CRN 11247: Final Projects
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*The final project will account for 25% of your course grade. | *The final project will account for 25% of your course grade. | ||
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*Projects will be assigned on '''Thursday, November 11'''. | *Projects will be assigned on '''Thursday, November 11'''. | ||
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*'''Topics:''' | *'''Topics:''' | ||
| − | # The Schroeder-Bernstein Lemma (Exercise 1.5.11, 1.5.7) | + | # '''Cecilia, Jocelynn, Leslie:''' The Schroeder-Bernstein Lemma (Exercise 1.5.11, 1.5.7) |
| − | # Perfect Sets (Section 3.4, 1st part) | + | # '''Daniel, Pedro:''' Perfect Sets (Section 3.4, 1st part) |
| − | # Connected Sets (Section 3.4, 2nd part) | + | # '''Citlali, Mariah, Saul:''' Connected Sets (Section 3.4, 2nd 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]* | ||
| − | # Sets of Discontinuity (Section 4.6) [no graduate students] | + | # '''Daniela, Italia, Jacqueline:''' Sets of Discontinuity (Section 4.6) [no graduate students] |
# [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)* | ||
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# Uniform Convergence I* (Section 6.2, pp. 173-176) | # Uniform Convergence I* (Section 6.2, pp. 173-176) | ||
# 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) | ||
| + | # '''Adrian, Dennise, Julien:''' The Arzela-Ascoli Theorem (Exercises 6.2.14 , 6.2.15) | ||
[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/202010_3341/RubricFP.pdf Grading Rubric]<br> | [http://helmut.knaust.info/class/202010_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 11:52, 12 November 2021
- The final project will account for 25% of your course grade.
- Six groups of three (or 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 final exam period on Tuesday, December 7 at 13:00-15:45. 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 11.
- Topics:
- Cecilia, Jocelynn, Leslie: The Schroeder-Bernstein Lemma (Exercise 1.5.11, 1.5.7)
- Daniel, Pedro: Perfect Sets (Section 3.4, 1st part)
- Citlali, Mariah, Saul: Connected Sets (Section 3.4, 2nd part)
- Baire's Theorem (Section 3.5)
- A Proof of the Fundamental Theorem of Algebra*
- Daniela, Italia, Jacqueline: Sets of Discontinuity (Section 4.6) [no graduate students]
- 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)
- Adrian, Dennise, Julien: 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 $\pi$.
