Talk:High School Mathematics Extensions

I feel a bit ambivalent about this page; most of the content is in other sections which is not really a bad thing in itself because of the way this is presented as a extension topic thing, but I think this should be different; perhaps as a Mathematics extension topics, for students at all levels, not just high school?

What do we think? Dysprosia 10:20, 29 Sep 2003 (UTC)

The work on the included pages looks great to me. Lets not bother the author with strictures. If the work can be used later in other spots then so be it but redundancy is not a problem. Let him be free to write as he desires, especially now in such early stages. --Karl Wick

Well, Dysprosia, I think each book has its intended audience. The online book on High school extensions are aimed at 14-18 year olds. The language we'll use to write the book are more accessible to high schools student with no university-type rigour. For this reason we need new material written just for the high school students, with the appropriate theme, tone, register and whatever else. I totally disagree with what you did to the project! I will be converting it back to what it was like. A new book aimed at 14 -- 18 year olds. Xiaodai

Ok, sorrysorrysorrysorrysorry... Dysprosia 06:53, 30 Sep 2003 (UTC)

Ok, you are forgiven. We are trying our best to contribute. That's good to see.Xiaodai

To Whoever wrote the Crytography basic thing: I'm not familiar with the cryptography side of things, so if you wrote a section on it and it will be great.

Would the proof for the infinitude of primes fit in the chapter on Primes or in the chapter on Mathematical proofs? Lord Emsworth 01:45, 29 Oct 2003 (UTC)

Give it in the primes page.

Content removed?
Why was so much content removed from the front page? I don't mind reading that the first two chapters are easier than the rest, nor that Australian high schools may not offer enough material. What happened?


 * The reason why I removed them is because I didn't want people to think I'm bossy and that to edit this book they need to follow all those rules. I want this to be more rules-free, so anyone can contribute without having to worry too much about what they write or how they go about writing it.

Premise
Hmm...not sure I understand the intended premise of this book. Is it simply a collection of math topics not covered by the Australian school system? Or is there a more continuous thread running through it? --Spikey 19:48, 14 Dec 2003 (UTC)


 * This online-book is intended to be a "teach yourself" kind of book. High school students are its intended audience. This textbook covers topics not taught in Australian high schools, and it's not meant to be taught, it's meant to be read. To answer your question regarding thread, this book may seem disconnected, but it does have a few interesting things that are threaded e.g. Fibonacci numbers in Matrices, Infinite Processes and Mathematical programming; Logic and Mathematical Proofs come hand in hand; also Probabilities & counting is connected with Infinite processes. Modular arithmetic together with Matrices will make an interesting section on cryptography. As you can see, the chapters, although independent on their own, are connected, or if you liked threaded. Is that what you meant by a thread? -- Xiaodai GMT+10:00 11:53 (15 Dec 03)


 * Yeah, that explains it. Thanks!  Sounds like something I'd love to work on.  --Spikey 02:04, 20 Dec 2003 (UTC)

Navigation
Can we decide on something along the lines of Contents on the top of each chapter? Meanwhile though, just type HSE into the top bar and press Go - it's a redirect. r3m0t 21:57, 1 Jan 2004 (UTC)

Too big, what can I do? Also I'll change it to blue... r3m0t (cont) (talk) 11:55, 26 Mar 2004 (UTC)

Well, I'm going to add a simple nav... r3m0t (cont) (talk) 11:45, 27 Mar 2004 (UTC)

Raven paradox
Can we fit this in somewhere? *grin* Raven paradox r3m0t 23:15, 3 Jan 2004 (UTC)
 * I dont know enough about it to write it, maybe someone more knowledgeable (perhaps you) could add it. Xiaodai

"Further modular arithmetic"?
What's this, and why is it on the Topics list (haven't noticed it before) without being in the Plan section? r3m0t 19:57, 4 Jan 2004 (UTC)


 * The modular arithmetic section didn't go far enough into this beautiful subject. So i thought an extension would be nice, just haven't written up a plan. Xiaodai 07:59, 5 Jan 2004 (UTC)

Puzzle
Anybody tell the area of the rectangle inside this other rectangle of area 1?

