@article{chayes2013mathematics,
  abstract = {Dr Chayes’ talk described how, to a discrete mathematician, ‘all the world’s a graph, and all the people and domains merely vertices’. A graph is represented as a set of vertices V and a set of edges E, so that, for instance, in the World Wide Web, V is the set of pages and E the directed hyperlinks; in a social network, V is the people and E the set of relationships; and in the autonomous system Internet, V is the set of autonomous systems (such as AOL, Yahoo! and MSN) and E the set of connections. This means that mathematics can be used to study the Web (and other large graphs in the online world) in the following way: first, we can model online networks as large finite graphs; second, we can sample pieces of these graphs; third, we can understand and then control processes on these graphs; and fourth, we can develop algorithms for these graphs and apply them to improve the online experience.},
  author = {Chayes, Jennifer},
  doi = {10.1098/rsta.2012.0377},
  eprint = {http://rsta.royalsocietypublishing.org/content/371/1987/20120377.full.pdf+html},
  interhash = {3993b23ca636e9fb8497a1e918be7acf},
  intrahash = {3f77f26601231ba891aa65a702b8c867},
  journal = {Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  number = 1987,
  title = {Mathematics of Web science: structure, dynamics and incentives},
  url = {http://rsta.royalsocietypublishing.org/content/371/1987/20120377.abstract},
  volume = 371,
  year = 2013
}

@article{dudley1983trisector,
  address = {New York},
  author = {Dudley, Underwood},
  interhash = {1bd2d0854c76b9070e6b9a1c81909c0d},
  intrahash = {1f7857c3d17534019af8dcbb6494fe6e},
  journal = {The Mathematical Intelligencer},
  number = 1,
  pages = {20--25},
  publisher = {Springer-Verlag},
  title = {What To Do When The Trisector Comes},
  volume = 5,
  year = 1983
}

@article{hoffman1987loves,
  abstract = {Paul Erdös is certainly the most prolific - and probably the most eccentric - mathematician in the world.},
  author = {Hoffman, P.},
  interhash = {2ddef33fea560e77d5bfab5b6a221bf8},
  intrahash = {947cc4cf4cbfdd3df48916237c7cd694},
  journal = {The Atlantic Monthly},
  month = nov,
  pages = {60--74},
  title = {The man who loves only numbers},
  url = {http://www.jcu.edu/math/Faculty/Shick/erdos.pdf},
  year = 1987
}

@book{feller1968introduction,
  address = {New York},
  author = {Feller, William},
  interhash = {5913bc93a52c1fad7ce8b0993debf407},
  intrahash = {cf464e5e44fbad2b68e11a80cbded06e},
  isbn = {0-471-25708-7},
  publisher = {Wiley},
  title = {An introduction to probability theory and its applications},
  url = {http://opac.bibliothek.uni-kassel.de/DB=1/PPN?PPN=177850175},
  year = 1968
}

@incollection{ganter1998stepwise,
  abstract = {Lattices are mathematical structures which are frequently used for the representation of data. Several authors have considered the problem of incremental construction of lattices. We show that with a rather general approach, this problem becomes well-structured. We give simple algorithms with satisfactory complexity bounds.},
  address = {Berlin/Heidelberg},
  author = {Ganter, Bernhard and Kuznetsov, Sergei},
  booktitle = {Conceptual Structures: Theory, Tools and Applications},
  doi = {10.1007/BFb0054922},
  editor = {Mugnier, Marie-Laure and Chein, Michel},
  interhash = {6ab4d800575b90bf787ade575b38994b},
  intrahash = {0c986e520647b86c202633cc6945d524},
  isbn = {978-3-540-64791-1},
  pages = {295--302},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {Stepwise construction of the Dedekind-MacNeille completion},
  url = {http://dx.doi.org/10.1007/BFb0054922},
  volume = 1453,
  year = 1998
}

@book{ganter1999formal,
  abstract = {This is the first textbook on formal concept analysis. It gives a systematic presentation of the mathematical foundations and their relation to applications in computer science, especially in data analysis and knowledge processing. Above all, it presents graphical methods for representing conceptual systems that have proved themselves in communicating knowledge. Theory and graphical representation are thus closely coupled together. The mathematical foundations are treated thoroughly and illuminated by means of numerous examples.},
  address = {Berlin/Heidelberg},
  author = {Ganter, Bernhard and Wille, Rudolf},
  interhash = {1b0bf49069eadcdfac42e52addf4eb9d},
  intrahash = {ae14b00b5489de8da6e4578ac3062bfc},
  publisher = {Springer},
  title = {Formal Concept Analysis: Mathematical Foundations},
  year = 1999
}

@book{knuth1989concrete,
  address = {Reading},
  author = {Graham, Ronald L. and Knuth, Donald E. and Patashnik, Oren},
  interhash = {a1450d7bb87f0107150d43a314a88326},
  intrahash = {ccef670ef39186763ecd379d2cca1e0a},
  publisher = {Addison-Wesley},
  title = {Concrete Mathematics: A Foundation for Computer Science},
  year = 1989
}

@book{MacKenzie,
  abstract = {Most aspects of our private and social lives -- our safety, the integrity of the financial system, the functioning of utilities and other services, and national security -- now depend on computing. But how can we know that this computing is trustworthy? In Mechanizing Proof, Donald MacKenzie addresses this key issue by investigating the interrelations of computing, risk, and mathematical proof over the last half century from the perspectives of history and sociology. His discussion draws on the technical literature of computer science and artificial intelligence and on extensive interviews with participants.

MacKenzie argues that our culture now contains two ideals of proof: proof as traditionally conducted by human mathematicians, and formal, mechanized proof. He describes the systems constructed by those committed to the latter ideal and the many questions those systems raise about the nature of proof. He looks at the primary social influence on the development of automated proof -- the need to predict the behavior of the computer systems upon which human life and security depend -- and explores the involvement of powerful organizations such as the National Security Agency. He concludes that in mechanizing proof, and in pursuing dependable computer systems, we do not obviate the need for trust in our collective human judgment.},
  author = {MacKenzie, Donald},
  interhash = {f08e669708b78682b3102f298632372b},
  intrahash = {3ea6b663f1ba9a440b352c887e1173cf},
  isbn = {978-0-262-13393-7},
  month = {October},
  publisher = {The MIT Press},
  title = {Mechanizing Proof:
Computing, Risk, and Trust},
  url = {http://mitpress.mit.edu/catalog/item/default.asp?tid=8635&ttype=2},
  year = 2001
}