Mathematical Reasoning –


(3 credits)

This course presents an introduction to advanced mathematical concepts and historical perspectives. Students examine truth tables and develop competence with formal logical proof techniques. Students investigate the real number system and also explore mathematical language, functions, and theoretical geometry.

This undergraduate-level course is 5 weeks. This course is available to take individually or as part of a degree or certificate program. To enroll, speak with an Enrollment Advisor.

Basics of Logic

  • Create sentences using standard mathematical terms.
  • Utilize truth tables to represent logical concepts.
  • Identify mathematical laws in logical statements.

Formalities and Techniques of Logic

  • Differentiate among axioms, theorems, corollaries, and lemmas.
  • Analyze arguments for validity.
  • Construct valid logical arguments.

Theoretical Geometry

  • Define geometric terms such as lines, points, rays, and angles.
  • Demonstrate an understanding of geometric proofs.

Sets and Numbers

  • Differentiate among number systems.
  • Utilize Venn diagrams to represent logical concepts.
  • Utilize the rules of arithmetic (axioms) to create mathematical proofs.

Significant Historical Proofs

  • Compare and contrast the work of two historically significant mathematicians.
  • Decipher proofs of historical significance.

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