# CRN11378: Final Projects

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- The final project will account for 25% of your course grade.

- Groups of two students each will work on one of the final projects.

- Deliverables consist of a complete written solution (target length: five pages) and a 10-minute presentation. (There are some starred 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!

- The projects will be presented during the last class day on
**Thursday, December 5, at 12:00-13:20.**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
**Tuesday, November 12**.

**Topics:**

- The Schroeder-Bernstein Lemma (Exercise 1.4.13)
- Dirichlet’s and Abel’s Tests (Exercises 2.7.12-2.7.14)
- A comparison of the Root and Ratio tests* (W. Rudin, Principles of Mathematical Analysis)
- Double Series and the Cauchy product* (E. Hairer and G. Wanner, Analysis by Its History)
- Perfect Sets* (Section 3.4, 1st part)
- Connected Sets (Section 3.4, 2nd part)
- Sets of Discontinuity (Section 4.6)
- The Euler-Mascheroni Constant
- A Continuous Nowhere Differentiable Function (Section 5.4)
- The Cantor Function (Exercise 6.2.13)

Advice on Giving a Good PowerPoint Presentation, by Joseph Gallian.