Advice for Honours Astrophysics/Applied Mathematics

[Oriako]

NOTE: This is a very long post!

Hello,
I will be attending the University of Calgary next year and intend to graduate after 5 years with honours majors in Astrophysics and Applied Mathematics. I designed what my schedule would look like over the next 5 years after some painstaking effort (with correct pre-requisites) and I am looking for some feedback.

Background Information Academically:
100% in AP Calculus, 100% in Physics 30, 98% in Pure Math 30, done lots of extracurricular reading and working on Multivariable Calculus through MIT OCW, etc. Hard work ethic and have no trouble studying for 5 hours straight.

Main Questions:
-Is this workload too much? Particularly the two semesters where I have to take 5 science/math courses.

-What have you heard about the University of Calgary? Are there research opportunities during the spring/summer? Are the professors good?

-Have I staggered the math/physics courses in the correct order so that I am sufficiently ahead on the math that will be applied in the physics classes I'm taking afterwards?

-Are there any glaring omissions in the program from what would be expected knowledge for the Physics/Math GRE?

-Are two honours majors a bit excessive before heading into graduate school or would it be great preparation? I want to avoid burnout, would it be a better idea to do only one of them as an honours degree and the other as just a major?

Other than that any general feedback would be great, here is the schedule I am planning on:

-

First Year

FALL:

MATH 273 - Honours Mathematics: Numbers and Proofs
Proofs, functions, sets, relations, integers, euclidean division algorithm, prime factorization, induction and recursion, integers mod n, real numbers, sequences, completeness, open and closed sets, complex numbers.

MATH 251 - Calculus I
Functions, graphs, limits, derivatives, and integrals of exponential, logarithmic, and trigonometric functions. Fundamental theorem of calculus. Applications.

PHYS 227 - Classical Physics
Kinematics and statics of rigid bodies; conservation laws; rotational mechanics.

CHEM 201 - General Chemistry: Structure and Bonding
Fundamental links between electronic structure, chemical bonding, molecular structure and the interactions of molecules using inorganic and organic examples.

[Faculty of Arts Elective]

WINTER:

MATH 213 - Honours Linear Algebra I
Systems of equations and matrices, vectors, matrix representations and determinants. Complex numbers, polar form, eigenvalues, eigenvectors. Applications.

MATH 283 - Honours Calculus II
Limits and continuity; Differentiation of functions of one real variable; the Mean Value Theorem and its consequences; Riemann integrations; fundamental theorem of calculus; applications and rigorous approach.

PHYS 255 - Electromagnetic Theory I
Electrostatics, DC circuits, calculation of magnetic intensity from currents, motion of charged particles in electric and magnetic fields, electromagnetic induction, transient effects in capacitors and inductors, electric and magnetic properties of materials.

ASPH 213 - Introduction to Astrophysics
Observations and physical interpretations of stars, galaxies, and the interstellar medium; distances and motions in the universe; radiation and telescopes; celestial mechanics.

CPSC 217 - Introduction to Computer Science
Introduction to problem solving, analysis and design of small-scale computational systems and implementation using a procedural programming language.

Second Year

FALL:

MATH 381 - Honours Calculus III
Functions of several variables; differentiability, extrema. Implicit and inverse function theorems. Integration of functions of several variables; line integrals; surface integrals.

MATH 313 - Honours Linear Algebra II
Diagonalization. Canonical forms. Inner products, orthogonalization. Spectral theory.

MATH 321 - Mathematical Probability
Sample spaces. Discrete probability. Discrete and continuous random variables. Standard distributions. Mathematical expectation and variance. Moments and moment generating functions. Central limit theorem. Functions of random variables. Statistical inference.

PHYS 325 - Modern Physics II
Origins of quantum mechanics, a historical perspective. Concepts of wave mechanics and applications: atoms, molecules, and solids. Kinetic theory of gases; distribution functions; statistics of quantum gases with applications.

[Faculty of Arts Elective]

WINTER:

AMAT 311 - Differential Equations I
Classification of ordinary differential equations, first and second order equations with applications, series solutions about regular points and singular points, special functions, Laplace transform.

