About writing a Highschool Math Research Paper Hello, I am…
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About writing a Highschool Math Research Paper
Hello, I am currently a Korean senior in a Highschool(Private School), planning on majoring mathematics, if not theoretical physics. I was recently thinking of writing a research paper on Mathematics.
**For convenience,**
My interest(not experience) in mathematics spans in Abstract Algebra(Especially in Complex Multiplication Theory or Differential Galois Theory) and Number Theory(Regarding Transcendentality of numbers and functions). I can proudly say I have a stable intuition towards the concepts I have mentioned, of which can be proved by how well I can explain these concepts to my peers, along with my ability of being highly rigorous in proofs(Though, correct me if it seems as if I am unable to distinguish between being rigorous and being tedious).
However, I lack the ability to apply the concepts I learned to solving problems, despite being convenient with proofs. Basic excercises I can solve, but problems that require an integrated field of the concepts I learned makes me stump
(For instance, I can prove whether a Galois Group is solvable or not, or find the isomorphisms of a given Elliptic Function, but have a hard time solving problems that are about the applications of Galois Groups to Torsions of Elliptic Functions).
The only levels of problem solving I am, at some extent,confident in, are elementary problems in Ring Theory and a few differential equations of 2nd order. Other than that, I highly lack pragmatic problem solving skills(My grades in math aren't even that great compared to other kids at my school, though I wouldn't call my grades severly underperforming).
I know that I am not capable of proving any conjectures or coming up with new theorems. But I know that there is not more of math than that, such as giving alternate proofs for an already known theorem, explaining a concept or theory in an alternate method of intuition, etc.
For those who don't really get what I'm saying, I provide a list of concepts I stumbled upon, that might make clear what I'm suggesting:
\- How Ramanujan's Constant(Though known for its name as a result of a hoax) is an "almost integer" explained through Ring Theory and Complex Multiplication
\- An alternate proof of the Abel Ruffini Theorem using Riemann Manifolds in the complex space.
\- A rigorous analysis of "Action" from the Least Action Principle in phase space, using gauge symmetry(I forgot where the paper was, but I'll upload it if possible).
\- Relation to the 2nd coefficient of the j invariant q-expansion and the order of the biggest simple sporadic group
\- Unprovability of Goodstein's theorem in the Peano Arithmetic(I haven't finished my attempt in completely being able to formulate this, but got an overall understanding of the proof)
I really love math(and I am sure I made it apparent), and even discovered some original theorems myself(which had almost no applicability, leaving me in dissatisfaction). But I know I lack the mathematical maturity to acheive any signficant result in my personal research in Mathematics. However, as much as I have put time and effort to learning math, I wanted to make a meaningful result out of it, which makes me ask these questions:
**What would suffice as a "decent" mathematical research paper(and I'm talking about "pure" mathematics)?**
**What other objectives there are in mathematical papers other than proving conjectures or developing theories?**
**Is it possible for anyone with this amount of limited knowledge and skills to write a research paper?**
**Could anyone provide some suggestions or simple directions I might follow or other aspects I need to approve(or possibly provide me with examples of thesis papers)?**
Sorry for my terrible English.
#science
source
Hello, I am currently a Korean senior in a Highschool(Private School), planning on majoring mathematics, if not theoretical physics. I was recently thinking of writing a research paper on Mathematics.
**For convenience,**
My interest(not experience) in mathematics spans in Abstract Algebra(Especially in Complex Multiplication Theory or Differential Galois Theory) and Number Theory(Regarding Transcendentality of numbers and functions). I can proudly say I have a stable intuition towards the concepts I have mentioned, of which can be proved by how well I can explain these concepts to my peers, along with my ability of being highly rigorous in proofs(Though, correct me if it seems as if I am unable to distinguish between being rigorous and being tedious).
However, I lack the ability to apply the concepts I learned to solving problems, despite being convenient with proofs. Basic excercises I can solve, but problems that require an integrated field of the concepts I learned makes me stump
(For instance, I can prove whether a Galois Group is solvable or not, or find the isomorphisms of a given Elliptic Function, but have a hard time solving problems that are about the applications of Galois Groups to Torsions of Elliptic Functions).
The only levels of problem solving I am, at some extent,confident in, are elementary problems in Ring Theory and a few differential equations of 2nd order. Other than that, I highly lack pragmatic problem solving skills(My grades in math aren't even that great compared to other kids at my school, though I wouldn't call my grades severly underperforming).
I know that I am not capable of proving any conjectures or coming up with new theorems. But I know that there is not more of math than that, such as giving alternate proofs for an already known theorem, explaining a concept or theory in an alternate method of intuition, etc.
For those who don't really get what I'm saying, I provide a list of concepts I stumbled upon, that might make clear what I'm suggesting:
\- How Ramanujan's Constant(Though known for its name as a result of a hoax) is an "almost integer" explained through Ring Theory and Complex Multiplication
\- An alternate proof of the Abel Ruffini Theorem using Riemann Manifolds in the complex space.
\- A rigorous analysis of "Action" from the Least Action Principle in phase space, using gauge symmetry(I forgot where the paper was, but I'll upload it if possible).
\- Relation to the 2nd coefficient of the j invariant q-expansion and the order of the biggest simple sporadic group
\- Unprovability of Goodstein's theorem in the Peano Arithmetic(I haven't finished my attempt in completely being able to formulate this, but got an overall understanding of the proof)
I really love math(and I am sure I made it apparent), and even discovered some original theorems myself(which had almost no applicability, leaving me in dissatisfaction). But I know I lack the mathematical maturity to acheive any signficant result in my personal research in Mathematics. However, as much as I have put time and effort to learning math, I wanted to make a meaningful result out of it, which makes me ask these questions:
**What would suffice as a "decent" mathematical research paper(and I'm talking about "pure" mathematics)?**
**What other objectives there are in mathematical papers other than proving conjectures or developing theories?**
**Is it possible for anyone with this amount of limited knowledge and skills to write a research paper?**
**Could anyone provide some suggestions or simple directions I might follow or other aspects I need to approve(or possibly provide me with examples of thesis papers)?**
Sorry for my terrible English.
#science
source
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