Math 448 – Fall 2026: Problem Sets

Welcome to Math 448! 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.

• 0. Read the course syllabus.  There is a link to it below. Report typos.
• 1. Read over Chapter 0 in the Lecture Notes and Appendices A,B,C,D in the textbook.  This should be easy light reading and mostly familiar material. You don’t need to obsess over it, just refresh the ideas and terms.
• 2. Write up and hand in any questions you have or concepts you are not familiar with in that background material so we can go over it on Thursday.  See the syllabus for instructions on how to write up your assignments. Type them up in Lurch by clicking here and save the resulting file to your Dropbox folder according to the instructions in the syllabus.

1. Read the Lurch Quick Start Guide for Students if you have any questions either ask me or one of the students who had me for Math 299.
2. Open the Writing and Checking Proofs with Lurch worksheet. Answer all of the questions in there and check your work with Lurch. As it says in the syllabus, save the completed file (using the Lurch File menu, not the browser File menu) in your Dropbox folder in a subfolder labeled assignment 02. Be sure the file name contains your name and the assignment number and ends in .lurch.
3. Prove both theorems in this Lurch document. Save it in the same folder as the previous worksheet. You will probably have questions, so just ask me or each other. No AI or Google! Yuk! 🤮 I don’t expect everyone to get every assigned proof, so just give it your best shot even if it’s not entirely correct.
Most of all.. have fun!

1. Read over Chapters 1.1 and 1.2 in the Lecture Notes below and in the textbook. In particular read the proof of the Division Algorithm Theorem in the textbook in Chapter 1.1
2. Prove the theorem in this Lurch document. Save it in your Dropbox folder in a subfolder named assignment 03 (lower case, one space, a zero before the 3, no # or hyphens). No AI or Google! Yuk! 🤮

1. Prove the theorems in this Lurch document. Save it in your Dropbox folder in a subfolder named assignment 04 (lower case, one space, a zero before the 3, no # or hyphens). No AI or Google! Yuk! 🤮
2. Putnam Training! (optional bonus points) Look at the problems in Round 1 of this year’s USAMTS competition. We will follow the same rules and regulations of the competition itself, but you will only submit any solutions you find to me, not to the contest (since you aren’t eligible!). Solutions should be handed in a folder named USAMTS Round 1 in your Dropbox folder before 10pm Eastern on October 13, 2026. You don’t need to verify them in Lurch, but you should write up your solutions either in Lurch or LaTeX. Game on!

1. Prove the theorems and answer the questions in this Lurch document. Note that the first one is the half finished proof we started in class. Save it in your Dropbox folder in a subfolder named assignment 05 (lower case, one space, a zero before the 5, no # or hyphens). No AI or Google! Yuk! 🤮
2. Putnam Training! (optional bonus points) Continue to optionally work on the bonus problems in Round 1 of this year’s USAMTS competition. Game on!

1. Prove the theorems and answer the questions in this Lurch document. Save it in your Dropbox folder in a subfolder named assignment 06 (lower case, one space, a zero before the 6, no # or hyphens). No AI or Google! Yuk! 🤮
2. Putnam Training! (optional bonus points) Continue to optionally work on the bonus problems in Round 1 of this year’s USAMTS competition. Game on!