## Before the Lecture

• Read Sections 4.3, 4.4, 4.6, 5.1:
• Watch the videos related to these sections (after reading them):
• Write down all questions about the above topics to bring to our (online) lecture. (You can also type them in the file "Questions.tex" in SageMathCloud.) Comments about the videos are welcome!
• Work on the assigned problems for these sections. (See Related Problems below.) You don't need to finish them, but try to work on as many as you can and the bring your questions to class.

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## Related Problems

The "turn in" problems are due on 06/28 (Homework 5) by 11:59pm.

 Section 4.3: Turn in: 14, 16. Extra Problems: 2, 4, 9, 12, 21. Section 4.4: Turn in: 6, 22. Extra Problems: 2, 3, 9, 15. Section 4.6: Turn in: 13, 20. Extra Problems: 4, 8, 16. Section 5.1: Turn in: 9(b), 17(b). Extra Problems: 9(a), 11, 13, 17(a).

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## In Class

In class:

• We will discuss the reading and pace.
• I will discuss the main points.
• I will answer any other questions.
• We can work on the HW problems.

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## Outcomes

After the assignment (reading and videos before class) and class, you should:

• understand graphic representation of relations (Problem 4.3.5);
• understand relations on a (single) set;
• understand (and be able to identify) reflexive, symmetric and transitive relations (most problems from 4.3);
• know what an antisymmetric relation is;
• know what are total and partial orders (and their difference -- Problem 4.4.2);
• know what least/greatest (or smallest/largest) and minimal/maximal elements are (and their difference) (Examples 4.4.5, 4.4.7, Problem 4.4.3);
• know what upper/lower bound are and what greatest lower bound and least upper bound are (Example 4.4.10, Problem 4.4.3);
• know what equivalence relation and equivalency class are;
• know what a partition is;
• know the relation between partitions and equivalence relations;
• know what are congruences modulo $n$ (as in $a \equiv b \pmod{n}$);
• understand functions as relations (and be able to prove basic facts about them).

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