How difficult is to write a Maths EE?

[Kil- STRO]

How hard should I work? What approaches should I take?

Would it be difficult to get an A, than a physics or any-other EE??

[kw0573]

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.

[Kil- STRO]

1 hour ago, kw0573 said:

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.

Hey thx for the reply,

I was actually thinking about this research question: "How does the Schrodinger's equation preserve its normalization?"

Now the concepts and theories in this questions heavily relate to physics and in-fact the question stated above was my RQ for my EE of physics, the subject I initially chose to work. Unfortunately, my teacher, when I presented my RQ to him today, he said that the RQ was way to theoretical and that IB considers theoretical essays, that solely rely on secondary data and not consider any experiments, to be ugly (hence a connotation for IB giving me a C or even less). So me taking my teachers advice that he switching my entire EE subject to maths, and focus on the mathematical reasoning behind how the equation's unitary functions preserve it's inner products, therefore keep the SE equation normalized at all times. 

I don't know if you understand QM... but it seems like you have pretty good experience with IB maths. If do understand QM, is it cool if we continue the conversation in depth and I share my EE structure, and hear u're thoughts??

 

 

[kw0573]

I don't understand QM but I have taken a 4th year university level chemistry course in it. I don't want to offer so much help somehow my role overshadows that of a supervisor. The wave's normalization is preserved but that's not the most interesting mathematical aspect out of SE. Certainly the core maths are in the eigenvalues, the orthogonality, and the differential equations. 

[Kil- STRO]

7 hours ago, kw0573 said:

I don't understand QM but I have taken a 4th year university level chemistry course in it. I don't want to offer so much help somehow my role overshadows that of a supervisor. The wave's normalization is preserved but that's not the most interesting mathematical aspect out of SE. Certainly the core maths are in the eigenvalues, the orthogonality, and the differential equations. 

Hey, 

I just looked at the EE guide and found that we could use secondary data and the candidate may very well get a high grade for the theoretical physics EE

From guide it says:

"Students can choose to answer their research question with an essay based solely on theory or one based on data and theory."

"Student using data elsewhere can assess all assessment criteria and achieve the highest marks"

So what do you think... is the explanation of the SE preserving it's norm a more mathematical based EE or physics based. I understand if I consider a mathematical basis of this question I would have to go pretty deep into complex mathematics such as eigenvectors, vector calculus and as an IB student it way over me and I probably won't have time to even study them individually for my essay. Whilst the physics I may make use of my calculus and highs school mathematics and merge them with explaining the physics behind the norm of particle in a box and how it stays normalized with of time

 

[kw0573]

I am not familiar with a science EE, so I can't offer much help. Sorry  I am not sure what data you'll be using??? Like basically for SE you choose a potential function and you solve it mathematically, so it's more challenging to show personal engagement in physics than it is in math. 

[Kil- STRO]

18 minutes ago, kw0573 said:

I am not familiar with a science EE, so I can't offer much help. Sorry  I am not sure what data you'll be using??? Like basically for SE you choose a potential function and you solve it mathematically, so it's more challenging to show personal engagement in physics than it is in math. 

 

Essentially I was thinking of this structure for my essay: 

- A consider a particular function with a normalization condition 

- Then I would evolve the function in time and show that it is normalized for all time

- With that out of the way... I would explain why the SE stays normalized and here I dicuss the mathematical propertise of SE and it's unitary functions; time evolution. Essentially researching what gives away to the preservation of the wavefunction. 

I understand the explanation is more mathematical than physics, but what I really fear is writing a maths EE with complex mathematical explanations. 

Infact, do you need complex mathematics such as vector calculus and eigenvectors to make my EE good for A or at-least a B, what exactly are the examiners looking for? 

Or I'm I good explaining the whole preservation thing with some IB calculus and some-what uni-level mathematics?

Edited May 17, 2019 by Kil- STRO

[kw0573]

Quality of math only worth 30%. The guide will say what examiners are looking for. The math behind normalization is straightforward. The down side is that it's hard to show personal engagement regardless math or physics. You are doing a lot of explaining, but not much original content.

[Kil- STRO]

5 hours ago, kw0573 said:

Quality of math only worth 30%. The guide will say what examiners are looking for. The math behind normalization is straightforward. The down side is that it's hard to show personal engagement regardless math or physics. You are doing a lot of explaining, but not much original content.

 

I not necessarily working out normalization of a particular wave-function, and just explaining the normalization , but my EE as I have mentioned before is explaining HOW the unitary operator (time evolution) of the SE work to preserve the inner products of the function thus preserving the SE's norm for all times. I don't really know how much of a mathematical explaining I have got to do for this.. but the actual explaining of the mathematical operator of SE, I guess gives it away.

