~ Proper sequence of mathematics to learn

From: Adam (addam_at_rogers.com)
Date: 07/26/04 

Date: Mon, 26 Jul 2004 14:14:23 GMT

Hi,

I will be studying physics at university this September. I am trying to
prepare myself for the material by learning pure mathematics, also just as a
hobby. I really only need to know applied mathematics, but I do not like it
much at all. I would like to know what most people would recommend that I
learn in sequence. For instance, I have been studying set theory, and am now
learning introductory group theory using online pdf documents. After group
theory, I wish to use the knowledge to learn linear algebra. I am not sure
if there is anything I should learn in between group theory and LA.

Basically, my intention is to understand pure mathematics well-enough that I
will be able to easily understand the mathematics that I will encounter when
studying physics and so can focus on the actual ideas instead. I truly enjoy
set theory, proofs, and am liking group theory so far, but I know that I
will not have to do proofs in my upcoming physics courses. I wish to
understand the mathematics fully and how it is related. That is why I
learned logic and then worked on set theory.

I'd appreciate any additions or changes to the material/order of study if
you are experienced with such things. As far as I can tell, the sequence of
logic, set theory, group theory, and, finally, linear alegbra, should be
followed. However, there might be something that I have not thought
included.

The math curriculum:
1) Set theory + proofs
2) Group theory
3) Linear Algebra
4) Single-variable calculus
5) Multi-variable calculus
6) Ordinary differential equations
7) Partial differential equations
8) Calculus with complex number

The physics curriculum: - not sure of the order
Introductory physics
Classical mechanics - not sure if this includes general relativity. Maybe
just Newtonian mechanics.
Quantum mechanics
Quantum physics (molecules, solids, nuclei, particles)
Thermal physics
Electrodynamics
Atmospheric physics
Nuclear physics
Material physics - semiconductors

I also bought a used book on quantum fluids, but it seems way over any of
the other texts I have in terms of mathematics used. 

-- 
"Don't just read it; fight it! Ask your own questions, look for your own 
examples, discover your own proofs. Is the hypothesis necessary? Is the 
converse true? What happens in the classical special case? What about the 
degenerate cases? Where does the proof use the hypothesis?"
  --- Paul Halmos (1916 - )
addam@rogers.com

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