Updated: Dec 16, 2020
We're about a month into our stay-at-home adventure, and though I've provided some puzzles and problems in some of my past articles (try some prisoner-themed puzzles or go outside and learn about the Fibonacci sequence!) for you to try at home, I realized I haven't yet given you all the ideas I have for exploring math on your own. If you'd like to learn more math (or investigate anything else you're interested in), I encourage you to take advantage of this time! This article is more of a list, so feel free to read whatever sections excite you the most. So without further ado, here are some ideas for my GLeaM members!
1. Read some math books! Whether you're just beginning or you're already super excited about math, I have lots and lots of book recommendations in the Resources section of this site. Books are one of the main reasons I'm so inspired about math today. The right books showed me that math is so much more than what's been drilled into us in school, and I was so inspired by the stories of the mathematicians on the pages and by the elegance of the math they created.
I'd immediately recommend Things to Make and Do in the Fourth Dimension by Matt Parker to older grades (and adults!) and Go Figure and Why Pi? by Johnny Ball to younger grades.
I'm also currently reading Humble Pi by Matt Parker, an entertaining exploration into all the "real-world mathematical disasters" that happen around the globe, and So You Think You've Got Problems? by Alex Bellos, which is an amazing collection of more than 150 fun and surprising puzzles that invites you to solve and engage with them.
I have a massive collection of math books (I think I'm near 80 now?), so just check out my interactive resource hub for more specific recommendations! There's something for everyone there!
2. Find some mathy articles! Books aren't always free, so if you're looking to read something fun and accessible online, look for some articles! I especially like Quanta Magazine for all sorts of STEM articles, and Scientific American also has great content.
Also, look for math sections on some of the larger news sources. The New York Times has a math section, and they do a great job covering material well, though they focus more on the people and the stories than the math itself.
Quanta Magazine is far and away the best source I've found for explaining both the math and the story, and I'd definitely recommend you check it out!
3. Watch some math videos! If you've been reading my articles for a little while, you definitely know how much I like math videos. I love to embed them in my articles, and I find that a video is one of the best mediums for math because it's so visual and engaging. I'd love to start making videos for GLeaM if I had a bit more time, but for now, definitely check out some mathy YouTube channels. Numberphile is a channel with hundreds of interviews of famous mathematicians across both the United States and the United Kingdom, and 3Blue1Brown is another channel where math is explained brilliantly through visuals the creator programs himself. I also love standupmaths and ViHart, and I recommend even more channels in the videos resources section of my site. There are even some full-length movie recommendations there!
For specific video recommendations, I actually wrote an article entirely about my favorite math videos on YouTube, so definitely check that out if you want your mind blown! It's a fun article to both read and watch, and I hope it gives you an engaging tour of the fun, accessible side of math.
4. Try some math websites! There are definitely some great math-based websites out there. AoPS (www.artofproblemsolving.com) is the most extensive math website with articles, hundreds of forums to talk to other math-minded people, and most importantly, lots of online math courses! I'd definitely recommend checking their site out. They post puzzles in the "Keep Learning" section of their site under Resources, and they do all they can to prepare you for math competitions if you're into that.
More specifically, try looking at some neat databases, like the Online Encyclopedia of Integer Sequences, a compilation of all the integer sequences in the world (started in 1964) at oeis.org. Surf the web, and see what kind of fun sites you can find and leave them in the comments for me! Here's one I found: a database of biographies of lots of female mathematicians.
5. Attend online math events! There are some online math events now if you'd like to attend something live. AoPS has weekly events called Math Jams that are free to the public! Find their schedule here: https://artofproblemsolving.com/school/mathjams
I've also heard that renown mathematician and national coach of the winning USA International Mathematical Olympiad team, Po-Shen Loh, is doing live streams online where you can ask him anything: https://www.poshenloh.com/live/
6. Solve some mathy puzzles! One foolproof way to explore math is to try some puzzles! As I mentioned earlier, AoPS has some puzzles and Alex Bellos' new book So You Think You've Got Problems? is a great collection, but you can also try more traditional puzzles like Sudoku, Kakuro, and Ken-Ken. I even did a whole project at Georgia's Governor's Honors Program (GHP) on a type of puzzle called nonograms. There are now so many apps on the app store that let you try out nonograms (the one we used was called Pixelogic), and they're a super fun puzzle to try!
You can find puzzles pretty much anywhere online from riddles to logic puzzles to, of course, mathy ones, and here are two great places to get you started: https://www.mathsisfun.com/puzzles/ and http://www.mathpuzzle.com/.
7. Try some competition math! I know a lot of my GLeaM members participate in math team and attend math competitions like MathCounts. Math competitions are a super fun way to get excited about math, and I'd definitely recommend checking them out if you haven't seen them.
