| Topic: |
Science > Physics |
| User: |
"Amine" |
| Date: |
17 Mar 2007 06:03:17 PM |
| Object: |
Choosing a math course for a physics M.Sc. |
Hi,
If you guys with M.Sc. and Ph.D.'s out there were to choose one of the
two following math courses, which one would be the most relevant for a
first-year M.Sc. student in physics? Here are the descriptions of the
courses:
(A) Advanced linear algebra: Abstract vector spaces: subspaces,
dimension theory. Linear mappings: kernel, image, dimension theorem,
isomorphisms, matrix of linear transformation. Changes of basis,
invariant spaces, direct sums, cyclic subspaces, Cayley-Hamilton
theorem. Inner product spaces, orthogonal transformations, orthogonal
diagonalization, quadratic forms, positive definite matrices. Complex
operators: Hermitian, unitary and normal. Spectral theorem. Isometries
of R2 and R3.
(B) Complex Variables: Theory of functions of one complex variable,
analytic and meromorphic functions. Cauchy's theorem, residue
calculus, conformal mappings, introduction to analytic continuation
and harmonic functions.
Which one of these two courses is of the most ubiquitous utility in
physics at a M.Sc. level? Any comments as to the pros and cons of
either one are welcome.
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| User: "Androcles" |
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| Title: Re: Choosing a math course for a physics M.Sc. |
17 Mar 2007 06:56:39 PM |
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"Amine" <tfovid@yahoo.com> wrote in message =
news:1174172597.792311.287850@e1g2000hsg.googlegroups.com...
Hi,
=20
If you guys with M.Sc. and Ph.D.'s out there were to choose one of the
two following math courses, which one would be the most relevant for a
first-year M.Sc. student in physics? Here are the descriptions of the
courses:
=20
(A) Advanced linear algebra: Abstract vector spaces: subspaces,
dimension theory. Linear mappings: kernel, image, dimension theorem,
isomorphisms, matrix of linear transformation. Changes of basis,
invariant spaces, direct sums, cyclic subspaces, Cayley-Hamilton
theorem. Inner product spaces, orthogonal transformations, orthogonal
diagonalization, quadratic forms, positive definite matrices. Complex
operators: Hermitian, unitary and normal. Spectral theorem. Isometries
of R2 and R3.
=20
(B) Complex Variables: Theory of functions of one complex variable,
analytic and meromorphic functions. Cauchy's theorem, residue
calculus, conformal mappings, introduction to analytic continuation
and harmonic functions.
=20
Which one of these two courses is of the most ubiquitous utility in
physics at a M.Sc. level? Any comments as to the pros and cons of
either one are welcome.
Hmm... 6 of one and half a dozen of the other, take both.
Complex variables are useful for electronics, linear mapping=20
and matrix algebra for just about anything and everything.
If you have to make a choice then IMO the linear algebra
since the latter is less physics oriented.
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| User: "" |
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| Title: Re: Choosing a math course for a physics M.Sc. |
17 Mar 2007 06:07:35 PM |
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In article <1174172597.792311.287850@e1g2000hsg.googlegroups.com>, "Amine" <tfovid@yahoo.com> writes:
Hi,
If you guys with M.Sc. and Ph.D.'s out there were to choose one of the
two following math courses, which one would be the most relevant for a
first-year M.Sc. student in physics? Here are the descriptions of the
courses:
(A) Advanced linear algebra: Abstract vector spaces: subspaces,
dimension theory. Linear mappings: kernel, image, dimension theorem,
isomorphisms, matrix of linear transformation. Changes of basis,
invariant spaces, direct sums, cyclic subspaces, Cayley-Hamilton
theorem. Inner product spaces, orthogonal transformations, orthogonal
diagonalization, quadratic forms, positive definite matrices. Complex
operators: Hermitian, unitary and normal. Spectral theorem. Isometries
of R2 and R3.
(B) Complex Variables: Theory of functions of one complex variable,
analytic and meromorphic functions. Cauchy's theorem, residue
calculus, conformal mappings, introduction to analytic continuation
and harmonic functions.
