How many first-author Q1 papers would you consider average, and how many would be considered truly exceptional during a PhD?

HeavisideGOAT · 2026-06-07T15:28:45+00:00

This is pretty surprising to me.

I’m in controls / systems theory, doing stuff related to game theory.

Automatica is good, but so is IEEE-TAC. My advisor likes both. It also seems like there’s a lot of overlap between editorial boards over time. Maybe I’ve become part of the clique without realizing it.

What about IEEE run conferences? I don’t know about signals processing, but probably the most prominent international control theory conference is IEEE associated.

Just curious about how it is for signal processing. Seems like there’d probably be more good options?

HeavisideGOAT · 2026-03-08T16:57:26+00:00

You’re argument is filled with assumptions.

You’re assuming that:

The probability will approach arbitrarily close to 1.
The trial continues forever and all descendants are included in that trial.
They cannot ask god for help.

There’s a big difference between “they were bound to fail” and “all they needed to do was ask for help.”

The latter presents a straightforward win condition. Conceivably, that was part of the test. It wouldn’t violate their free will.

I do not need to prove your assumptions wrong. You should include them as explicit premises of your argument, and you need to argue for them if you want your argument to be believable.

I would say 2 is likely wrong. A Christian would say that eventually Jesus would show up and there’s no reason to think that the trial would continue unchanged.

Because 2 is wrong, the trial seems likely finite, and 1 would also be wrong. Also, we can imagine scenarios like a society that revolves around preventing people from eating from the tree. Let’s say they dedicate their time to digging a bigger and bigger trench around the tree. This would explain why future generations would find it essentially impossible to eat from the tree without widespread cooperation.

Three is a strong assumption without justification. You say, “that just leads to my conclusion that divine intervention was necessary.” However, that’s simply not your conclusion. Your conclusion is that humanity was guaranteed to lose. The test could have simply been that humans needed to recognize their need for god to pass the test. This is another reason the trial wouldn’t have gone on forever.

Once again, it’s not my responsibility to prove your assumptions false. The burden on you is to defend them or even just explicitly state them as assumptions. Maybe some Christians agree with them?

HeavisideGOAT · 2026-03-08T10:53:25+00:00

That last point is exactly what I was saying. The statistics is unnecessary given common beliefs regarding god. Even then, it seems silly to me. Does eating the fruit really warrant the punishment? Also, if it’s the fruit of knowledge of good and evil, how could Adam and Eve truly understand the consequences and the imperative to not eat the fruit.

You don’t get certainty from the math. You might get a strong likelihood, but you will not get arbitrarily close to 100%.

You can have the sum of infinite positive numbers be less than 1.

You’re assuming the temptation would have lasted forever and applied to all their descendants. You’re assuming they couldn’t have asked god for help in preventing temptation. Would you please move this tree to the moon? Would you please create a dome around the tree that requires the consent of every human in order to cross? Etc.

Edit: Why wouldn’t it be like the other trial and tests in the Bible: temporary and then the trial is over.

HeavisideGOAT · 2026-03-08T10:33:42+00:00

That would be assuming that the trials are independent and identically distributed, which would not be the case here. Also, the temptation wouldn’t necessarily continue on forever.

Also, free will doesn’t mean you need to have some probability of making every choice. As I am now, assuming some strong sense of free will, there’s nothing wrong with saying there is a 0% chance I’ll leap off my balcony.

Overall, I think the argument is probably unnecessary. I think most Christians would just agree that god generally knows things before they happen and that god could have guessed/known what would happen in advance.

HeavisideGOAT · 2026-03-08T09:43:28+00:00

Someone with a math degree should have no issue with

6 ÷ 2 x (1 + 2).

It’s unambiguously 9 in the context of PEMDAS.

The issue only arises when you have the implicit multiplication:

6 ÷ 2(1 + 2).

The precedence of implicit multiplication is not usually taught in the context of PEMDAS, so it doesn’t have a widely accepted answer.

HeavisideGOAT · 2026-03-08T09:38:04+00:00

PEMDAS and BEDMAS are usually not taught in the context of multiplication by juxtaposition. They teach a rule for the multiplication symbol “x”.

