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Author Topic: Class of 2021 Math Club  (Read 15210 times)

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Bri MT

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Class of 2021 Math Club
« on: July 04, 2018, 05:26:48 pm »
+5


Quite a few of you have expressed interest in pursuing maths at a more difficult level than is currently offered to you, so I thought I'd make this thread as:

a) a place to share how you have extended your mathematical studies
b) a discussion thread for anything & everything related to your math journeys
c) a place to share interesting problems/resources that you've come across


Here are some introductory questions to kick things off:
1) What's your favourite aspect of maths?
2) Do any key moments stand out to you so far?
3) How far do you plan on going with maths? Do you see it playing a key role in your future?
4) What's your favourite form of mathematical learning?

turtlesforeveryone

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Re: Class of 2021 Math Club
« Reply #1 on: July 05, 2018, 06:40:33 pm »
+9
Thank you for this opportunity. I'd love any chance to share my passion for math and to meet like-minded people :D

I guess I'll start. Math is appealing to me in many ways. In the technical sense, it's a useful tool as it is essentially the formal application of logic. This means math can be universally used and understood, as we humans have an innate sense of logic. Thus, math is also a way to express our logical thoughts and arguments. This also leads to another neat application: math provides a platform to translate our world into just a few equations. It allows us to predict the world and understand it better (for example, someone from the US and china could both look at the same set of equations, and immediately know what it is describing). Even more amazingly, we have had many discoveries in math that had seemed just theoretical, but later (sometimes even centuries later) would be found to be the exact tool that fits a scenario in physics, engineering, or the life sciences. In some mystical way, the mathematical application is often discovered before the physical application, but always seems to predict the usage.

Personally, I like math mostly because math is beautiful. Attempting math problems gives you a sense of completion, because in many ways math is very black and white: it is either right or wrong. This allows us to prove or disproves claims efficiently (however there are quite a lot of problems that are too complicated to solve). In school, math is a list of steps, while in higher math, it is more of an art - an exploration. So I look forward to when my math education changes from rigid, uncreative processes to a more interesting and fun task.

I'm not sure what role math will play in my future yet, I'm just eager to learn and explore. So looking forward to how this thread grows!

(This year I tried starting up a math and science club in my school but sadly not a lot of people were interested and the teachers I tried to work with stopped communication, so it never got up and running :( I just wanted some people to talk with...)

Bri MT

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Re: Class of 2021 Math Club
« Reply #2 on: July 20, 2018, 10:37:18 am »
+1
snip

Love your username!

I'm glad that you've really connected to this thread & in a broader sense that you have such a keen appreciation and interest in maths - as you've recognised, it truly is adaptive and relevant and relevant to every one.

Congratulations for actually taking the initiative to create a new club and invest in the communication necessary for that. It sucks that this time you didn't get to achieve the vision you had in mind, but I hope that this doesn't discourage you from reaching out in the future. In my course we talk about collecting as many "no"s as possible, because if you never fail and no one ever says "no" that just means you should be aiming higher and you aren't stretching your limits enough.

Nevertheless, I hope that you continue to connect here on atarnotes and that we can help you find some of the community you seek :)

turtlesforeveryone

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Re: Class of 2021 Math Club
« Reply #3 on: July 21, 2018, 07:02:10 pm »
+13
List of free mathematics resources
(will be continually updated)

Youtube Channels
Vihart: Creative math through doodles
Numberphile: Videos featuring mathematicians talking about many interesting areas and problems in math.
3Blue1Brown: 3Blue1Brown provides explanations driven by animations, making difficult problems simple to understand, with changes in perspective.
PBS Infinite Series: "Ambitious content for viewers that are eager to attain a greater understanding of the world around them . . .With each episode you’ll begin to see the math that underpins everything in this puzzling, yet fascinating, universe."
Yaymath: Math videos filmed in a live classroom. Covers many high school math topics in a fun, inviting school atmosphere.
Eddie Woo: Math videos filmed in a classroom in a public school in Sydney, Australia. "I think learning is awesome, and love being able to share what I've learned with others!" Here's an introduction to who Eddie Woo is and what he does.
Think Twice: Elegant geometric proofs shown visually through animations.
Mathloger: "Enter the world of the Mathologer in which beautiful math(s) rules." Fun little explorations into math.
PatrickJMT: Our favourite online math teacher. "Free math videos for the world".

