khaled Posted July 24, 2011 Posted July 24, 2011 I'm computer science researcher, but I'm not really good at math, that I want to improve myself, I studied: Basic Calculus, Basic Geometry, Discrete Mathematics, Basic Linear Algebra, Basic Probability & Statistics I know how to get math courses, but in what order should I go .. I want to know the path where I can then understand Quantum, Super mathematics, ..etc best regards, khaled
DJBruce Posted July 25, 2011 Posted July 25, 2011 Books that you'll probably want to get to develop the basics: Spivak's Calculus Kunz and Hoffman's Linear Algebra Spivaks Analysis on Manifolds Artin's Algebra Covering this would probably give you a good foundation to move onto higher level mathematics. As for what you would specifically need for quantum mechanics I don't know, but I would bet you'd need these to get there.
khaled Posted July 25, 2011 Author Posted July 25, 2011 well, first .. I asked for the order of mathematical topics\courses, not books, in order to reach a level to understand Quantum Theory ... besides, I don't know how I'm going to jump from specific types of calculus into Analysis on Manifolds, not even knowing Numerical\Functional analysis ... I need something general, if I can simplify it in a phrase "I want to learn everything in mathematics, what is the path" ...
ajb Posted July 25, 2011 Posted July 25, 2011 (edited) I studied: Basic Calculus, Basic Geometry, Discrete Mathematics, Basic Linear Algebra, Basic Probability & Statistics That is enough to start to tackle quantum physics, especially quantum mechanics. From there one can move on to field theory and beyond. To understand quantum mechanics well one needs a bit of functional analysis; Banach and Hilbert spaces, operator algebras and their representations etc. A little group theory goes a long way also. Key to a lot of physics is the notion is a Lie group and a Lie algebra. Probably if I had to single out one area of mathematics to be familiar with it would be Lie theory. Edited July 25, 2011 by ajb 1
CaptainPanic Posted July 25, 2011 Posted July 25, 2011 But books take you by the hand, and start at something relatively basic, and build it up from there. Don't worry, each book only teaches you a tiny bit about maths... it's gonna take a lot more than the 4 books DJBruce wrote down to learn "everything in mathematics". If you want to be able to upgrade your maths skills from what you describe, to a level able to work and understand the quantum mechanics, then I would advise you first to let go of the idea that 4 books are too much. You're probably looking at more than 4 books. Also, if the money for 4 books is too much, then you might want to look at used books (Amazon has used books at lower prices). You're looking at quite an endeavour, so you might as well realize what resources you need to achieve it: lots of time, dedication and also some books. And possibly a teacher too. It takes regular students in a university a couple of years to learn and properly apply the maths. It'll take you even longer if you do it alone (unless you're a genius).
uncool Posted July 25, 2011 Posted July 25, 2011 (edited) well, first .. I asked for the order of mathematical topics\courses, not books, in order to reach a level to understand Quantum Theory ... besides, I don't know how I'm going to jump from specific types of calculus into Analysis on Manifolds, not even knowing Numerical\Functional analysis ... I need something general, if I can simplify it in a phrase "I want to learn everything in mathematics, what is the path" ... The courses you need will be presented as followed: Course: prerequisites. Basic linear algebra: basic Real analysis: basic Group theory: basic Ring theory: requires group theory and basic linear algebra Field theory: requires ring theory Multidimensional real analysis: requires real analysis and basic linear algebra Point-set topology: requires multidimensional real analysis Complex analysis: requires multidimensional real analysis, should include Fourier analysis Functional analysis: requires multidimensional real analysis (and possibly complex analysis) Advanced linear algebra: requires field theory Manifold topology: requires point-set topology and basic linear algebra Advanced ring theory (commutative and noncommutative): requires advanced linear algebra and field theory, should include module theory Homology theory: requires module theory Algebraic topology: requires homology theory, manifold topology Differential topology: requires manifold topology, advanced linear algebra Lie algebra: requires advanced linear algebra, complex analysis, and a small amount of differential topology Operator theory: requires Lie algebra, noncommutative ring