Lecture 8

Navigation

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

Before the Lecture

• Read Sections 5.2-3 and 6.1-2:
• Watch the videos related to these sections (after reading them):
  • Problem 5.2.7.
  • Problems 5.2.8(a) and 5.2.9(b).
  • Problem 5.2.17.
  • Problem 5.3.9.
  • Problem 5.3.11.
  • Review of Section 6.1.
  • Problem 6.1.4.
  • Problem 6.1.11.
  • Problem 6.1.14.
  • Problem 6.2.11.
  • Problem 6.2.14.
  • Tower of Hanoi Problem.
• 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.

 

Related Problems

The "turn in" problems are due on 07/01 (Homework 6) by 11:59pm.

Section 5.2:	Turn in: 8(b), 9(a).
	Extra Problems: 3, 6, 11, 18.
Section 5.3:	Turn in: 10, 12.
	Extra Problems: 4, 6.
Section 6.1:	Turn in: 9(b), 16.
	Extra Problems: 4, 9(a).
Section 6.2:	Turn in: 3, 6 (here you can use, without proving, the Triangle Inequality: if $a, b \in \mathbb{R}$, then $|a+b| \leq |a|+|b|$).
	Extra Problems: 5, 10.

 

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:

• know the definitions of one-to-one/injective and onto/surjective functions;
• know how to prove statements involving one-to-one and onto functions, including those involving compositions;
• understand the definition of the inverse function;
• know the necessary and sufficient conditions to the existence of the inverse (e.g., Theorems 5.3.4-5);
• understand the process of induction and how/why it works;
• be able to use induction to prove formulas (Example 6.1.1, Problems 6.1.4, 6.1.16), inequalities (Example 6.13, Problem 6.1.14) and divisibility questions (Example 6.1.2, Problem 6.1.9);
• be able to prove by induction statements that are not formulas, such as statements on finite sets (Examples 6.2.1, 6.2.2, Problem 6.2.3), combinatotics (Problem 6.2.10) and geometry (Examples 6.2.3, 6.2.4).