YEAR 3: Computational Math

Projects utilizing computer algebra systems, technical writing, research skills. Topics include complex variables, computational geometry, matrix algebra.

Course Outline

Part I

Complex Numbers
Polar Form. Euler's Formula.
Trigonometry.
- Trigonometric Functions: Sine, Cosine, and Tangent. Solving Right Triangles.
- Radian Measure.
Computational Geometry
- Volumes of Solids: Parallelepipeds, Prisms, Pyramids, Cones, Spheres, Polyhedron.
- Inscribed and Circumscribed Circles of a Triangle. Radii of Inscribed and Circumscribed Triangles.
- Heron's Formula.
Plane Geometry with Complex Numbers.

Part II

Matrix Algebra.
- Elimination. Row Reduction.
- Determinants. Cramer's Rule.
- Parametrization of Lines and Planes.
Computational Methods for Roots of Polynomials.
- Bezout's Theorem for Roots of Polynomials.
- Descarte's Rule of Signs. Number of Real Roots.
- Cubic and Quartic Roots Formula.
- Solution of Equations in Terms of Radicals.
- Rational Root Theorem.
Plane Transformations.
- Isometries. Composition. Inverse.
- Dilations. Reflections. Rotations.
- Matrix of a Transformation.

Part III

Logarithms.
- Solving for Exponents.
- Exponential Growth and Decay.
Semi-Algebraic Sets.
- Inequalities in Two Variables
- Optimization Problems. Linear Programming in Dimension Two.
Diophantine Equations.
- Pythagorean Triples.
- Pells Equation.
- Gaussian Integers

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