| Tasks | Draft submission deadline | |
|---|---|---|
| #1 |
Download a LaTeX distribution that is compatible with your operating system.
I strongly recommend that you use TexShop if you are a Mac user or TexWorks if your are working with Windows. If you like to work online you can use Overleaf. Type your first LaTeX document with a title ''Term Paper of Firstname Lastname'' and a first section ''Mathematical Logic''. Write between 150 and 200 words about Mathematical Logic (e.g. origins, types of logic, applications...) and try to familiarize yourself with the software (helpful tutorials, Wikibook LaTeX). By Friday September 01, 8am you must upload in Canvas two files: the .tex file and the .pdf file. The names of the files must be of the following form: yourlastname_draft1.tex and yourlastname_draft1.pdf. | Friday 09/01 |
| #2 | In your section called Mathematical Logic draw the truth tables of the following logical connectives: negation, conjunction, disjunction, implication. Make sure that your tables have a caption and are centered. Then, reproduce the statement of Problem 1.14 in the homework problem set (you will need to create an environment for problems) and provide a solution (use the proof environment). By Friday September 08, 9am you must upload in Canvas two files: the .tex file and the .pdf file. The names of the files must be of the following form: yourlastname_draft2.tex and yourlastname_draft2.pdf. | Friday 09/08 |
| #3 | In your section called Mathematical Logic: First recall the two DeMorgan Laws. Then, state the following exercise and provide a solution. Exercise: Are the statement forms P∨((Q∧R)∨ S) and ¬((¬ P)∧(¬(Q∧ R)∧ (¬ S))) logically equivalent? By Friday September 15, 9am you must upload in Canvas two files: the .tex file and the .pdf file. The names of the files must be of the following form: yourlastname_draft3.tex and yourlastname_draft3.pdf. | Friday 09/15 |
| #4 | Create a section called Principle of Mathematical Induction. Write no more than 200 words about the Peano Axioms. By Friday October 6, 9am you must upload in Canvas two files: the .tex file and the .pdf file. The names of the files must be of the following form: yourlastname_draft4.tex and yourlastname_draft4.pdf. | Friday 10/06 |
| #5 | Prove that the principle of mathematical induction is equivalent to the principle of strong mathematical induction. More precisely you need to provide a proof for the following two statements: 1. The principle of mathematical induction implies the principle of strong mathematical induction. 2. The principle of strong mathematical induction implies the principle of mathematical induction. By Friday October 13, 9am you must upload in Canvas two files: the .tex file and the .pdf file. The names of the files must be of the following form: yourlastname_draft5.tex and yourlastname_draft5.pdf. | Friday 10/13 |
| #6 | Create a new section called "An introduction to Set Theory" and a subsection called "A soft introduction to topology". In this subsection write a short essay describing the field of mathematics called "Topology" (no more than 200 words). Then, reproduce the template for the project on a soft introduction to topology. Provide a solution for exercise 3 in the template. By Friday October 20, 9am you must upload in Canvas two files: the .tex file and the .pdf file. The names of the files must be of the following form: yourlastname_draft6.tex and yourlastname_draft6.pdf. topology project helper | Friday 10/20 |
| #7 | In the subsection called "A soft introduction to topology". Provide a solution for exercises 1,2, and 4 from the project on a soft introduction to topology. By Friday October 27, 9am you must upload in Canvas two files: the .tex file and the .pdf file. The names of the files must be of the following form: yourlastname_draft7.tex and yourlastname_draft7.pdf. | Friday 10/27 |
| #8 | In the section called "An introduction to Set Theory" create a new subsection called "A soft introduction to measure theory". In this section reproduce the template for the project on a soft introduction to measure theory. Provide a solution for exercises 1-2-3 in the template. By Friday November 03, 9am you must upload in Canvas two files: the .tex file and the .pdf file. The names of the files must be of the following form: yourlastname_draft8.tex and yourlastname_draft8.pdf. | Friday 11/03 |
| #9 | In the subsection called "A soft introduction to measure theory". Provide a solution for exercises 4-5-6-7 from the project on a soft introduction to measure theory. By Friday November 10, 9am you must upload in Canvas two files: the .tex file and the .pdf file. The names of the files must be of the following form: yourlastname_draft9.tex and yourlastname_draft9.pdf. measure project helper | Friday 11/10 |
| Last day to resubmit Task #1-#5. | Friday 11/17, 5pm | |
| Last day to resubmit Task #6-#9. | Sunday 11/26, 5pm | |
| #10 | In the subsection called "A soft introduction to topology". Provide a solution for exercise 5 from the project on a soft introduction to topology. In the subsection called "A soft introduction to measure theory". Provide a solution for exercise 8 from the project on a soft introduction to measure theory. By Saturday December 2, 11:59 pm you must upload in Canvas two files: the .tex file and the .pdf file. The names of the files must be of the following form: yourlastname_final_paper.tex and yourlastname_final_paper.pdf. topology project helper measure project helper | Saturday 12/02, 11:59 pm |