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Note 1: Wikipedia states that Lagrange's "academic advisor" (in what sense is unclear if there was no dissertation) was Leonhard Euler, whose advisor was Johann Bernoulli; the line continues back as Jacob Bernoulli (his brother), Gottfried Leibniz (the co-inventor of calculus seems to have done two theses in philosophy and law) and Erhard Weigel (mathematician, astronomer and philosopher, 1625-1699) where the line seems to end. Euler was one of the most prolific mathematicians in history and the inventor of graph theory in his famous solution to the Konigsberg bridges problem (1736). According to Barabasi, this initiated the subject of networks; Lagrange and Euler could not be better ancestors for work in dynamic networks.
Note 2: The date for a dissertation is not clear. From http://www-history.mcs.st-andrews.ac.uk/Biographies/Fourier.html: "Later in 1794 Fourier was nominated to study at the Ecole Normale in Paris. He was taught by Lagrange, who Fourier described as the first among European men of science, and also by Laplace, who Fourier rated less highly, .... In 1797 he succeeded Lagrange in being appointed to the chair of analysis and mechanics.... he does not appear to have undertaken original research during this time....It was during his time in Grenoble that Fourier did his important mathematical work on the theory of heat. His work on the topic began around 1804 and by 1807 he had completed his important memoir On the Propagation of Heat in Solid Bodies. The memoir was read to the Paris Institute on 21 December 1807 and a committee consisting of Lagrange, Laplace, Monge and Lacroix was set up to report on the work. Now this memoir is very highly regarded but at the time it caused controversy. ....The first objection, made by Lagrange and Laplace in 1808, was to Fourier's expansions of functions as trigonometrical series, what we now call Fourier series. Fourier was elected to the Academie des Sciences in 1817... the Academie published his prize winning essay Theorie analytique de la chaleur in 1822. (This is referred to as a book elsewhere.) It seems 1807 is the most likely year for a dissertation.
Note 3: Wikipedia lists Simeon Poisson as a second advisor. Poisson's advisor is unclear but may be taken as Lagrange: "This success at once procured for Poisson an entry into scientific circles. Joseph Louis Lagrange, whose lectures on the theory of functions he attended at the Ecole Polytechnique, early recognized his talent, and became his friend (the Mathematics Genealogy Project lists Lagrange as his advisor, but this may be an approximation); while Pierre-Simon Laplace, in whose footsteps Poisson followed, regarded him almost as his son."
Note 4: Wikipedia states that he had a second supervisor, Julius Plucker, from whom the line continues back mostly in German mathematics through Christian Gerling (physics, astronomy), notably Carl Friedrich Gauss (arguably the founding father for signals and systems ideas used in EE) and then Johan F Pfaff and Abraham Kastner (1719-1800); there is no article about Kastner's advisor, given as Christian Hausen.
I was admitted to University of Sydney, Australia, in 1995. Prof. David Hill was my Ph.D. advisor. David was also the Head of School of Electrical and Information Engineering during my study. I was supported by the Overseas Postgraduate Research Scholarship (OPRS) from Australian Government. I obtained my Ph.D. degree in 1999.
Special thanks to Prof. Dvid Hill for providing this information to me in 2007.