When you try to master ( can any one master some established discipline now a days ? ) something , too often ,depth is emphasized more than it ought to be .
Take the case of Mathematics as I have encountered it.
After 10th , I have not studied Mathematics formally. I learned bulk of my math through self learning . I started with Differential Calculus and to further my knowlege , I was forced to learn Trignometry. Then , TrignoMetry made sense. When I learned Integral Calculus , Differential Calculus began to make sense. When It reached Differential Equations , Integral calculus began to make sense. When I learned , Partial differentiation , Ordinary differential equations began to make sense to me. When Closed form solutions for some problems evaded me , I learned that Numerical methods are the way to go.
When I learned Numerical Methods (by writing Computer Programs ) , things like Continuity , Limiting operations , Linearity (Matrix stuff ) began to make more sense.
I got interested in Computer Graphics Programming. This gave more insights into Co-Ordinate Systems , Co-ordinate Transformation , Vector DotProduct , Cross Product , Matrix Algebra , Orthogonality , OrthoNormality etc etc
Then came Finance which helped me to brush my arithematic and algebra for sure. Then , found applications for Non linear root findings for computing Internal Rate of Return (IRR) , Progression for deriving formula for EMI , Statistics for calculating Beta , Regression analysis and Trend Projection.
Then , came Stochastic Analysis of Finance models. This was really an eye opener where I really understood stuffs like Discrete Random Variables , Continuous Random Variable , Sampling , Monte Carlo Simulation , Continuous time finance ( e , base of natural logarithm ) etc.
Emphasis should be on breadth first learning as using mathematics is different from doing mathematics. By trying to spread thin , you find more opportunity to apply the math you have come across and appreciate mathematics much more.
Take the case of Mathematics as I have encountered it.
After 10th , I have not studied Mathematics formally. I learned bulk of my math through self learning . I started with Differential Calculus and to further my knowlege , I was forced to learn Trignometry. Then , TrignoMetry made sense. When I learned Integral Calculus , Differential Calculus began to make sense. When It reached Differential Equations , Integral calculus began to make sense. When I learned , Partial differentiation , Ordinary differential equations began to make sense to me. When Closed form solutions for some problems evaded me , I learned that Numerical methods are the way to go.
When I learned Numerical Methods (by writing Computer Programs ) , things like Continuity , Limiting operations , Linearity (Matrix stuff ) began to make more sense.
I got interested in Computer Graphics Programming. This gave more insights into Co-Ordinate Systems , Co-ordinate Transformation , Vector DotProduct , Cross Product , Matrix Algebra , Orthogonality , OrthoNormality etc etc
Then came Finance which helped me to brush my arithematic and algebra for sure. Then , found applications for Non linear root findings for computing Internal Rate of Return (IRR) , Progression for deriving formula for EMI , Statistics for calculating Beta , Regression analysis and Trend Projection.
Then , came Stochastic Analysis of Finance models. This was really an eye opener where I really understood stuffs like Discrete Random Variables , Continuous Random Variable , Sampling , Monte Carlo Simulation , Continuous time finance ( e , base of natural logarithm ) etc.
Emphasis should be on breadth first learning as using mathematics is different from doing mathematics. By trying to spread thin , you find more opportunity to apply the math you have come across and appreciate mathematics much more.
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