Studying Optimizing Your Math Study Plan: Tips and Textbook Recommendations

[DianaElQassim]

I want to study physics, but I am really not that good in mathematics. I need some sort of a hierarchy or a study plan with good textbooks included. I want to start from the very basics, a study plan that covers everything from vectors, algebra, geometry, to calculus. If anyone could suggest a good study plan with textbooks or even online courses, that would be very helpful.

 

[S.G. Janssens]

You may find the "Insights" by this author helpful, particularly those about (self-)studying.

 

[heff001]

I also have a related question regarding a ( more pure) math study plan - Her is my list below (I reviewed many sources to arrive at this)...the questions I have are (1) Why is Linear Algebra so late in the list? (2) Is this list accurate?
•Logic
•Set Theory (Set-class Theory)
•The Natural Numbers
•Category Theory
•Order Theory
•Group Theory
•The Integers and Number Theory
•Ring Theory
•The Rationals
•Field Theory
•Point-set Topology
•The Real Numbers
•The Complex Numbers
•Linear Algebra (why so late?)
•Measure Theory
•Real Analysis
•Complex Analysis
•Functional Analysis
•Differential Equations

 

[symbolipoint]

I want to study physics, but I am really not that good in mathematics. I need some sort of a hierarchy or a study plan with good textbooks included. I want to start from the very basics, a study plan that covers everything from vectors, algebra, geometry, to calculus. If anyone could suggest a good study plan with textbooks or even online courses, that would be very helpful.

How do you mean, "really not that good in mathematics"? Best response depends on knowing what that means for you.

 

[member 587159]

I also have a related question regarding a ( more pure) math study plan - Her is my list below (I reviewed many sources to arrive at this)...the questions I have are (1) Why is Linear Algebra so late in the list? (2) Is this list accurate?
•Logic
•Set Theory (Set-class Theory)
•The Natural Numbers
•Category Theory
•Order Theory
•Group Theory
•The Integers and Number Theory
•Ring Theory
•The Rationals
•Field Theory
•Point-set Topology
•The Real Numbers
•The Complex Numbers
•Linear Algebra (why so late?)
•Measure Theory
•Real Analysis
•Complex Analysis
•Functional Analysis
•Differential Equations

Category theory should be far down the list. Where will you get your examples without topology and abstract algebra? A course on logic seems unnecessary: you learn this while doing mathematics. Same thing with set theory; well maybe some set theory course can be useful later introducing ZFC formally but I think formal set theory will obscure things without the proper background. The set theory course and logic course can be replaced by one discrete math course imo. Also, linear algebra way too late on the list. Can easily be in top 5. Also, all the number systems should be basic and higher in the list. Merge them as one thing.

 

[PeroK]

How do you mean, "really not that good in mathematics"? Best response depends on knowing what that means for you.

The OP is long gone from PF.

 

[symbolipoint]

The OP is long gone from PF.

Post #3 came on Friday, which was only TWO days ago, and an Alert came to me about this topic; so I HAD a response.

 

[heff001]

There can be debated a lot in this list, but my first question:

why would you want to do all this if youCategory theory should be far down the list. Where will you get your examples without topology and abstract algebra? A course on logic seems unnecessary: you learn this while doing mathematics. Same thing with set theory; well maybe some set theory course can be useful later introducing ZFC formally but I think formal set theory will obscure things without the proper background. The set theory course and logic course can be replaced by one discrete math course imo. Also, linear algebra way too late on the list. Can easily be in top 5. Also, all the number systems should be basic and higher in the list. Merge them as one thing.

I really appreciate the reply. This is perfect.