Links to use with Newer Math, summer 2004

Page Topic (with link)
iThe title, Newer Math, refers to an instructional fad called "New Math". What was the "new math"? Here are the lyrics to Tom Lehrer's song, New Math.
i Who was G. H. Hardy?
i Who was Richard W. Hamming?
iiWho was Carl Jung?
1Who was Benjamin Franklin?
1Who is Lawrence Lessig?
2Discussion of the RSA patent
4Lagrange interpolation: This reference states, "The formula was first published by Waring (1779), rediscovered by Euler in 1783, and published by Lagrange in 1795."
10Here's a description of how the Euclidean algorithm can solve ax=b mod c. And here's an online "visual" realization of the Euclidean algorithm by Paul Garrett.
14Here's another reference, a whole book available on the web: The Handbook of Applied Cryptography. S. Landau wrote in a recent review (July, 2004, Bulletin of the AMS) of many crypto books, "If I were limited to only one cryptography text on my shelves, it would be the Handbook of Applied Cryptography".
15Here is a list of cryptography "maxims", or rules, including the most famous, Kerckhoff's maxim. This link goes to a copy of the original articles by Kerckhoffs and lists all six of Kerckhoff's design principles.
17 More recent developments in the factorization of RSA challenge numbers can be found here . Thanks to S. Radomirovic for sending me this link.
17Here is a brief description by S. Landau of some attacks on RSA. And here is D. Boneh's comprehensive article entitled Twenty Years of Attacks on the RSA Cryptosystem.
19The original RSA paper ( A method for obtaining digital signatures and public-key cryptosystems) is available in PDF or Postscript versions. You can also see what Rivest is up to recently. A few weeks ago I heard a very interesting talk he gave about the prospects and problems of electronic voting.
19Adelman and Rivest and Shamir jointly won the 2002 Turing Award (a computer science Nobel prize). Here are their presentations as they accepted the award.
19A sketch of The Prehistory of Public Key Cryptography.
21Discussion of the nature of a sonnet.
25The prize: One million dollars and P vs NP.
An essay by a Rutgers first year student, J. Palumbo, written in fall 2003, about Minesweeper as an example of P vs NP, .
26The pure, the beautiful, the original ... Euclid
25 & 27 PRIMES is in P
27DNA Computing , a way to use molecular biology to develop highly parallel computation
27Information about quantum computing
35The original Diffie-Hellman paper, New Directions in Cryptography.
37Random numbers
38A short history of probability
39Who was Goethe?
47 Here's a formal proof of the Binomial Theorem.
54Here is the text, so far, of Probability on Trees and Networks by Russell Lyons and Yuval Peres. Peres also has several recent papers (written in the last two years) analyzing "games" like JvN and NvJ: these things are not so simple!
58 M & M colors
64 Brief information about Ramsey numbers (perhaps already more than you must know!). But even more information is available.
Ramsey games: "games" coloring edges of graphs. The strategies and goals originate in Ramsey theory.
67 A little bit about Erdös. -- for more, consult one of the biographies mentioned.
68 The structure and function of complex networks by Mark Newman, and some pictures of networks.
68 Mapping the internet

Maintained by and last modified 6/21/2004.