Learning platforms, online communities, computing tools and online courses specifically tailored for higher-mathematics enthusiasts!
You know this one right? Starting from being a math-tutorial YouTuber to being discovered by Bill Gates and subsequently backed by several private foundations, Salman Khan would go on to found Khan Academy — a non-profit organisation with the goal of providing free, world-class education to the world.
While much of the educational contents on Khan Academy are built to supplement an applied-math-based curriculum with a learning philosophy skewed towards video-based learning, many of their math topics — such as the ones on Probability & Statistics, Calculus, Differential Equations and Linear Algebra — nevertheless remains valuable to millions of college/university students worldwide.
In addition to topic-based materials, Khan Academy also offers preparatory modules on standardized admission tests such as SAT and GMAT — always at zero cost to the interest students and their parents.
Back in the old days, standardized test preparation can cost up to several hundreds of dollars. With the advent of the Internet and the associated technologies, access to affordable test preparation is now possible to most computer users within a few clicks.
Built as an online testing platform with the goal of providing a robust test preparation experience, Magoosh now offers test materials for the ACT, SAT, GRE, GMAT (among other tests) in the form of timed practice questions and video lessons.
Available both on the Web and in the form of mobile application, Magoosh’s testing platform also allows its users to track their own progress, create customized practice sessions and receive assistance from the support team. While admittedly not a replacement for one-to-one instructions, it is nonetheless an great tool for those who prepare a test by studying on their own.
THE GREAT COURSES
In case you're wondering, The Great Courses is one of the earliest pioneer educational companies which team up with world-renowned experts in various fields to produce top-notch courses in textual, audio and visual formats.
In particular, they offer 40+ courses in mathematics with topics ranging from elementary algebra, mental arithmetic, financial mathematics, calculus to formal logic, discrete mathematics, geometry and statistics (among other topics). In our case for example, we are particularly fond of the Secrets of Mental Math and Joy of Mathematics by Arthur Benjamin — An outstanding mathemagician whose work inspired our vision of a thriving mathematical culture and a society of mathematical excellence.
Despite being a relatively recent act, Udemy has quickly made its way into one of the de-facto marketplaces for course buyers and course sellers. Yes, you've heard that right: any eligible person can become an instructor or a student on Udemy!
With 45,000+ courses (and counting) in pretty much any subjects you can think of, Udemy is clearly out there to reinforce the idea that "learning is not just a goal but a process." For our mathematics enthusiasts, Udemy offers a variety of courses from standardized test prep, calculus, linear algebra, discrete math to number theory, geometry, probability and statistics (among other topics).
On the other hand, since Udemy aims to be a democratic marketplace for courses, the educational value and production quality of a course can vary from one instructor to another — who might or might not be as expert as they claim to be!
Originally developed based on the popular computer algebra system Mathematica, Wolfram Alpha — an answer engine aiming to provide knowledge and answers to its users via dynamic computations — has since then morphed into one of the most extensive computing engine and one of the most frequently visited site on the Web.
Indeed, from decimal approximation, solving recurrence relations to function optimization and derivative/integral calculation, Wolfram Alpha seems to leave nothing mathematical untouched. For example, it can also be used to compute truth tables, create Venn Diagrams, solve differential equations and factorize large numbers (among other surprising features).
To be sure, the full capabilities of Wolfram Alpha actually extends much beyond the simple act of mathematical computations, so this would be another reason why you simply have to try this tool out on your own!
As a powerful HTML5 online graphing calculator, Desmos has established itself as a free web/mobile application with minimalist user interface and stunning graphic / animation capabilities.
From graphing equations and inequalities to creating tables and regression models, Desmos has all kinds of functionalities in its toolbox — which is also summarized in its very concise 12-page user manual.
If you want to learn all the stuffs you can do with Desmos, then this definitive guide can definitely get you going, and you haven’t heard of Desmos Art, then this guide on computational sketching will certainly make sure that you are not missing out!
Yet another powerhouse hailing from the Silicon Valley, Quora touts itself as a website with “the best answer to any question“. Launched fairly recently in 2010, it has since gained enough traction to become one of the most visited website in the world.
Despite being predominantly a more general question-and-answer community, with its MathJax integration in May 2015, Quora is increasing becoming a landing spot where math students can ask ultra-specific questions, and other mathematics enthusiasts can answer them — and have the answers voted by the fellow members!
A community website devoted to the intellectually-gifted, Brilliant.org aims to provide a social learning platform whereby students of math-related disciplines — be it mathematics, physics, quantitative finance and computer science — can practice their problem-solving skills through the access to its ever-growing repertoire of user-generated questions.
Additionally, these questions are classified by their subtopic and tailored to an individual’s level of proficiency. On the top of that, Brilliant.org users also have the options to create their own problem sets or wikis for other users, making it a formidable accelerated learning tool of for anything mathematics and beyond.
ART OF PROBLEM SOLVING
One of the earliest and the most celebrated Math Olympiad training hubs, the Art of Problem Solving (AoPS) was started by Richard Rusczyk in 2003 as a humble textbook publisher, and would go on to become an educational powerhouse providing mathematical training to high-performing students all over the world.
In its current form, AoPS now features accredited online school, textbook series, customized online learning system and community forum, with additional resources comings from its YouTube channel, online games, collection of math competition materials and a lot more!
A specialized question-and-answer website for math students and professionals alike, Mathematics StackExchange provides a relatively-clean LaTeX-integrated platform where topics from different branches of higher mathematics — be it number theory, calculus, abstract algebra, probability theory, combinatorics, group theory, analysis or graph theory — can survive and thrive.
Although generally not intended for students/instructors at the K-12 levels, it’s nonetheless a favorite place among the technically inclined. Indeed, it's not far-fetch to say that some math research papers are developed in part due to the discussions found on Mathematics StackExchange! .