Educational Websites
Maths Is Fun: "We offer mathematics in an enjoyable and easy-to-learn manner, because we believe that mathematics is fun". The site is a great resource for simply and intuitively explained topics from Kindergarten to Year 12.
Brilliant:  "Math and Science done right". Great for interactive learning, problem solving, and creative thinking.
NRICH: Provides free interesting mathematical games, problems and articles.
Paul's Online Math Notes: Provides a complete set of free online (and downloadable) notes and/or tutorials for classes that the author teaches at Lamar University. Topics cover Algebra, Calculus I, II and III, Differential Equations, and reviews. This site also provides cheat sheets such as Algebra, Trig, Calculus, and Laplace Transform cheat sheets.
Mathigon: "Textbooks come to life!" Mathigon provides a fun and interactive way to learn new mathematics. At every step students have to actively participate, explore, and discover new ideas. Mathigon encourages engaging through problem solving, reasoning and creativity. Every course is filled with colourful illustrations, puzzles, animations and real-life applications.
Cut The Knot: "An encyclopedic collection of math resources for all grades. Arithmetic games, problems, puzzles, and articles."
Purplemath: A good resource for learning many aspects of math. Purplemath is often cited, and is frequently referenced in google searches.
Plus magazine: "Plus is an internet magazine which aims to introduce readers to the beauty and the practical applications of mathematics. Plus provides articles and podcasts on many aspects of math, a news section, showing how recent news stories were often based on some underlying piece of maths that never made it to the newspapers, reviews of popular maths books, and puzzles for you to sharpen your wits.
Stat Trek: Online tutorials and tools to help you learn statistics.
Art of Problem Solving: This is a must for people who wish to undertake mathematical thinking, or are preparing for a math competition.
Better Explained: Math concepts explained in often a new or intuitive way. Gives you something to think about, covers everything from number systems, to calculus, to computer science.

Puzzles/Problems
Project Euler:  Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help, the use of a computer and programming skills will be required to solve most problems.The intended audience includes students for whom the basic curriculum is not feeding their hunger to learn.
mathpuzzle: A site dedicated to posting math puzzles and mathematical recreations, inspired by Martin Gardner (who you may recognise from his section in the Scientific American, titled Mathematical games).
Crux Mathematicorum: "Crux Mathematicorum is an internationally respected source of unique and challenging mathematical problems published by the CMS. Designed primarily for the secondary and undergraduate levels, and also containing some pre-secondary material, it has been referred to as 'the best problem solving journal in the world'."

Entertainment Websites
Coolmath Games: A bunch of kid-friendly non-violent logic and math related games. Categories include strategy, skill, numbers, logic, and trivia. This used to be the go-to game website us kids would log on at school during primary.
Math with bad drawings: Math blog by a person who loves math but is bad at drawing.
r/badmathematics: "A place for sharing the bad math that plagues reddit and the internet as a whole." A good laugh at how people misuse or misunderstand mathematics.
What's Special About This Number?: A distinctive fact about each number from 1 to 9999.
The Geometry Junkyard - Origami: Lots of mathematical origami designs.

PDFs and books
How To Solve It by George Pólya: A short volume underlining different approaches to solving a mathematical problem. The ideas in this volume are so useful that they can be used not just for solving mathematical problems, but for solving any problem in any field.
How to write proofs: a quick guide by Eugenia Cheng: Short volume covering topics such as: What does writing a proof look like, the general shape of a proof, and common bad ways to write proofs.
The Art and Craft of Problem Solving by Paul Zeitz: Good for a breather in competition mathematics, but is aimed a bit higher than the lower level competitions. Lots of interesting mind exercises and mathematical problems.

A bit of everything
What's New: Terrence Tao's blog. The side bar has links to other math related and non-math related websites. Terrence Tao covers such a wide range of topics that it's hard to describe simply. This is an entry on career advice in math, covering primary school to post-doctoral level.
Math3ma: Tai-Danae Bradley's blog, originally created as a tool to help her transition from undergraduate to graduate level mathematics. Some topics covered include category theory, complex analysis, topology, set theory, and much more. Most entries are either a brief (and mostly non-technical) introduction to the topic, or an elaboration of the basic idea via mathematics.
Tao Manifesto: Why choose Tau.
Pi Day and The Pi Manifesto: Why choose Pi.
The Math Forum: The Math Forum has a rich history as an online hub for the mathematics education community. It contains such sections like Ask Dr. Math, the year game, and problems of the week.
Project Euclid: Project Euclid's mission is to provide powerful, low-cost online hosting and publishing services for theoretical and applied mathematics. It provides free online access to scholarly articles and published journals.
Mathematics Stack Exchange: A question and answer forum. You can browse through answers, or look for answers to your own questions. Covers a wide range of topics.
Gower's Weblog: Sir Timothy Gower - a fields medal recipient - 's blog.
The unfinished PDE coffee table book: "During 2000-2001 a group project based in the Oxford University was begun to write this book. Many people at Oxford and around the world contributed drafts, which were then extensively rewritten and edited to help bring about a uniform style and mathematical level. Unfortunately, the project is stalled, with no plans at present to complete it." This project is still very beautiful, despite being unfinished.
Mathblog: Mathblog.com is dedicated to promoting the beauty of Mathematics at every level. It covers many topics, including applied math, basic math (arithmetic, geometry, algebra, calculus etc), math education, and statistics.
Mathvault: "Resource hub for people pursuing higher mathematics through digital publishing and other nerdy gimmicks."
Desmos: Graph functions, plot data, evaluate equations, explore transformations, and more. It's like the ultimate graphing tool.
Math pages by Stan Brown: Articles covering how to use a graphing calculator, how to show your work and succeed as a student in math, how to teach math, and more topics such as algebra, trig, statistics, and calculus.
Mathsnacks: Collection of pdfs containing small packets of beautiful mathematics. Perfect for posters.
« Last Edit: October 13, 2018, 08:37:58 pm by turtlesforeveryone »

