MA502 SPATIAL VISUALIZATION, SHAPE, AND MEASUREMENT. (3 Cr.)
COURSE DESCRIPTION
Prerequisite
Mathematics education major or minor or elementary education major with
mathematics concentration; required course in the Master of Science in
Mathematics (MSME) program.
General Introduction and Goals
Historical and philosophical foundations of mathematics and their
relationships to measurement, Euclidean and non-Euclidean geometries, analytical
geometry, trigonometry, transformations, shape and dimension, and applications.
Objectives
This course will deepen students' understanding of the mathematical foundations
of different geometries. Students will explore the role of visualization,
shape, and measurement in relation to understanding, describing, and solving
problems encountered throughout history, and they will become more aware of
connections between topics studied in this course and topics taught in the
elementary and secondary curriculum.
Content Outline
This course will examine selected topics from the following areas of
mathematics:
- Euclidean and non-Euclidean geometries (e.g., historical underpinnings of
geometry; axioms; significance of Euclid's parallel postulate and consequences
of alternative postulates)
- Analytical geometry (e.g., Descartes' work; two- and three-dimensional
coordinate representations; rectangular and polar coordinates; analytic
solutions to geometric problems)
- Spherical geometry and trigonometry (e.g., great circles and spherical
coordinates; measurement and navigation in two and three dimensions;
relationships between trigonometric functions and "right-triangle
trigonometry")
- Measurement (e.g., length, distance, area, volume, surface-area
measurements; measurement applied to selected plane and solid figures;
accuracy and precision)
- Graphs (e.g., graphical representation of functions; translations,
reflections, rotations, and dilations; graphing calculators and software)
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