Which one of these two courses is of the most ubiquitous utility in
physics at a M.Sc. level? Any comments as to the pros and cons of
either one are welcome.
In the ultimate account, both are valuable, but if you really can pick
just one, pick the first, as it is directly relevant to lots of
physics. The second is of value mostl;y for some calculational
techniques, when needed you should be able to learn the relevant parts
on your own.
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
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| User: "BioFreak" |
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| Title: Re: Choosing a math course for a physics M.Sc. |
18 Mar 2007 07:19:06 AM |
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On 17 Mar 2007 16:03:17 -0700, Amine wrote:
If you guys with M.Sc. and Ph.D.'s out there were to choose one of the
two following math courses, which one would be the most relevant for a
first-year M.Sc. student in physics? Here are the descriptions of the
courses:
Don't masturbate with physics.
--
"yeki ro tuye deh rAh nemidAdan sorAghe kadkhodAro
migereft."
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| User: "Eric Gisse" |
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| Title: Re: Choosing a math course for a physics M.Sc. |
18 Mar 2007 12:58:14 AM |
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On Mar 17, 3:03 pm, "Amine" <tfo...@yahoo.com> wrote:
Hi,
If you guys with M.Sc. and Ph.D.'s out there were to choose one of the
two following math courses, which one would be the most relevant for a
first-year M.Sc. student in physics? Here are the descriptions of the
courses:
(A) Advanced linear algebra: Abstract vector spaces: subspaces,
dimension theory. Linear mappings: kernel, image, dimension theorem,
isomorphisms, matrix of linear transformation. Changes of basis,
invariant spaces, direct sums, cyclic subspaces, Cayley-Hamilton
theorem. Inner product spaces, orthogonal transformations, orthogonal
diagonalization, quadratic forms, positive definite matrices. Complex
operators: Hermitian, unitary and normal. Spectral theorem. Isometries
of R2 and R3.
(B) Complex Variables: Theory of functions of one complex variable,
analytic and meromorphic functions. Cauchy's theorem, residue
calculus, conformal mappings, introduction to analytic continuation
and harmonic functions.
Which one of these two courses is of the most ubiquitous utility in
physics at a M.Sc. level? Any comments as to the pros and cons of
either one are welcome.
A is important. So is B. But A is more fundamental to and ubiquitous
in modern physics than B.
You can get pretty far without knowing a whole bunch of complex
analysis. The most useful parts - complex form of trig, inverse trig,
and log functions - you can teach yourself in short order. In fact,
you probably know the basics to complex analysis as well as the
complex forms of such functions if you are a first year masters
student.
Good luck getting very far in physics without A though.
I'm a senior undergraduate so take it as you will. I don't know what
you are studying, but if I had to choose I'd pick A. I have had to use
precious little complex analysis - it has its' uses here and there,
but most of that is stuff I either already knew or learned within the
first 3 weeks. On the other hand, understanding inner product spaces
and related topics has been a far more useful concept - how will you
understand Fourier analysis or quantum mechanics without that?!
.
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| User: "Douglas Eagleson" |
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| Title: Re: Choosing a math course for a physics M.Sc. |
17 Mar 2007 06:38:56 PM |
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On Mar 17, 7:03 pm, "Amine" <tfo...@yahoo.com> wrote:
Hi,
If you guys with M.Sc. and Ph.D.'s out there were to choose one of the
two following math courses, which one would be the most relevant for a
first-year M.Sc. student in physics? Here are the descriptions of the
courses:
(A) Advanced linear algebra: Abstract vector spaces: subspaces,
dimension theory. Linear mappings: kernel, image, dimension theorem,
isomorphisms, matrix of linear transformation. Changes of basis,
invariant spaces, direct sums, cyclic subspaces, Cayley-Hamilton
theorem. Inner product spaces, orthogonal transformations, orthogonal
diagonalization, quadratic forms, positive definite matrices. Complex
operators: Hermitian, unitary and normal. Spectral theorem. Isometries
of R2 and R3.
