# How difficult is to write a Maths EE?

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Data processing is not a requirement. Once you check out the youtube channel in greater detail you'll know what I mean (especially the pi series, and regularities in prime).

I believe what you mean is the "magnitude". It is important to use precise terminology.

The magnitude is constant in time because the potential function is constant in time. If the potential function is a function of time then the wave function changes with time. (From ODE to PDE). It seems to me that if you don't even have the right terms down I doubt you understand the fundamentals of the Schrodinger equation. This is not to insult your intelligence, but a reflection of the fact that INTRO to quantum mechanics is taught as a full semester course in third or fourth year university and it may as well be risky to write the EE on it. The math requirement to "understand" basic quantum involves all of Math HL Calculus, the Calculus Option, second order ODEs, PDEs, and exposures to double, triple, path, line, and surface integrals.

The other thing is that examiners will check for errors and them not knowing quantum is not an insurmountable barrier. With their MS or even PhD in Math they can quickly read the wikipedia page to know the basics, because they know the aforementioned math concepts.

As a bad analogy, this is like doing chemistry report only knowing stoichiometry. Yes the experiment can be correct, but there is so much missing maths knowledge that the probability of saying erroneous statements is near unity. I am not saying this is a bad topic. And I hope that the constant-length thing that you have been going on and on about is just a small, maybe insignificant part, so that you can focus on parts you understand well from your previous project. I could be entirely wrong but wave function preserving constant magnitude is not worth 4000 words (around 15 pages with diagrams).

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22 minutes ago, kw0573 said:

Data processing is not a requirement. Once you check out the youtube channel in greater detail you'll know what I mean (especially the pi series, and regularities in prime).

I believe what you mean is the "magnitude". It is important to use precise terminology.

The magnitude is constant in time because the potential function is constant in time. If the potential function is a function of time then the wave function changes with time. (From ODE to PDE). It seems to me that if you don't even have the right terms down I doubt you understand the fundamentals of the Schrodinger equation. This is not to insult your intelligence, but a reflection of the fact that INTRO to quantum mechanics is taught as a full semester course in third or fourth year university and it may as well be risky to write the EE on it. The math requirement to "understand" basic quantum involves all of Math HL Calculus, the Calculus Option, second order ODEs﻿, PDEs, and exposures to double, triple, path, line, and surface integrals.

The other thing is that examiners will check for errors and them not knowing quantum is not an insurmountable barrier. With their MS or even PhD in Math they can quickly read the wikipedia page to know the basics, because they know the aforementioned math concepts.

As a bad analogy, this is like doing chemistry report only knowing stoichiometry. Yes the experiment can be correct, but there is so much missing maths knowledge that the probability of saying erroneous statements is near unity. I am not saying this is a bad topic. And I hope that the constant-length thing that you have been going on and on about is just a small, maybe insignificant part, so that you can focus on parts you understand well from your previous project. I could be entirely wrong but wave function preserving constant magnitude is not worth 4000 words (around 15 pages with diagrams).

I think you for your honest comment. Actually when I mentioned vector length... I assumed you'd know it's a magnitude. But that's besides the point. You initially mentioned what potential I am working with, in-fact I am taking a particle in closed box with infinite potential, and the box is in 1D, and this simplifies the math. And to be honest, my EE is very straight forward, and I am sorry if I was not able to provide the correct picture. When it comes to the "magnitude" of the wave-function vector staying constant or preserved.... all comes down to the unitary operator. And all I am trying to show mathematically therefore, the property of unitary operator with relation to the Hamitonian. I know this is a very very very broad topic and I am trying to narrow and simplify a lot of the mathematics down to a math EE level. I have already looked at linear algebra and studied various concepts related to my RQ from 3B1B and from Khan Academy, truly the visualizations did strengthen my understanding.

And also another thing, I don't really see how the potential play a part in the vector length  or magnitude of the wave-function, if theres' a reading you can link me into, that'll be helpful. Well since I am assuming an infinite potential, I don't think it will play a part, RIGHT?

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For the infinite potential well, the potential function is made up of two Heaviside functions. When you plug in different geometries, the potential function would change and you would get a different eigenvalue when solving the differential equation. The whole point that this particular geometry has a time-independent magnitude, because by definition. When you are trying to model systems where particles have relative motion (eg 2 particles colliding forming one), then you would use a time-dependent potential function. The resultant eigenvalue will be dependent on time. Most of my sources are written for students with the necessary math background. I think you know a reasonable amount for a Y1 student, but I don't think you should spend pages discussing this detail. I like the rest about property of the Hamiltonian as a unitary operator.

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Posted (edited)
8 minutes ago, kw0573 said:

but I don't think you should spend pages discussing this detail

True because the infinite potential box is just a situation, a mere constraint. This doesn't really need a major emphasis to the main point of my essay, as it deals with the mathematics of just conservation of the normalization. Thanks for all your valuable help!

Edited by Kil- STRO

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@kw0573 I had another question, do we have to have an annotated bibliography for a maths EE?

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An annotated bibliography is a reference list with a sentence or two explaining the source. You do not need to do that for any EE. You do need a complete bibliography with in-text citation for any maths discussed outside of the HL Syllabus.

