CRN 10459: Final Projects
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*Groups of three students each will work on one of the final projects. | *Groups of three students each will work on one of the final projects. | ||
| − | *Deliverables consist of a 10-minute presentation and, in | + | *Deliverables consist of a 10-minute presentation and, in most 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 presentation 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 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. | ||
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*'''Topics:''' | *'''Topics:''' | ||
# The Schroeder-Bernstein Lemma (Exercise 1.5.11, 1.5.7) | # The Schroeder-Bernstein Lemma (Exercise 1.5.11, 1.5.7) | ||
| + | # [http://helmut.knaust.info/class/202610_3341/3341limsup.pdf Limes Inferior and Limes Superior] | ||
| + | # [http://helmut.knaust.info/class/202610_3341/3341accpts.pdf More on Accumulation Points] | ||
# Perfect Sets (Section 3.4, 1st part) | # Perfect Sets (Section 3.4, 1st part) | ||
# Baire's Theorem (Section 3.5) | # Baire's Theorem (Section 3.5) | ||
# [http://helmut.knaust.info/class/201220_4303/FTAlgebra.pdf A Proof of the Fundamental Theorem of Algebra]* | # [http://helmut.knaust.info/class/201220_4303/FTAlgebra.pdf A Proof of the Fundamental Theorem of Algebra]* | ||
| − | # | + | # [http://helmut.knaust.info/class/202610_3341/3341monotone.pdf Monotone Functions] |
# [http://helmut.knaust.info/class/202010_3341/Euler-M.pdf The Euler-Mascheroni Constant] | # [http://helmut.knaust.info/class/202010_3341/Euler-M.pdf The Euler-Mascheroni Constant] | ||
# A Continuous Nowhere Differentiable Function (Section 5.4)* | # A Continuous Nowhere Differentiable Function (Section 5.4)* | ||
| Line 24: | Line 26: | ||
# Uniform Convergence II* (Section 6.2, pp. 176 bottom-179, including Theorem 6.2.6) | # Uniform Convergence II* (Section 6.2, pp. 176 bottom-179, including Theorem 6.2.6) | ||
# The Cantor Function (Exercise 6.2.12) | # The Cantor Function (Exercise 6.2.12) | ||
| − | # The Arzela-Ascoli Theorem (Exercises 6.2.14 , 6.2.15) | + | <!-- # The Arzela-Ascoli Theorem (Exercises 6.2.14 , 6.2.15)--> |
| + | |||
| + | [http://helmut.knaust.info/class/202610_3341/Teams.pdf Project teams] | ||
[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/202610_3341/RubricFP.pdf Grading Rubric]<br> | [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 $\pi$.] | ||
Latest revision as of 18:44, 13 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 most 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 presentation 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 Tuesday, November 18.
- Topics:
- The Schroeder-Bernstein Lemma (Exercise 1.5.11, 1.5.7)
- Limes Inferior and Limes Superior
- More on Accumulation Points
- Perfect Sets (Section 3.4, 1st part)
- Baire's Theorem (Section 3.5)
- A Proof of the Fundamental Theorem of Algebra*
- Monotone Functions
- 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)
Advice on Giving a Good PowerPoint Presentation, by Joseph Gallian. | PPT version
Grading Rubric
An example: Exploring Machin's Approximation of $\pi$.
