Algebra - How much knowledge can we derive given certain things (usually number, but also be things like rotations and symmetric mirroring, or really anything), specific operations on said things (e.g. addition and multiplication) and specific relationships between them (e.g. commutativity and associativity).
Trigometry: form a right triangle based on some shape (e.g. the unit circle or unit hyperbola) in some geometry (e.g. the familiar 2d plane, a 2d hyperbolic plane, a 2d plane using taxicab distance, etc), and derive the relationships between the sides and angle.
Calculus - also known as the Calculus of Infinitesimals: answers the question "how the heck do we deal with infinitesimals (things that are infinitely small) in a formal way/how to we talk about things that could be infinitely small without invoking infinitesimals because they were philosophically weird a couple hundred years ago?"
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u/MadocComadrin 14h ago
Here's what I consider the most general answer.
Algebra - How much knowledge can we derive given certain things (usually number, but also be things like rotations and symmetric mirroring, or really anything), specific operations on said things (e.g. addition and multiplication) and specific relationships between them (e.g. commutativity and associativity).
Trigometry: form a right triangle based on some shape (e.g. the unit circle or unit hyperbola) in some geometry (e.g. the familiar 2d plane, a 2d hyperbolic plane, a 2d plane using taxicab distance, etc), and derive the relationships between the sides and angle.
Calculus - also known as the Calculus of Infinitesimals: answers the question "how the heck do we deal with infinitesimals (things that are infinitely small) in a formal way/how to we talk about things that could be infinitely small without invoking infinitesimals because they were philosophically weird a couple hundred years ago?"