Math 299 – Spring 2026: Training Workouts

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.

• Read the course syllabus (see below).  Let me know if you have any questions.
• Read the introduction to the lecture notes.
• Read Problem #1 on the 2021 Prove it! admissions test and then play the Scrambler! Product Catalog game until you figure out how to reliably beat any goal on all three machines (Juggler, Frogger, Whirligig). You do not have to answer parts (a)-(f) of the question or hand in anything, but you should try figure out a strategy that is guaranteed to beat all three machines no matter what goal comes up when you select “New Goal”. I will ask you in class how to solve each machine. Optional: If you figure out all three levels, you can try the more advanced Scrambler game. Beware! The later levels are hard!

• 0. For each assignment that you hand in in Dropbox, make a folder called “Assignement #n”, where n is the Assignment number I have posted here. So for this assignment, put it in a subfolder of our shared Dropbox folder called “Assignment #1” and put your document in there. All assignments must be handed in prior to class on the day they are due. Be sure to name your files as explained in the syllabus below.
• 1. Answer Problem #2.4 at the end of Chapter 2 in the lecture notes. Type up your answer (you can use any editor for this assignment) and save your file to Dropbox as described above.
• 2. Try to figure out how to consistently beat Trix Game at all levels.  This is another example of a Toy Proof system. I’ll ask for volunteers in class. Write up your solution and put it in the same document as the previous problem.

Reminder: For each assignment that you hand in in Dropbox, make a folder called “Assignement #n”, where n is the Assignment number I have posted here. So for this assignment, put it in a subfolder of our shared Dropbox folder called “Assignment #2” and put your documents in there. All assignments must be handed in prior to class on the day they are due. Be sure to name your files as explained in the syllabus below.

• 1. Prove each of the following Circle-Dot theorems. You must use the Toy Proof software to ensure that your proofs are correct. Prove them using the software, and then print that web page to a PDF document and place that pdf document in your Dropbox homework folder with the appropriate file name. You can prove all four parts in one proof if you want, rather than proving them separately (but its ok if you prove then separately too). If you put one pdf for each problem below, name the files so I know which one is which. You can also just insert the printout into a larger document so that you can type comments or mark up the pdf with a stylus (for my iPad users).
  • Thm B: $\bullet\bullet\bullet$
  • Thm J: $\bigcirc\bigcirc\bigcirc$
  • Thm N: $\bigcirc\bullet\bigcirc\bullet\bigcirc\bullet$
  • Thm P:  $\bigcirc\bigcirc$
• 2. (Bonus) Can you explain why every circle-dot expression is a theorem in the Circle-Dot toy system, or if not, determine with certainty exactly those expressions which are not? Write up your answer in a pdf document (using whatever editor you like for now) and put it in the same Dropbox folder with this assignment.
• 3. Bring your laptops to class from now on.

Reminder: For each assignment that you hand in in Dropbox, make a folder called “Assignement #n”, where n is the Assignment number I have posted here. So for this assignment, put it in a subfolder of our shared Dropbox folder called “Assignment #3” and put your documents in there. All assignments must be handed in prior to class on the day they are due. Be sure to name your files as explained in the syllabus below.

• 1. Answer problem 3.1 in the lecture notes.
• 2. Answer problem 3.2 in the lecture notes.
• 3. Answer parts (a) thru (g) of problem 3.3 in the lecture notes.

Reminder: For each assignment that you hand in in Dropbox, make a folder called Assignment #n, where $n$ is the Assignment number I have posted here. So for this assignment, put it in a subfolder of our shared Dropbox folder called Assignment #4 and put your documents in there. All assignments must be handed in prior to class on the day they are due. Be sure to name your files as explained in the syllabus below.

• 1. Read and follow the instructions in the Lurch Quick Start Guide. You don’t need to hand anything in for this question (but you do for the next one).
• 2. Answer the questions in this document in Lurch and use the Lurch File menu to save it to your homework folder in Dropbox. It should be named Assignment 4 - firstname.lurch where firstname is replaced with your first name. It should validate with all green checks if you type it correctly.

• 1. Answer question #4.1 in Chapter 4 of the new lecture notes. Use the Lurch File menu to save it to your homework folder in Dropbox. It should be named Assignment 5 - firstname.lurch where firstname is replaced with your first name. It should validate with all green checks if you type it correctly. Can you see why they are correct?

Click on this link and fill in the proofs in the Lurch document that opens.

• Your proofs should have only one meaningful expression per line.
• Every claim should be justified with a reason (using non-meaningful black text after the claim as we did in the example in class).
• You can add extra explanation or ask questions using the expository text.
• You cannot add any Rule, Premise, or Theorem environments to the document. You can (and should) add Subproof environments, of course.
• Type your name at the top after the word Name.

Save frequently to your Dropbox folder using the Lurch File > Save menu option.

Click on this link and fill in the proofs in the Lurch document that opens.

• Your proofs should have only one meaningful expression per line.
• Every claim should be justified with a reason (using non-meaningful black text after the claim as we did in the example in class).
• You can add extra explanation or ask questions using the expository text.
• You cannot add any Rule, Premise, or Theorem environments to the document. You can (and should) add Subproof environments, of course.
• Type your name at the top after the word Name.

Save frequently to your Dropbox folder using the Lurch File > Save menu option.

Click on this link, read everything, and fill in the proofs in the Lurch document that opens. Feel free to ask me questions by email if you are stuck.

Click on this link, read everything, and fill in the proofs in the Lurch document that opens. Feel free to ask me questions by email if you are stuck. Put your files in Dropbox as usual.

• 1. Memorize the rules for Propositional Logic and Predicate Logic from Chapter 5 and Chapter 6 of the lecture notes for an in-class quiz on Tuesday.
• 2. Click on this link, read everything, and fill in the proofs in the Lurch document that opens. Feel free to ask me questions by email if you are stuck. Put your files in Dropbox as usual. Let your genius shine!

Click on this link, read everything, and fill in the proofs in the Lurch document that opens. Feel free to ask me questions by email if you are stuck. Put your files in Dropbox as usual.