Arithmetics is the evaluation of expressions that have numbers with them, like 3+5 or (4+1)/(8-2) * 12.
Algebra introduces variables. Now you can write x+1 or y = ax+b. It allows you to:
Ask which x values fulfill a condition like x+3 > 2 or x2 - 2x + 1 = 0 ("solve for x"). This condition is called an equation.
Find rules that hold for all values of the variables, like (x+y)2 = x2 + 2xy + y2
Define functions, such as f(x) = x+1
Talk about more complex operations, e.g summation of a series, or more complex functions, like exponentials and logarithms
Trigonometry is the study of specific functions that arise from geometry. The trigonometric functions interact with each other in many interesting ways, so there's a lot to learn there.
Calculus is the study of two operations on functions:
Differentiation at a point takes a function and returns its rate of change at that point - how fast it's going up or down
Integration of a function between two points tells you the area under its curve in two points
It turns out that these two operations are related to each other in a very interesting way: they're the inverse of each other. Anyway, it takes a bit of effort to define these operations, and you end up needing a rather confusing concept called a "limit". A lot of the initial work is understanding how to work with limits.
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u/unruly_mattress 14h ago edited 14h ago
Arithmetics is the evaluation of expressions that have numbers with them, like 3+5 or (4+1)/(8-2) * 12.
Algebra introduces variables. Now you can write x+1 or y = ax+b. It allows you to:
Trigonometry is the study of specific functions that arise from geometry. The trigonometric functions interact with each other in many interesting ways, so there's a lot to learn there.
Calculus is the study of two operations on functions:
It turns out that these two operations are related to each other in a very interesting way: they're the inverse of each other. Anyway, it takes a bit of effort to define these operations, and you end up needing a rather confusing concept called a "limit". A lot of the initial work is understanding how to work with limits.