If someone thinks that computational mathematics is a specialization that has been studied enough, then you can argue with him. Let such an opinion exist, because it is still not fundamental.
Computational mathematics is a field of mathematical science, the subject of which is the development and research of approximate methods and algorithms for the numerical solution of problems of mathematics and its applications.
For a thesis on computational mathematics, you can take a whole list of topics that have been touched to one degree or another and are currently interesting:
1. The theory of approximate methods and numerical algorithms for solving problems of algebra, differential and integral equations, problems of discrete mathematics, extremal problems, control problems, ill-posed problems of other problems of linear, nonlinear and stochastic analysis.
2. Theory and methods of parallel computing.
3. Numerical methods and algorithms for solving applied problems arising from the mathematical modeling of natural science, scientific, technical, social and other problems.
- mathematical analysis;
- differential equations;
- Theory of Probability and Mathematical Statistics;
- discrete mathematics and mathematical cybernetics;
- mathematical modeling, numerical methods and program complexes.
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