Mathematics

All mathematics teachers (5-8 and 8-12) shall meet the following requirements:

1. Algebra (Courses in which Algebra is evident)

• Pre-Calculus
• Classical Algebra
• Elementary Functions
• Introduction to Functions of Several Variables
• Multi-variable Calculus
• Partial Differential Equations
• Integral Calculus, Infinite Series
• Vector Calculus and Linear Algebra
• Computer Algebra
• Problem Solving

2. Euclidean geometry (Courses in which Geometry is evident)

• Classical Geometry
• Foundations of Geometry
• Geometric Structures
• Differential Geometry
• From Euclid to Einstein
• Introduction to Algebraic Topology
• Topology and Geometric Analysis
• Geometry and Manifold Theory
• Complex Algebraic Geometry
• Fractal Geometry
• Analytic Geometry and Calculus

3. Trigonometry (Courses in which Trigonometry is evident)

• Introduction to Functions of Several Variables
• Pre-Calculus
• Multi-variable Calculus
• Differential Calculus
• Partial Differential Equations
• Integral Calculus, Infinite Series
• Vector Calculus and Linear Algebra

4. Discrete/finite mathematics
(The following courses usually engage this content)

• Methods of Discrete Mathematics
• Discrete Mathematics and Graph Theory
• Finite Mathematics
• Number Theory
• Topics in Analysis
• Numerical Analysis
• Numerical Methods
• Set Theory
• Introductory Data Analysis
• Data, Functions, and Graphs
• Optimization
• Foundations of Cryptography
• Mathematics of Finance
• Problem Solving
• Discrete Mathematics for Computer Science

5. Introductory calculus through integration
(The following courses usually engage this content

• Multi-variable Calculus
• Differential Calculus
• Partial Differential Equations
• Integral Calculus, Infinite Series
• Optimization
• Combinatorics and Calculus

6. History of mathematics
(The following courses usually engage this content)

• History of Mathematics
• Development of Mathematics

7. Use of technology
(The following courses usually engage this content)

• Mathematical Theory of Computation
• Mathematical Foundations of Computer Science
• Discrete Mathematics for Computer Science
• Multivariable Calculus with Computers
• Mathematical Software-Scientific Programming
• Mathematics of Computer Graphics
• Software Techniques for Scientific Computation
• Linear Programming and Extensions
• Optimization
• Mathematics in the Age of Information
• Introduction to Logic and Computability
• Nonlinear Programming
• Computer-Assisted Mathematical Problem-Solving

Additional requirements for 8-12 teachers:

1. Abstract algebra
(The following courses usually engage this content)

• Introduction to Abstract Algebra
• Linear Algebra
• Vector Calculus and Linear Algebra
• Fields and Galois Theory
• Modern Algebra
• Lie Algebras
• Representation of Continuous Groups
• Linear Algebra and Differential Equations

2. Number theory
(The following courses usually engage this content)

• Number Theory
• Algebraic Number Theory

3. Calculus through differential equations
(The following courses usually engage this content)

• Differential Calculus
• Vector Calculus and Linear Algebra
• Linear Algebra and Differential Equations
• Partial Differential Equations
• Ordinary Differential Equations
• Integral Calculus, Infinite Series
• Multi-Variable Calculus
• Measure Theory and Integration
• Calculus of Variations
• Combinatorics and Calculus
• Dynamical Systems and Calculus
• Differential Equations: Dynamics and Chaos

4. Probability and statistics
(The following courses usually engage this content)

• Probability Theory
• Discrete Probability and Mathematical Theory of Sample Surveys
• Introduction to Mathematical Statistics
• Probability and Matrices
• Stochastic Processes
• Topics in Combinatorics
• Combinatorics and Calculus
• Dynamical Systems and Calculus

5. Non-Euclidean and transformational geometries
(The following courses usually engage this content)

• Geometry and Transformations
• Differential Geometry
• From Euclid to Einstein
• Introduction to Algebraic Topology
• Topology and Geometric Analysis
• Geometry and Manifold Theory
• Complex Algebraic Geometry
• Fractal Geometry
• Metric Differential Geometry
• Differential Topology
• Classical Geometry: Projective

6. Applied mathematics or mathematics modeling
(The following courses usually engage this content)

• Introduction to Applied Mathematics
• Advanced Methods in Applied Mathematics
• Partial Differential Equations of Applied Mathematics
• Applied Linear Analysis
• Topics in Analysis
• Mathematical Physics and String Theory
• Linear Programming and Extensions
• Mathematical Modeling
• Introduction to Mathematical Mechanics
• Numerical Computation
• Optimization
• Math Games and Theory of Games
• Introduction to Cryptography
• Introduction to Mathematical Economics
• Mathematical Tools for the Physical Sciences
• The Mathematics of Medical Imaging and Measurement