I don't know if this counts as "math help," but if anyone is interested, let know your opinion on this. The main reason for this is because I want to go back through all the math I've ever learned and fill in the holes that haunted me the entire time I was in college (a poor geometry and trig background), and then maybe expand what I know into other branches. Maybe start at the beginning and work my way up over the course of a couple years. I'm hoping that having a good foundation will make this easier than the first time I studied math, when I started at Calculus I when I really should have shored up my weaknesses first.
I think the list should probably be something like this:
Algebra
Geometry (informal)
Trigonometry
Calculus I, II, III, IV (or whatever way it's broken up in your institution)
Geometry (proof heavy)
Linear Algebra
Probability and Statistics
Differential Equations
Partial Differential Equations
Transition to Higher Math (whatever name is used at your institution)
Abstract Algebra
Real Analysis
Vector Analysis
Complex Analysis
Numerical Analysis
Topology
Number Theory
Combinatorics/Graph Theory
As for the upper division and borderline graduate courses starting with Abstract Algebra, I honestly am not sure the best order. I did take Abstract I and II, and Intro to Real Analysis, and the latter was much more difficult for me. Abstract algebra felt very natural to me. Real analysis not so much. So I'm assuming the different types of analysis courses listed here require basic real analysis first. Based on what little I know of introductory topology, it seems similar in essence to real analysis, so I'm assuming it probably helps to have real analysis down first before topology as well.
So what would your ideal order be? I think I left out discrete math in there, but I imagine in some abstract algebra courses you get some exposure to it.
I think the list should probably be something like this:
Algebra
Geometry (informal)
Trigonometry
Calculus I, II, III, IV (or whatever way it's broken up in your institution)
Geometry (proof heavy)
Linear Algebra
Probability and Statistics
Differential Equations
Partial Differential Equations
Transition to Higher Math (whatever name is used at your institution)
Abstract Algebra
Real Analysis
Vector Analysis
Complex Analysis
Numerical Analysis
Topology
Number Theory
Combinatorics/Graph Theory
As for the upper division and borderline graduate courses starting with Abstract Algebra, I honestly am not sure the best order. I did take Abstract I and II, and Intro to Real Analysis, and the latter was much more difficult for me. Abstract algebra felt very natural to me. Real analysis not so much. So I'm assuming the different types of analysis courses listed here require basic real analysis first. Based on what little I know of introductory topology, it seems similar in essence to real analysis, so I'm assuming it probably helps to have real analysis down first before topology as well.
So what would your ideal order be? I think I left out discrete math in there, but I imagine in some abstract algebra courses you get some exposure to it.
