Nobua Yoneda was a Japanese mathematician and computer scientist (1930-1996) from whom the famed Yoneda Lemma gets its name. It is ultimately a grand generalization of Cayley's Theorem in group theory.
His doctoral advisor was Shokichi Iyanaga. Iyanaga in turn studied under Teiji Takagi who was instrumental in developing Japanese encryption systems in World War 2.
He has done work on dialects of ALGOL (formerly known as International Algebraic Language, or IAL).
The Farey series gets its name from British geologist Farey.
It is notable that a geologist had such an impact on the theory of numbers.
In 1816, Farey published a statement that the middle of three successive terms is the "mediant" of the other two.
The proof was supplied by Cauchy (or Baron Augustin-Louis Cauchy, to give him his full title).
Studies of nonlinearity often bring us to the badlands between physics and mathematics.
One such exponent is Professor Pierre Raphael who specializes in the study of nonlinear waves.
Pierre Raphael joined Cambridge's Department of Pure Mathematics and Mathematical Statistics (DPMMS) in 2019. He has a PhD from Cergy Pontoise (since January 2020 known as CY Cergy Paris university).
At Cambridge, PR is the Herchel Smith Professor of Pure Mathematics (named after organic chemist Herchel Smith who was an undergraduate at Emmanuel College, Cambridge).
Super-able mathematical expositors are valuable to PyCryptos requiring mathematical intuition to be ingested speedily in order to achieve success in algorithmic implementation.
Examples of such worthy expositors include:
Walter Warwick Sawyer - lots of good essays and expository book on Numerical Functional Analysis. Essays include "AMA Revisted".
Harold Edwards - lots of good essays and expository book on Riemann Zeta Function (1974)
An article slightly tangential to natural language processing but provides useful background considerations to PyCryptos operating in this space, as well as to programmers designing conversational interfaces, is this article on how phrasing affects memorability. Cornell professor Jon Kleinberg co-authors.
Arithmetic dynamics is a fascinating area which amalgamates number theory and dynamical systems. Number-theoretic properties of integer points (and integral-related points e.g. rational points) under the repeated application of an algorithmic rule that expresses a polynomial or rational function are studied. Joseph Silverman from Brown University is one of the field's exponents.
It is not difficult to understand the need for and the objective of the calculus of variations.
The classical brachistochrone problem and the isoperimetric problem associated with Dido of Carthage are cases in point.
However, the prerequisites for competency are not as apparent.
A suggested list of pre-competencies are listed below.
An nonpareil familiarity with function spaces is essential to make the theoretical arguments stick. One can even say that function spaces are the biosphere in which the calculus of variations exists and flourishes.
If you don't live and breathe function spaces you may find the journey down the road of calculus of variations somewhat tough.
We can start with a simple example of C[0,1] as a warm-up example. This is the set of all functions defined and continuous on the closed interval bounded by 0 and 1.
