## Before the Lecture

• 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

No problem will be turned in, but solve the problems below to practice for the final.

 Section 6.3: Turn in: None. Extra Problems: 2, 5, 9, 12, 16. Section 6.4: Turn in: None. Extra Problems: 4, 6, 7, 19.

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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 recurrence and recursive definitions;
• be able to apply induction to prove summation formulas (Problems 6.3.2, 6.3.5, 6.3.9);
• be able to apply induction to prove formulas recursively defined sequences (Example 6.3.3, Problem 6.3.16);
• be able to apply induction to more complex inequalities (for integers -- Example 6.3.1, Problem 6.3.12);
• understand and know how to use strong induction (Theorem 6.4.2);
• understand more complex examples of recursively defined sequences (Problem 6.4.4);
• know what Fibonacci numbers are and be able to prove simple statements about them (Theorem 6.4.3, Problems 6.4.6, 6.4.7).

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