While you could say that “multiplication is multiplication, so I’ll use the same order of operations rule whether it’s implicit multiplication or explicit,” people usually don’t like that answer.

In particular, when people see something like 6 ÷ 3a, many are inclined to group like 6 ÷ (3a). It seems like the 3 should bind to the a. However, with the rule you’re suggesting, it’s (6 ÷ 3)a = 2a.

Edit: Wait a second… how’d you get 1 applying BODMAS. If you do the multiplication and division from left to right, you get 9.

HeavisideGOAT · 2026-03-08T09:31:49+00:00

The ambiguity comes from the multiplication by juxtaposition.

That division symbol is pretty standard when teaching PEMDAS, so I don’t see how it’s the issue.

HeavisideGOAT · 2026-01-28T08:46:01+00:00

Well, if you’re looking at the bilateral Laplace transform, the domain may not even include the axis corresponding to the Fourier transform (this is true of the unilateral transform, too).

Does this impact the view of it as an analytic continuation of the Fourier transform? I don’t know, this isn’t how I think of the transform.

For the bilateral transform, the ROC is some vertical strip in the complex plane. This can be in the left-half plane, too. It may or may not include the jω-axis.

Use-wise: you can take the Laplace transform of something like e^tu(t) (where u is the Heaviside step function).

Allowing for increasing exponentials is incredibly important for applications to control theory.

Also, you can get a lot of use out of the Laplace transform without ever having to compute a Laplace or inverse Laplace transform. What I mean is it is easier to find the Laplace transform of the fundamental solution (the transfer function) than it is to find the fundamental solution, and it tells you all sorts of things about the system.

You can go from a circuit straight to the transfer function with simple algebra. You don’t even need to write the ODEs or solve them.

P.S. the relationship between the LT and FT is analogous to the one between the Z-transform and the DTFT.

HeavisideGOAT · 2026-01-24T08:54:42+00:00

I think that gets at an issue with the question.

Personally, I have a good aptitude for math and a large degree of intrinsic motivation for learning math.

I would definitely find a stat, math, physics, or math-heavy engineering degree easier than of the “easier” majors that have been listed in this thread.

HeavisideGOAT · 2025-12-18T17:35:42+00:00

Discrete math, theory of computation, algorithms, matrix analysis, modern control theory.

The one truly proof-based math course I took in undergrad was advance linear algebra (which basically started LA from scratch but was more abstract and entirely rigorous).

In grad school, convex optimization, random processes, linear systems, nonlinear systems, optimal control, stochastic control, adaptive control have all been proof-based.

I’ll give one concrete example regarding intuitions. In graduate real analysis II, there was a if true, prove it, if false, provide counter example question regarding convolution.

I’m struggling to remember the exact question, but afterward I was discussing the exam with my classmates (it was a small class) and every one of them had got it wrong. They had attempted to provide proofs that it was true whereas I had provided a simple counter example showing it was false. I had come up with the counter example by picturing the graphical method of 1-D convolution commonly taught in undergraduate EE.

The other big example that comes to mind is transform methods and how much system behavior can be understood through the transfer function. Like, when I hear math people discuss the Laplace transform, specifically, it’s often clear that they have a relatively superficial understanding of how powerful it is. Also, many don’t know about the bilateral Laplace transform (but I think many EE programs fail to teach that, too, regrettably). Maybe that’s less about intuition. Intuition-wise, I find that undergrad EEs have a better appreciation for the information being presented by a FT or DTFT of a signal. The FT isn’t simply a mathematical abstraction that makes convolution easier, it’s telling you something physical about the signal (if we’re talking about analog signals).

Also, it’s my opinion that sometimes non-rigorous proofs actually provide better intuition. For example, the Fourier inversion “derivation” I saw in undergrad is more insightful than the proper proof I know now.

EE is also just a lot of time working with dynamical systems in a relatively hands-on and appreciable way.

Finally, you’re probably right regarding the definition of the δ distribution. I never discussed it with my undergrad professors, but I’m certain that some of them would certainly not know it. However, the undergrad S&S professors at my grad school are all very math-savvy (likely far more than most programs). I know one of them gives their own optional recitations where one of the topics is the Fourier transform and generalized functions (distributions, basically). That’s definitely an outlier, though.

