- #1
Super Kirei
- 14
- 0
Hi everybody, I've been out of school for 4 years and I'd like to learn some physics.
I'll give a summary of my background and I'd like suggestions as to what I should study and in what order. There's an abundance of resources that can be found through Google, but it's hard to decide what is and is not worth pursuing and in what order they ought to be pursued. I'm hoping someone who's already been there will grant me some pointers.
So here are the math and physics courses I took in college:
Physics I and II with calculus: Calculus based physics intro. Newtons's laws, work and energy, momentum and impulse, rotational dynamics, acoustic vibrations, thermodynamics, electricity, magnetism, basic circuits, Maxwell's equations, electromagnetic waves and geometrical optics. I remember learning the stuff but remember very little of the stuff on electricity and magnetism.
Calc. 1-3: A standard calculus sequence covering limits, continuity, differentiation, integration, sequences and series, vector integration and differentiation, functions of several variables, double and triple integrals and a small sprinkling of vector anlysis including path and surface integrals.
Discrete mathematics: Standard compsci oriented lower division sampler pack. Turned me on to math.
Differential Equations: The usual course in ODEs taken by science majors. Separation of variables, integrating factors, constant coefficients, variation of parameters, series solutions, and laplace transforms.
Linear Algebra: linear systems, gauss jordan elimination, properties of matrices, vector spaces, linear maps, dot products and orthogonality, eigenvectors and eigenvalues.
Number Theory: How to solve linear diophantine equations, uniqueness of prime factorization, how to work with and solve congruences, chinese remainder theorem, fermat's little theorem. Can't remember much of it, it's a blur.
Graph Theory: ...purged from my memory. Something about Konigsberg and taking a walk.
Combinatorics: Pigeonhole principle, combinations and permutations, binomial coefficients, inclusion exclusion, recurrence relations.
Math Stats: discrete and continuous probability, survey of useful distrubutions and probability densities along with their properties. Very fuzzy memory.
Intro to Adv. Math: Bridge course on logic and proofs. Covered naive set theory, predicate logic, functions and relations.
Advaned Calculus: First six chapters of baby Rudin. Class was weak, book was hard, prof pitched to LCD, learned very little.
Complex Variables: Complex numbers, functions of a complex argument, differentiation, path integration, the integral theorems, power series, laurent series. Learned little for same reason as in adv. calc.
Partial Differential Equations: The use of separation of variables and Fourier series to solve boundary value problems.
Algebraic Structures: Groups and rings.
Topics in Algebraic Structures: More rings and modules.
Axiomatic Set Theory: ZF axioms, ordinals, cardinals. I had the hardest time with this one. Earned a C. I have no intuition in this area, can't visualize.
If you've read this much you have my supreme gratitude. The descriptions became terser near the end as I grew tired of typing. So, based on my background, what would be the best way for me to self-study the physics contnent of the usual undergraduate curriculum?
I'll give a summary of my background and I'd like suggestions as to what I should study and in what order. There's an abundance of resources that can be found through Google, but it's hard to decide what is and is not worth pursuing and in what order they ought to be pursued. I'm hoping someone who's already been there will grant me some pointers.
So here are the math and physics courses I took in college:
Physics I and II with calculus: Calculus based physics intro. Newtons's laws, work and energy, momentum and impulse, rotational dynamics, acoustic vibrations, thermodynamics, electricity, magnetism, basic circuits, Maxwell's equations, electromagnetic waves and geometrical optics. I remember learning the stuff but remember very little of the stuff on electricity and magnetism.
Calc. 1-3: A standard calculus sequence covering limits, continuity, differentiation, integration, sequences and series, vector integration and differentiation, functions of several variables, double and triple integrals and a small sprinkling of vector anlysis including path and surface integrals.
Discrete mathematics: Standard compsci oriented lower division sampler pack. Turned me on to math.
Differential Equations: The usual course in ODEs taken by science majors. Separation of variables, integrating factors, constant coefficients, variation of parameters, series solutions, and laplace transforms.
Linear Algebra: linear systems, gauss jordan elimination, properties of matrices, vector spaces, linear maps, dot products and orthogonality, eigenvectors and eigenvalues.
Number Theory: How to solve linear diophantine equations, uniqueness of prime factorization, how to work with and solve congruences, chinese remainder theorem, fermat's little theorem. Can't remember much of it, it's a blur.
Graph Theory: ...purged from my memory. Something about Konigsberg and taking a walk.
Combinatorics: Pigeonhole principle, combinations and permutations, binomial coefficients, inclusion exclusion, recurrence relations.
Math Stats: discrete and continuous probability, survey of useful distrubutions and probability densities along with their properties. Very fuzzy memory.
Intro to Adv. Math: Bridge course on logic and proofs. Covered naive set theory, predicate logic, functions and relations.
Advaned Calculus: First six chapters of baby Rudin. Class was weak, book was hard, prof pitched to LCD, learned very little.
Complex Variables: Complex numbers, functions of a complex argument, differentiation, path integration, the integral theorems, power series, laurent series. Learned little for same reason as in adv. calc.
Partial Differential Equations: The use of separation of variables and Fourier series to solve boundary value problems.
Algebraic Structures: Groups and rings.
Topics in Algebraic Structures: More rings and modules.
Axiomatic Set Theory: ZF axioms, ordinals, cardinals. I had the hardest time with this one. Earned a C. I have no intuition in this area, can't visualize.
If you've read this much you have my supreme gratitude. The descriptions became terser near the end as I grew tired of typing. So, based on my background, what would be the best way for me to self-study the physics contnent of the usual undergraduate curriculum?