Expanding the Wiki - Algebra! - Calvin Lin

$\color{#D61F06} {\text{Updated! October 8 } }$ .

I have added these skills to the Algebra Map, and you can check them out. More than 100 skills have been added, and I look forward to seeing the Wiki Contributions.

If there are any skills that you would like to see, please let me know. I have not added Subtopics of Matrices or Abstract Algebra as yet.

For problem creators, I would appreciate if you can start assigning the skills to your Algebra problems. You can do so by selecting "Edit" in the dot dot dot menu, and then selecting the topic o Algebra (again), and going through the skill tree system to find the relevant skill to add. Let me know if any part seems confusing, and we can work on improving clarity. If you are uncertain what to tag a problem with, please reply to my comment below, and provide a title / link back to your problem.

Thanks!

Thanks for your suggestions for the Number Theory Map. I encourage you to check it out, and contribute to the Wiki where you can.

Given the success of Expanding the Wiki, I would like to continue with it for the Algebra map. I am interested in building it out beyond what is covered in high school, and it will include skills that are used in Olympiad Problem Solving. Please take a look at Upcoming Skill Maps - Algebra Extension for the (most updated) proposed extension.

I have the following questions. Please reply to the appropriate comment, to make it easy for me to track.

1) Are there any subtopic that I missed out? Are people interested in Matrices? Abstract Algebra?
2) Inequalities Chapter - I would like help with specifying all the skills. This is currently limited to “inequalites that you deal with in high school”. The “Olympiad inequality proofs” are placed in Advanced Inequalities
3) Advanced Polynomials - Anything else to add?
4) Advanced Equations - Anything else to add?
5) Advanced Inequalities - How should this be organized? There should also be a ton more skills here.
6) Induction subtopic - Any other specific areas that I should also include?
7) Functional Equations - This needs more work. Any one would like to look into categorizing the skills here?
8) Any other comments?

Note: To keep the discussion on topic, I will be removing irrelevant comments.

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Problem Creators - Please start to assign skills to your Algebra Problems. Reply to this comment if you have any difficulties, or if you have suggestions for improvements.

@Daniel Liu @John Aries Sarza @Trevor B. @Pi Han Goh @Joshua Ong @Arpit Dhimanj @Mursalin Habib @Anqi Li @Sreejato Bhattacharya @Gabriel Merces @Prakkash Manohar @megh choksi @Shenal Kotuwewatta @Tunk-Fey Ariawan @Matt Enlow @Tan Li Xuan @David Altizio @Zi Song Yeoh @Justin Wong @Ahaan Rungta @minimario minimario

Calvin Lin Staff - 6 years, 8 months ago

1) Are there any subtopic that I missed out? Are people interested in Matrices? Abstract Algebra? Anything else (please specify)?

Matrices are good. I'm interested.

isaiah simeone - 6 years, 8 months ago

I am also intrested in matrices and determinants

Aman Sharma - 6 years, 8 months ago

@isaiah simeone @Aman Sharma @Samuel Jones I have added Matrices to the Upcoming Skill maps. Feedback on expanding this would be appreciated.

Can I add problems and contribute a wiki to the up coming matrices map ?

Abdulrahman El Shafei - 6 years, 5 months ago

@Abdulrahman El Shafei – You can always add a new wiki on any topic that you choose. I can incorporate that into the Matrices Map when I push it out.

You will be unable to attach a matrices skill to problems, because those do not exist as yet. However, if you created a wiki page, you can post from there, and the problem will have the skill attached.

Calvin Lin Staff - 6 years, 5 months ago

@Calvin Lin – Thanks for your response, I have two further questions:

1- How can I add old problems to the wiki from my profile without posting them again?

2- How can I add photos from my computer to the wiki ?

@Abdulrahman El Shafei – 1)

From your problem, select Edit Select the corresponding topic/subtopic/chapter/skill (this follows the practice section structure), Click Save.

See this note for more details

@Calvin Lin – Thanks :-)

Can you please add Complex numbers and things like rotation theorem, geometric interpretation of complex numbers, roots of unity on a unit circle etc. Also, Determinants and Matrices.

Samuel Jones - 6 years, 8 months ago

Complex Numbers and Roots of unity have been added, and I welcome specific skills that you would like to supplement the list with.

I will be working on expanding out the matrices chapter. Suggestions are welcome.

non-euclidean geometry would be great!

Julian Poon - 6 years, 8 months ago

Please put matrices :) thank you

Giovanni Alonso - 6 years, 2 months ago

4) Advanced Equations - Anything else to add?

2) Inequalities Chapter - I would like help with specifying all the skills. This is currently limited to “inequalites that you deal with in high school”. The “Olympiad inequality proofs” are placed in Advanced Inequalities

You can add different types of problems based on different inequalities like AM-GM-HM-QM, Cauchy, Chebyshev's Sum, Triangle Inequality etc. They are very helpful especially in finding maximum and minimum value and are frequently asked questions in olympiads.

Yash Singhal - 6 years, 8 months ago

Can you state what those skill names will be like? I already listed out some of these inequalities in the document, and my thinking is that these problems should be sorted into those skills.

However, I can see why having them be placed separately could make sense

@Calvin Lin – The skill names can be the names of respective inequalities like AM-GM-HM-QM, Cauchy etc. These can be added under the head Special Inequalities(or any other name which you like) and at the end of this head, you can provide a review of all the inequalities, just as you do for all other topics. You can also add them under Advanced Inequalities Head. Keeping the inequalities of different types in different heads would be more systematic and organized in my opinion. Rest, all depends on you Sir.

@Yash Singhal – Thanks! I decided to go with "Statements" and "Applications", because I felt that it was better to have 2 chapters of numerous skills, then numerous chapters of 2-3 skills each. I will check with the community and see which approach is better.

@Calvin Lin – That's also fine!

8) Any other comments?

You can add Square Root of a complex number under the Complex Numbers Head. Vieta's Root Jumping is also a good topic.

I feel that square roots is covered under the current Complex numbers subtopic already. Though, finding just square roots do not have a skill by themselves. Would it make sense to add "Square roots" as a skill in De Moivre's Theorem?

Thanks for suggesting Vieta's Root Jumping. I've added it to System of Equations.

When are you posting Expanding the Wiki- Combinatorics. I have a lot of stuff to add to its practise section. Thanks!!!

Let me work out the Number Theory and Algebra sections first, and then I will make another post. Keep your eyes open.

If you have organized a lot of skills, you can also send me an email listing them out. I can add that to the document directly :)

@Calvin Lin – You can add Simon's Favourite Factoring Trick under the Factorization head of Algebra. I would like to do its write-up.

7) Functional Equations - This needs more work. Would any one like to look into categorizing the skills here?

6) Induction subtopic - Any other specific areas that I should also include?

5) Advanced Inequalities - How should this be organized? There should also be a ton more skills here.

3) Advanced Polynomials - Anything else to add?

can you add arithmetic progressions and geometric progressions too?

Palash Som - 6 years, 8 months ago

We already have a chapter on Arithmetic and Geometric Progressions. Are there additional skills that you wish to see in it?

maybe make a basic about HM/GM , they are underatted

math man - 6 years, 8 months ago

@Math Man – That is currently covered under the Power Mean inequality.

Do you feel that there is sufficient material to devote an entire page to just HM/GM?

Sir please add graph theory.
Because graphical solutions are very attractive

U Z - 6 years, 8 months ago

That would come under combinatorics.

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$