PMAT 317 - Honours Algebra I
Basic ring theory: rings and fields, the integers modulo n, polynomial rings, polynomials over the integers and rationals, homomorphisms, ideals and quotients, principal ideal domains, adjoining the root of an irreducible polynomial; basic group theory: groups, examples including cyclic, symmetric, alternating and dihedral groups, subgroups, cosets and Lagrange's theorem, normal subgroups and quotients, group homomorphisms, the isomorphism theorems, further topics as time permits, e.g., group actions, Cayley's theorem, etc.

PHYS 341 - Classical Mechanics I
Forced and damped harmonic oscillations with real and complex numbers; anharmonic oscillators central force motion and scattering; non-inertial frames; 2- and 3-body problems; applications of linear differential equations and complex numbers.

ASPH 309 - Solar System Astrophysics
Orbital mechanics. Planetary interiors, surfaces, atmosphere, ionospheres and magnetospherees. Solar magnetism and activity cycles. Comets, asteroids, meteorites. Origin of the solar system.

[Faculty of Arts Elective]

Third Year

FALL:

AMAT 413 - Introduction to Partial Differential Equations
Orthogonal sets of functions, Fourier series, solution of potential equation, heat equation and wave equation. Numerical solution of partial differential equations.

AMAT 433 - Mathematical Methods in Physics
Fourier analysis. Laplace Transforms. Partial differential equations. Complex analysis. Residue integrals. Extensive physical applications.

PHYS 343 - Classical Mechanics II
Rotating frames of reference; general rotations of rigid bodies; moment of inertia tensor; eigenvalues and eigenvectors; Lagrangian and Hamiltonian mechanics; potential theory and tides; perturbation theory.

PHYS 449 - Statistical Mechanics I
State-counting; classical distributions; origins and role of entropy; equilibrium; microcanonical, canonical, and grand canonical ensembles; concepts of work, heat, and temperature; equations of state; heat capacity; equipartition theorem; engines; laws of thermodynamics; non-equilibrium systems; Maxwell-Boltzmann distribution; enthalpy and free energies.

ASPH 401 - Galactic Astrophysics
The galaxy; space distribution of stars and interstellar material; kinematics and dynamics of stellar systems; rotation and spiral structure; classification and global properties of galaxies; active galaxies.

WINTER:

AMAT 411 - Differential Equations II
Existence and uniqueness theorems, comparison and oscillation theorems, Green's functions, Sturm-Liouville problems, systems of equations, phase portraits, stability.

AMAT 491 - Numerical Analysis I
Interpolation and approximation, numerical integration, numerical methods for the solution of nonlinear equations, systems of linear equations and the eigenvalue problem.

PMAT 455 - Honours Real Analysis I
Real and complex numbers, topology of metric spaces, sequences and series, continuity, differentiation, Riemann-Stieltjes integration. Rigorous approach throughout.

PHYS 381 - Computational Physics I
Solution of problems associated with the analysis of physical systems, using digital computers, high level programming languages, and mathematical computation systems.

[Faculty of Arts Elective]

Fourth Year

FALL:

PMAT 521 - Complex Analysis
A rigorous study of functions of a single complex variable. Consequences of differentiability. Proof of the Cauchy integral theorem, applications.

PHYS 443 - Quantum Mechanics I
Basic postulates of quantum mechanics. Mathematical formalism of the theory and its physical interpretation. Schrodinger's time-dependent and time-independent equations. Single particle in a potential field (square well, potential barrier, harmonic oscillator, Kronig-Penney, Coulomb) and rigid rotator. The applicability of these potentials to atomic, molecular, nuclear, and solid state physics will be indicated.

PHYS 451 - Statistical Mechanics II
Gibbs' paradox; bosons and fermions; quantum counting; classical-quantum transition; blackbody radiation; phase transitions; fluctuations and critical phenomena; complex systems; self-organized criticality; cellular automata.

ASPH 403 - Stellar Structure and Evolution
Observational properties of stars; equations of stellar structure; physics of stellar interiors; structure and evolution of stars; white dwarfs, neutron stars, black holes; observational aspects of stellar atmospheres; radiative transfer in stellar atmospheres; opacity; spectral line formation.

[Faculty of Arts Elective]

WINTER:

PMAT 545 - Honours Real Analysis II
Sequences and series of functions; theory of Fourier analysis, functions of several variables: Inverse and Implicit Functions and Rank Theorems, integration of differential forms, Stokes' Theorem, Measure and Lebesgue integration.

