Basic Mathematics of Science

Logic and Proof

Core

Propositional Logic. Predicate Logic. Implications. Negations.

Optional

Converse and equivalence. Quantifiers. Definitions. Theorems.

Experimentalist

Examples and counterexamples.

Theorist

Reading proofs.

Honors

Write an essay about a related topic.

Set Theory

Core

Operations on Sets. Cartesian products. Relations. Functions.

Optional

Order Relations. Equivalence Relations. Cardinal Numbers. Ordinal Numbers.

Experimentalist

To be determined.

Theorist

Uncountabe Sets.

Honors

Write an essay about a related topic.

Algebra

Core

Algebraic Structures. The Number System. Theory of Polynomials. Theory of Equations.

Optional

Number Theory. Groups. Rings. Fields.

Experimentalist

Constructions.

Theorist

Euclidean and Complex Spaces

Honors

Write an essay about a related topic.

Analytical Geometry

Core

Analytical Geometry of the Line. Vectors. Conic Sections. Euclidean Three-Space.

Optional

Analytical Geometry of the Circle. Graphs of Functions. Parametric Equations. Vectors in 3-Space.

Experimentalist

Polar Coordinates

Theorist

Geometric Transformations

Honors

Write an essay about a related topic.

Matrices

Core

Matrices. Binary Operations on Matrices. Matrix Multiplication. Transposition and Trace of a Matrix.

Optional

Determinants. Systems of Linear Equations. Elementary Operations. The Inverse Matrix.

Experimentalist

The Method of Least Squares.

Theorist

Transformation Matrices.

Honors

Write an essay about a related topic.

Trigonometry

Core

Trigonometric Functions. Trigonometric Identities. Inverse Trigonometric Functions. Vectors.

Optional

Right Triangles. Angle Measurement. Trigonometric Equations. Complex numbers.

Experimentalist

Fitting Trigonometric Functions

Theorist

Exponential and Logarithmic Functions.

Honors

Write an essay about a related topic.

Differential Calculus

Core

Techniques of Differentiation. Differentials. Implicit Differentiation. Extrema of Functions.

Optional

Linear Approximations. One-Sided Limits. Infinite Limits. Continuity.

Experimentalist

Sketching Curves.

Theorist

Uniform Continuity and the Mean Value Theorem.

Honors

Write an essay about a related topic.

Integral Calculus

Core

Definite Integrals. The Fundamental Theorem of Calculus. Area. Integration by Substitution and by Parts.

Optional

Volume. Integration by Partial Fractions. Trigonometric Integrals. Curve Length.

Experimentalist

Probability.

Theorist

Moments and Centroids.

Honors

Write an essay about a related topic.

Differential Equations

Core

First-Order Differential Equations. Second-Order Differential Equations. Higher-Order Differential Equations. Power Series Methods.

Optional

Laplace Transforms. Linear Systems. Nonlinear Systems. Numerical Methods of Solution.

Experimentalist

Deriving differential equations from experimental/observational results.

Theorist

Operators.

Honors

Write an essay about a related topic.

Vector Analysis

Core

Partial Derivatives. Multiple Integrals. Vector Differentiation. Vector Integration.

Optional

Maxima and Minima of Vector Functions. The Geometry of Euclidean Space. Directional Derivatives. Lagrange Multipliers.

Experimentalist

To be determined.

Theorist

Implicit and Inverse Function Theorems.

Honors

Write an essay about a related topic.

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