---
tags: tutorial
---

# 數學文獻搜尋

## 常用連結
- [arXiv](https://arxiv.org/)
- [國立中山大學圖書館](https://lis.nsysu.edu.tw/)
- [數學研究推動中心](https://web.math.sinica.edu.tw/mrpcwww/periodicalservice_19.php)
- [MathSciNet](https://mathscinet.ams.org/mathscinet)
- [Mathematics Genealogy](https://www.genealogy.math.ndsu.nodak.edu/)
- [Overleaf](https://www.overleaf.com/)
- [AMS Journal Abbreviation](https://mathscinet.ams.org/msnhtml/serials.pdf)
- [2010 Mathematics Subject Classification](https://mathscinet.ams.org/msc/msc2010.html)
- [~~Journal Citation Reports - Clarivate~~](https://jcr.clarivate.com/)

## Copyright
- Everything is owned by someone --- being online $\neq$ you can share, print, redistribute, or sell
- A sentence / paragraph without citation $\implies$ plagiarism

##### Exercise
The following picture is from [Wikipedia: Linear Algebra](https://en.wikipedia.org/wiki/Linear_algebra).
(Source: [Wikipedia: Linear Algebra](https://en.wikipedia.org/wiki/Linear_algebra))
- Find the author of the picture.
- Find the copyright liscense.
- What do you need to be aware of if you use this picture?

## Search for a term
- Google: Wikipedia, book, paper
- [MathSciNet](https://mathscinet.ams.org/mathscinet): book, paper

##### Exercise
- What is a *unimodular* matrix?
- Give me an example and a counterexample of a unimodular matrix.
- What is a *totally unimodular* matrix?
- Give me an example and a counterexample of a totally unimodular matrix.

##### Exercise
- What is *Sylvester's law of inertia*?
- What is the meaning of "*congruent*"?
- Find all congruent matrices of the identity matrix.

## Search for a paper
- Journal website
- [arXiv](https://arxiv.org/)
- [國立中山大學圖書館](https://lis.nsysu.edu.tw/)
- [數學研究推動中心](https://web.math.sinica.edu.tw/mrpcwww/periodicalservice_19.php)

##### Exercise
- Find [1] on journal's website. Is this the first paper that introduced the notion of *Braess' paradox for graphs*? If not, which is the first paper?
- Find [2] and describe the eigenvalue--eigenvector identity. Can you find the source file(s)?

[1] Lorenzo Ciardo. The Braess' paradox for pendent twins. *Linear Algebra and its Applications*. 590:304--316, 2020.
[2] Peter B. Denton, Stephen J. Parke, Terence Tao, and Xining Zhang. Eigenvectors from Eigenvalues: a survey of a basic identity in linear algebra. *arXiv:1908.03795*.

## Search the papers of a person
- Personal website
- [MathSciNet](https://mathscinet.ams.org/mathscinet)

##### Exercise
- How many paper does "the" Euler have according to MathSciNet?
- Think about your potential advisor. Search for his/her publications.

## Know more about someone
- Personal website
- [Mathematics Genealogy](https://www.genealogy.math.ndsu.nodak.edu/)
- [Collaboration distance](https://mathscinet.ams.org/mathscinet/collaborationDistance.html)

##### Exercise
- Suppose you want to study aboard and work with Professor Steve Butler at Iowa State University. Find his website and check how many PhD students have graduated under his guidance.
- If you want to work with someone, you'd better know more about the person's research. Once you've found your potential advisor's publications, find keywords that you found interested --- if you don't understand something, remember you know how to "[Search for a term](#Search-the-papers-of-a-person)" now.
- Find the collaboration distance between Shing-Tung Yau and Albert Einstein.

---

## The bibliography
- Whenever you quote, apply, or mention results of others, make sure to add proper citation and give credit to the authors.
- Different journals (and NSYSU thesis) have different citation style.
- Most of math paper lists the references in alphabetical order.

##### Exercise
- Find one or two papers and look at their references/bibliography. See what information are contained in each cited item (e.g., title, author(s), etc.).
- Visit [國立中山大學論文查詢系統](https://etd.lis.nsysu.edu.tw/eThesys/index.php) and look for one or two thesis from our department (e.g., 楊宗穎 or 梁育菖). See what information are contained in each cited item (e.g., title, author(s), etc.). Compare the style a NSYSU thesis with those you found earlier.

## $\LaTeX$ bibliography
- [Overleaf](https://www.overleaf.com/); see an example [here](https://www.overleaf.com/read/ggdcqmppqfqm)

Knuth's \TeX{} book \cite{texbook} is a wonderful reference for learning \TeX{}, a typesetting program.  For drawing pictures using TikZ, one may refer to the manual \cite{tikz}.

\begin{thebibliography}{9}
\bibitem{texbook} D. Knuth.  \emph{The \TeX{}book}.  Reading, Massachusetts: Addison-Wesley, 1984.
\bibitem{tikz} Till Tantau.  \emph{The TikZ and PGF Packages Manual}.  Available on CTAN.
\end{thebibliography}

##### Exercise
- Typeset the following by $\LaTeX$.

I love linear algebra. There are many elegant formulas in linear algebra, for example, the eigenvalue--eigenvector identity surveyed in [2]. It is also very powerful. Ciardo [1] uses linear algebra to study the Braess' paradox for pendent twins.

[1] Lorenzo Ciardo. The Braess' paradox for pendent twins. *Linear Algebra and its Applications*. 590:304--316, 2020.
[2] Peter B. Denton, Stephen J. Parke, Terence Tao, and Xining Zhang. Eigenvectors from Eigenvalues: a survey of a basic identity in linear algebra. *arXiv:1908.03795*.

## BibTeX
- BibTeX is a program that help you to generate the reference.
- You need a `bib` file as a database for your references. Here is an example of `my_ref.bib`.

@misc{DPTZ19,
    author    = "Peter B. Denton and Stephen J. Parke and Terence Tao and Xining Zhang",
    title     = "Eigenvectors from {E}igenvalues: a survey of a basic identity in linear algebra",
    howpublished = "arXiv:1908.03795",
}

@article{Ciardo20,
    author    = "Lorenzo Ciardo",
    title     = "The {B}raess' paradox for pendent twins",
    journal   = "Linear Algebra and its Applications",
    volume   = "590",
    pages    = "304--316",
    year      = "2020",
}

- In your `tex` file, replace the `thebibliography` environment by the following.

\bibliographystyle{plain}
\bibliography{my_bib}

##### Exercise
- Do the previous exercise by BibTex.