EGMT 1520: Building Truth from Scratch

How do we know a mathematical claim is true? In this course, we will explore the nature of mathematical proof through an interactive, collaborative approach by building, testing, and refining mathematical arguments from first principles. Rather than memorizing established results, we will distinguish among examples, counterexamples, conjectures, and formal proofs, learning to recognize both the power and limitations of empirical evidence in mathematics. Through problem-solving sessions and “math battles,” students will practice evaluating the success or failure of proofs, sharpen their ability to communicate abstract ideas, and rigorously challenge one another’s claims. By experiencing mathematics as a creative process - where logical structure and empirical observations combine to form reliable conclusions - students will cultivate a deeper awareness of how and why certain arguments achieve certainty. Along the way, we will experience mathematics as a creative, empirical discipline where logical reasoning transforms intuition into certainty.