To me, Distance, Space and Time are the ever-most important ingredients for mathematical based sciences and mathematics itself at the most. Every human being know and understand mathematics according to their needs and careers. There may be fundamental keys for other areas for example Machine learning is based on discriminant analysis or finding roots of the linear/nonlinear equations or finding first derivative of the model/function, equating it to zero and finding roots or optimal points at the given domain.
Dear RG members on individual specificity bases may you describe the fundamental keys/pillars of your research areas? (For similar example, as I described above for mathematics and machine learning. You may explain your answers more explicitly please!!!
Dear Muhammad Ali
It is a very general question. Distance, space and time, etc. is equivalent to define the suitable manifold structure and atlas charts that are the best to describe the environment (Universe) of your mathematical model. Concerning the question about the set of the fundamentals, say {F} that are needed to study the field or topic P. In general, the essential tools of mathematics like calculus, linear algebra, differential equations, and the undergraduate elementary mathematics are strongly needed in almost all branches of sciences. But for some specific topics, special preliminaries are needed too. Examples: (1) General topology is a prerequisite of Algebraic or differential topology. (2) Multivariable calculus is a prerequisite for optimization theory. (3) Advanced Matrix theory is strongly recommended as a prerequisite to study the dynamical systems and control theory. (4) Group theory is needed to understand Galois theory. (5) Probability theory is a must for decision making. Etc. Best regards
Dear Issam Kaddoura,
Thank you very much, for replying to this discussion. I much appreciate your comments.
With Best Regards.
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