Admissions Direct Entry to PhD Program -- Advice Please

[Darmstadtium]

I am a second-year combined honour in physics and math with prerequisites for 4th-year math courses. I am hoping for a direct entry (if possible) into a top US PhD physics program in quantum with a current unofficial cGPA of 3.9/4 (88%). Since I am in Canada, we only have percentage grades that are not boosted (class average around the 60s for upper-level math/physics).

1. How would the receiving school perceive an 88%?

2. Additional to current summer research in quantum coherent control, is there any other way to be competitive with direct entry to PhD? (GRE?) (Co-op?) (Contact with potential grad school supervisor?) With research and combined honours, I will graduate as a 5-year undergrad rather than the typical 4. Is there any repercussion?

3. Another interest of mine is quantitative finance. Would a summer as a quantitative intern (unrelated to physics other than computational experience) outweigh the opportunity for another summer of physics research?

4. What are some undergrad math electives I should take to prepare for a program in QFT or quantum information (computing) and be competitive? The issue is that I will not have enough elective credits to take all of them since the combined honour requirements already took a big chunk.

• Probability: Probability spaces, random variables, distributions, expectation, conditional probabilities, convergence of random variables, generating and characteristic functions, weak and strong laws of large numbers.
• Complex Analysis: Residue theorem, the argument principle, conformal mapping, the maximum modulus principle, harmonic functions.
• Group Theory: Groups, cosets, homomorphisms, group actions, p-groups, Sylow theorems, composition series, finitely generated Abelian groups.
• Stochastic Processes?
• Fields and Galois Theory?
• Topology?
• Grad version of these courses?

 

[CrysPhys]

I am hoping for a direct entry (if possible) into a top US PhD physics program ...

In case there's a misconception on your part, let me clarify that for PhD physics programs in the US, admission to the programs upon completion of a bachelor's (not a master's) is the norm, not the exception. So if you think that the bar is higher for "direct entry", that's not true.

 

[Haborix]

Three main things to get right: (1) get good grades, (2) show interest in research (ideally be an author on a peer-reviewed paper), and (3) the enthusiastic approval of your professors (strong rec letter that will go beyond "Darmstadtium got an A in my class and seemed to be engaging with the material"). But before all that, you have a lot of time to change your mind (second year out of five years), and you have divergent interests. You will need to revisit most of this in about two years.

As for your electives list, I would say the first three are the highest priority. As between those three, I think complex analysis should be a required course for physics majors. A lot of other math you will just have to pick up as you go. Taking math courses from the math department can have diminishing returns, at least as far as it concerns helping you do physics.

 

[mathwonk]

As a mathematician, I have to ask the physicists for verification of my guesses here, but I would think the course described above on (finite) group theory would have less value, and might perhaps be replaced by one on (infinite) linear groups, i.e. advanced linear algebra. Of course the concepts of group, subgroup, homomorphism, group action, are basic, but Sylow subgroups are peculiar to finite groups. The structure of finitely generated abelian groups is also a bit special, but does have a generalization to the setting of linear algebra in the guise of finitely generated modules over Euclidean domains. I would think you would also want to look specifically at linear groups like O(n), U(n), etc...and group representations. But since I am not a physicist, I could well be wrong about the usefulness of the finite group theory....???

 

[Mordred]

I could well be wrong about the usefulness of the finite group theory....???

You need finite groups as well

 

[mathwonk]

thank you. it dawned on me that finite permutation groups may be relevant, which of course is all finite groups.

 

[Vanadium 50]

If you took a class in Economics, you would learn something called "opportunity costs". If you take a bunch of math classes, that's a bunch of physics classes that you are not taking. You should check with your advisor that this is not counterproductive.

 

[Mordred]

Permutation groups is one type of finite group you will need. There are others including cyclic group Z_n.
Group theory is incredibly useful in physics so it's a solid skill to develop. However how much will apply will depend on which field of physics your taking.
Some fields don't really require group theory. Best to always check with your curriculum.

 

[WWGD]

Just a technical point: isn't 3.9/4 in your GPA closer to 98% than to 88%?

 

[berkeman]

Just a technical point: isn't 3.9/4 in your GPA closer to 98% than to 88%?

You're always so mathematical. Oh wait...

 

[WWGD]

You're always so mathematical. Oh wait...

How Nyquist frequently from you.

 

[gwnorth]

Just a technical point: isn't 3.9/4 in your GPA closer to 98% than to 88%?