theory Physics side: Basic mechanics: basic Basic electromagnetics: requires basic mechanics Waves and basic perturbation theory: requires basic mechanics, Fourier analysis Advanced mechanics: requires basic perturbation theory, functional analysis Advanced electromagnetism: requires basic electromagnetics, multidimensional real analysis Special relativity: requires advanced mechanics, advanced electromagnetism Quantum mechanics: requires noncommutative algebra, basic mechanics Quantum field theory: requires quantum mechanics, advanced mechanics, special relativity General relativity: requires special relativity, differential topology Theories of everything: needs general relativity and quantum field theory. =Uncool- Edited July 25, 2011 by uncool 1
khaled Posted July 25, 2011 Author Posted July 25, 2011 But books take you by the hand, and start at something relatively basic, and build it up from there. Don't worry, each book only teaches you a tiny bit about maths... it's gonna take a lot more than the 4 books DJBruce wrote down to learn "everything in mathematics". If you want to be able to upgrade your maths skills from what you describe, to a level able to work and understand the quantum mechanics, then I would advise you first to let go of the idea that 4 books are too much. You're probably looking at more than 4 books. Also, if the money for 4 books is too much, then you might want to look at used books (Amazon has used books at lower prices). You're looking at quite an endeavour, so you might as well realize what resources you need to achieve it: lots of time, dedication and also some books. And possibly a teacher too. It takes regular students in a university a couple of years to learn and properly apply the maths. It'll take you even longer if you do it alone (unless you're a genius). I'm currently only a bachelor in computer science .. but, just like great scientists, I'm a scientist in more than one field, Logic, Computer Science, Artificial Intelligence, Psychology, Philosophy, Theoretical Computer Science, Theoretical Physics, and Mathematics -- and that's why I want to learn everything .. I've my whole life to this, I believe if I become good at all mathematics, I will be able to do researches in all of my fields in high level, knowing all kind of models I can utilize to solve a problem, or work a model ..etc ps. thanks uncool for the list, but I will need to see the complete list, of everything in math .. even complex topics such as super-manifolds, supersymmetry, ..etc
uncool Posted July 25, 2011 Posted July 25, 2011 I forgot to include differential geometry, which needs differential topology and advanced ring theory. That should include super-manifolds. Supersymmetry will certainly be covered in theories of everything. Do you want me to be more specific, or to include more advanced topics? =Uncool-
khaled Posted July 25, 2011 Author Posted July 25, 2011 I forgot to include differential geometry, which needs differential topology and advanced ring theory. That should include super-manifolds. Supersymmetry will certainly be covered in theories of everything. Do you want me to be more specific, or to include more advanced topics? =Uncool- .. are there any more advanced topic ?
uncool Posted July 25, 2011 Posted July 25, 2011 .. are there any more advanced topic ? None that I can think of that relate to advanced particle physics, which seemed to be what you were aiming towards. There are a lot more advanced topics in both fields. I don't know them quite as well. Set theory: basic. Point-set topology may require this. Model theory: requires set theory Category theory: requires set theory, can be used as a basis for group theory, field theory, topology. Good basis for homology theory. Basic statistics: basic Measure theory: requires real analysis Advanced statistics: requires basic statistics, measure theory Basic number theory: requires group theory. Advanced number theory: requires basic number theory, commutative ring theory Cryptography: requires number theory Thermodynamics: requires advanced statistics Plasma physics: requires advanced electrodynamics and thermodynamics, may require particle physics Condensed matter: requires advanced electrodynamics and thermodynamics, may require particle physics Astrophysics: requires plasma physics Graph theory: basic Combinatorics: Basic Differential equations: requires real analysis Partial differential equations: requires differential equations, good basis for advanced mechanics Ordinary differential equations: requires differential equations Chaos theory: requires partial differential equations That's most of the areas I can think of off the top of my head.
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