MA501 MATHEMATICAL REPRESENTATION, REASONING, AND PATTERNS. (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 problem solving and applications; proof, logic, and
mathematical reasoning; algebraic structures and functions; mathematical
representations and coding.
Objectives
This class will deepen students' understanding of the nature of mathematical
reasoning and proof, and the concomitant need for symbolism. Students will
learn how algebraic thinking and structure can lead to applications, 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:
- Logic and set theory (e.g., syllogisms and the contributions of Aristotle,
Euler, Venn, Carroll; Godel's and Cantor's work)
- Algebraic structures (e.g., groups, rings, fields)
- Code theory (e.g., Fermat's work; Turning machines; enigma machines;
public key encryption system; matrices; modular arithmetic)
- Problem solving and recreational mathematics (e.g., algebraic methods;
systems; classic problems)
- History of mathematics (e.g., Greek mathematics; figurate numbers;
Fibonacci numbers; cardinality)
- Applications (e.g., discovering patterns involving the topics above that
have led to applications in biology, weather, photography, computers, etc.)
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