| Tasks | 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 January 17, 9 a.m. you must upload to Canvas two files: the .tex file and the .pdf file. The names of the files must be of the following form: yourlastname_task1.tex and yourlastname_task1.pdf. | Friday 01/17, 9 a.m. |
| #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 January 24, 9 a.m. 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_task2.tex and yourlastname_task2.pdf. | Friday 01/24, 9 a.m. |
| #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 January 31, 9 a.m. 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_task3.tex and yourlastname_task3.pdf. | Friday 01/31, 9 a.m. |
| Last day to submit the final version of Tasks #1-#3. | Friday 02/14, 9 a.m. | |
| #4 | Create a section called Principle of Mathematical Induction. Write no more than 200 words about the Peano Axioms. By Friday February 21, 9 a.m. you must upload to Canvas two files: the .tex file and the .pdf file. The names of the files must be of the following form: yourlastname_task4.tex and yourlastname_task4.pdf. | Friday 02/21, 9 a.m. |
| #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 February 28, 9 a.m. you must upload to Canvas two files: the .tex file and the .pdf file. The names of the files must be of the following form: yourlastname_task5.tex and yourlastname_task5.pdf. | Friday 02/28, 9 a.m. |
| #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 from Definition 1 up to Exercise 1 included and provide a solution for Exercise 1. By Friday March 07, 9 a.m. you must upload to Canvas two files: the .tex file and the .pdf file. The names of the files must be of the following form: yourlastname_task6.tex and yourlastname_task6.pdf. | Friday 03/07, 9 a.m. |
| Last day to submit the final version of Tasks #4-#5. | Friday 03/14, 9 a.m. | |
| #7 | In the section called "An introduction to Set Theory" create a new subsection called "A soft introduction to measure theory". In this subsection write a short essay describing the field of mathematics called "Measure Theory" (no more than 200 words). In this section, reproduce the template for the project on a soft introduction to measure theory from Definition 1 up to Exercise 1 and provide a solution for Exercise 1. By Friday March 21, 9 a.m. you must upload to Canvas two files: the .tex file and the .pdf file. The names of the files must be of the following form: yourlastname_task7.tex and yourlastname_task7.pdf. | Friday 03/21, 9 a.m. |
| #8 |
In the subsection called "A soft introduction to topology", reproduce and provide a solution for Exercise 2 from the project on a soft introduction to topology.
In the subsection called "A soft introduction to measure theory", reproduce and provide a solution for Exercises 2-3 from the project on a soft introduction to measure theory. By Friday March 28, 9 a.m. you must upload to Canvas two files: the .tex file and the .pdf file. The names of the files must be of the following form: yourlastname_task8.tex and yourlastname_task8.pdf. | Friday 03/28, 9 a.m. |
| Last day to submit the final version of Tasks #6-#7. | Friday 04/04, 9 a.m. | |
| #9 |
In the subsection called "A soft introduction to topology", reproduce and provide a solution for Exercise 3 from the project on a soft introduction to topology.
In the subsection called "A soft introduction to measure theory", reproduce and provide a solution for Exercises 4-5 from the project on a soft introduction to measure theory. By Friday April 4, 9 a.m. you must upload to Canvas two files: the .tex file and the .pdf file. The names of the files must be of the following form: yourlastname_task9.tex and yourlastname_task9.pdf. | Friday 04/04, 9 a.m. |
| #10 |
In the subsection called "A soft introduction to topology", reproduce and provide a solution for Exercise 4 from the project on a soft introduction to topology.
In the subsection called "A soft introduction to measure theory", reproduce and provide a solution for Exercises 6-7 from the project on a soft introduction to measure theory. By Friday April 11, 9 a.m. you must upload to Canvas two files: the .tex file and the .pdf file. The names of the files must be of the following form: yourlastname_task10.tex and yourlastname_task10.pdf. | Friday 04/11, 9 a.m. |
| Last day to submit the final version of Tasks #8-#9. | Friday 04/18, 9 a.m. | |
| #11 |
In the subsection called "A soft introduction to topology", reproduce and 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", reproduce and provide a solution for Exercise 8 from the project on a soft introduction to measure theory. By Friday April 18, 9 a.m. you must upload to Canvas two files: the .tex file and the .pdf file. The names of the files must be of the following form: yourlastname_task11.tex and yourlastname_task11.pdf. | Friday 04/18, 9 a.m. |
| Last day to submit the final version of Tasks #10-#11. | Friday 04/25, 9 a.m. |