Mathematics
"Mathematics is the most beautiful and most powerful creation of the human spirit."- Stefan Banach
Calculus
The essence of Calculus is an introduction to Calculus explaining its nature. However, this is not recommended as a formal tutorial but more as an easy way for you to understand "what is calculus". If you want to learn Calculus but are afraid of its difficulty, then this one is the best for you as a start.
The Calculus course held by prof. Gilbert Strang is an official and formal tutorial for undergraduate students to fully comprehend the single variable calculus. However, this is not difficult; instead, it is pretty comprehensible with details and thorough explanations. Try this if you want to master Calculus!
The official AP Calc class held by College Board is a comprehensive and easy-to-understand tutorial for you to get a 5 in the AP exam. However, you may find this course a bit slow and elementary in teaching calculus. If you solely aim at a 5, then this one is best for you!
YouTube Channels
Dr Tom Crawford - Mathematician at the University of Oxford and St Edmund Hall, Numberphile, Naked Mathematician, YouTube 'Creator on the Rise', OxTALENT and IOP award-winner, lover of rock music and Maths tattoos (12 and counting)...
Maths, but not as you know it.
Videos about numbers and mathematics. Videos by Brady Haran since 2011.
3Blue1Brown, by Grant Sanderson, is some combination of math and entertainment, depending on your disposition. The goal is for explanations to be driven by animations and for difficult problems to be made simple with changes in perspective.
Summer Programs
RSI brings together about 70 high school students each summer for six stimulating weeks at MIT. This rigorous academic program stresses advanced theory and research in mathematics, science, and engineering. Participants attend college-level classes taught by distinguished faculty members and complete hands-on research. Open to high school juniors, the program is free of charge for those selected.
Canada/USA Mathcamp is an intensive 5-week-long summer program for mathematically talented high school students, designed to expose these students to the beauty of advanced mathematical ideas and to new ways of thinking. More than just a summer camp, Mathcamp is a vibrant community, made up of a wide variety of people who share a common love of learning and passion for mathematics. At Mathcamp, students can explore undergraduate and even graduate-level topics while building problem-solving skills that will help them in any field they choose to study.
Stanford University Mathematics Camp (SUMaC) welcomes a select group of mathematically talented rising high school juniors and seniors from around the world for intensive study in advanced mathematics. When you attend Stanford University Mathematics Camp, not only will you engage in a deep exploration of mathematics and develop as a mathematician, but you will be immersed in a community of others who share your mathematical talent and curiosity. For three weeks you will participate in online classes, make new friends, and be challenged intellectually. Many participants say the experience changed their lives.