Proof for Feedback:
choose #3, 4 or 5 (your choice) from the Existence Proofs Worksheet
- Wednesday is a proof test! It will be an existence proof. For more practice, see Hammack, Chapter 7, exercises 12, 17, 18, 20 (uses the symbol “divides”; it says “11 divides 2^n-1”).
- Finish your existence proofs worksheet; choose one of them to request feedback on from the grader (put it first in what you hand in). In class we will take up the solutions. (Of course, don’t look at this before you do your proof for feedback, that would be kind of silly.)
- With what time remains, read Hamkins, Chapter 3 up to end of 3.2 (Number Theory, Prime Numbers and Fundamental Theory of Arithmetic). This involves an existence proof.
No proof for feedback, because there’s a test.
- Study for your test on Wednesday. You can hand in some practice problems on canvas. Resources/info:
- Test will be 20 minutes at the end of class, on counting problems. The problems will be short-answer problems (not proofs), grades mainly based on getting the answer correct.
- Materials from class are all available under “Materials Archive” tab. In particular, the main topics are:
- Multiplication, addition, subtraction, and division principles
- How to count all sorts of things by use of the principles above
- How to count the number of ways to order k elements chosen from n elements (and why it works)
- How to count the number of subsets of a set of size n (and why it works)
- How to count the number of subsets of size k chosen from a set of size n (binomial coefficient and its formula and why it works)
- Here are some example test problems I’ve given in the past. For hints, discuss on discord (use the “spoiler” feature on discord if hinting/spoiling anything). For full solutions, see this solution set. BUT I suggest you use the full solutions only when you are confident you have solved it yourself — asking for a hint is a better way to proceed for more effective learning.
- Hammack chapters 3.1-3.4 exercises are excellent practice.