No the grading scale in Canada is different

A = 85-89%, 3.9
A+ = 90-100%, 4.0

The actual percentages assigned don't matter as the GPA and letter scales align basically the same and they're what are reported on transcripts, not percentages.

 

[WWGD]

No the grading scale in Canada is different

A = 85-89%, 3.9
A+ = 90-100%, 4.0

The actual percentages assigned don't matter as the GPA and letter scales align basically the same and they're what are reported on transcripts, not percentages.

I don't get it; 3.9/4=0.975%. Isn't that an A+?

 

[Vanadium 50]

I don't get it

Canadian math. Same reason their football fields are too big.

 

[WWGD]

Canadian math. Same reason their football fields are too big.

They computed it oot of the hoose, eh? ( Generic , stale, joke about Canadians)

 

[berkeman]

No the grading scale in Canada is different

A = 85-89%, 3.9
A+ = 90-100%, 4.0

The actual percentages assigned don't matter as the GPA and letter scales align basically the same and they're what are reported on transcripts, not percentages.

So if I get straight-A's in Canada, my GPA is less than 4.0? That's really depressing.

And in the job applications I've seen as a hiring R&D EE here in Silicon Valley, you enter your GPA, not your average letter grade. That puts applicants from Canada at a disadvantage, IMO. Frustrating.

 

[gwnorth]

Most universities in Canada use a +/- grading scale so an A- is a 3.7, an A is a 3.9, and an A+ is a 4.0. If applying to the US you'd need to recalculate the GPA. Many universities in Canada don't use the 4.0 scale anyway so you would need to convert it either way. That's why credential evaluation companies like Scholaro and WES exist, to be able to convert the credentials of international students to the US equivalence. This the converted GPA Scale for Ontario.

Ontario Grading Scale:​

Grade	Scale	US Grade Points	Notes

A+	90 - 100	4.0
A	80 - 89.99	4.0
B	70 - 79.99	3.0
C	60 - 69.99	2.0
D	50 - 59.99	1.0

 

[mathwonk]

excuse me for the overly brief flip remark, I was referring to the fact that every finite group occurs as a subgroup of a permutation group, so in that sense all finite groups are, not full permutation groups, but sub groups of them. I.e. each element of a group permutes the elements of that group by multiplication, hence every group element of G can be viewed as a permutation of the points of G. Thus G can be viewed naturally as a subgroup of the full permutation group of the elements of G. Certainly the most important cases are the simplest ones, the cyclic groups. Given any group G, and any element a, the set of all powers a^k forms a cyclic subgroup of G.

As a further comment on finite group theory, a basic result, due essentially to Gauss (before the creation of general group theory), is that the number of elements of a subgroup of G divides the number of elements of G. The big theorem, Sylow's theorem, gives a partial converse to this. I.e. although there are groups G of order n, such that certain factors of n do not occur as the order of any subgroup, nonetheless any factor of n having the form p^r, where p is prime, does occur as order of some subgroup. I.e. if G has order n = p^r.q^s...., where p,q are prime, then G does have subgroups of orders p, p^2,...p^r, q, q^2,...,q^s,....

 

[WWGD]

excuse me for the overly brief flip remark, I was referring to the fact that every finite group occurs as a subgroup of a permutation group, so in that sense all finite groups are, not full permutation groups, but sub groups of them. I.e. each element of a group permutes the elements of that group by multiplication, hence every group element of G can be viewed as a permutation of the points of G. Thus G can be viewed naturally as a subgroup of the full permutation group of the elements of G. Certainly the most important cases are the simplest ones, the cyclic groups. Given any group G, and any element a, the set of all powers a^k forms a cyclic subgroup of G.

As a further comment on finite group theory, a basic result, due essentially to Gauss (before the creation of general group theory), is that the number of elements of a subgroup of G divides the number of elements of G. The big theorem, Sylow's theorem, gives a partial converse to this. I.e. although there are groups G of order n, such that certain factors of n do not occur as the order of any subgroup, nonetheless any factor of n having the form p^r, where p is prime, does occur as order of some subgroup. I.e. if G has order n = p^r.q^s...., where p,q are prime, then G does have subgroups of orders p, p^2,...p^r, q, q^2,...,q^s,....

Is that Cayley's Theorem?