PHYS 455 - Electromagnetic Theory II
Macroscopic Maxwell equations. Scalar and vector potentials. Energy and momentum in Maxwell's theory. Electrostatics and magnetostatics. Dielectric and magnetic properties of materials. Superconductors.

PHYS 543 - Quantum Mechanics II
Theory of angular momentum and applications, perturbation theory and applications. identical particles. introduction to relativistic wave equations.

ASPH 503 - The Interstellar Medium
Multiwavelength observations of gas and dust in our Galaxy; distribution and physics of neutral atomic hydrogen and molecules; interstellar chemistry; physics of dust grains; HII regions; interstellar shocks; gas dynamics; star formation.

[Faculty of Arts Elective]

Fifth Year

FALL:

AMAT 505 - Calculus on Manifolds
Integral and differential calculus on manifolds including tensor fields, covariant differentiation, Lie differentiation, differential forms, Frobenius' theorem, Stokes' theorem, flows of vector fields.

PHYS 457 - Electromagnetic Theory III
Electromagnetic wave solutions to Maxwell's equations, in vacuum and in insulating and conducting media. Waveguides. Electromagnetic radiation from accelerated charges. Relativistic formulation of electrodynamics.

ASPH 507 - Senior Astrophysics Laboratory
Lectures and laboratory sessions in observational astronomy. Modern methods of observation, data reduction, and analysis.

ASPH 509 - High Energy Astrophysics and Cosmology
Clusters of galaxies; microwave and X-ray background radiation; dark matter and dark energy; overview of cosmology; general relativistic considerations; large-scale structure and expansion of the universe; nucleosynthesis; gamma ray bursts and cosmic rays.

[Faculty of Arts Elective]

WINTER:

AMAT 507 - Introduction to Relativity Theory
Mathematical theories of space and time. Special Relativity. Electro-dynamics. General Relativity.

PMAT 431 - Algebra I
Group theory: Sylow theorems, solvable, nilpotent and p-groups, simplicity of alternating groups and PSL(n,q), structure theory of finite abelian groups; field theory: gilds, algebraic and transcendental extensions, seperability and normality, Galois theory, insolvability of the general quintic equation, computation of Galois groups over the rationals.

PHYS 501 - Special Relativity
Lorentz transformations in classical mechanics; relativistic kinematics; spacetime diagrams; relativistic energy and momentum conservation; Geometrical interpretation; applications of relativistic kinematics; four-vector formalism and tensors; applications, primarily to relativistic electrodynamics.

PHYS 599 - Honours Thesis
Each student will be assigned a research project in Physics with consultation of an adviser. A written report and oral presentation are required.

[Faculty of Arts Elective]
-

Potential problems:
-How late I take the Electromagnetic Theory sequence?
-How late I take PMAT 431 - Algebra I?
-No coverage of Optics or Plasma Physics?

Thanks for reading if anyone did take the time, I appreciate any feedback on my schedule or plans.

 

[Nano-Passion]

I don't think I have much to contribute here but I thought your thread was interesint and read through every singly description of your classes...

and I must say, my head was spinning form all the unfamiliar terms in the math classes. It was a little discouraging seeing soo many unfamiliar names but I'm sure its just a matter of getting acquainted with it. Before I took trig and pre-calc all the names sounded alien-ish to me too but they ended up easy so I'm not too discouraged lol. =]

 

[Oriako]

Thanks for being interested, unforunately you haven't really been through any schooling so you can't be of much help... D:

I don't mean to be too persistent, but could anyone who has been through the academic process through to a PhD/Post-Doc/Professorship please answer my questions! There are some deadlines coming up and I need to get everything to do with residence in order if I don't pursue this plan and instead take an Honours Astrophysics degree at the University of Alberta.

Thanks again.

 

[Nano-Passion]

unforunately you haven't really been through any schooling so you can't be of much help... D:

Which is why I stayed clear from trying to give advice. Hopefully some of the veterans here will help you out soon enough.

 

[Skrew]

Your lack of general education classes I yearn for.

 

[mege]

Your lack of general education classes I yearn for.

He has a gen-ed class per semester earmarked.