If you'd like to learn a little more competition math, you can find my recommendations for competition prep books for middle schoolers here in the resources hub. There are also hubs for elementary and high schoolers on that page, so check them out too!
There are some places online you can find competition problems for free, such as AoPS's compilation of all the problems of the most widespread national competition, the AMC (American Math Competition) series. Go here for the AMC 8, here for the AMC 10, and here for the AMC 12.
If you'd like something for MathCounts, you can also go here for the MathCounts Trainer and
here for a popular game called For the Win. Both are fun, engaging ways to learn more math and explore MathCounts-style problems.
I'm still developing my competition math resources hubs, but they already have a lot of resources for competitions. Even at home, competition problems are definitely an exciting way to try some math.
There are even going to be some online math competitions. On June 6, there is an online competition for middle school girls. It's called Math Invitational for Girls, and you can sign up at this link and learn more about it here! (Yes, I was asked to promote this, but yes, it is super awesome!) I'll keep my eye out for more online competitions, and I'll let you know about them.
8. Investigate some math! If this sounds super open-ended, that's because it is! If there's ever something you've wanted to find out, see if you can use math to explain it.
When I was a lot younger, I randomly became interested in square numbers and a type of number called oblong numbers (I didn't know the name at the time... oblong numbers are basically numbers that are the products of 2 consecutive numbers, like 1*2 = 2, 2*3 = 6, 3*4 = 12, 4*5 = 20, etc.) One of the things I found out was that every number can be expressed as either the difference of two oblong numbers or two square numbers, and it turns out that these differences have something to do with the factorizations of the original number (hint: it has something to do with how far apart the numbers are).
More recently, in the nonogram investigation I mentioned earlier, my partner and I explored what initial clues for a nonogram result in a solvable puzzle (meaning one that has one and only one solution). There were some interesting properties and conditions we discovered, but I won't give them away now! Maybe I'll write an article about it someday.
If you're interested in those investigations, feel free to ask some more questions about my setups and test them out! If you're interested in something else, try investigating that too. Math really is about asking questions and seeing where they take you. There's no set way to go about investigating it. It's really just where your curiosity takes you.
Emory Math Circle has a summer camp called the Week of Mathematical Exploration that does a wonderful job introducing students to mathematical investigations (and presentations) that I would definitely recommend, but as that's not something you can do from home, I'll provide you with a couple ideas and resources (but make sure to search for more if you're interested!)
First, here's a pirate-coconut riddle. See if you can expand it and ask some questions about it:
Seven pirates wash ashore on a deserted island after their ship sinks. In order to survive, they gather as many coconuts as they can find and throw them into a central pile. As the sun sets, they all go to sleep.
One pirate wakes up in the middle of the night. Being the greedy person he is, this pirate decides to take some coconuts from the pile and hide them for himself. As he approaches the pile, though, he notices a monkey watching him. To keep the monkey quiet, the pirate tosses it one coconut from the pile. He then divides the rest of the pile into seven equally sized bunches and hides one of the bunches in the bushes. Finally, he recombines the remaining coconuts into a single pile and goes back to sleep. (Note that individual coconuts are very hard, and therefore indivisible.)
Later that night, a second pirate wakes up with the same idea. She tosses the monkey one coconut from the central pile, divides the pile into seven bunches, hides her bunch, recombines the rest, and goes back to sleep. After that, a third pirate wakes up and does the same thing. Then a fourth. Then a fifth, and so on until all seven pirates have hidden a share of the coconuts.
In the morning, the pirates look at the remaining central pile and notice that it has gotten quite small. They decide to split the pile into seven equal bunches and take one bunch each. (Note: The monkey does not get one this time.)
If there were N coconuts in the pile originally, what is the smallest possible value of N?
Here's two more links to explore:
https://ibmathsresources.com/maths-ia-maths-exploration-topics/ (some topics to think about)
https://www.icts.res.in/sites/default/files/media/attachments/files/Maths-Circle-Explorations.pdf (some investigation questions!)
On top of investigations, you can always try some other fun activities you might find. Maybe even try crocheting a hyperbolic plane (like I hid in the cover image)!
9. Learn how to code! Coding is one of the skillsets that goes hand in hand with math, so think about using this time to learn how to program! There are so many online courses for coding from Udemy to edX to code.org, so find the one that works for you!
10. Use this site! You can always use this site to find resources and read articles, so feel free to keep coming back here over the coming months! I'd especially like to see all of you start to use the forum more. I'll be answering any sorts of questions you have for me over there or in the comments, and you can always discuss anything with each other at the forum. We can all stay strong together despite our current circumstances!
If you have any more ideas for mathy things to do over quarantine, leave them in the comments below! I'd always love to see more resources and more ideas in this department. If you have any questions for me (or just want a book recommendation), feel free to email me at email@example.com or just leave a question in the comments below! Have a great week everybody!