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Academic Guidance Academic Guidance - Academic guidance for those pursuing a college degree... what college? Grad school? PhD help?


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October 24th, 2015, 10:52 AM   #1
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linear algebra vs complex analysis

I am studying math and physics...I generally like to take math courses that I can apply to physics courses. I am kind of in between second and third year in terms of courses..

I have already taken some linear algebra, this course is a kind of continuation. But I haven't done too much with complex numbers...

I would take both courses but they conflict with each other so I have to decide one or the other...What do you think would be more useful between these two courses??:


This is the linear algebra course description:

Review and further study of vector spaces over arbitrary fields. General linear transformations. Kernel and range. Invertibility. Matrices of linear transformations. Similarity. Isomorphism. Complex vector spaces and inner product spaces. Unitary, normal, symmetric, skew-symmetric and Hermitian operators. Orthogonal projections and the spectral theorem. Bilinear and quadratic forms. Jordan canonical form.

And the complex analysis course description:

Algebra and geometry of complex numbers, complex functions and their derivatives; analytic functions; harmonic functions; complex exponential and trigonometric functions and their inverses; contour integration; Cauchy's theorem and its consequences; Taylor and Laurent series; residues.

Last edited by Kinroh; October 24th, 2015 at 10:56 AM.
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October 24th, 2015, 12:06 PM   #2
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Although you haven't described the physics courses, I would think that the complex analysis course should be chosen. What do you intend to do when you've qualified?
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October 24th, 2015, 12:43 PM   #3
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Future physics courses I'd like to take:

Classical Mechanics

Advanced treatment of the mechanics of particles and of rigid bodies; Lagrangian and Hamiltonian methods; Poisson brackets, applications to the theory of small oscillators and central force motions, elements of chaotic motions.

Quantum Mechanics

Postulates about states, observables, probabilities, change of state in a measurement, and time evolution. Dirac's bra and ket notation; representation and transformation theory. Two-level systems. Complete set of commuting observables and classification of states. Symmetries and their usage in classification of states.

Relativity Theory and Black Holes

Review of Special Relativity and Minkowski space-time. Introduction to General Relativity theory; the space-time metric, geodesics, light cones, horizons, asymptotic flatness; energy-momentum of particles and light rays. Curvature and field equations. Static black holes (Schwarzschild metric), properties of light rays and particle orbits. Rotating black holes (Kerr metric).


Not sure what I'll do after graduating.

Last edited by skipjack; October 24th, 2015 at 11:41 PM.
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October 24th, 2015, 01:01 PM   #4
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Complex analysis is generally a good course and needs to be taken at some point. However with the courses you mentioned I would say that neither really comes up in Classical Mechanics, nor in Relativity. QM, on the other hand, makes extensive use of Linear Algebra.

-Dan
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October 25th, 2015, 07:58 AM   #5
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I thought there was a fair bit of complex analysis in GR.

Certainly you need lots of linear algebra to do quantum. I don't think the choice is terribly important though because you probably need both to get a physics degree. These are fundamental courses on which many others will build.
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October 25th, 2015, 09:48 AM   #6
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Originally Posted by CRGreathouse View Post
I thought there was a fair bit of complex analysis in GR.
.
Not that I've noticed. However I haven't studied much of the practical side of the calculations either, just the basic theory.

-Dan
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October 26th, 2015, 03:44 PM   #7
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So its sounds as if linear algebra may be the more pertinent choice?

I heard complex numbers are used a lot in quantum? But may be a awhole course in complex analysis isn't necessary for quantum?

I am thinking about potentially studying electrical engineering later on.

Also, Ive heard about how complex analysis leads to a method of integrating REAL functions more easily? What kind of integration does it help with?

Last edited by Kinroh; October 26th, 2015 at 03:49 PM.
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October 26th, 2015, 05:03 PM   #8
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Before deciding which Math course to take, can you find out when the courses will be offered next? For example, let's say you are registering for Semester 1, need Courses X and Y, and can't take X and Y both. If Course X is offered every semester and Course Y is only offered in odd semesters, you should take Course Y in Semester 1 and Course X in Semester 2. If you took Course X in Semester 1, you would need to wait to Semester 3 to take Course Y. Given that you're between year two and year three, if both Math courses are prerequisites for a required Physics course, you should take both Math courses as fast as possible. You posted courses descriptions but have you looked at prerequisites? First you should make sure you have met prerequisites for both Math courses.
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October 26th, 2015, 05:10 PM   #9
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Quote:
Originally Posted by Kinroh View Post
So its sounds as if linear algebra may be the more pertinent choice?

I heard complex numbers are used a lot in quantum? But may be a awhole course in complex analysis isn't necessary for quantum?

I am thinking about potentially studying electrical engineering later on.

Also, Ive heard about how complex analysis leads to a method of integrating REAL functions more easily? What kind of integration does it help with?
There are a lot of complex numbers floating around in QM but you don't need what is called "Complex Analysis," which refers to such topics as complex integration, until you get past the basics in Grad. school.

EE will likely require at least some complex analysis.

-Dan
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