Content in Math EE

[yangmillsexists]

Hello,

I recently finished the process of writing a math EE on cylindrically symmetric stationary vacuum solutions to the Einstein field equations of general relativity. I included a derivation of this family of solutions and a rather detailed analysis of various properties that offered my own perspectives on things and did some illustrative calculations. However, the fluidity of the essay assumes knowledge of differential geometry and topology (i.e. theory of differentiable manifolds), as well as Riemannian geometry, tools essential to general relativity. My adviser recommended the inclusion of appendices explaining the advanced topics to a reader who would hypothetically only be familiar with the math HL curriculum, but the problem is that the content is simply so vast that the appendices are dreadfully long and I feel that they detract from the point of the essay. Most of the stuff I explain in them could be found in any respectable general relativity textbook. Would it really be necessary to include these appendices if my discussion in the essay illustrates that I am proficient in the material? 

Thanks

[kw0573]

It shouldn't be necessary to provide appendices solely for explanatory purposes. Examiners are not required to read appendices so if you do write in depth explanations in the APPENDIX it's a waste of time. It should be enough in your essay to provide a few sentences introducing each topic outside of the HL syllabus. Eg. "The ____ method describes _____ and it states ______. It is applicable in the calculation because _______. [proceeds to use the method in the calculation.]" Similarly, all of your calculations should be briefly justified to demonstrate clear coherent thought process which will earn you marks. Your goal is to convince examiners that you know what you are talking about, not to simply get the right answers. If you were to feel that explanations are too brief, then maybe you could cut one of the less important notes to just consolidate all your other points. Remember that there is a maximum number of marks you can get for knowledge and understanding; you should easily get the highest mark for that criterion with the EE you are doing, so don't jam too much content if you weren't able to explain them all. 

[yangmillsexists]

Thanks for the reply! My only source of worry is that the basic language of the essay operates outside of the HL syllabus, so it would kill any fluidity to try to explain absolutely everything from ground up. I feel like it would be unnecessary to halt all discussion to define some term whose definition could easily be found in a reference. I think that my essay communicates that I know what I'm talking about, but also I think I shouldn't be responsible for breaking it down to a high school/early undergraduate mathematics level. It would just be redundant and almost condescending. I'm really only bothered because the guide says "it should communicate clearly, not just to an examiner who is likely to be more mathematically sophisticated than the student, but also to an interested reader with a similar mathematical competence to the student". 

[kw0573]

I do have a sense of what you are talking about. So what I was suggesting was that you only include certain aspects of your work that effectively and concisely demonstrate both your communication and math skills. The EE should be, as best to your abilities, should be understandable by another (high-performing) HL student who may have not exactly know about manifolds. Such a student should be able to largely following your work without doing too much extra research. Suppose you want to explain quantum mechanical model of the atom to a chemistry student, but they don't know how to solve partial differential equations. Certainly you can explain the consequences of such a theory and shape of orbitals without having to painstaking explore the mathematical intricacies. So you don't have to explain to the point that another student can produce a similar EE but just that they understand the main points.

Take another example, Newton invented certain aspects of calculus to solve his physics problems. Of course, other physicists at the time cannot immediately grasp his math but they understand that somehow he quantified concepts of conservation of energy and mass, as well as non-constant acceleration that they were all quite familiar with. That should be your goal when writing your EE: another HL student doesn't have to follow any of the math to a great extent but they should be satisfied as to what motivates you to use certain math concepts, hopefully some are similar to what they know already. 

[yangmillsexists]

Ok, I see what you mean. This clarifies a lot. In that case, I think I should be fine. Thank you!