Does anyone know the order of mathematic topics starting with the simplest to most advanced? Like algebra, geometry, trigonometric, calculus, statistics? Is there a name for the area of math children learn in grade school like counting, addition/subtraction, multiplication? I am just curious what the order of math would be starting from the beginning of learning to the very advanced for someone who would become a mathematician.
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before algebra you learn arithmetic.
Then there is algebra I, geometry, and algebra II,
Not necessarily in that order.
Finite math or business math can get thrown in there somewhere too.
Next would be calculus, statistics, or linear algebra.
After calculus its sort of a free-for-all.
Algebra (groups, rings, modules, fields, vector spaces, lattices, categories)
Foundations of math
Number theory
Differential equations
Partial differential equations
Probability theory
Linear modeling
History of mathematic
Philosophy of mathematics (not really a math class.)
Logic (not really a math class)
and that's all I can think of off the top of my head.
Then there is algebra I, geometry, and algebra II,
Not necessarily in that order.
Finite math or business math can get thrown in there somewhere too.
Next would be calculus, statistics, or linear algebra.
After calculus its sort of a free-for-all.
Algebra (groups, rings, modules, fields, vector spaces, lattices, categories)
Foundations of math
Number theory
Differential equations
Partial differential equations
Probability theory
Linear modeling
History of mathematic
Philosophy of mathematics (not really a math class.)
Logic (not really a math class)
and that's all I can think of off the top of my head.
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arithmetic => algebra => geometry => trig => pre-calc => calc
After calc, the course of study diverges depending on discipline.
For a mechanical engineering student in college, it would probably be like calc 1 (basic calc) => calc 2 ( mostly integrals), differential and linear equations => calc 3 (mostly surfaces, 3d math), numerical methods (complex number math, transforms, nonlinear dynamics) => computational methods (comp programming to solve problems beyond analytical methods). Around calc 2 and calc 3, you throw in a variety of electives like probability and statistics, control theory, and courses that specialize in certain aspects of math like vibrations, acoustic, fluids, combustion, etc.
For pure math, the progression would largely be based on the direction the math student wants to go.
After calc, the course of study diverges depending on discipline.
For a mechanical engineering student in college, it would probably be like calc 1 (basic calc) => calc 2 ( mostly integrals), differential and linear equations => calc 3 (mostly surfaces, 3d math), numerical methods (complex number math, transforms, nonlinear dynamics) => computational methods (comp programming to solve problems beyond analytical methods). Around calc 2 and calc 3, you throw in a variety of electives like probability and statistics, control theory, and courses that specialize in certain aspects of math like vibrations, acoustic, fluids, combustion, etc.
For pure math, the progression would largely be based on the direction the math student wants to go.