What is the order of Mathematical Tiers?

Math only follows a linear order like that up until calculus. From there, it branches out into many different directions.

The earliest mathematical concepts you learn are associating the natural numbers to physical quantities (groups of objects) and learning to count. From there, you pick up on the basic operations (+, -, *, /). This naturally leads into additional basic arithmetic involving fractions, decimals, percents, proportions/ratios, etc. Toward the end of middle school or the beginning of high school, you'll take algebra, followed by geometry, followed by advanced algebra, followed by pre-cal/trigonometry, followed by calculus, with the possible option of taking statistics.

At the university level, you can continue you education of calculus. Calc is often split into three separate courses: differential, integral, and vector/multivariable calculus. You can also take differential equations at some point in there (usually after the second or third course in calc). Many people will also take an introductory course in linear algebra at this time (if they are pursuing a degree in math, or something related).

This is about the point math branches out. From here, you could take number theory, real analysis, complex analysis, more linear algebra, abstract algebra, numerical analysis, topology, etc. Although it would be highly advisable to take some of these before others (I would highly advise against taking topology right after calculus), they don't follow the same kind of linear progression that math classes in high school do. You can take number theory before or after real analysis, and it would make absolutely no difference since they are completely different branches of math.

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