So, You Want To Study Mathematics?

Wow, wonderful post covering what one needs to get started in Math!

Math has a bad reputation. I believe it is the most beautiful form of human thought, but most people see it as a sterile rule system made to punish students. This disconnect is due to the way our schooling system approaches math — it focuses on the mechanics and not the why. While the basics are necessary, they can hide the deeper beauty that math contains. Luckily, it is easier than ever to get an amazing mathematics education on your own thanks to the internet.

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Before I begin my subject recommendations, there are some things to keep in mind. These pieces of advice come from my own experience with 10+ years of self-studying math and working as a college math teacher. I have provided sources where relevant if you want to see why I recommend these practices.

• First, accept that this will be hard. Math is a new language that has to be mastered. It is much less flexible and more demanding than any spoken language. Expect to run into roadblocks and to have to push yourself. Some ideas will take a long time to get comfortable with; you are literally forming new connections in your brain as you study math!
• The best way to study anything is with consistency, not 3-hour marathon sessions once a month. Your brain works better on 15 solid minutes a day. My rule of thumb is to never miss two days in a row. Life gets in the way, and I can’t always make every day work, but I go out of my way to never let that happen twice.
• I remind my students about this all the time: the only way to learn math is to actually do problems. Following along with a video is an important step, but you do not understand something until you can solve the problems on your own. My recommended resources are largely based on the quality of their problems.
• Studying math can be lonely, but it doesn’t have to be. Find someone who wants to learn the same content and work together. This will help you both with accountability and increase your understanding as you talk through the content with each other. Maybe we can create an online community of people learning different topics: any interest?
• AI can be an excellent tool for self-studying math, if used correctly. There is no substitute for a good teacher, but AI can give intuitive explanations and help check your work. Resist the temptation to use it to overcome every obstacle you face, but it can be wonderful for checking your work or offering hints when there aren’t answers provided.
• Interested in one-on-one tutoring and guidance for your studies? Send me a message; maybe I can help
• Take breaks! Schools know this and have many breaks throughout a semester and even longer breaks between semesters. If an idea isn’t sticking, sometimes you need to walk away and do something else for it to click. Let your subconscious tackle it for a while. Rest is just as important as the work.
• And most importantly, have fun! You are doing this for you. Discipline can only take you so far; remember why you are self-studying math in the first place.

Part of the problem with standard college mathematics curriculum is that it heavily emphasizes calculus. I love teaching calculus, and I think the subject is really fun, but this sequence is based on outdated priorities left over from the space race. Calculus certainly has its place, but it is not the only subject to study.