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Let's get started. Work your way down this list of tasks. Remember to check back during the week, as tasks may get added:
In addition to Wednesday's list,
A. Read Useful Lemma to learn about it. What other questions can we apply it to?
B. It seems to me that people are not too familiar with what roots of unity are, and how to use them. This is a advanced topic, that pushes your understanding of polynomials. Try working on the following questions from the book, with a focus on using roots of unity (somewhere) in the solution. If you can't solve them after Sunday, make a post on Help Wanted.
C. Write a comment in What I Learnt. I'm sure a lot of you have learnt from this past week, but there are only 2 comments there.
In addition to Monday's list,
B. For those who haven't seen Vieta's Formula, read the attached note. Solve the 2 questions added at the end (and struggle with the third).
C. Work on Sharky's problem Vieta might come in handy.
D. Work on Eddie's note on Having No Rational Roots.
E. Write a comment in What I Learnt.
A. Read through pages 245 - 250 of Problem Solving Strategies. (Not the whole chapter)
B. If you have any questions about the material, ask them in Help Wanted.
C. Know the following terms:
- Polynomials, Coefficients, Degrees
- Division, Quotient, Division Algorithm
- Remainder Factor Theorem, Rational Root Theorem
- Vieta's Formula
- Roots of unity
D. Work on the following problems in the book, listed on pages 254-255. Try not to refer to solutions at the end of the chapter.
F. Write a comment in What I Learnt.
G. Provide feedback, so that we can improve this experience for you.
The goal of this set is to provide exposure to problems which you likely have not encountered in school. You will learn new techniques, apply known ideas, and improve your problem solving skills. For those who are new, you can review How This Will Work to understand the expectations.