Hierarchy of Knowledge/Continued Education

[dimensional]

I plan on continuing my education to pursue a second degree sometime soon, and I was wondering if some of the more brilliant and experienced academics here might be able to help me out. Essentially what I am looking for is a very thorough overview of the hierarchy of knowledges that physics adheres to in particular, however a general charting is acceptable as well. In addition to a formal hierarchy, I'm also looking for recommendations on books that would take me from basic Algebra all the way through QM and beyond.

I certainly do appreciate any contributions to my topic and my personal quest for knowledge. If my request is a bit vague I'll be glad to clarify, however I am trying to be succinct in order to prevent any confusion.

 

[someperson05]

You may find this website quite helpful

http://www.openproblems.net/

In particular the links it provides to,

http://superstringtheory.com/math/math2.html
http://math.ucr.edu/home/baez/books.html

EDIT:

This website may be even better for your needs, another link on that website.

http://www.phys.uu.nl/~thooft/theorist.html

 

[dimensional]

Wow, thanks a lot! Especially the last link, that looks just great. I'll have some fun looking through these. Thanks!

 

[intwo]

I actually just started making a list of topics/books yesterday. It needs some tweaking at the moment, but it should still be helpful. Just pick one or two books from each category starting from the top and you're set. I've italicized books that I recommend.

This list also contains topics I'd like to learn, so some sections can be omitted. You don't need Calculus /w Analysis if you dislike proofs, but it'll be worthwhile to take a look at it later in your education. Matlab is good for making graphs (you can purchase a student edition for $100) but can be ignored until upper level classes. Engineering Statics & Dynamics and Mechanics of Materials are engineering topics.

Precalculus

Precalculus: Mathematics for Calculus - Stewart, Redlin, Watson
https://www.amazon.com/dp/0840068077/?tag=pfamazon01-20

Calculus

Calculus - Larson & Edwards
https://www.amazon.com/dp/0547167024/?tag=pfamazon01-20

Calculus - Stewart
https://www.amazon.com/dp/0538497815/?tag=pfamazon01-20

Thomas' Calculus - Thomas, Weir, Hass
https://www.amazon.com/dp/0321587995/?tag=pfamazon01-20

Calculus /w Analysis

Calculus - Spivak
https://www.amazon.com/dp/0914098918/?tag=pfamazon01-20

Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus - Spivak
https://www.amazon.com/dp/0805390219/?tag=pfamazon01-20

Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra - Apostol
https://www.amazon.com/dp/0471000051/?tag=pfamazon01-20

Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications - Apostol
https://www.amazon.com/dp/0471000078/?tag=pfamazon01-20

Introductory Physics

The Feynman Lectures on Physics - Feynman, Leighton, Sands
https://www.amazon.com/dp/0465023827/?tag=pfamazon01-20

Fundamentals of Physics - Halliday, Resnick, Walker
https://www.amazon.com/dp/0470469080/?tag=pfamazon01-20

Physics for Scientists and Engineers - Giancoli
https://www.amazon.com/dp/0131495089/?tag=pfamazon01-20

Physics for Scientists and Engineers - Serway & Jewett
https://www.amazon.com/dp/1439048444/?tag=pfamazon01-20

University Physics - Young & Freedman
https://www.amazon.com/dp/080532187X/?tag=pfamazon01-20

Introductory Physics Supplements

An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements - Taylor
https://www.amazon.com/dp/093570275X/?tag=pfamazon01-20

Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving - Mahajan & Mead
https://www.amazon.com/dp/026251429X/?tag=pfamazon01-20

Matlab Programming

Getting Started with MATLAB: A Quick Introduction for Scientists and Engineers - Pratap
https://www.amazon.com/dp/0199731241/?tag=pfamazon01-20

Matlab: A Practical Introduction to Programming and Problem Solving - Attaway
https://www.amazon.com/dp/0750687622/?tag=pfamazon01-20

Ordinary Differential Equations

Differential Equations - Blanchard, Devaney, Hall
https://www.amazon.com/dp/0495012653/?tag=pfamazon01-20

A First Course in Differential Equations: The Classic Fifth Edition - Zill
https://www.amazon.com/dp/0534373887/?tag=pfamazon01-20

Ordinary Differential Equations - Tenenbaum, Pollard
https://www.amazon.com/dp/0486649407/?tag=pfamazon01-20

Engineering Statics & Dynamics

Engineering Mechanics: Combined Statics & Dynamics - Hibbeler
https://www.amazon.com/dp/0138149291/?tag=pfamazon01-20

Engineering Mechanics: Statics & Dynaics - Bedford & Fowler
https://www.amazon.com/dp/0136142257/?tag=pfamazon01-20

Vector Mechanics for Engineers: Statics and Dynamics - Beer, Johnston, Eisenberg, Cornwell, Mazurek
https://www.amazon.com/dp/0077275551/?tag=pfamazon01-20

Mechanics of Materials

Mechanics of Materials - Beer, Johnston, DeWolf, Mazurek
https://www.amazon.com/dp/0077221400/?tag=pfamazon01-20

Mechanics of Materials - Gere & Goodno
https://www.amazon.com/dp/0495438073/?tag=pfamazon01-20

Mechanics of Materials - Hibbeler
https://www.amazon.com/dp/0136022308/?tag=pfamazon01-20

Linear Algebra

Introduction to Linear Algebra - Strang
https://www.amazon.com/dp/0980232716/?tag=pfamazon01-20