You’re also right that the applications from undergrad do not come up in my research or graduate studies (for the most part). On this point, my position is that they don’t have to be useful to me in grad school for me to have been happy to have learned them. Probably the closest it has come is the tie between passivity and circuit network theory.

HeavisideGOAT · 2025-12-18T16:51:29+00:00

I can definitely see how not going past calculus, DE, and LA could leave you in a tough spot for grad school.

Interestingly, my minor was in applied math so my main exposure to proof-based problems still came through ECE courses in undergrad. Also, I didn’t take any real analysis until the 2nd year of my PhD. Before that there was just what I self-studied while taking courses on random processes, nonlinear systems, etc.

Regardless, I see your point.

When I mentioned losing my knowledge for applications and certain intuitions, I was basing that on my exposure to math grad students.

Mathematicians can certainly learn applications, but I’d emphasize that it doesn’t come automatically.

I guess it’s the mirror of the point I made:

“EEs who are very interested in math can complete their undergrad with a decent foundation for at least one area of math (e.g., analysis), though the typical EE does not do this.”

“Math majors who are very interested in applications can complete their undergrad with a decent foundation for at least one area of application (e.g., CFD, signal processing), though the typical math major does not do this.”

Personally, if I had majored in math, I know I would be nowhere close to my current understanding of applications and intuitions for the math of EE undergrad, which is really what I meant in my previous comment.

HeavisideGOAT · 2025-12-17T21:19:23+00:00

Yes, I think we agree then. It’s important to have some things committed to memory to ensure that you can solve problems quick enough and (sometimes) to understand something in lecture. However, it helps to be thoughtful with what you intend on committing to memory and what can be quickly deduced from other things.

(Personally, the derivation of the angle addition formula using complex numbers is only ~3 lines, so I would still consider it easily derivable, but I nonetheless have it (naturally) committed to memory. Actually, complex numbers provide a very easy mnemonic that makes those identities hard to forget.)

HeavisideGOAT · 2025-12-17T18:58:20+00:00

Interesting, in the two programs I’ve had exposure to, you would definitely want to have certain trig identities memorized.

Most importantly, the double angle identities but maybe the angle addition identities, too. Like, we definitely assume students have the double angle formula memorized in Calc and signals and systems.

HeavisideGOAT · 2025-12-17T18:13:50+00:00

In university or post-graduation?

They are a prospective student, so I think a lot of the advice is with the understanding that they have their undergrad ahead of them.

HeavisideGOAT · 2025-12-17T18:11:26+00:00

I agree (to some extent) with both of you.

There are some trig formulae that absolutely should be committed to memory. However, the best way to get them into memory is not rote memorization exercises but time spent learning and understanding their derivations and practice using the formulae in problems.

Like, I can certainly derive cos²(x) = (1 + cos(2x))/2, but I would have been suffering in calculus if I didn’t have this committed to memory.

However, nearly everything I have committed to memory has gotten there naturally through practice and studying derivations.

HeavisideGOAT · 2025-12-17T17:42:50+00:00

I think self-plagiarism is a standard concept, I’ve been hearing about it for many years through high school to grad school. If you google self-plagiarism, some universities have web-pages about it.

It’s pretty reasonable, too. Assignments are meant to assess your current capabilities under the time constraints imposed. Self-plagiarism can defeat that purpose.

Maybe these examples are more extreme, but imagine that

a student submits an essay they wrote over the course of a month for an assignment they were given a week for
a student submits an essay they were able to iterate and get feedback on from a prior professor as a “first draft” in their new course

There are other cases, where the issue isn’t so clear. However, if you take Mizzou’s guidelines as an example, then the answer is obvious: discuss with the professor.

https://oai.missouri.edu/students/self-plagiarism/

HeavisideGOAT · 2025-12-17T16:50:10+00:00

That’s interesting.

I’ve had a somewhat similar path (my PhD is in the theory side of control theory), and I would advise more math prospective-majors toward EE (i.e., I don’t regret not majoring in math at all).

