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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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