Formal letter

Dear teacher, could you please currect this letter? Thank you so much.

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Dear Dr. Ronald Gil,

I would like to express my interest in the PhD position in differential equations and branching processes at the Faculty of Science , in the Mathematical Institute of the Department of Mathematics, at AB University.

I am particularly eager to contribute to this project because it perfectly aligns with my plans to continue my education and pursue a career in the area of partial differential equations (PDEs) and probabilities. In particular, my research would be investigate how nonlinear PDEs may be studied by complex stochastic processes, which make possible to quickly calculate challenging Bayesian perspective.

While studying for my BA in mathematics at the +++ University in [country], I took courses in statistics probabilities (I, II) and learned fundamental concepts. Thereafter, I was admitted to the +++ University, [sity] branch for my MSc, in Applied Mathematics- Numerical Analysis. My master's thesis, under the supervision of Dr. Rab, was on "Using mathematical techniques for solving Fokker-Planck equations" which gave me a deeper knowledge of stochastic process, PDEs and probability theory. By solving the Fokker- Planck equation, a probability distribution function is obtained. Extracting and solving this equation requires knowledge of stochastic processes, brownian motion and probability theory, On the other hand, courses like "Numerical Methods for Integral Equations" and "Numerical Method for Ordinary Differential Equations " with a high grade and the methods I learned, give me more efficient knowledge of solutions of linear differential equations and linear partial differential equations. Given that I learned some methods of solving linear differential equations during my master's degree, I am very interested in pursuing my PhD in researching new methods of solving nonlinear differential equations and expanding my knowledge in this field. Furthermore, I have always been interested in interdisciplinary activities and researching solutions to real-world problems and problems in physics by using mathematical algorithms be appeals to me.

I now wish to advance my academic career in the international environment and I cannot imagine a better be place to study than the AB University, at the Faculty of science that there are 6 departments to make a fundamental connection with: Biology, Chemistry, Information and Computing Sciences, Mathematics, Pharmaceutical Sciences, and Physics, six disciplines, Combined, they reinforce each other and are the driving force behind the technology we use in our daily lives. In my opinion, it is the ideal place to do interdisciplinary projects.

Considering the content of the master's thesis, combined with knowledge I have stocked from my previous studies, I am confident that I can do the research project successfully. I recognise the importance of studying this field. I believe that these skills and experience will allow me to effectively complete a larger-scale project such as a PhD.

After completing the PhD, I intend to pursue a postdoc in stochastic processes. With a lifelong interest in nonlinear differential equation, I am keen to continue my education in this area and to perform my own research in order to help extend the knowledge in this field. Thank you so much for considering my application.

Yours sincerely,

Mona Mi