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1 hour ago, kw0573 said:

An annotated bibliography is a reference list with a sentence or two explaining the source. You do not need to do that for any EE. You do need a complete bibliography with in-text citation for any maths discussed outside of the HL Syllabus.

And BTW... since I will be using a lot of linear algebra in my EE, should I be required to explain every process of doing the basics of linear algebra like finding the determinant, linear combination, matrix multiplication, etc. Or should I just stick to the mathematical explanation that is only relevant to the thesis.

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For linear algebra, I would suggest explain the basics using 10-15% of the EE. The goal is to demonstrate your maths understanding, so highlight why and when each operation is used. This is best done at the beginning, instead of throughout the EE. It would be bad to go "oh I need to introduce determinants now, oh 3 pages from now I need multiplication. It's simple to just explain all of linear algebra that you need, and throughout the EE you are referring back to the intro. It should flow nicely this way.

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On 7/10/2019 at 12:27 AM, kw0573 said:

For linear algebra, I would suggest explain the basics using 10-15% of the EE. The goal is to demonstrate your maths understanding, so highlight why and when each operation is used. This is best done at the beginning, instead of throughout the EE. It would be bad to go "oh I need to introduce determinants now, oh 3 pages from now I need multiplication. It's simple to just explain all of linear algebra that you need, and throughout the EE you are referring back to the intro. It should flow nicely this way.

What about the word count? I saw in the guide, that for EEs in Maths word count, don't matter!

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Word count is not appropriate to measure the length of a Maths EE. Usually If you have a lot of equations and figures, I would say around 16 pages, if it is mostly text then maybe 10-12 pages. However, the EE should be about twice as long as the IA. However, you still cannot exceed 4000 words. Very rarely does a Maths EE goes over 3000 words.

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@kw0573 How important is a personal connect for a Mathe EE? I mean I am working on maths with relation to QM, how can I show personal connect throughout my essay?

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Reflection criterion is graded through the RPPF forms.

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6 minutes ago, kw0573 said:

Reflection criterion is graded through the RPPF forms.

wait so the "personal content" thing is not really part of the essay, like I don't have to explicitly say or show, personal engagement!

It's all in the reflection?

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You don't have to mention personal engagement in the EE itself.

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In addition, beware of differences between the "Personal Engagement" of the IA and "Reflection" of the EE.

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5 minutes ago, kw0573 said:

In addition, beware of differences between the "Personal Engagement" of the IA and "Reflection" of the EE.

Reflection includes the full assessment of the research process and perseverance, while the personal engagement is something about your IA topic that relates to your life. Right? Therefore... the personal engagement must be mentioned in an IA, yes?

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Stronger PE tends to include struggles and perseverance as well. Personal Engagement is emphasis on the "engagement" not on the "personal". PE also includes if you are able to draw connections between quantum and core HL Math. DO NOT just simply state how quantum changed your life and hope for full points in PE.

Because I wrote my EE before 2018, I am not too familiar with how RPPF works. I think reflection also includes how you gathered information and tackled this topic. It probably also includes what you thought you could do differently if you had more time or know more about linear algebra/calculus. Or possibly some remaining question that are unanswered.

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@kw0573 Hey, I had an off topic question. I am not sure if u took physics for your subject but I just hope you can comment a little bit on what I am doing for my physics IA. I am still unsure about my RQ for my physics IA, but in essense what I am doing is looking at a simple experiment for an electric generator and seeing how "maxwell's equation" applies to it. I don't know if u heard about maxwell's equation, if u haven't it's essentially a bunch of vector calculus stuff like divergence and curls with relation to electric fields and magentic fields. Now I am trying make an IA to show how does the "curl" of electric field that is produced due to the generator gets effected with an independent variable which would be a magnetic field that creates that electric field. NOW the "curl" itself is quite mathematical...and tbh throughout my IA I am trying to display this bridge between physics and mathematics (ie I am going to physically interpret a curl) SO what do u think?

I hope I didn't explain it with some heavy complexity.

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Posted (edited)

In the future, please start a new thread or start a private message for off topic discussions.

It sounds like you are doing Faraday's Law. Now both electric and magnetic field will be functions of space (distance) and time. So either you measure both at the same place or you justify why the electric field is approximately the same across a region. [Redacting this sentence as it is misleading]. This is a standard and self-explanatory experiment, so if you get stuck there are plenty of explanations available online. I am not too sure if it is necessary or even if you have sufficient data to "visualize" a curl by comparing to the electric field. Basically you would need to find a whole vector field and it is pretty time consuming and meticulous. There is no merit in discussing math for the sake of discussing math.

Edited by kw0573
see strikethroughs and bolded text. For clarification

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If math is your hands-down definitive best subject, then it's doable to get an A. Keep in mind that C is the average grade across all subjects. Basically if you have always been 1-2 years ahead in math than your peers, or are able to pick up math quicker than the others than Math EE can be an option. You want to first read the Math chapter in the EE guide, understand the criteria, and brainstorm on some possible topics. Keep your options open and find topics in other subjects as well.

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