I don't really understand what you really mean by personal engagement (is it to show how enthusiastic am I about the topic, idk I hope you can explain)

like you menstioned about "not much original content" .... ofcourse in the guide it say that restating secondary research or not giving any personal research at all is not good for a "good enough grade".

I think by personal engagement you mean... when some himself/herself do some personal research (correct me if I am wrong), but to me undestanding why the SE stay or not stay normalized over a period of time seems quite intriguing and I literally don't have a clue about how to answer and approach my RQ as stated at the very beginning. Although the answer to the RQ is pretty well know to the scientific community... to me it's just a black canvas. So, could me myself actually trying to learn, deciphering and demonstrating my understanding be the reason behind the preservation be a personal engagement???

Again I want to appreciate the awesome help you're providing me with and helping me understand the whole situation. 

😁😁😀 U're the BEST!

Edited May 17, 2019 by Kil- STRO

[kw0573]

I said personal engagement because that's the phrase in the HL IA and I thought you might recognize it. So out of 34 points in the EE, 12 is critical thinking and 6 is engagement. Critical thinking is taking what you know, and combine the ideas to infer about additional facts. Engagement is based on the reflection form in which you discuss the research process and any obstacles. 

Again I don't know exactly what you are trying to do (mostly because I don't understand QM very well) but it sounds like a complicated version of the distributive (or associative?) property. It's not that hamiltonian preserves the magnitude, it's that by taking the hamiltonian, the wave magnitude change, so you add a reciprocal pre-factor (coefficient) to "cancel" what the operator did. Say the operator does (× 5), then in the wave function you might add a coefficient of 1/5, so the two operations cancel each out to maintain the same wave integral over space and time.

I think learning basic vectors and complex numbers are a must, so it could be easier to relate eigenvalues/eigenvectors to HL than some of the other topics. 

[Kil- STRO]

18 hours ago, kw0573 said:

I said personal engagement because that's the phrase in the HL IA and I thought you might recognize it. So out of 34 points in the EE, 12 is critical thinking and 6 is engagement. Critical thinking is taking what you know, and combine the ideas to infer about additional facts. Engagement is based on the reflection form in which you discuss the research process and any obstacles. 

Again I don't know exactly what you are trying to do (mostly because I don't understand QM very well) but it sounds like a complicated version of the distributive (or associative?) property. It's not that hamiltonian preserves the magnitude, it's that by taking the hamiltonian, the wave magnitude change, so you add a reciprocal pre-factor (coefficient) to "cancel" what the operator did. Say the operator does (× 5), then in the wave function you might add a coefficient of 1/5, so the two operations cancel each out to maintain the same wave integral over space and time.

I think learning basic vectors and complex numbers are a must, so it could be easier to relate eigenvalues/eigenvectors to HL than some of the other topics. 

Hey I just read the guide... it say IB discourages student from taking topics, that are too complicated. Do you think, my topic is way to complicated for a Maths EE?

[kw0573]

I like to first correct something I said in the last post

The magnitude of the wave function is chosen so that ∫ψ* • ψ dτ = 1, and changes of applying the hamiltonian and potential functions are stored in the eigenvalue. So what you had before is right

No I didn't think this topic is very complicated for a Year 1 student, but you need to make that decision!

[Kil- STRO]

2 minutes ago, kw0573 said:

I like to first correct something I said in the last post

The magnitude of the wave function is chosen so that ∫ψ* • ψ dτ = 1, and changes of applying the hamiltonian and potential functions are stored in the eigenvalue. So what you had before is right

No I didn't think this topic is very complicated for a Year 1 student, but you need to make that decision!

Well I since, I am quite interested in the topic and I did do prior research on normalization before DP1 and in-fact did my Grade 10 personal project on Schrodinger's equation. I guess for my EE, I might as well take it further by talking about the intricate mathematics of the equation.   

[Kil- STRO]

What is the actual point what were are tryna demostrate in our EE? Is it simply just explaining your topic mathematically, demonstrating research skills and showing personal connect?? 

 

[kw0573]

For starters, EE usually are more than twice as long as an IA, and it's the same for mathematics. One key difference is that for the IA, you have to connect multiple areas of maths, but not for the EE (though you probably should anyways).

You pretty much got the idea. I would add that the EE has to be organized and coherent: the EE overall has to support a central research question. 

[Kil- STRO]

1 hour ago, kw0573 said:

For starters, EE usually are more than twice as long as an IA, and it's the same for mathematics. One key difference is that for the IA, you have to connect multiple areas of maths, but not for the EE (though you probably should anyways).

You pretty much got the idea. I would add that the EE has to be organized and coherent: the EE overall has to support a central research question. 

 

Will a good EE be measured by the amount of mathematical rigor and its corresponding explanation? 

