Prof. Dr. Marian Mureşan

Prof. Dr. Marian Mureşan

I am a dreamer. A naïve dreamer. I am a naïve and optimistic dreamer. This combination can be lethal for a man. And still, I navigate through life with these talents.

I send a grateful thought to teacher Neculae Cojocaru and Professor Tiberiu Popoviciu.

Over the years, I’ve been fascinated by various mathematics and computer science problems. I think a considerable part of my activity has been the intertwinement between pure mathematics, applied mathematics and software development. Throughout the years, I have explored these passions in various publications.

Inspired by Professor T. Popoviciu’s suggestion I studied the minimum number of multiplications needed to calculate the value of a fundamental polynomial of the interpolation polynomial of Lagrange[1] and the best bounds for successive permutations[2].

I began my career (under the laws back then) at a territorial calculation center in Cluj-Napoca, Romania and worked on some interesting programs written in assembly language[3]. Around the same time, my interest was sparked by problems relating to burning in an axial-symmetric combustion chamber and Navier-Stokes equations. The programs in question were written in FORTRAN.

My interest towards the Fubini numbers materialized in publications [8], [11] and [18].

For a long period of time I was fascinated by a few qualitative problems regarding differential equations, mostly the 16th problem of D. Hilbert regarding limit cycles. This interest is also reflected in publications [13], [14], [15], [16], [17], [19], [20], [21], [22], [25], [26], [28], [29], [32], [37], [39], [41] and [45]. My best publications on this list are [37], [41] and [45].

For another period of time I investigated different types of numerical integration methods of differential equations (implicit, semi-explicit and reduced number of evaluations at every step). Publications [23], [24] and [27] reflect this interest.

A lot of qualitative aspects of the differential inclusions were studied in publications [30], [31], [33], [34], [35], [36], [38], [40] and [48]. My best publications around this topic are [34], [35] and [40].

My fascination for applications of various economics problems is explored in publications [42], [43], [46], [47], [49] and [50].

The controllability of differential equations and differential inclusions is an important subject relating to optimal control and to the qualitative theory of differential inclusions. See publications [44], [48], [51], [53] about this topic, particularly number [52].

A fascinating topic is the approximation of multifunctions and my interest in this topic is highlighted in publications [54] and [55].

A new method of studying classic and modern problems involves using calculation and graphics software. I’ve opted for the Mathematica® package and using this software I wrote a study about the problem of brachistochrone curves with/without friction and with/without initial velocity as well as the problem of moon landing in certain conditions. Publications [56], [57], [58] and [59] look at this issue in more detail.

Out of all the books I’ve written so far, the one that brought me the most satisfaction was the last one, publication [9] in the List of books. The title of the book contains the word ‘concrete’.  Approximately 20 years ago, Concrete Mathematics was published, by L. Graham, D. E. Knuth and O. Patashnik, Addison-Wesley, 1994. This book underlines the necessity of a vision regarding concrete aspects of mathematical analysis. The book contains a lot of competition level problems, combinations related to the calculation of pi (the BBP method and others), the W-Z method, algorithm analysis and many others. With my book, I wanted to demonstrate that a first year maths or computer science student can tackle problems that might seem difficult at first sight. Now I am hoping to finish the second edition, which will have many more applications and will rely more on the use of the Mathematica® software.

Because I am a naïve and optimistic dreamer, I hope to make progress in the writing of a book about variation calculus and optimal control. The book will comprise of a few chapters relating to smooth and a few chapters relating to nonsmooth aspects. I am also hoping that many if not all problems will have calculations and figures made with Mathematica®.

[1] A combinatorial problem connected to the Lagrange interpolation polynomial, in T. Popoviciu, Numerical Analysis. Introductory Notions of Approximative Calculus, Editura Academiei RSR, 1975, p. 190, Romanian

[2] Best evaluations to the lower and upper bounds of the number of successive permutations satisfying a minimum condition, in my Master thesis, Cluj, 1975, Romanian

[3] (2, 3, 4 and 7 in the Publications list)