| 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 16, 11:59 p.m. you must upload to Gradescope 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 01/16, 11:59 p.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 23, 11:59 p.m. you must upload in Gradescope 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 01/23, 11:59 p.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 30, 11:59 p.m. you must upload in Gradescope 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 01/30, 11:59 p.m. |
| #4 | Create a section called ``Mathematics by Mathematicians'' and write a short biography (between 200 and 250 words) of George Boole focusing on his scientific work. Follow the regular procedure to submit your files in Gradescope. | Friday 02/06, 11:59 p.m. |
| Last day to submit the final version of Tasks #1-#3. | Friday 02/13, 11:59 p.m. | |
| #5 | Create a section called ``Introduction to number theory''. State the fundamental theorem of arithmetic (it can be found in the lecture notes) and prove that there are infinitely many prime numbers. Follow the regular procedure to submit your files in Gradescope. | Friday 02/20, 11:59 p.m. |
| #6 |
Create a section called Principle of Mathematical Induction. Then,
1. Write no more than 200 words about the Peano Axioms. 2. 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: (i) The principle of mathematical induction implies the principle of strong mathematical induction. (ii) The principle of strong mathematical induction implies the principle of mathematical induction. Follow the regular procedure to submit your files in Gradescope. | Friday 03/06, 11:59 p.m. |
| #7 | 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 3 included and provide a solution for Exercises 1-3. Follow the regular procedure to submit your files in Gradescope. | Sunday 03/15, 11:59 p.m. |