MATH 4150 - Advanced Perspectives for Math Teachers

• After completion of the course, the student will be able to contextualize the mathematics content learned for their program in the content they will teach at the high school level.
• Analyze common mathematical problems and real-world models using functions.
• Analyze solutions of mathematical problems to determine alternative means of solving and/or representing the solution, and ways of extending and/or generalizing the problem.
• Analyze the origins, representations, and applications of mathematical concepts.
• Apply and prove the Division Algorithm and Euclidean Algorithm.
• Construct and analyze proofs using mathematical inductions.
• Describe the various ways of representing and defining of functions.
• Develop and apply algebraic properties of modular arithmetic systems.
• Explain the construction of the real and complex number systems and various ways of representing real and complex numbers.
• Extend the Division and Euclidean Algorithm to polynomials.
• In particular, the student will be able to perform, analyze, and see the connections between the following skills and concepts and to the application of these skills to high school mathematics instruction. The skills/processes include:
• Recognize and prove various logical equivalences to mathematical induction.
• Relate integer congruence to real-world applications. Prove and apply the Chinese Remainder Theorem.
• Relate properties of the real and complex number systems to general ordered fields.
• Use the theory of functions in solving equations and inequalities.