Quiz Study Guide

Items will appear here as the semester progresses

1.

Quiz 1 will be over section 1.2 in Rosenlicht and will possibly ask for the definition of indexing family and intersection and union of sets over an indexing family. There will also be proofs similar to problem 5 in Chapter 1 in Rosenlicht.

2.

Quiz 2 will be over section 1.3 in Rosenlicht and will possibly ask for the definition(s) of image of a set under a function, inverse image of a set under a function, one-to-one, onto. There will also be a proof similar to part of problem 8 in Chapter 1 in Rosenlicht.

3.

Quiz 3 will be over section 1.4 in Rosenlicht and the handout on countable sets. It will possibly ask for the definitions of finite set, infinite set, infinite sequence, countably infinite, countable and uncountable. It may ask you for Theorems 2 or 4 on the hand out on countable sets, or exercise 5, which may be proved using any preceding exercise or Theorem.

4.

Quiz 4 will be over sections 2.1 and 2.2 in Rosenlicht. You should know the definition of absolute value and its properties 1-5 on page 22. You should able to use correctly all of Properties I-VI, F1-F10,O1-09. Anticipate problems such as 5 and 7 on page 30.

5.

Quiz 5 will be over sections 3.1 in Rosenlicht. You should know the definition of metric space and be able to work problems such as 1a and 1c in chapter 2.

6.

Quiz 6 will be over section 3.2 in Rosenlicht. You should know the definition of open set, open ball, closed set, closed ball, and the propositions about open and closed sets in section 3.2. Be able to show that the finite union of a collection of bounded sets is a bounded set and that finite subsets of a metric space are closed.

7.

Quiz 7 will be over problem 16b in chapter 3.

8.

Quiz 8 will ask for proofs such as showing that a convergent sequence is a bounded sequence or that if b_n is a sequence of non-zero real numbers that converges to the non-zero real number b then 1/b_n converges to 1/b.

9.

Quiz 9 will ask for proofs such as those of the third Proposition on page 52 and the Corollary on page 53.

10.

Quiz 10 will ask for proofs such as

• Problem 32 of chapter 3
• Show that if p is cluster point of a set S then there is a sequence of points of S that converges to p.

11.

Quiz 11 will cover Strichartz, 4.1.1. To prepare, reread the entire section carefully and understand the explanations and developments that he gives. The quiz may ask about some of these as well as ask you for some examples and/or true/false questions regarding continuous functions and limits. In order to imagine what some of these might be, take the definitions of ``domain of a function'', ``range of a function'', ``continuous function'' , ``uniformly continuous function'', ``limit of a function'' and ``bounded set'' and ``unbounded set'' and think about combining them in different ways.

12.

Quiz 12 will cover Strichartz, 4.1.3-4. To prepare, reread the entire section carefully and understand the explanations and developments that he gives. The quiz may ask about some of these as well as ask you for some examples and/or true/false questions regarding continuous functions, Lipschitz continuity and open sets. In order to imagine what some of these might be, take the definitions of ``domain of a function'', ``range of a function'', ``continuous function'' , ``uniformly continuous function'', ``Lipschitz Continuity'', ``open set'', ``bounded set'' and ``unbounded set'' and think about combining them in different ways.

13.

Quiz 13 will cover Strichartz, 4.2.1-2. To prepare, reread the entire section carefully and understand the explanations and developments that he gives. The quiz may ask about some of these as well as ask you for some examples regarding continuity, the intermediate value theorem and connected sets.

14.

Quiz 14 will cover Strichartz, 5.1. To prepare, reread the entire section carefully and understand the explanations and developments that he gives. The quiz may ask about some of these as well as ask you about problems 7 and 8.

15.

Quiz 15 does not exist, everyone gets 10/10.

16.

Quiz 16 will cover Strichartz, 5.3 and will also have problems similar to problems 1 and 7 in section 5.3.

17.

Quiz 17 will cover Strichartz, 6.1.1. Know definitiion 6.1.1 with all the details and problem 2 in section 6.1.5.

18.

Quiz 18 will cover both parts of the Fundamental Theorem of Calculus, (Integration of the Derivative and Differentiation of the Integral) along with their proofs and other interpretations.