study-notes.tex

\input{preamble.tex}
\input{toc.tex}

\begin{document}

    \listoftodos

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        \makeatletter
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    \input{parts/special-relativity}

    \part{\href{https://trello.com/c/jzmmeXHp}{A First Course on General Relativity}}
    \chapter{Special Relativity}
    \input{parts/first-course/chapter-1}

    \part{Mathematics}
    \chapter{Topology}

    \tcbsidebyside[sidebyside adapt=right, blanker,sidebyside gap=5mm]{
        The name of this division (``Topology") is in honor of, from my sincere respect, the great book by George F.
        Simmons, \href{https://trello.com/c/3EPccNTa}{Introduction to Topology and Functional Analysis}
    }{
        \includegraphics[width=0.1\textwidth]{胡桃-26.png}
    }

    \input{parts/mathematics/topology}
    \chapter{Linear Algebra}
    \input{parts/mathematics/linear-algebra}
    \chapter{Riemannian Geometry}
    \label{ch:riemannian-geometry}
    This chapter was raised by the discussion of \hyperlink{green-theorem-proof}{Green's Theorem}

    There are lots of texts around the topics of Riemannian Geometry. Here is a list of threads in which great people
    recommended good books on it

    \begin{itemize}
        \item \href{https://physics.stackexchange.com/a/247415}{Riemannian and Pseudo-Riemannian Geometry}
        \item \href{https://math.stackexchange.com/questions/1546037/beginners-book-for-riemannian-geometry}{Beginner's book for Riemannian geometry}
        \item \href{https://math.stackexchange.com/questions/499945/need-help-finding-a-good-book-on-riemann-geometry}{Need help finding a good book on Riemann Geometry}
        \item \href{https://mathoverflow.net/questions/19505/introductory-text-on-riemannian-geometry}{Introductory text on Riemannian geometry}
    \end{itemize}

    One will need quite a solid backgound in topology, and especially differential geometry. I would recommend the book
    series by Lee: Introduction to topological manifolds / introduction to smooth manifolds/ introduction to riemannian
    manifolds.\footnote{\href{https://www.reddit.com/r/math/comments/tt2klk/comment/i2v4nud/?utm\_source=share\&utm\_medium=web3x\&utm\_name=web3xcss\&utm\_term=1\&utm\_content=share\_button}{Book recommendations}}

    \todo[inline]{Study notes on Riemannian Geomery}

    \input{parts/mathematics/manifolds}

    \part{Electromagnetism}

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        This question arose because I noteiced Einstein dedicated a huge portion of his famous
        \hyperlink{sr-original-paper}{Special Relativity paper} on its application in Electromagnetism.

        In fact, Einstein was trying ridiculously hard to unify his General Theory of Relativity with
        Electromagnetism\footnote{\href{https://en.wikipedia.org/wiki/Unified_field_theory}{\ldots Albert Einstein, who attempted to unify his general theory of relativity with electromagnetism \ldots}, Wikipedia}. Why?

        Relativity describes our Universe pretty good but works horribly in the microscopic world like subatomic
        particles, whereas Quantum Physics works from the opposite. Relativityis, in some sense, \textit{not complete}

        Those who are familiar with Maxwell's Equations know by heart that Electrodynamics is a beautifully
        \textit{complete} and successful theory. It has become a king of paradigm for physicists: an ideal model that
        other theories strive to emulate.

        Studying Electromagnetism is same thing as studying the standard model of Physics which shall guide my study of
        General Theory of Relativity.
    \end{tcolorbox}

    \chapter{Mathematics}
    \input{parts/electromagnetism/mathematics}
    \input{parts/electromagnetism/gauss}
\end{document}