The following general topics can be used to guide your more specific topic selection:

• Explain the process of constructing the real number system beginning with the natural numbers.
• Prove implications of axioms and properties of the real number system.
• Describe the concept of an ordered field as it applies to the real number system.
• Describe the idea of a limit of a function at a point.
• Determine whether a given function is continuous, discontinuous, or uniformly continuous.
• Explain the connection between the continuity of a function at a point and the function being differentiable at a point.
• Prove and apply the fundamental theorem of calculus in finding the value of specific Riemann integrals of functions.

1. Document the proof in detail with comprehensive supporting information, specifically:
   1. Ensure mathematical representations (equations, diagrams, graphs, etc.) are clear and appropriate.
   2. Ensure that your use of mathematical terminology and notation is accurate.
   3. Present all of the main elements of the mathematical proof, including axioms and theorems.
   4. Explain the significant mathematical concepts involved in your proof.
2. Provide a thorough oral defense, speaking clearly and effectively.
3. Organize your presentation in a logical way and pace the transitions so that the material is easily accessible to your audience of peers.