If you are a declared Math major will you need to take some of the applied-math classes intended for scientists? They may be redudant with the more pure math classes. Also, if you've taken AP Calculus already - why are you planning on taking Calc I (and depending on what you did in High school, Calc II) at University?

I don't envy your 2nd Year Fall, perhaps if you do shift your math 'earlier' a semester (due to Calc I being comped by AP) that can aleviate that term a bit.

 

[micromass]

Hi Oriako!

That are some nice courses there. The workload should be OK and your prerequisites should check out.

I do think you're taking PMAT 431 - Algebra I a little bit late, it's two years after your first algebra I class. Chances are that you forgot most of it already.

Also, you say you're going for applied math, but you're classes don't look so applied to me. The only applied classes you have are mathematical analysis and probability. You don't even have a statistics class! (which is fine, I'm just saying that you don't have much applied classes).

Also, if you already know calculus, why are you taking Calc I and Calc II, if you were you, I'd take something else.

 

[JNBirDy]

Hi Oriako!

That are some nice courses there. The workload should be OK and your prerequisites should check out.

I do think you're taking PMAT 431 - Algebra I a little bit late, it's two years after your first algebra I class. Chances are that you forgot most of it already.

Also, you say you're going for applied math, but you're classes don't look so applied to me. The only applied classes you have are mathematical analysis and probability. You don't even have a statistics class! (which is fine, I'm just saying that you don't have much applied classes).

Also, if you already know calculus, why are you taking Calc I and Calc II, if you were you, I'd take something else.

It's a Canadian university, I don't think he has a choice. Calc I and Calc II aren't the same as in the U.S.

 

[Oriako]

Well, I think I may be allowed to skip Calc I, but they don't know my AP test mark yet because I have to send it in after I receive my grade. I will try and fill that spot with Intro to computer science so that second semester I can take an arts course and then balance out some semester in 2nd or 3rd year so I don't have to take 5 sciences courses ever.

Thanks for pointing that out! As for PMAT 431 being very late, I do agree with you micromass. Do you have any ideas for remedying that problem because the schedule seems fairly tight as is! AMAT are called Applied Math and PMAT are called Pure Math, so... maybe U of C is more Pure Math oriented and that's why even the applied courses focus a lot more on theory than just numerical methods/computational mathematics.

I appreciate the advice everyone, is it a problem that I do not cover any Optics? I heard that Optics will be on the GRE, is this true?

 

[tqk]

I'm a student at the UofC.

There are research opportunities over the spring/summer. See for example http://phas.ucalgary.ca/undergraduate/summer-opportunities for physics-related ones (but since I don't have a physics major I won't say more about those).

What you should keep in mind is that most courses are not offered every term. For example, I don't recall AMAT 491 ever having been offered in a winter term.

To get a general idea of what might be reasonable to expect, you could browse through which courses have been offered in some past terms at http://math.ucalgary.ca/courses (for math courses) and at http://phas.ucalgary.ca/courses (for physics courses). However, the future could be different...

A couple more points

• even if the courses you want are offered in the right terms, they may be scheduled at conflicting times (in some cases you might be able to get approval to take them anyway, but you might not like missing classes)
• what courses exist may change over the duration of your degree.

I guess my overall point is that plans made so far in advance will be very difficult to follow precisely.

 

[christoski]

This is probably too late but here's my thoughts anyway...

I'm also a UofC student, 5th year, double majoring in Physics and Astrophysics. I will say that your plan is ambitious, and probably overkill. There are a few scheduling conflicts I can see just from browsing through your list, for example Phys 457 is only offered in winter, and I suggest doing it immediately following Phys 455. Phys 543 is only offered in the fall. Also, if you do end up taking all of those applied math courses, you can likely get out of AMAT 433 (and possibly others), since it is a condensed version of complex analysis and partial differential equations. Most 300-400 level classes and above are only offered once a year, so you'll likely have to rearrange some things. On the other hand most 200 level classes are offered year round so you will have more options, and once you're in first year you will have more time to figure out the rest of your schedule for the following years.

If you intend on pursing graduate studies in astrophysics, I would say an honours in applied math is entirely unnecessary, in fact even a major in it is not that crucial. I originally intended on doing a minor in applied math, but after discussing things with the department head, I decided it would be of little to no benefit in the long run.

Overall I'm quite happy with the UofC, and there are plenty of research opportunities available.