(B) Complex Variables: Theory of functions of one complex variable,
analytic and meromorphic functions. Cauchy's theorem, residue
calculus, conformal mappings, introduction to analytic continuation
and harmonic functions.
Which one of these two courses is of the most ubiquitous utility in
physics at a M.Sc. level? Any comments as to the pros and cons of
either one are welcome.
Linear algebra.
All physics appears the set of differential equations as inferred from
the Hilbert.
A difficult realm is about to be entered and the complex variable is
an importent topic, but not foundational.
A solution to the dilemma was to write the foundations of physics
without complex terms in matrix space. How is this done?
NO big deal square then triple then quadruple the space of the
Hilbert. Then learn inversion. LEARN ALL MATRIX METHOD. Learn each
eightX eight space equation of matirx reference.
Learn why complex variables disappear.
.
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| User: "Eric Gisse" |
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| Title: Re: Choosing a math course for a physics M.Sc. |
18 Mar 2007 01:01:41 AM |
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On Mar 17, 3:38 pm, "Douglas Eagleson" <eaglesondoug...@yahoo.com>
wrote:
[...]
Learn why complex variables disappear.
Oh Douggie, please expand on this.
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| User: "Douglas Eagleson" |
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| Title: Re: Choosing a math course for a physics M.Sc. |
18 Mar 2007 06:04:03 AM |
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On Mar 18, 2:01 am, "Eric Gisse" <jowr...@gmail.com> wrote:
On Mar 17, 3:38 pm, "Douglas Eagleson" <eaglesondoug...@yahoo.com>
wrote:
[...]
Learn why complex variables disappear.
Oh Douggie, please expand on this.
Sure;
Here is a basic vector:
1=3.5e12quanta/unit acceleration*|h|
Where h is a four state vector. In hamilton's matrix.
Unit analysis for vector appears to allow tran. An operation of some
notorious existence.
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| User: "Timo A. Nieminen" |
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| Title: Re: Choosing a math course for a physics M.Sc. |
18 Mar 2007 12:18:24 AM |
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On Sun, 17 Mar 2007, Amine wrote:
(A) Advanced linear algebra: Abstract vector spaces: subspaces,
dimension theory. Linear mappings: kernel, image, dimension theorem,
isomorphisms, matrix of linear transformation. Changes of basis,
invariant spaces, direct sums, cyclic subspaces, Cayley-Hamilton
theorem. Inner product spaces, orthogonal transformations, orthogonal
diagonalization, quadratic forms, positive definite matrices. Complex
operators: Hermitian, unitary and normal. Spectral theorem. Isometries
of R2 and R3.
(B) Complex Variables: Theory of functions of one complex variable,
analytic and meromorphic functions. Cauchy's theorem, residue
calculus, conformal mappings, introduction to analytic continuation
and harmonic functions.
Which one of these two courses is of the most ubiquitous utility in
physics at a M.Sc. level? Any comments as to the pros and cons of
either one are welcome.
I recommend (A). More generally useful in my experience, which is likely
to be affected by computational physics being about 50% linear algebra
(and about 35% numerical analysis, and the remainder specialised
techniques). If you have any inclination towards computational physics,
definitely (A).
If you loathe computational work, then perhaps (B), since you're likely to
meet all of the elements of (A) that you'll need in non-computational
theoretical physics integrated into your physics courses (since it's such
an integral part of mathematical physics). It depends on how much of the
stuff in (A) and (B) you've already encountered elsewhere.
Whether or not either course is useful in practice depends on exactly what
is taught, and how it is taught. The content can be fine in principle, but
the course can consist of definition-theorem-proof only, which is fine for
learning mathematics for its own sake, but the applications of the maths
are what are useful for physics. Look at past exams for the courses. If
those for one course look like they're all about memorised definitions and
proofs, and the other one has the material applied to problems, choose the
applied course. If both are memorise-and-regurgitate ...
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
.
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