The Mathematical Proof: Origins, Importance, and Construction
Course enrollment will be available for this course once it is scheduled.
The Pythagorean Theorem. The area of a circle. The quadratic formula. We know how to use these things, but where did they come from? In this course, students will not only be afforded a glimpse into the origins of these and other famous and familiar mathematical ideas and formulas, but they will also be equipped with the tools to compose their own mathematical proofs.
From the inception of mathematical thought and discourse, mathematicians (such as Newton, Descartes, Pythagoras, and Einstein) have investigated matters regarding numeration, shapes and special reasoning, the idea of infinity, and other pertinent mathematical concepts that eventually had to be rigorously proven. Through analytical reasoning, critical thinking, and logical pathways to understanding, many foundational formulas and concepts (including the aforementioned) became a lasting part of the study of mathematics, and are still central in the 21st Century.
As an instructor of not only mathematics, but also of mathematics education, I view the understanding of "proof" as foundational to understanding and appreciating the logical and analytical habits of mind that a successful math learner possesses. As such, I am structuring the course in which the goal is not only to learn "proof", but to use it as a vehicle to help advance students logical, critical, and analytical processes, which will benefit them as they pursue further studies (and maybe careers) in math and science.
By the end of the course, the students will be able to:
• Identify key mathematical concepts and the method(s) by which they were proven
• Identify common strategies of mathematical proof
o Direct Proof
o Proof by Induction
o Proof by Contradiction
• Construct their own mathematical proofs
• Improve their skills in logical induction and deduction and analysis
• Critique their own reasoning and the reasoning of others, regarding the level of rigor in constructed proofs
There are no formal prerequisites for this course, but it will be beneficial to the student to have successfully completed courses in basic and advanced algebra, geometry, and trigonometry. Completion of courses in trigonometry and calculus is also welcomed.