Lecture 10

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• Before the Lecture
• Related Problems
• In Class
• Outcomes

• Read Sections 4.4 and 4.6. (Note: Look at the section Outcomes to see what you are expected to get from the reading, perhaps after also some in class help.)
• Watch the videos related to these sections (after reading them):
  • Remarks on Section 4.4.
  • Problem 4.4.8.
  • Problem 4.4.20.
  • Problem 4.4.23(a).
  • Remarks on Section 4.6.
  • Problem 4.6.15.
  • Problem 4.6.22(a) and (b).
  • Problem 4.6.9.
• Write down all questions about the above topics to bring to our (online) lecture. Comments about the videos are welcome! You can also post questions you'd like us to discuss on
• Piazza. Just make sure to choose the correct folder (in Piazza) for the lecture.
• 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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All of these are to be turned in on 06/22 (Homework 6) by 11:59.

Section 4.4: Turn in: 6, 22. Discuss in Meeting: 2, 3, 9, 15.

Section 4.6: Turn in: 13, 20. Discuss in Meeting: 4, 8, 16.

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In class:

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

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

• know what an antisymmetric relation is;
• know what are total and partial orders (and their difference);
• know what least/greatest (or smallest/largest) and minimal/maximal elements are (and their difference);
• know what upper/lower bound are;
• know what greatest lower bound and least upper bound are;
• 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 $a \equiv b \pmod{n}$).

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