Homework will be assigned most class meetings. Students are expected to complete each assignment prior to walking into the next class meeting. The significant majority of our time in class will be devoted to students presenting some subset (maybe all) of the proofs/solutions that are due that day.

During class, you are encouraged to annotate your work in light of presentations made in class; however, you must use a different color than what you used to complete your homework. Homework assignments will be collected at the end of class. No late homework will be accepted. Instead, I will drop your lowest 3 homework scores.

When it comes to completing assignments, you should not look to resources outside of the context of this course for help. You should not be consulting the web, other textbooks, other faculty, or students outside of this section of the course in an attempt to find solutions to the problems you are assigned. This also includes websites like Chegg and Course Hero, or generative AI such as ChatGPT or Gemini. On the other hand, you are allowed and encouraged to utilize each other, the textbook, me, your course mentor Seb, and your own intuition. If you need additional resources, please come talk to me and we will work together on a plan of action.

As we proceed through the problem/theorem sequence in the textbook, you may wonder which results you are allowed to use. In general, you may use the basic algebra and ordering of the integers, the Well-Ordering Principle, standard logic and proof techniques such as cases, contradiction, contraposition, and induction, any result we have proven earlier in the sequence, and anything I have explicitly granted us. When in doubt: prove it before you use it. Many of these proof techniques will be discussed as we encounter them. When using a previous result from the textbook you should cite it by number.

Numbered items below, such as 1.4, are problems and theorems from Number Theory Through Inquiry, which you can read online at no cost through the Grinnell College Library.