Lecture 4

Navigation

• Back to Main Page.
• Back to the Lectures.
• Before the Lecture
• Related Problems
• In Class
• Outcomes

Before the Lecture

• Read Section 3.1-4.
• Watch the videos related to this section (after reading it):
  • Problem 3.1.3.
  • Problem 3.1.5.
  • Problem 3.1.11.
  • Problem 3.2.1.
  • Problem 3.2.3.
  • Problem 3.2.6.
  • Problem 3.3.8.
  • Problem 3.3.14.
  • Problem 3.3.16.
  • Remarks on Section 3.4..
  • Problem 3.4.9.
  • Problem 3.4.15.
  • Problem 3.4.23.
• 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 Sage Math Cloud.) 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.

 

Related Problems

The "turn in" problems are due on 06/18 (Homework 3) by 11:59pm.

Section 3.1:	Turn in: 6, 10.
	Extra Problems: 2, 15, 16.
Section 3.2:	Turn in: 4, 7.
	Extra Problems: 2, 9, 12.
Section 3.3:	Turn in: 10, 15.
	Extra Problems: 2, 4, 18, 21.
Section 3.4:	Turn in: 10, 16.
	Extra Problems: 3, 8, 24.

 

In Class

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.

 

Outcomes

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

• understand what a proof is;
• be able to write (Problems 3.1.6 and 3.1.10) and read (Problems 3.1.2) simple proofs;
• be able to prove simple statements of the form $P \rightarrow Q$ (Example 3.1.2, Problems 3.2.2, 3.2.4);
• be able to prove simple statements of the form $P \rightarrow Q$ using the contrapositive (Example 3.1.3, Problems 3.1.10);
• be able to prove simple negative statements (i.e., of the form $\neg P$ -- Example 3.2.1, Problem 3.2.7);
• be able to prove statements by contradictions (Examples 3.2.2, 3.2.3)
• be able to use assumptions of the forms $P \rightarrow Q$ and $\neg P$ in proofs (Example 3.2.5, Problem 3.2.9);
• be able to prove simple statements involving quantifiers (most problems of 3.3);
• be able to use in proofs assumptions involving quantifiers (most problems of 3.3);
• know the notation ($a \mid b$) and definition for "$a$ divides $b$" and how to prove statements involving divisibility (Theorem 3.3.6, Problem 3.3.18);
• be able to prove and use statements connected by "and"s (Example 3.4.1, Problem 3.4.3);
• know how to approach proofs on containment (Problems 3.4.4, 3.4.8, etc.) equalities of two sets (Example 3.4.4, Problem 3.4.16);
• know how to approach proofs on iff statements (Examples 3.4.2, 3.4.3, Theorem 3.4.6, Problem 3.4.8).