I did a little investigate as well as couldn’t find any source which is improved for summing up a vital branches of arithmetic than wikipedia. According to them a vital fields as well as topics have been as follows.
Quantity: Arithmetic- healthy numbers to formidable numbers etc.
Space: Geometry, Trigonometry, Differential Geometry, Topology, Fractal Geometry
Change: Calculus, Vector Calculus, Differential Equations, Dynamical Systems, Chaos Theory
Structure: Number Theory, Abstract Algebra, Group Theory, Order Theory
Foundations as well as Philosophy: Mathematical Logic, Set Theory, Category Theory
Discrete Mathematics: Combinatorics, Theory of Computation, Cryptography, Graph Theory
Applied Mathematics: Mathematical Physics, Mathematical Fluid Dynamics, Numerical Analysis, Optimization, Probability Theory, Statistics, Financial Mathematics, Game Theory
1. According to your believe does this list total up all a categorical branches/topics of math or does it tumble short?
2. I’m gifted in math as well as investigate it in my giveaway time. we would similar to to sense a basics/introductory element for any bend (I know any particular bend by itself might have some-more element than a single can sense in a lifetime if we go in depth). we know it will take prolonged as well as though a highbrow it will take even longer, though we do not mind. This is a hobby of mine.
In what sequence we should investigate these categorical topics so which we do not confront any report gaps along a way, in what sequence should we investigate them for a many continuity?
Also, does investigate of any of a listed categorical branches need a little in abyss believe of alternative branches over a basics?
3. If we did sense a basis of all these branches, what percent of well known arithmetic will we know- would we be only scratching a surface?
4. What textbooks would we suggest for a little or all of these branches of math for study?
Thank we for your advice.

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