IF YOU ARE ENROLLED IN 441, GO TO THE 441 CANVAS SITE to see and (in some cases) turn in assignments. This version of the assignments is provided only for those who are not yet enrolled in the class, but hope to be.
Remember that you may turn in reports on both parts on 9/29, or you may postpone the report on part 2 until Tuesday. Follow the Reading Response Guidelines EXCEPT if you are not yet enrolled, write and submit your response to Professor Arms at arms@math.washington.edu.
Part 1. Read §§1-2 of Chapter 1 in Munkres, but follow the instructions below. If you find yourself spending a lot of time on §1, postpone some of it until later, because it's important that you read §2 (with the handout replacing part of it) before Monday's class.
Section 1 reviews basic ideas from Math 300, but has one notation convention that may be different from your previous classes. Read about inclusion and proper inclusion at the bottom of p. 4. We will follow the text's convention for notation for these concepts.
For the rest of §1, you should be able to scan through, looking at words or sentences in italics (e.g., disjoint on p. 6 and DeMorgan's laws on p. 11) and at the subsection titles (e.g., p. 5 The Union of Sets and the Meaning of "or"). If each of these seems familiar and you think you could explain it to a classmate, you probably don't need to read about it. If you feel uncertain about something, read what Munkres says.
One more comment on §1: There's a paragraph on p. 13 that describes an ordered pair as a collection of sets. We won't use that description. Note that Munkres himself says "most mathematicians think of an ordered pair as a primitive concept;" that is, they don't use the "collection of sets" description.
For §2, replace pp. 15-16 with this handout: functions.pdf. Read the handout and then p. 17 through the rest of §2. (On p. 17 when Munkres mentions the "rule" of a function, he just means the function as a subset of the product of the domain and codomain.)
RR on Part 1: For A, answer these questions. Did the reading feel like it was all review of things you know pretty well? If not, what were the things that seemed least familiar? Did you have to postpone any part of §1 until later? Don't forget to do parts B & C! See RRguidelines19.pdf.
We will come back to §3 when we start using "relations" in Chapter 2. Consult §§4-7 if you need to recall something about properties of integers or real numbers, induction, or showing sets are finite or countable or uncountable. In particular you should know that the integers are countably infinite and the real numbers are uncountable. §§8-11 are completely optional.
Part 2. Read this handout: metricspaces.pdf. When reading material the first time, before sending me a RR, it's OK to skip details in proofs and examples if you're getting bogged down in them. Be sure then to say, as one of your "questions," where you found material challenging enough to decide to postpone the details.
Remark: We will work with this handout before starting Chapter 2 because most students like to build from a familiar example to its generalization. If you prefer to start with the general definition, then see how a familiar example fits the definition you are welcome to look ahead to pp. 75-78 and 119-120 now, to see how metric spaces, and in particular Euclidean spaces, are one kind of topological space.
RR on Part 2: Have you worked with the concept of a metric (with its 3 defining properties) in any previous class? Have you encountered any other metric besides the Euclidean metric? Don't forget parts B & C!
§2, p. 21: Exer. 1, 4(c) & (e). This means make a conjecture about what you can say in each case, and then prove your conjecture. Of course, because this is a Warmup Problem, "prove" means it is OK to give just an outline of the proof, or if you can't prove it, evidence of serious attempt to find a proof: write down any steps you did prove, relevant definitions, and/or investigate an example, etc.
You should read all the parts of exercise 4 and think about them a bit, because you might need to use part (a) or (b) or (d) later (for instance, in exercise 5, which will be a Followup Problem).
Because you aren't enrolled and so can't get to Canvas to submit this assignment, you may either scan or take photos of your work and email them to the TA Tafari James, tafarij@uw.edu, or you may turn in a hard copy at the START of class on Monday. (Use one, not both, of these methods. If you turn in a hard copy at the start of class, have a second copy to keep for working with your group.)
If (and only if) you didn't send a report on both parts of the reading on Sunday, remember to email your RR on part 2 to Professor Arms at arms@math.washington.edu by 1:30 (or as soon after as you can) on Tuesday.
§2, p. 21, Exercise 5. Remember that "yes or no" questions as in part (d) always mean "and prove your answer is correct." For each question in part (d), that means either give an example showing it is possible, or give a proof that the left, respectively right, inverse is unique.
From Metric Spaces handout (link above in Reading assignment):
p. 4-5, Exercises 3.7 and 3.11.
Be sure to review the Followup Problem Guidelines before you finish writing up this first assignment. When done, don't forget to estimate your time doing this assignment and put that time next to your name on the front page.
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Most recently updated on September 28, 2019.