turtlesforeveryone

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Re: Class of 2021 Math Club
« Reply #4 on: August 17, 2018, 09:29:03 pm »
+6
Well this thread has gone a bit dead :0. Still happy to share my interests in math with anyone else!
Well recently I had gone to a bridge building competition and managed to win a prize, despite this being our school's first year participating. I'm quite happy - we took a look at the different types of bridges and analysed them mathematically to decide on our design.

SChMurpel

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Re: Class of 2021 Math Club
« Reply #5 on: August 17, 2018, 09:37:37 pm »
0
My maths teacher is so trash, Idek why she's the year 9 co-ordinator
In maths, she said 2 + 7 = 8 -_-
And always say "never question my judgment, it's always right"
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Bri MT

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Re: Class of 2021 Math Club
« Reply #6 on: August 18, 2018, 08:19:35 am »
0
Well this thread has gone a bit dead :0. Still happy to share my interests in math with anyone else!
Well recently I had gone to a bridge building competition and managed to win a prize, despite this being our school's first year participating. I'm quite happy - we took a look at the different types of bridges and analysed them mathematically to decide on our design.

I've been to one of these contests before,  could you elaborate on how they work?

My maths teacher is so trash, Idek why she's the year 9 co-ordinator
In maths, she said 2 + 7 = 8 -_-
And always say "never question my judgment, it's always right"

Everyone makes careless errors now and then,  sounds exactly like the type of careless thing I would do in a test :P

It seems a bit odd that she'd say that,  could she have been joking?
« Last Edit: August 18, 2018, 01:45:34 pm by miniturtle »

turtlesforeveryone

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Re: Class of 2021 Math Club
« Reply #7 on: August 18, 2018, 11:34:12 am »
+1
I've been to one of these contests before,  could you elaborate on hire they work?

I don't want to elaborate too much because it can be traced back to me, but basically every school could register a team of three to participate. We would be mailed a set of materials and could only use those materials (balsa wood, cardboard, string, and glue). Then we had about 6 weeks to make the final project. It would be tested using a machine placed in the middle of the bridge (btw we got a full day to scienceworks for free, because the competition was hosted there).

SChMurpel

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Re: Class of 2021 Math Club
« Reply #8 on: August 18, 2018, 09:58:26 pm »
0
Everyone makes careless errors now and then,  sounds exactly like the type of careless thing I would do in a test :P

It seems a bit odd that she'd say that,  could she have been joking?
She's like so serious
She said to my class you guys are all gonna fail VCE maths (just because one person doesn't do homework or paste in 20 pages of notes)
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aspiringantelope

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Re: Class of 2021 Math Club
« Reply #9 on: December 04, 2018, 03:46:45 pm »
+2
Here are some introductory questions to kick things off:
1) What's your favourite aspect of maths?
2) Do any key moments stand out to you so far?
3) How far do you plan on going with maths? Do you see it playing a key role in your future?
4) What's your favourite form of mathematical learning?

1) My favourite aspect of Maths is knowing that you've gotten the answer correct, giving you the satisfaction.
2) Um, one key moment stood out when I knew I had got some of the last 5 AMC Intermediate Questions correct.
3) I just feel that Math is something I am strong at, but don't see it going to play a major in my future life.
4) Does it mean my favourite topic in math or how I learn it?
My favourite topics are Algebra, Trigonometry and Quadratics (easiest for ME)
And I learn simply by practising and consolidating formulas.

