Students in Mathematical Approaches courses develop an appreciation of the power of Mathematics and formal methods to provide a way of understanding a problem unambiguously, describing its relation to other problems, and specifying clearly an approach to its solution. Students in Mathematical Approaches courses develop a variety of mathematical skills, an understanding of formal reasoning, and a facility with applications.
- These goals are met by courses that treat formal reasoning in one or more of the following areas.
- Mathematical reasoning: The ability to use such techniques as abstraction, definition, symbolic computation, calculation, and proof.
- Data-based reasoning: The ability to work with numeric data, to reason from those data, and to understand what can and cannot be inferred from those data;
- Logical reasoning: The study of formal logic, at least to the extent that is required to understand mathematical proof.
- Algorithmic reasoning: The ability to analyze a problem, to design a systematic way of addressing that problem using an algorithm, and to implement that algorithm in a formal language such as a computer programming language.
- Where these skills or methods are taught within the context of a discipline other than mathematics or computer science, they must receive greater attention than the disciplinary material.