## Calendar

Your syllabus has a rough calendar of what we will be covering each class.  After each class I will post what we were actually were able to cover here:

1. 8/29 – Today we went over the syllabus and discussed the first assignment, I encourage you to start working on that sooner rather than later. We also when through an opening day class activity to help preview some of what we will be doing this semester.
2. 9/1 – Today we worked through the material in Chapter 2 of your text by looking at the sample explanations of Newton’s method linked below. First we practiced comparing texts. Next we discussed reading a text in detail in order to make sure we could understand why and how the author was doing what they where doing, not just the what. You should now start looking at assignment 2 listed below and due 9/12/2022.
3. 9/8 – Today we discussed material from chapters 3 and 4 on writing mathematics. We looked at some samples of poorly written mathematics (sample trig problem and sample calculus problem) and discussed how we could more clearly write up the given solutions. We will continue exploring these ideas on Monday.
4. 9/12 – Today we finished writing up the calculus example from last time. We also discussed proper notation/terminology and we looked at a problem with errors (sample problem with errors) so that we could practice proofreading. You should read through chapters 3 and 4 in your text if you haven’t done so already and start working on the assignment due 9/19/2022, which does need to be typed.
5. 9/15 – Today we started looking at chapter 5, in particular we looked at Polya’s four steps for problem solving: Understand, Plan, Execute, Review. We worked through a couple of problems in class and will do another next class. You should read through chapter 5. Next time we will also start looking at the material in chapters 6 through 13, all of this should be review from MAT 141 so we won’t be spending a lot of time on it. Since we only got through a couple examples of problem solving today I moved the due date of the problem solving exercises to 9/29. Finally, don’t forget that you have a writing assignment due next class and it needs to be typed.
6. 9/19 – Today we looked at two more examples of problem solving. We solved the projectile problem by asking more questions in order to make sure we understood the problem and how the assumptions were used/needed. We solved the problem $\forall\, n\in\mathbb{N},\ \exists\, x,y,z\in\mathbb{N}:x^2+y^2=z^n$ by looking at examples and sorting examples until we were able to see patterns which lead to a solution. Next class we will review material on implications from MAT 141. We should also have time to answer brief questions ahead of the exam on Monday 9/26.
7. 9/22 – Today we discussed some comments on writing up your work, in particular being careful not to write as if you are assuming what you want to prove. Then we started discussing implications, much of what we discussed can be found in chapters 6-8. Monday is the exam, so we will pick up with the new material next Thursday.

## Assignments

Unless specifically specified otherwise, all assignments must be typed and in complete sentences. Proper submission formatting may count for up to 10% of the assignment grade.

1. Due 9/8/2022 – Writing Up Mathematics Assignment. This assignment does not need to be typed.
2. Due 9/12/2022 – Reading Assignment: Hand in your annotated copy of chapter 1 and your work for problem (iv) on page 12. Recall that for this you should be completing/explaining the underlined statements and answering included questions. This assignment does not need to be typed, in fact much of it you can complete by writing directly on a copy of chapter 1.
3. Due 9/15/2022 – Extra Credit What is Mathematics? Assignment: Read this article What is Mathematics? by Jenny Quinn (MAA Focus Vol, 42 No. 4), then write a brief reflection on your own thoughts. This should be typed, double spaced, with 1 inch margins, and about a page long. Be sure to include …
• What sort of things you think about when you are “doing math.”
• What you think math is based on your experiences and on what you personally got out of the article.
4. Due 9/19/2022 – Writing Assignment: Rewrite these poorly written out solutions:  Hey isn’t this good enough Prof? Due 9/19/2022
5. Due 9/29/0222Problem Solving Assignment: Demonstrate that you have used all of Polya’s steps by solving these Chapter 5 problems (For this assignment turn in your rough work along with your final typed solution):
• p.49 (iv), and (vi),
6. Due 10/10/2022 – Conjecture Exercise: This assignment does not need to be typed, in fact much of it you can complete by writing directly on a copy of the Conjecture Exercise handout.
7. Due 10/24/2022 – Direct Style Proofs: From the text:
• p.146 – (ii); p.153 – (ii); p.159 – (i) and (vii)
8. Due 11/7/2022 – Contradiction and Contrapositive Proofs: From the text:
• p.164 – (iv); p. 165 – (xii) (Hint: First prove the lemma: If $$n^3$$ is even, then $$n$$ is even.);
• p. 183 – (iii) (Hint: Look at p.165 – (i)).
9. Due 11/17/2022 – Induction Proofs: From the text:
• p.172 – (ii), (vii), (iii)<- Prove once directly and then again using (vii) ;
• Extra Credit p.173 – (vi) or (viii)
10. Due 12/15/2022 by 4pm – Number Theory Assignment from the text:
• p. 194 – (ii), (iv); p.206 – (ii), (iv)ab; p.216 – (xi)bd, (xiv);
• Extra Credit p.207 (viii)
11. Due 12/15/2022 by 4pm – Proofs Portfolio: Remember that this must contain an example of: direct proof, proof by cases, proof by contradiction, proof by contrapositive, and proof by induction. For each proof you should include at least two drafts; one that you completed earlier in the semester and that I commented on and at least one revision of that.

## Exams

1. Exam 1 on Monday 9/26 covers chapters 1 through 5
2. Exam 2 on Thursday 10/13 will cover the material from chapter 6 through 18 with an emphasis on understanding implications, quantifiers, and reading theorems and proofs.
3. Exam 3 on Thursday 10/27 will cover direct proofs, proofs by cases, divisibility, modular equivalence, and the division algorithm.
4. Exam 4 on Thursday 11/10 will cover proofs by contradiction and by contrapositive.
5. Exam 5 on Monday 11/21 will cover proofs by induction, you need to know the P.M.I., Strong Induction, the general format of a proof by induction.
6. Exam 6 on Thursday 12/15 @ 11am (During Finals!) will cover Number Theory, the topics will include:
• Divisibility
• Division Algorithm
• Well Ordering Principle
• Fundamental Theorem of Arithmetic
• Greatest Common Divisor and Least Common Multiple
• Euclidean Algorithm
• Chinese Remainder Theorem
• Wilson’s Theorem
• Euler’s $$\phi-function$$ and Euler’s Theorem (Fermat’s Little Theorem)