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.