Spring 2017

Professor: Erika L.C. King

Email:eking@hws.edu

Office: Lansing 304

Phone: (315)781-3355

**Our first exam is Tuesday (February 21) 7:15PM-9:15PM in Gulick 206A. You will turn in your journal at the beginning of the exam. I will
randomly grade three to five of the entries
completely. Then I will count to see how many total entries you have. Note that it is highly likely that
the graded entries will be those things we did not specifically go over in class or have on a quiz. Remember to follow the
journal guidelines (hightlighting exercise/problem numbers or the start of a question, etc.).**

- Vocabulary List
- One Question you had followed by an answer for each journal assignment for a total of 10 questions with answers.
- Section 1.2: problems 2, 4, 6 and 7
- Check Yourself problems 1 and 2 at the end of Section 1.3
- Check Yourself problems 1, 2 and 3 at the end of Section 1.4
- The "nice version" of Example 1.4.7 as requested on page 13
- Check Yourself problems 1 and 2 at the end of Section 1.5
- Problem 17 in Section 1.7
- On page 18, Prof. belcastro introduces existence proofs/theorems. In your journal, describe what they are and what makes them different from other proofs/theorems.
- Here is an existence theorem: "There exists an integer whose cube equals its square." Try writing a nice proof of this theorem.
- Check Yourself problems 1-6 at the end of Section 2.2
- Problem 13 and 15 in Section 1.7
- Check Yourself problems 1, 4, 5, and 8 at the end of Section 2.3
- Richard Hammack's book: Section 2.6 numbers 3 and 13, and Section 2.10 numbers 1, 2, 4 and 8
- Problem 5 in Section 2.9
- Section 2.4: problems 1, 2 and 3
- Consider the symbolic statement $(P\land Q)\Rightarrow (R\vee Q)$. Negate this statement. Then illustrate a truth table for the negation.
- Section 2.4: problems 5, 6 and 7
- Check Yourself problems 1-3 at the end of Section 2.5
- Write down the two main steps for a proof by contraposition, then do the same for contradiction. (Hint: the two steps should start with "Assume" and "Show"!)
- On Thursday, Christian presented the first half of the proof for part II number three on this worksheet. In your journal, write the second half of the proof!
- In your journal, write all ten ways of expressing the statement: If f is a differentiable function, then f is a continuous function.
- Problems 4(a)-(c), 8 and 9 in Section 2.4
- Problem 4(d) and (e) in Section 2.4
- Richard Hammack's book: Section 1.8 numbers 1, 4 and 5
- Check Yourself problems 1 and 2 at the end of Section 3.2
- Prove the Theorem: Let $A$, $B$ and $X$ be sets. If $X\subseteq A$ or $X\subseteq B$, then $X\subseteq A\cup B$.
- Problems 15, 21 and 23 in Section 2.9