Math Resources for Independent Learning

The math club at my school is now teaching through distance learning.

I compiled a list of some publicly available resources teaching math, or other topics related to math to share with my peers at my school. I thought others in this community might find it useful too.

  1. The Essence of Calculus Series – presented by 3Blue1Brown, is an extraordinary series that walks you through the /invention/ of calculus. It has many episodes covering topics from the number e to Taylor Series. I highly recommend it to students of ALL grades, as it focuses on the conceptual and not as much the technical part of calculus. Totally worth the time.
    Link to The Essence of Calculus Series: https://youtu.be/WUvTyaaNkzM

  2. If you like the series, consider watching more of 3Blue1Brown’s content. It also looks at linear algebra in the same intuitive manner. Currently 3Blue1Brown does a very interesting series of livestreams sharing some great insights about the topics that are commonly taught in our curriculum.

  3. Eddie Woo – learning mathematics. Eddie Woo has many lessons available online covering many topics relating to our curriculum. I recommend watching his Emoji Maths Puzzle solution first :slight_smile: https://youtu.be/FjE3CPEzM4w

The next relate to improving the contest math skills:
4. Math olympiad problems – presented by blackpenredpen. His channel currently has amazing videos covering questions including those from the International Math Olympiad. I highly recommend watching his Math for fun playlist, and if you have the chance, then totally watch his videos from before where he uses different proof techniques. https://www.youtube.com/user/blackpenredpen/featured

The next resources are from Centre for Education in Mathematics and Computing.
5. Enrichment, Extension, and Application Exercises – CEMC Courseware. CEMC has Courseware covering a wide range of Ontario math courses. There are courses for Grades 9, 10, 11, 12 and they can help you review or prepare for any future math courses that you might be taking. If you are in Grade 11 or 12, I encourage you to work through the Enrichment, Extension, and Application exercises. https://cemc.uwaterloo.ca/resources/courseware/courseware.html

  1. If you are interested in learning programming, and you are learning from scratch or looking to review any topics that you have learned previously, then definitely consider learning Python or web programming with University of Waterloo’s Open Computer Science and CS Circles. It is a great way to learn, once again for students of all grades.
    https://open.cs.uwaterloo.ca/
    https://cscircles.cemc.uwaterloo.ca/

  2. If you are already familiar with all concepts outlined in CS Circles, then take a look at their list of things to focus on next:
    https://cscircles.cemc.uwaterloo.ca/resources/

If you hope to have a go at some contest math, then check out these resources:
8. Art of Problem Solving has fantastic resources. Puzzles: https://artofproblemsolving.com/keeplearning
and past AMC Problems and Solutions: https://artofproblemsolving.com/wiki/index.php/AMC_Problems_and_Solutions

  1. CEMC’s Problem of the Week is available for Grades 9/10 and 11/12. https://cemc.uwaterloo.ca/resources/potw.php

Another suggestion that is learning mathematical communication. A mark-up language such as LaTeX that is very common in academic writing might be of interest for you. Overleaf provides very helpful resources in terms of learning LaTeX


Just go to https://www.overleaf.com/learn and start exploring! If you start feeling comfortable in LaTeX, you might want to consider this post https://www.quora.com/Does-anybody-use-LaTeX-to-take-notes-especially-during-class-If-not-what-do-you-use-especially-when-you-need-to-write-down-equations/answer/Gilles-Castel-1

P.S. Another parthway is CSS. There is a helpful video that introduces CSS and explains the syntax of the language https://youtu.be/0afZj1G0BIE

Also, one specific learning resource that I found through CEMC’s CS Circles is Project Euler. I have not yet tried any questions but it seems very interesting. https://projecteuler.net/

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This is a great list. When I saw this thread I was getting ready to link the CEMC resources, but you already go them. The CEMC was incredibly influential in nurturing my love of math and my (unsuccessful) journey to make the Canadian IMO team. They’re the gold standard in my mind when it comes to advanced mathematics education and problem solving.

Project Euler is my favourite way to learn a new programming language, as the problems give you a fun way to stretch your brain, to make getting used to a new language less painful.

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