Understand mathematical problem solving and the use of mathematics in other disciplines.

Understand reasoning processes, including inductive and deductive logic, and spatial reasoning.ean and non-Euclidean geometry.

Understand and communicate the meaning of mathematical concepts and symbols.

Understand number theory and the principles and properties of the real and complex number systems.

Understand the principles and properties of algebraic operations

Apply principles and techniques of algebra to model and solve problems involving linear relations.

Understand and apply methods for using graphic representations to analyze and interpret linear relations.

Apply principles and techniques of algebra to model and solve problems involving quadratic relations.

Understand and apply methods for using graphic representations to analyze and interpret quadratic relations.

Understand the principles and properties of polynomial, rational, radical, absolute value, exponential, and logarithmic functions;  and apply algebraic and graphic techniques to problem solving situations involving these functions.

Understand the principles and properties of Euclidean geometry.

Understand measurement and the properties of two- and three-dimensional figures.

Understand the principles and properties of coordinate geometry.

Apply mathematical principles and techniques to model and solve problems involving vector and transformational geometries.

Understand right triangle trigonometry and the conceptual foundations of calculus.

Understand the principles, properties, and techniques of probability and their applications.

Understand the principles, properties, and techniques of statistics and their applications.

Understand how techniques of discrete mathematics (e.g., graphs, matrices, recurrence relations) are applied to model and solve problems.