic, computer programming languages, geometry, number theory, chemical equations and electron-dot notations.
- Mathematical models
Students are able to develop and understand mathematical models for problems that arise in various disciplines. Though these problems are often not explicitly mathematical, mathematical models should be used to gain insights into how systems work, how their component parts interact or contribute to the system’s output and, in many cases, to make predictions about how the system will behave.