Instructor: Florent Baudier
Office: Blocker 525C
Office hours: MW 2:30-5:00 p.m. or by appointment
Term Paper Instructions

	Tasks	Suggested 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. Type your first LaTeX document with a title ''Term Paper of Firstname Lastname'' and a first section ''Mathematical Logic'' and try to familiarize yourself with the software (helpful tutorials, Wikibook LaTeX).	Friday 09/07
#2	In your section called Mathematical Logic draw the truth table of the implication. Make sure that your table has a caption and is centered.	Friday 09/14
#3	Create a new section called "Proof Techniques" and explain what is Modus Ponens.	Friday 09/21
#4	In the section called "Proof Techniques" create a subsection called "Proof by contradiction" and a subsection called "Proof by cases". In the subsection "Proof by contradiction" state the following theorem "log(3) is irrational" and provide a proof. (see homework 3.17 for a hint). When you write a theorem use the theorem environment (\begin{theorem} write the theorem here \end{theorem}). To write your proof use the proof environment (\begin{proof} write the proof here \end{proof}). To be able to use the proof environment your document class needs to be \documentclass{amsart} or you need to call the package amsmath. Your term paper should have two sections and two subsections now.	Friday 10/05
#5	Create a new section called "The Principle of Mathematical Induction". State the PMI theorem and detail one example of your choice of a proof by induction. Your term paper should have three sections and two subsections now. This assignment must be turned in (by the deadline indicated). You will send me an email with the subject ``MATH 220 term paper of (write your last name)'' with two files attached: the .tex file and the .pdf file. The names of the files must be of the following form: yourlastname_draft.tex and yourlastname_draft.pdf.	Tuesday 10/15, midnight
#6	Create a new section called "Introduction to Set Theory". Define the arbitrary union, arbitrary intersection of a collection of sets. State the two DeMorgan's laws for arbitrary unions and arbitrary intersections (Theorem 13 from the lecture notes) and prove only one of them.	Monday 11/05
#7	In the subsection "Proof by cases" include the proof of the statement of your choice whose proof is based on distinguishing cases. In the section "Introduction to Set Theory" reproduce the statement of Problem 7.17 OR Problem 7.18 from the homework problem set and provide a solution.	Monday 11/12
#8	In the section "Introduction to Set Theory" include the formal definitions of the power set of a set. Illustrate this notion with a simple example.	Monday 11/19
#9	Create a new section "Functions" and include the formal definition of a function, and of the following notions: injectivity, surjectivity, bijectivity. Illustrate with simple examples. This assignment must be turned in (by the deadline indicated). You will send me an email with the subject ``MATH 220 term paper of (write your last name)'' with two files attached: the .tex file and the .pdf file. The names of the files must be of the following form: yourlastname_final_version.tex and yourlastname_final_version.pdf.	Monday 11/26, 11:59 p.m.