 

Edited July 3, 2019 by Kil- STRO

[kw0573]

Rigor is important but it alone will not get you an A/B. Treat the reader as a strong student who does not know much beyond HL. Explain any math that is not in the syllabus. For example in my EE, I used partial derivatives on a page. I didn't explain it, because it's so similar to ordinary derivatives. But if you talk about anything in the realms of matrix transformations, complex models, graph theory, multivariate calculus, etc then you should definitely explain them properly. A rule of thumb is that you don't need to over explain a topic any strong HL student can understand from 5 minutes of reading wikipedia. Think the reader as a skeptic waiting to be persuaded by you.

Not sure if I understood your question precisely. Feel free to provide more details if this is not the desired answer.

[Kil- STRO]

9 hours ago, kw0573 said:

Rigor is important but it alone will not get you an A/B. Treat the reader as a strong student who does not know much beyond HL. Explain any math that is not in the syllabus. For example in my EE, I used partial derivatives on a page. I didn't explain it, because it's so similar to ordinary derivatives. But if you talk about anything in the realms of matrix transformations, complex models, graph theory, multivariate calculus, etc then you should definitely explain them properly. A rule of thumb is that you don't need to over explain a topic any strong HL student can understand from 5 minutes of reading wikipedia. Think the reader as a skeptic waiting to be persuaded by you.

Not sure if I understood your question precisely. Feel free to provide more details if this is not the desired answer.

 

No, it's really an amazing answer thank you. But I was meaning to ask you this, with relation to my EE and would it be a correct approach. After some research I have arrived to the conclusion that the preservation of the normalization of the wave-function is due to the conservation of the length (or inner products) with the evolution of time. Now to actually mathematically explain the conservation of length is not really mathematical... it's just intuition, that when u rotate any fixed object, the length doesn't really change! So in my EE to show the mathematical rigor I have considered taking a longer and a backward route to explain the conserved  length. We know it's a property of the unitary operator to preserve the vector length (or inner product), the essentially the property of the unitary operator itself emerges from the hamilitonian, and the professor I have been doing my internship with, said most of the mathematical rigor exists within the hamiltonian.

So essentially I was thinking to expand broadly and backwardly, but expanding on the the hamiltonian... therefore going into the unitary then connecting to the explanation of how the unitary preserve the length or inner products and then connecting the length to the normalization of the wave-function and how the normalized wave-function stay constant with time. Will this be fine??

Edit**

I would also like to add, that my supervisor said that some sort of data is required for math EE, to show some graphical interpretation or something. Is "data" really required when it comes to my maths EE or it's just a physics EE thing?

Edited July 3, 2019 by Kil- STRO

[kw0573]

I have merged these two threads as it's pretty much you and I.

I'll answer the easy question first, which is that it would be nice if you visualize the mathematics. I would recommend https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw for visualization tips. Notice how he connects rigor with intuition.

I am not sure what do you mean by length. I do still have my quantum mechanics book so I can still look up technical information. What is the potential you are working with? 

Your EE needs to be full of logical reasoning and cannot be just hand-wavy. I understand that this is not what you hoped but it's the harsh truth. I would say a C or above is unlikely if there you cannot justify most of your claims rigorously.

There are two main Maths EE approaches. The first way is to talk about one specific problem and involve many techniques while solving/exploring it. The other main method is to apply a single theorem or idea across multiple contexts, then compare and contrast between them. 

[Kil- STRO]

1 hour ago, kw0573 said:

I have merged these two threads as it's pretty much you and I.

I'll answer the easy question first, which is that it would be nice if you visualize the mathematics. I would recommend https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw for visualization tips. Notice how he connects rigor with intuition.

I am not sure what do you mean by length. I do still have my quantum mechanics book so I can still look up technical information. What is the potential you are working with? 

Your EE needs to be full of logical reasoning and cannot be just hand-wavy. I understand that this is not what you hoped but it's the harsh truth. I would say a C or above is unlikely if there you cannot justify most of your claims rigorously.

There are two main Maths EE approaches. The first way is to talk about one specific problem and involve many techniques while solving/exploring it. The other main method is to apply a single theorem or idea across multiple contexts, then compare and contrast between them. 

Thanks again, I understand that every mathematics I implement have to be understood in a clear and logical way. Which makes sense to me absolutely, because the chance of the examiner actually understanding QM is very low... so he therefore want to be followed along, when I say "length" what do I exactly mean. 

But what I was implying is that...the true mathematical elegance of my RQ is really within the hamiltonian (the energy operator; which is found in the schrodinger's equation) and really I arrived to the hamiltonian after unpacking the claim that the vector length (where the wavefunction is a vector) stays constant with time. So in my EE I am trying to expand from Hamiltonian to unitary operator to the wavefunction and therefore preserving the vector length. I hope this makes sense, and if it does, does my expansion on the idea from the Hamiltonian to my claim a logical one?

Also will any mathematical data or data processing be a requirement for an EE or maybe make a better EE?