Guidelines and Rubric: Topic Selection

Overview

The topic of 2 selections should be a three-pages submission detailing the topic you selected for your final project, a synchronous live oral defense of your mathematical proof. The topic description should provide sufficient detail to show the appropriateness of the topic. If you are using an alternative format for the slides other than PowerPoint, you need to let the instructor know in this submission.

NOTE: The topics should be intimately connected to the structure of real numbers, sequences, continuity, differentiation, and Riemann integration real numbers. The following general topics can be used to guide your more specific topic selection, select two topics of those as followed:

  • Explain the process of constructing the real number system beginning with the naturalnumbers.
  • Prove implications of axioms and properties of the real numbersystem.
  • Describe the concept of an ordered field as it applies to the real numbersystem.
  • Describe the idea of a limit of a function at apoint.
  • Determine whether a given function is continuous, discontinuous, or uniformlycontinuous.
  • Explaintheconnectionbetweencontinuityofafunctionatapointandthefunctionbeingdifferentiableatapoint.
  • Prove and apply the fundamental theorem of calculus in finding the value of specific Riemann integrals offunctions.

Review A Brief Note on Proofs in Pure Mathematics for a description of the components of a mathematical proof.

Specifically the following critical elements must be addressed:

Provide a description of the selected topic, describing:

  • Thespecifictopicofthemathematicalprooftobepresented,includingtheappropriateaxiomsandtheoremsandwhichmethodofproofyoumayuse (e.g., direct proof, proof by construction, proof by contradiction, proof by induction,etc.).
  • Ananalysisofwhythistopicisappropriateforasynchronousliveoraldefenseofyourmathematical proof, forexample,cananappropriatelevelofdetail bepresentedwithin5to10minutestoprovidea clear,logicalargument?

Rubric

Guidelines for Submission: Milestone One: Topic Selection should follow these formatting guidelines: One page, double spacing, 12-point Times New Roman font, one-inch margins, and citations in APA format.

This activity uses an integrated rubric in Blackboard. Students can view instructor feedback in the Grade Center. For more information, review these instructions.

Instructor Feedback: Students can find their feedback in the Grade Center.

Critical Elements / Proficient (100%) / Needs Improvement (55%) / Not Evident (0%) / Value
Mathematical Topic / Selects and comprehensively explains a topic to defend in the mathematical proof / Selects and explains a topic to defend in the mathematical proof; however, explanation is insufficient or inaccurate / Does not select or accurately identify a topic for mathematical proof / 40
Analysis / Demonstrates comprehensive analysis of the topic, demonstrating the appropriateness of the topic choice / Demonstrates minimal analysis of the topic; minimallydemonstrates appropriateness of topicchoice / Does not demonstrate analysis of the topic/show the appropriateness of the topic / 40
Articulation of Response / Submission has no errors related to citations, grammar, spelling, syntax, or organization / Submission has major errors related to citations, grammar, spelling, syntax, or organization that negatively impact readability and articulation of main ideas / Submission has critical errors related to citations, grammar, spelling, syntax, or organization that prevent understanding of ideas / 20
Earned Total / 100%