Linear Algebra - Shilov
https://www.amazon.com/dp/048663518X/?tag=pfamazon01-20

Advanced Introductory Mechanics

An Introduction to Mechanics - Klepper & Kolenkow
https://www.amazon.com/dp/0521198216/?tag=pfamazon01-20

Advanced Introductory E&M

Electricity and Magnetism - Purcell
https://www.amazon.com/dp/0070664951/?tag=pfamazon01-20

Electromagnetic Vibrations, Waves, and Radiation - Bekefi & Barrett
https://www.amazon.com/dp/0262520478/?tag=pfamazon01-20

E&M Supplements

Div, Grad, Curl, and all That: An Informal Text on Vector Calculus - Schey
https://www.amazon.com/dp/0393925161/?tag=pfamazon01-20

A Student's Guide to Maxwell's Equations - Fleisch
https://www.amazon.com/dp/0521701473/?tag=pfamazon01-20

Electronics

The Art of Electronics - Horowitz & Hill
https://www.amazon.com/dp/0521370957/?tag=pfamazon01-20

Special Relativity

Six Ideas That Shaped Physics: Unit R - laws of Physics are Frame-Independent - Moore
https://www.amazon.com/dp/0072397144/?tag=pfamazon01-20

Spacetime Physics - Taylor, Wheeler
https://www.amazon.com/dp/0716723271/?tag=pfamazon01-20

Special Relativity - French
https://www.amazon.com/dp/0393097935/?tag=pfamazon01-20

Introductory Quantum Mechanics

Introduction to Quantum Mechanics - French & Taylor
https://www.amazon.com/dp/0393091066/?tag=pfamazon01-20

Six Ideas That Shaped Physics: Unit Q - Matter Behaves Like Waves - Moore
https://www.amazon.com/dp/0072397136/?tag=pfamazon01-20

Partial Differential Equations

Partial Differential Equations: An Introduction - Strauss
https://www.amazon.com/dp/0470054565/?tag=pfamazon01-20

Partial Differential Equations for Scientists and Engineers - Farlow
https://www.amazon.com/dp/048667620X/?tag=pfamazon01-20

Partial Differential Equations with Fourier Series and Boundary Value Problems - Asmar
https://www.amazon.com/dp/0131480960/?tag=pfamazon01-20

Complex Analysis

Complex Variables - Fisher
https://www.amazon.com/dp/0486406792/?tag=pfamazon01-20

Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics - Saff & Snider
https://www.amazon.com/dp/0139078746/?tag=pfamazon01-20

Mathematical Methods

Mathematical Methods for Physicists - Arfken & Weber
https://www.amazon.com/dp/0120598760/?tag=pfamazon01-20

Mathematical Methods in the Physical Sciences - Boas
https://www.amazon.com/dp/0471198269/?tag=pfamazon01-20

Optics

Optics - Hecht
https://www.amazon.com/dp/0805385665/?tag=pfamazon01-20

Upper Level Mechanics

Analytical Mechanics - Hand & Finch
https://www.amazon.com/dp/0521575729/?tag=pfamazon01-20

Classical Dynamics of Particles and Systems - Thornton & Marion
https://www.amazon.com/dp/0534408966/?tag=pfamazon01-20

Classical Mechanics - Taylor
https://www.amazon.com/dp/189138922X/?tag=pfamazon01-20

Upper Level E&M

Electromagnetic Fields - Wangness
https://www.amazon.com/dp/0471811866/?tag=pfamazon01-20

Introduction to Electrodynamics - Griffiths
https://www.amazon.com/dp/013805326X/?tag=pfamazon01-20

Upper Level Quantum Mechanics

Introduction to Quantum Mechanics - Griffiths
https://www.amazon.com/dp/0131118927/?tag=pfamazon01-20

Thermal Physics

Equilibrium Thermodynamics - Adkins
https://www.amazon.com/dp/0521274567/?tag=pfamazon01-20

Fundamentals of Statistical and Thermal Physics - Reif
https://www.amazon.com/dp/1577666127/?tag=pfamazon01-20

Thermal Physics - Baierlein
https://www.amazon.com/dp/0521658381/?tag=pfamazon01-20

Thermal Physics - Kittel & Kroemer
https://www.amazon.com/dp/0716710889/?tag=pfamazon01-20

Solid State Physics

Introduction to Solid State Physics - Kittel
https://www.amazon.com/dp/047141526X/?tag=pfamazon01-20

Principles of the Theory of Solids - Ziman
https://www.amazon.com/dp/0521297338/?tag=pfamazon01-20

Solid State Physics - Ashcroft & Mermin
https://www.amazon.com/dp/0030839939/?tag=pfamazon01-20

Advanced Upper Level/Graduate Mechanics

Classical Mechanics - Goldstein, Poole, Safko
https://www.amazon.com/dp/0201657023/?tag=pfamazon01-20

Advanced Upper Level/Graduate E&M

Classical Electrodynamics - Jackson
https://www.amazon.com/dp/047130932X/?tag=pfamazon01-20

Advanced Upper Level/Graduate Quantum Mechanics

Modern Quantum Mechanics - Sakurai & Napolitano
https://www.amazon.com/dp/0805382917/?tag=pfamazon01-20

Principles of Quantum Mechanics - Shankar
https://www.amazon.com/dp/0306447908/?tag=pfamazon01-20

 

[General_Sax]

I appreciate that list. Thanks for taking the time.