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.


SemiAlgebraic Sets.

Inequalities in Two Variables

Optimization Problems. Linear Programming in Dimension Two.


Diophantine Equations.

Pythagorean Triples.

Pells Equation.

Gaussian Integers
