I would say everything you learn up to algebra is like the alphabet of math. Something you teach someone when you don’t expect them to actually understand how to form words into complex ideas, but you want to introduce them to the building blocks you’ll be using later on. Then you start taking English classes where you learn what a verb is, what tense is, parts of speech, rules of grammar, the exceptions and intricacies. The actual rules of English.
Algebra is the rules of math. Math is such a huge, enormous topic that you spend the first 8 years of your student life just learning the alphabet of math. It’s not until algebra that you really start digging into the rules of math. How to combine concepts. Stuff like that. You hit this stage where the strides you take each year are exponentially larger and larger. The math that you learn becomes more and more powerful.
If you are going into any major that requires math (basically anything in STEM) you will use algebra concepts every single day in at least one of your classes. Outside academia is a bit of a pot shoot. But even in my very paperwork-focused job, I use algebra every week. It’s woven into everything we do.
If you don’t get a math-heavy major and don’t go into a job that requires much or any math from you, then the exact topics may not be that useful to you. But Algebra is such a huge expansion in the logic that you can use and the tricks you need to rethink and reframe problems into a form you know how to solve. I truly think that these skills are going to be extremely helpful to anyone. The tools you have to develop to solve problems need to be very generic and apply to any number of different types of problems, so you will start learning how to solve problems outside of math as well. Critical thinking skills, thinking outside the box, approaching from multiple angles, sorting through what you know, what you do t know, and what’s required to traverse the gap between.
All studies used to be branches of philosophy. Math is what happened when logic grew so large that it split off from philosophy and became its own discipline. Math is what happens when you extend logic. Math is logic. If you can do basic logic, then you can do basic math. If you can do advanced math, advanced logic will be easier too.
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