CRN 10459: Final Projects
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[http://helmut.knaust.info/BD/Gallian.pdf Advice on Giving a Good PowerPoint Presentation], by Joseph Gallian. | [http://helmut.knaust.info/class/202010_5195/PPTs.pdf PPT version]<br> | [http://helmut.knaust.info/BD/Gallian.pdf Advice on Giving a Good PowerPoint Presentation], by Joseph Gallian. | [http://helmut.knaust.info/class/202010_5195/PPTs.pdf PPT version]<br> | ||
| − | [http://helmut.knaust.info/class/ | + | [http://helmut.knaust.info/class/202610_3341/RubricFP.pdf Grading Rubric]<br> |
[http://helmut.knaust.info/class/202010_3341/Machin.pdf An example: Exploring Machin's Approximation of $\pi$.] | [http://helmut.knaust.info/class/202010_3341/Machin.pdf An example: Exploring Machin's Approximation of $\pi$.] | ||
Revision as of 11:35, 11 November 2025
- The final project will account for 25% of your course grade.
- Groups of three students each will work on one of the final projects.
- Deliverables consist of a 10-minute presentation and, in some cases, a complete written solution (target length: five pages). (The starred projects are projects with no written report.) The paper does not need to be typeset if the handwriting is legible. Don't forget to include the references you use, in both the presntations and the written report! Do not use AI resources!
- The projects will be presented during the final exam period on Thursday, December 11 at 16:00-18:45. The accompanying papers are due before the start of the presentations.
- The student group will be graded as a group. All group members must contribute to both the written solution and the presentation in equal parts.
- The group will be graded foremost on the mathematical correctness and mathematical clarity of their presentation and their written report. Other criteria include the completeness of the written report, the quality of the group presentation, making effective use of the allotted time, and staying within the time frame of 10 minutes for the oral presentation.
- Projects will be assigned on Thursday, November 18.
- Topics:
- The Schroeder-Bernstein Lemma (Exercise 1.5.11, 1.5.7)
- Perfect Sets (Section 3.4, 1st part)
- Connected Sets (Section 3.4, 2nd part)
- Baire's Theorem (Section 3.5)
- A Proof of the Fundamental Theorem of Algebra*
- Sets of Discontinuity (Section 4.6)
- The Euler-Mascheroni Constant
- A Continuous Nowhere Differentiable Function (Section 5.4)*
- Uniform Convergence I* (Section 6.2, pp. 173-176)
- Uniform Convergence II* (Section 6.2, pp. 176 bottom-179, including Theorem 6.2.6)
- The Cantor Function (Exercise 6.2.12)
- The Arzela-Ascoli Theorem (Exercises 6.2.14 , 6.2.15)
Advice on Giving a Good PowerPoint Presentation, by Joseph Gallian. | PPT version
Grading Rubric
An example: Exploring Machin's Approximation of $\pi$.
