Welcome to Math 299, where mathematicians are born! I will post assignments and announcements here throughout the semester. Check back frequently. Below are links to some resources we will be using in the course.
Below are all of the Training Workouts for Math 299 – Spring 2023 to date. For the most recent Training Workout and additional information see the Math 299 Home Page.
Welcome to Math 299, where mathematicians are born! I will post assignments and announcements here throughout the semester. Check back frequently. Below are links to some resources we will be using in the course.
1. Type up a Formal proof of each of the following statements. You can only use the rules of Propositional Logic discussed in class. To do that, start your new document by using the Lurch menu File > Choose Topic.. > Logic > Propositional Logic > Blank Document. Put your name at the top. For each theorem, first state the theorem, then give a proof of it directly below the theorem as I did in the examples in class (I put a copy of both the original document I shared with you and the one I did in class in your Dropbox folder).
Number each statement in the proof, and give a reason for every statement (except Assumptions, which need no reason). Use the auto-numbered list in the Lurch to number the lines – don’t type the line numbers by hand. Be sure to give the line numbers for the statements used as the premises (i.e. inputs) immediately after the reason. Use the TAB key to indent your assumptions, and also to line up your reasons in a separate column. Do all of your work in Lurch. Save your work often! Lurch has been known to crash! You can use Lurch to check your work as I showed you in class.
If you have questions, just let me know. Put your assignment in Dropbox in a folder for Assignment 4. Save it as a .lurch file (not a pdf) so I can type in it and leave comments and grades. It’s ok to put the file in there when it is partially finished – I won’t grade it until after Tuesday, and if you get stuck or have a problem while working on the proofs I can open your file and help you figure it out.
If everyone loves themselves then everyone loves someone.
Mixed bag. Prove each of the following theorems and write up your semiformal proof in a single LaTeX file project. When you are done, download the pdf file from Overleaf and put it in your Dropbox folder in a subfolder named “Assignment #18”. The proof of each theorem can only use results from earlier chapters and the axioms, definitions, and previously proven results from the same chapter that the theorem is from.
0. Memorize the definitions of Functions in the table on page 68 (section 10.4) of the lecture notes for a short quiz at the start of class.
1. Start working on your Take Home Final Exam. To help keep you on track, put a draft of your Take Home Final Exam pdf in Dropbox before class on Thursday. It should use the Homework Template – Article style linked to below, not the usual Homework Template – Handout style. Create all of the necessary sections and pieces (Title, Abstract, Introduction section, Proof section, Summary section, bibliography) and you can start to fill in the commentary. Put your pdf in a Final Exam subfolder of your Dropbox folder, and call it ‘Final Exam Draft 1.pdf’.
You can start to pick out which of the six theorems you would like to prove in accordance with the instructions in your Dropbox folder, and you can include the theorem statements and even the proofs if you find some you like. You can always change your mind about which problems you want to answer at any time before the exam is due, and keep in mind that any problems that are assigned for homework or done in class are no longer eligible. So one good strategy would be to try to prove six easy one point proofs first, and then try to increase your score from there by upgrading some to two points or three points, or collect some of the bonus points for induction, or proof by cases, writing style, or diagrams. See the instructions for details.
0. Memorize the definitions of Functions in the table on page 68 (section 10.4) of the lecture notes for a short quiz at the start of class.