(grrr won't let me move the page)

The two midpoints are, well, midpoints, and the lines are perpendicular where obvious. r3m0t (cont) (talk) 10:57, 5 Feb 2004 (UTC)

In short, the answer is... variable. --Lemontea 09:29, 23 Feb 2005 (UTC)

ah hell i met that question in a math comp i put between 3/8 and 7/16, is it right???

-protecter


 * I'm going to agree with Lemontea. It's not at all obvious what the height/width aspect ratio of the outer rectangle is. If the aspect ratio is very small (short and wide), the area of the inner rectangle could be nearly 1/2 the outer rectangle. If the aspect ratio is exactly 2:1 (tall and narrow), the inner rectangle is exactly square with area 1/4 the outer rectangle.
 * So ... I suppose we could specify the height and width of the outer rectangle, and then solve for the area for that one aspect ratio. Or we could change the question and ask for a formula for the area as a function of the height/width aspect ratio. --DavidCary (talk) 08:35, 12 December 2008 (UTC)

Tjis is hard man I'm still working on the answer Miviwe (discuss • contribs) 17:07, 20 June 2018 (UTC)

Problems with coming up with problems
I've enormous trouble coming up with (hard) problems for this book. Can you guys please contribute some problems? Please. Xiaodai 06:03, 14 Jul 2004 (UTC)

curved geometry
sorry for asking but i really want to learn basic curved geometry, is it possible that you people can add it? or do you know any place that gives a introduction?


 * Sorry for not being able to answer this q for so long. I think most high school will teach that sooner or later, so i have no plan to do a chapter on it. But if later one of the chapters requires Cartesian geometry then i will add a supplementary section. So no plan to write such a section yet.
 * If you want to learn more the topic then search google for "coordinate geometry", "cartesian plane", "graphing functions" should turn up some useful pages. Xiaodai 8 July 2005 11:21 (UTC)

don't you think that modulo chapter is still difficult for beginners -- registered in wikipedia as "kushal_one"

Yeah. Everything can be improved. Maybe i will review the material once i have time. Xiaodai 12:59, 29 May 2006 (UTC)

Proposals for new topics?
After an overview of this wikibook (a very clever idea by the way), I observed that it mainly focuses on many algebraic topics. What about some extension topics more geometry-oriented, interesting topics. Examples: -Vectors (possibly with basic elements of Vector Analysis) -Elementary Topological Concepts . I am aware that this is a High School extension wikibook on maths but I believe that if a student is interested in maths, he or she will have a better and mainly broader understanding of what mathematics exists beyond high school books by exploring such topics. Could anyone provide any similar proposals?


 * Sounds like a good idea, although it will take lots of work. Go for it if you have the time. I am too busy doing my uni studies to do anything with book until perhaps next year.Xiaodai 02:49, 29 June 2006 (UTC)

Primes and Goldbach's Conjecture
As with Riemann's hypothesis, a lot of theory has been built presuming Goldbach's is correct. Some may be worth mentioning somewhere. For example, Schinzel proof that Goldbach's conjecture implies that every odd integer larger than 17 is the sum of three distinct primes.--Billymac00 04:07, 14 June 2007 (UTC)

Context?
There's a lot of information here, but personally I found it all too disjointed. It reads less like a book and more like scrap notes and collected stray thoughts. There's also a lot of information that is entirely unexplained. For instance, a large "X" with a bar over it. How is a student to understand what that is all about without any explanation? Step back and try to imagine it from a student's viewpoint. Petercorless (discuss • contribs) 17:31, 5 May 2011 (UTC)

New Topics
Since the most recent discussion conversations on here are very very very old, I don't expect this to garner too much attention. However, I think I might add the following topics and start them, because I think they pose wonderful mathematical ideas for high school students: And that is the current list as of so far. Additionally, I would like to import the knowledge from AoPSWiki and Wolfram Mathworld to assist in this. There's a bunch of mathematics not taught at the high school level that could deepen understanding of it and help benefit students in other areas of life.
 * Geometry
 * Complex Numbers and Analysis
 * Markov Chains
 * Polynomials