Mathematics

• Grade 6 Math

• Grade 7 Math

• Grade 8 Math

• Pre-Algebra

• Algebra I

• Geometry

• Algebra II

• Pre-Calculus

• Calculus

• Statistics

Mathematics is the fundamental language of the physical universe.  The physical universe, of course, has a structure based ultimately, within our current framework of understanding, on subatomic particles that appear to have properties of both matter and energy.  The manner in which we describe those particles and their interactions is mathematical.  The particles themselves can be represented as combinations of numerical values for a set of characteristic variables, and their behavior and interactions can be predicted (or can be shown to be unpredictable) through the solutions to mathematical expressions that incorporate those values.

Mathematics starts for students the way it comes into existence in the universe; through shapes and counting.  Even in the absence of more sophisticated symbolic mathematics--even in the absence of people--shapes and quantities exist.  Similarly, before we have any concept of a variable or an equation, we are able to discern similarities and difference between shapes and to count how many objects are in a given place.  We then begin to quantify the characteristics of shapes, determining the measures of line segments and angles; and we subdivide, rearrange, and regroup objects to develop concepts of arithmetic.  Before long, our interactions with shapes and measures become sufficiently complicated that we require additional language to describe them, and we advance into areas of study, such as algebra, geometry, and trigonometry, whose language reveals even deeper concepts and connections.

Each step on this journey of learning is a step of discovery.  We discover attributes of the physical universe and we create language to describe and predict their behavior.  This parallel journey of evolving language is the story of mathematics, a story that plays out over and over again in every person that cares to read it.

• Characteristics of a system may be represented as variables, symbols that may have different values in different circumstances.

• The behavior of a system or of a part of a system may be described with a mathematical expression.

• Descriptive expressions tell not only the relationships between variables but also which characteristics of a system are relevant to understanding it.

• By extension, all physical phenomena may be modelled mathematically.

• Mathematical models do not necessarily represent mechanisms, even when they predict probable outcomes.

• Mathematics is based on deductive reasoning, which may proceed from, but not be proved by, intuitive or inductive reasoning.

• Equations are true when their variable(s) assume the value(s) of the solution set.

• Solution sets may be represented as graphs in various dimensional spaces.

• Solutions to complex systems may be conceptualized as interactions between simpler sets that represent the solutions to interrelated parts of the system.

• We take courses in mathematics to learn another way to think; whether you ever use it is up to you.

• We take courses in mathematics so that we live in the kind of world in which people value mathematics.