S200

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Re: Class of 2021 Math Club
« Reply #10 on: December 04, 2018, 10:44:42 pm »
+2
^May I suggest instead learning from first principles?

this is particularly useful for Trig identities and Integration...
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AlphaZero

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Re: Class of 2021 Math Club
« Reply #11 on: December 04, 2018, 11:24:31 pm »
+7
Hey 2021ers,

I just finished my first year at University of Melbourne. Like many of you here, I've always loved maths and it's been a passion of mine ever since I can remember.

Since a few of you have taken interest in really extending/challenging yourselves, upon request, I'm more than happy to write some challenging questions for you all to work on together as a group (then, this will really become a maths club ;D).

Let me know if this is something you guys are interested in. I'm happy to post, say, one or two challenging questions per week :)
2015\(-\)2017:  VCE
2018\(-\)2021:  Bachelor of Biomedicine and Mathematical Sciences Diploma, University of Melbourne


aspiringantelope

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Re: Class of 2021 Math Club
« Reply #12 on: December 05, 2018, 05:13:43 pm »
0
Hey 2021ers,

I just finished my first year at University of Melbourne. Like many of you here, I've always loved maths and it's been a passion of mine ever since I can remember.

Since a few of you have taken interest in really extending/challenging yourselves, upon request, I'm more than happy to write some challenging questions for you all to work on together as a group (then, this will really become a maths club ;D).

Let me know if this is something you guys are interested in. I'm happy to post, say, one or two challenging questions per week :)
Yes! Please post the challenging questions!!



^May I suggest instead learning from first principles?

this is particularly useful for Trig identities and Integration...
Hey I just saw your post, may I know what you mean by first principles? Does it cover it in the Cambridge Math Methods 1/2 Textbook? Or do I have to do some online research on it. Thanks.

Mod edit: Merged double post; please make sure not to double post as it is against forum rules.
« Last Edit: December 05, 2018, 07:42:26 pm by miniturtle »

AlphaZero

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Re: Class of 2021 Math Club
« Reply #13 on: December 06, 2018, 12:15:55 am »
+8
Set 1 Questions: 6 Dec 2018 to 8 Dec 2018

Solve the following questions without the use of a calculator.

Question 1
Derive the quadratic equation. That is, show that the solutions of the equation \(ax^2+bx+c=0\) for \(x\) are given by \[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.\]

Question 2
Given that \(\log_2\left(\dfrac{1}{10}\right)=-3.322\), correct to three decimal places, evaluate \(\log_2\left(\dfrac{2}{5}\right)\) correct to three decimal places.

Question 3
Three identical circles of diameter \(12\ \text{cm}\) are placed tangent to each other as shown in the diagram below.

Find the exact area, in \(\text{cm}^2\), of the shaded region. Express your answer in the form \(a\sqrt{b}+c\pi\), where \(a\), \(b\) and \(c\) are integers \(\left(a,b,c\in\mathbb{Z}\right)\).
« Last Edit: December 08, 2018, 12:04:06 am by dantraicos »
2015\(-\)2017:  VCE
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aspiringantelope

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Re: Class of 2021 Math Club
« Reply #14 on: December 06, 2018, 10:25:04 am »
+3
Alrighty. Look like we're doing this. First, I'm going to give you a few short questions. I just want to find out where you guys are at in maths. I have no idea if these are too easy, too hard or just right, so let me know :)

Solve the following questions without the use of a calculator.
Ok using LaTex is complicating so I will just try with a equation copier LOL
1. \(x^2+\frac{bx}{a}+\frac{c}{a}=\(
2. \(\left(x+\frac{b}{2a}\right)^2-\frac{b^2}{4a^2}+\frac{c}{a}=0\)
3. \(\left(x+\frac{b}{2a}\right)^2=\frac{b^2}{4a^2}-\frac{c}{a}\)
4. \(\left(x+\frac{b}{2a}\right)^2=\frac{b^2}{4a^2}-\frac{4ac}{4a^2}\)
5. \(\left(x+\frac{b}{2a}\right)^2=\frac{b^2-4ac}{4a^2}\)
6. \(x+\frac{b}{2a}=+\ or\ -\sqrt{\frac{b^2-4ac}{4a^2}}\)  *anyone know how to write the + with a - sign underneath? thanks*
7. \(x+\frac{b}{2a}=\frac{\sqrt{b^2-4ac}}{2a}\)
8. \(x=-\frac{b}{2a}+\frac{\sqrt{b^2-4ac}}{2a}\)
9. \(x=\frac{-b+or\ -\sqrt{b^2-4ac}}{2a}\)
Please anyone know how to do +/- sign?
Thanks

q2. haven't learn logarithms yet.. (I have but fully forgotten because I am doing the textbook form the start to end)
q3 i dont know either omg this is embarrassing  :-[
« Last Edit: December 06, 2018, 10:31:29 am by aspiringantelope »