Here are some fun and useful resources accessible to (not only) secondary school students. (Page under construction)
- Art of Problem Solving: They have an excellent set of guides, courses you can take (WOOT is fab), books you can buy and a cool bot called Alcumus (which is free) that you can practice solving problems with. They also have an excellent collection of competition problems, but not that many have on-site solutions. You can ask in the forums, though they may look intimidating at first.
- Brilliant.org: Free, wide range of problems from contributors all over the world. Now covers a wider range than ever, from classics such as algebra, geometry, number theory and combinatorics to quantitative finance, electricity and magnetism, and JEE Math. Jeez. Problems are assigned different levels and you earn points for completing problems.
- NIMO (National Internet Math Olympiad): Team up with your friends and join the Online Math Open! There are also monthly contests that look fun.
Books on Problem-Solving:
- How to Solve it (George Polya): A classic on methods of problem-solving. Disclaimer: Just reading through it is NOT going to magically make you good at problem-solving. You actually have to do (a lot of) problems.
- The Art and Craft of Problem Solving (Paul Zeitz): Rich collection of problem-solving principles followed with examples and addictive problems.
- Problem-Solving Through Problems (Loren C. Larson): I found this much harder than Zeitz’s book, and only went through the first few chapters.
- ViHart: Who doesn’t love a hexaflexagon?
- Numberphile: Or a video on keeping hundreds of Klein bottles in your basement?
- LMS Popular Lecture Series: I recommend Prof. Takashi Tokieda’s Toy Models talk. It is freaking AMAZING. His site is also really cute. :3
Books that you actually read:
- 1089 and All That: A Journey into Mathematics (David Acheson): Short and fun. Easy to start with!
- Oliver Byrne’s 1847 printing of the First Six Books of the Elements of Euclid: When I first saw this, I cried rainbows. See picture below.
- A Mathematician’s Apology (G.H. Hardy)
- The Music of the Primes: Why an Unsolved Problem in Mathematics Matters (Marcus Du Sautoy): Engaging book on primes and how primes and Riemann’s conjecture relate to music, quantum mechanics, computing, and finance. <- Makes it sound more clinical than it is.
- Love and Math (Edward Frenkel): Inspiring but can get a bit technical / confusing.
- Coffee, Love and Matrix Algebra (Gary E. Davis): Okay this one was jokes.
- Wolfram Alpha: Not gonna lie, I used this to check the answers for a lot of weird integrals. There are far better things you can do with it, though.
- Wolfram Demonstrations Project: An incredible library of interactive online models.
- GeoGebra: Geometry package (free) that is great for exploring graphs, constructs and other figures. It’s free for desktop and mobile. Other packages include (1) the Geometer’s Sketchpad which is particularly good for exploring Euclidean Geometry, and (2) Autograph, which you can use to animate graphs and blow people’s minds. Basically.
I put this at the end because it’s the essential but often-seen-as-boring part, so hopefully on the way here you came across some interesting links.
- PatrickJMT: From calculus to linear algebra, he’s your man.
- Khan Academy: They’ve got simple exercises for practice on top of their excellent videos now.