 

[Darmstadtium]

Thanks for the responses. I now have a general idea of the math electives.
Since I am already taking most of the physics upper-level courses other than some bio/ medical/ zoological physics and some application/ experiment, the math electives are the only courses that are somewhat related to physics.
As Vanadium 50 pointed out, are there any less "counterproductive" pathways to show a stronger interest/intent for physics research? (I have taken multiple economics courses: micro, macro, game theory, international trade, and econometrics since I was considering double honours in physics and economics, but decided on combined physics and math in the end. Hence, there is a reduced number of elective credits remaining.)

Regarding the GPA, would the receiving school know the Canadian GPA conversion? Our transcript only shows percentage with a class average and letter grade?

 

[WWGD]

Zoological Physics?

 

[Darmstadtium]

Zoological Physics?

Yep:

PHYS 438 Zoological Physics​

Animal systems viewed from a physicist's perspective. Topics include sensory systems, energy budgets, locomotion, internal flows, physical advantages of grouping.

 

[Vanadium 50]

Zoological Physics?

You know, like Tadpole Feyman diagrams.

 

[mathwonk]

yes, according to the internet: "In group theory, Cayley's theorem, named in honour of Arthur Cayley, states that every group G is isomorphic to a subgroup of a symmetric group."

The proof is so easy I did not know it had a name.
i.e. x-->multiplication by x.

As often happens, maybe just thinking of it was the main step.

 

[Mordred]

You know, like Tadpole Feyman diagrams.

And here I was thinking tortoise coordinates. Lmao.

 

[Mordred]

excuse me for the overly brief flip remark, I was referring to the fact that every finite group occurs as a subgroup.

No worries As @Vanadium 50 already mentioned and I agree you can focus too much on the mathematics instead of the theories involved
For example you really don't require a strong understanding of group theory to get a Ph.D. it's sufficient to know the groups your field deals with and how the subgroups etc relate but which groups are involved (if any) depends on the field of physics chosen.
Knowing how to use thetensors and matrices however is definitely far more useful.

 

[symbolipoint]

Yep:

PHYS 438 Zoological Physics​

Animal systems viewed from a physicist's perspective. Topics include sensory systems, energy budgets, locomotion, internal flows, physical advantages of grouping.

Would this be better called, Biophysics? I do not insist it; I only ask.

 

[gwnorth]

Thanks for the responses. I now have a general idea of the math electives.
Since I am already taking most of the physics upper-level courses other than some bio/ medical/ zoological physics and some application/ experiment, the math electives are the only courses that are somewhat related to physics.
As Vanadium 50 pointed out, are there any less "counterproductive" pathways to show a stronger interest/intent for physics research? (I have taken multiple economics courses: micro, macro, game theory, international trade, and econometrics since I was considering double honours in physics and economics, but decided on combined physics and math in the end. Hence, there is a reduced number of elective credits remaining.)

Regarding the GPA, would the receiving school know the Canadian GPA conversion? Our transcript only shows percentage with a class average and letter grade?

The easiest ways to demonstrate research are to work as a research assistant either paid or voluntary, and to do a senior year thesis. Summer research awards like NSERC USRA or those specific to your university are really beneficial. If you can get a publication all the better but that's mostly not expected for students applying straight from undergrad. Letters of recommendation from research supervisors who can speak to your ability to do research are generally more valuable than those from professors whose classes you took (excepting maybe lab courses). Working as a TA lab demonstrator can help as well.

Re your GPA, many US universities are familiar with Canadian grading as they get many Canadian applicants, but also many formal transcripts provide a grading scale. I know for my son's university it's printed on the back. There are programs however that will require you to submit a formal credential evaluation from a company like WES (which can be costly and time consuming).

 

[StatGuy2000]

Would this be better called, Biophysics? I do not insist it; I only ask.

@symbolipoint , @Vanadium 50 , I believe the OP is referring to the following course offered at the University of British Columbia (UBC for short):

https://phas.ubc.ca/~oser/p438/

The textbook that is used for this course is written called "Zoological Physics" by Boye Ahlborn:

http://www.amazon.com/Zoological-Ph...-Limitations/dp/3540208461/?tag=pfamazon01-20

From the description of the text this course seems to be covering applications of nonlinear physics and statistical mechanics to biological systems, which is something that is somewhat different from the focus of biophysics.

Aside to the OP: I hope you did not mind disclosing this info (specifically, the school you are currently attending).

 

[symbolipoint]

Thanks, @StatGuy2000.
The course description is interesting but my limited awareness makes those feel like Biophysics and Zool. Physics are not too far apart or they overlap.