61 lines
4.8 KiB
TeX
61 lines
4.8 KiB
TeX
\documentclass{article}
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\usepackage{mla13}
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\usepackage{hyperref}
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% ========== Note to users =========
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% Remove these two packages after
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% you remove the example text.
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\usepackage{blindtext}
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\usepackage{lipsum}
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\usepackage{amsmath}
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\title{Mathematical Me} % Title for the paper
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\firstname{Krishna} % Author's first name
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\lastname{Ayyalasomayajula} % Author's last name
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\professor{Foresee} % Last Name of the professor
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\class{MATH 2415.008: Calculus III} % Name of the class
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\date{21 September 2025} % Uncomment to change due-date
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\sources{references.bib} % File holding all the sources
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\begin{document}
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% First create the title page on its own.
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\maketitlepage
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\newpage
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% Then create the table of contents on its own.
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%\tableofcontents
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\newpage
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% Paper content begins here.
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\makeheader % Adds the MLA-Style information
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\maketitle % Redefined to use MLA-Style
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% Put paper here.
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% Begin example text.
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The following equations encapsulate my life rather completely:
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\begin{align}
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K_{n+1} &= K_n + \alpha P_n + \beta C_n + \gamma R_n \label{eq:knowledge} \\[6pt]
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S(T,E) &= S_{\max}\!\left(1-e^{-\lambda T}\right) + \mu E \label{eq:skill} \\[6pt]
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\text{Premium} &= BS(S,K,r,\sigma,t) + \eta \cdot \mathcal{N}(0,1),
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\qquad \eta \to \infty \label{eq:trading} \\[6pt]
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I &= \kappa\cdot\mathrm{Skill}\cdot\mathrm{Intent} - \delta\cdot\mathrm{Risk}^2 \label{eq:impact} \\[6pt]
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F &= \int \frac{\partial \,\text{Immersion}}{\partial \,\text{Pages}}\,\mathrm{d}(\text{Pages})
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+ \int \frac{\partial \,\text{Immersion}}{\partial \,\text{Prose}}\,\mathrm{d}(\text{Prose}) \notag \\
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&\quad + \int \frac{\partial \,\text{Immersion}}{\partial \,\text{World}}\,\mathrm{d}(\text{World})
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+ \int \frac{\partial \,\text{Immersion}}{\partial \,\text{Characters}}\,\mathrm{d}(\text{Characters})
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\label{eq:fun}
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\end{align}
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In equation~\ref{eq:knowledge}, I am looking at my cumulative knowledge growth, which models how practical coding, challenges, and research accumulate over time. Mathematically, each component contributes linearly, so balancing them according to their weights maximizes overall growth, reflecting my approach to learning efficiently. In equation~\ref{eq:skill}, I am examining my skill as a function of time and efficiency. The partial derivatives \(\frac{\partial S}{\partial T}\) and \(\frac{\partial S}{\partial E}\) and the limit \(\lim_{T \to \infty} \frac{\partial S}{\partial T} = 0\) show that efficiency drives growth more than time, guiding me to focus on deliberate effort rather than long hours. In equation~\ref{eq:trading}, I am analyzing quantitative analysis premiums through a Black–Scholes model with an added stochastic noise term. The limit \(\lim_{\eta \to \infty} \text{Premium}\) demonstrates that randomness dominates, illustrating how real outcomes feel unpredictable despite understanding the formulas. In equation~\ref{eq:impact}, I am quantifying my real-world impact, combining skill, intent, and risk. The quadratic risk term shows nonlinear penalties, so I must carefully calibrate my actions to maximize meaningful contributions in projects like my research paper and work with the IT Army of Ukraine. Finally, in equation~\ref{eq:fun}, I am modeling fun as immersion derived from reading progression fantasy. Evaluating partial derivatives with respect to Pages, Prose, World, and Characters reveals which books provide the strongest engagement per axis, with \textit{Cradle} excelling in Pages and Characters, \textit{The Stormlight Archive} in World, and the \textit{Azura Ghost} series in Prose, allowing me to quantify and prioritize my enjoyment mathematically.
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In the past, a great positive influence on my journey into mathematics was Mrs. Kottwitz (A.K.A Godwitz), who taught me the intricate beauties of single-variable calculus. Along the same lines, my incredibly ill-tempered geometry teacher --- Mr. Lantiere --- taught me to hate geometric proofs by gifting the class impossibly long exams, leading to a class average of $62$ by the end of the year. This was counteracted by the success I was seeing in looking ahead into Pre-Calculus, a venture on which I found the amazing resources of the Internet. Chief among these stands the wonderful YouTube channel \href{https://en.wikipedia.org/wiki/3Blue1Brown#Early_life_and_education}{3Blue1Brown}, run by Grant Sanderson. Much earlier in my study of mathematics, around the age of 2 or 3, I was unable to count at precisely the number $3$. I could go from $1$ to $2$ or $7,6,5,4,\dots$ but never say the number $3$. I'm not exactly sure when I got past that roadblock though. Overall, especially recently, my comprehensive body of experience has left positive impressions deep in my mind regarding math, which is why I'm attempting this class.
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% End example text.
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% Put the works-cited on a separate page.
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\newpage
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\makeworkscited
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\end{document}
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