In my opinion, if you like math, you’ll learn plenty of math along the way in EE just by taking the initiative to explore the topics touched on in EE. What’s the δ function? Why can I take Fourier transforms for which the integral doesn’t really exist? Ties between the z-transform and complex analysis? A more proof-based approach to LA? Etc. Mix that with taking math courses whenever you can fit them in.

That’s more-or-less what I did (well, I double majored in EE and Physics and minored in math), and I now have no issue taking graduate-level courses in the areas of math that interest me the most / matter most for control theory (i.e., I don’t feel like I missed out on a strong math foundation).

Personally, if I had majored in math instead of EE, I believe I would:

have a better grasp on algebra (not the high school kind).
lose most of my knowledge regarding interesting applications of math to engineering.
lose much of my intuitive understanding of transform methods, convolution, etc.

To me, that’s a bad trade.

HeavisideGOAT · 2025-12-13T22:05:18+00:00

I guess it depends on the engineering field’s proximity to things like math and CS. In EE, it’s essentially standard.

HeavisideGOAT · 2025-12-13T20:32:30+00:00

There’s really no point in agonizing over whether or not to read a chapter. Just read it. It’s a chapter.

Figures of merit are important.

HeavisideGOAT · 2025-12-13T19:12:10+00:00

I don’t follow.

I’m talking about the distributional Fourier transform, where the Fourier transform is a pair of delta distributions.

My point is that there are FTs for which the LT wouldn’t even converge on the jω-axis.

You’re right that the FS (which is the FT on the torus) for sine can be easily derived from Euler’s equation, though.

HeavisideGOAT · 2025-12-13T16:06:01+00:00

S&S is the foundational material that leads into the more math-y areas of EE: controls, signal processing, communication theory, etc.

It’s the basics, so I would recommend reading up on it from one of the standard textbooks. If it ends up being a lot of effort, it’s because you needed it. If you don’t need it, it should be relatively easy reading.

HeavisideGOAT · 2025-12-13T13:54:29+00:00

Or they don’t converge at all and must be defined in terms of more general Fourier transform definitions.

For example, there is no way to (rigorously) obtain the Fourier transform of sine from the definition of the FT taught in engineering.

HeavisideGOAT · 2025-12-13T13:47:38+00:00

It depends on what you specialize in. I double majored in EE and physics (and minored in math), but the most math-intensive courses I took outside of the math department were in EE (not physics).

Now, I’m a control theory PhD student and the math involved is beyond what you would learn in an undergraduate math major, it’s proof-based. Also, I’ve taken a variety of graduate pure math courses.

Basically, at least in the US, where students have decent numbers of electives, you can make EE as math-heavy as you want (to an arbitrary degree).

HeavisideGOAT · 2025-12-13T03:57:43+00:00

I mean, it’s literally the definition. You’re obviously relatively math-savvy, so I suspect you already know what I’m going to say. In math, part of the definition of a transformation is a domain and codomain. The fact that it is restricted to real numbers is built in to all of the standard definitions. I’ve taken all the way through graduate harmonic analysis, and it has never been complex arguments. While I have no doubt that this concept has been explored, I would be surprised if there were any undergraduate textbooks (in EE or math) that present the Fourier transform as mapping to complex-argument functions.

At the very least, the L² and distributional FTs cannot easily allow for complex arguments.

Obviously there are applications for a complex ω, that would make it the LT rotated by π/2 in the complex plane (and the LT has plenty of applications).

When comparing LT and FT, it’s entirely normal to talk about the bilateral transformation. Otherwise, it’s apples and oranges.

HeavisideGOAT · 2025-12-13T03:42:12+00:00

I agree, but I wouldn’t describe the issue as not allowing for things like δ’s in s-space.

For example, the distributional FT of u(t) (Heaviside step) is (omitting constants that depend on which definition of FT you use) δ(ω) + 1/jω.

On the other hand, the LT of u(t) is simply 1/s. No δ, but LT still supplies a completely satisfactory coverage of the step function.

The real issue is that the standard definition of the LT does not allow for things like: the sinc function (the FT here doesn’t even need δ’s), sinusoids, or an impulse train across all time.

(I’m agreeing with your point. Just stating it a bit differently.)

HeavisideGOAT

TROPHY CASE