數學文獻搜尋

常用連結

• arXiv
• 國立中山大學圖書館
• 國立中山大學應用數學系圖數館 介紹影片
• 數學圖書期刊計畫—館際合作服務
• MathSciNet
• Mathematics Genealogy
• Overleaf
• Zotero
• AMS Journal Abbreviation
• 2010 Mathematics Subject Classification
• Journal Citation Reports - Clarivate

Copyright

• Everything is owned by someone –- being online
  $\ne$ you can share, print, redistribute, or sell
• A sentence / paragraph without citation
  $⟹$ plagiarism

Exercise

The following picture is from Wikipedia: Linear Algebra.

(Source: Wikipedia: Linear Algebra)

• Find the author of the picture.
• Find the copyright license.
• What do you need to be aware of if you use this picture?

Search for a term

• Google: Wikipedia, book, paper
• 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
• 國立中山大學應用數學系圖數館 介紹影片
• 數學圖書期刊計畫—館際合作服務
• 國立中山大學圖書館

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

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
• Collaboration distance

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" now.
• Find the collaboration distance between Shing-Tung Yau and Albert Einstein.

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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 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; see an example here

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.