Basic Principles of Science 1

The documents in the links that follow require either Mathematica 8 or later, or the free Mathematica CDF Viewer (you can find that here).

Mathematical Structures and Numbers

Core

Mathematics as the study of objects, their relationships, and the structures created by their relationships. Numbers and Sets as Mathematical Objects. Arithmetic Operations as Relationships Between Numbers. Sets of Numbers as Having Properties Determined by the Operations Relating Numbers.

Optional

Properties of Sets. Properties of Arithmetic Operations. Symbolic Manipulation Techniques. Introduction to Calculating in Mathematica.

Experimentalist

Using Numbers to Represent Measurable Quantities

Theorist

Truth Tables and Proof

Honors

Write an essay about a related topic.

Geometry

Core

Points and Sets of Points as Mathematical Objects. Distance, angles, and congruence as relationships. Triangles and Polygons. Coordinate Systems.

Optional

Circles. Solids. Conic sections. Introduction to Geometry in Mathematica.

Experimentalist

Plotting data.

Theorist

Geometric proofs.

Honors

Write an essay about a related topic.

Functions

Core

Equations and inequalities. Functions. Algebraic functions. Transcendental functions.

Optional

Trigonometric functions. Plotting functions. Vectors. Introduction to Functions, Plotting, and Equation-Solving in Mathematica.

Experimentalist

Probability.

Theorist

Approximation.

Honors

Write an essay about a related topic.

Calculus

Core

Limits. Differentiation. Integration. Series.

Optional

Applications of derivatives. Applications of integrals. Differential equations. Introduction to calculus in Mathematica.

Experimentalist

Error analysis.

Theorist

Methods of integration.

Honors

Write an essay about a related topic.

Measurement and Science

Core

The nature of science. What it takes to be a scientist. Units and dimensions. Estimation.

Optional

Observational error. Unit conversions. Modeling. Introduction to units and measurement in Mathematica.

Experimentalist

Propagation of error.

Theorist

Deriving formulas.

Honors

Write an essay about a related topic.

Mechanics

Core

Kinematics. Forces and mass. Dynamics. Conservation laws.

Optional

Projectiles. Oscillations. Collisions. Introduction to mechanics in Mathematica.

Experimentalist

Conduct an experiment or observation.

Theorist

Conduct a calculation or derivation.

Honors

Write an essay about a related topic.

Electrodynamics

Core

Vector analysis. Electric fields. Magnetic fields. Induction.

Optional

DC circuits. AC circuits. Maxwell's equations and waves. Introduction to electrodynamics in Mathematica.

Experimentalist

Conduct an experiment or observation.

Theorist

Conduct a calculation or derivation.

Honors

Write an essay about a related topic.

Quantum Physics

Core

Waves. Uncertainty. The Schrödinger equation. Bound states.

Optional

The photoelectric effect. The Compton effect. The quantum structure of matter. Introduction to quantum physics in Mathematica.

Experimentalist

Conduct an experiment or observation.

Theorist

Conduct a calculation or derivation.

Honors

Write an essay about a related topic.

Thermal Physics

Core

Thermodynamic properties. Thermodynamic laws. Kinetic theory. Statistical mechanics.

Optional

States of matter. The ideal gas. Quantum statistics. Introduction to thermal physics in Mathematica.

Experimentalist

Conduct an experiment or observation.

Theorist

Conduct a calculation or derivation.

Honors

Write an essay about a related topic.

Chemistry

Core

The periodic table of the elements. Chemical reactions. Stoichiometry. Chemical bonding.

Optional

Aqueous reactions. Solutions. Chemical equilibrium. Introduction to chemistry in Mathematica.

Experimentalist

Conduct an experiment or observation.

Theorist

Conduct a calculation or derivation.

Honors

Write an essay about a related topic.

Click here to return to the educational programs page.

Click here to return to the home page.