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Polynomials Sprint - Let's Get Started

\( \color{red} {\text{ The course is over.} } \)
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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:

Friday:
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.

\[ 18, 28, 37, 38 \]

Wednesday:
In addition to Monday's list,

A. The discussions on Polynomial Vieta and Polynomial Remainder have been opened. Join in, and share what you learnt.

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.

Monday:
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.
\[ 3, 4, 5, 11, 13, 16, 17, 18. \]

E. Work on the problems Polynomial Vieta and Polynomial Remainder. Solutions / Discussions will only be open in 2 days, so everyone can work on them.

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.

Note by Calvin Lin
3 years, 3 months ago

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For roots of unity practice you might want to try my problem

David Lee - 3 years, 3 months ago

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Where can I get the book ? Do I need to purchase a hard copy of book or is it a pdf available for free ?

Aman Sharma - 2 years, 2 months ago

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You can try looking for pdf copies of it online.

Calvin Lin Staff - 2 years, 2 months ago

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Sir, can you please tell me the name of the book ?

Aman Sharma - 2 years, 2 months ago

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Why has there been so little activity? Is it because it's been a while since the last update (June 27)? Or is it because everyone is celebrating July 4?

Colin Tang - 3 years, 3 months ago

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When can we expect another update? Or is there something that I'm missing?

Colin Tang - 3 years, 3 months ago

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That was the end. The note was published on Friday, and unlocked on Monday for discussion through the rest of the week.

I would appreciate feedback, thanks!

Calvin Lin Staff - 3 years, 3 months ago

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@Calvin Lin When is the next course starting?

Colin Tang - 3 years, 3 months ago

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What's root of unity

Daniel Lim - 3 years, 3 months ago

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Refer to Help Wanted. There is an active discussion initiated by @Ananay Agarwal about root of unity.

Calvin Lin Staff - 3 years, 3 months ago

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ok

Daniel Lim - 3 years, 3 months ago

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Are we expected to purchase a copy of the book? Or is there someway to view it for free?

Chris Quinones - 3 years, 3 months ago

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http://f3.tiera.ru/2/MMathematics/MSchSchool-level/Engel%20A.%20Problem-solving%20strategies%20(for%20math%20olympiads)(Springer,%201998)(ISBN%200387982191)(O)(415s)MSch.pdf

For free. Hopefully it's virus-free as well.

Colin Tang - 3 years, 3 months ago

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Google "arthur engel problem solving strategies" and follow the first link, which should be a pdf. By the way the above link works if you surround italicized text with "_"s.

Colin Tang - 3 years, 3 months ago

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thank you

Chris Quinones - 3 years, 3 months ago

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Great work! (y)

Ayush Gupta - 3 years, 3 months ago

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which book should i read?

Johan Setiawan - 3 years, 3 months ago

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I've updated it with a link to the book that we're using. Thanks!

Calvin Lin Staff - 3 years, 3 months ago

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Where is the link sir ?

Aman Sharma - 2 years, 2 months ago

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Hello! I actually feel that apart from referring to the book as a resource, some notes may be added to facilitate better understanding of certain topics that may be covered in the future. Eg- Functional eqaution may be covered, but for a beginner it will be very difficult to understand without proper directive. Thnx! :)

Krishna Ar - 3 years, 3 months ago

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