Terminology To Know

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These are important terms and notations for this section.

Mathematical Reasoning A technique of problem solving that relies on deductive reasoning and symbolic manipulation.

Deductive Reasoning A form of inference that uses a set of given information, and extracts new information that must be true as a result.
For example (eg): Given the information:

It has rained
There is no cover for the ground

Then we can deduce that the ground is wet. This would be a logical deduction, or “deductive reasoning”.

Information A collection of knowledge or observations used to problem solve.

Data Quantified versions of information.

Model A (collection of) mathematical expressions used to represent a specific situation.

Generalize A process of going from a (somewhat) specific problem (eg a numeric model) to a methodology or (Generalized) Model to attain answers to (less specific) variations of the original problem.

(Mathematical) Symbol A mathematical symbol (usually referred to simply as ‘symbol’ when context is clear) is a non-numeric piece of writing (typically a letter) that holds the place of some (typically numeric) value, to be decided (or deduced) later.

The conceptual definition (Not to be used as the actual definition): A symbol is a letter, in some alphabet, that is a temporary stand-in for a piece of information. It is typically either a variable or replaced by a concrete value when one forms a model.

Author’s Note: This is included as we use the term ’symbol’ many times throughout this section and thus it should have a formal definition. However this term will not be tested on in discussion quizzes or on exams. It is necessarily abstract given it’s usage, but the abstraction is so deep as to be beyond the scope of this course.

Variable A symbol used to represent an unknown piece of data.

Independant Variable A variable whose value is unspecified, but will be provided by the statement of the problem.

Dependent Variable A variable whose value is unknown and is generated by the Model. In most cases dependent variables are determined (solved for) by the Model (See Arbitrary Constant Below).

Arbitrary Constant A symbol that is unaffected by independent variables, and whose value is determined by the model and initial conditions of the system.