Teaching and Research in Mathematics

Parisa Fatheddin is a senior lecturer at the Ohio State University, Marion, where she teaches various courses and conducts research in Mathematics. Her main area of research is stochastic partial differential equations, in which she has contributed to the literature by publishing results on stochastic Navier-Stokes and Schrodinger equations in well-established journals in stochastic Analysis. Dr. Fatheddin is also active in research in applied fields such as in optics and cyber security. As a visiting assistant professor at the Air Force Institute of Technology, she became involved in an optics laboratory and made a publication on her research results in the journal of Optics Communications. She also held a visiting position at the University of Pittsburgh, where she collaborated with well-known mathematicians in fluid dynamics and taught many courses. In the field of cyber security, Dr. Fatheddin has contributed a chapter to the textbook, Mathematics in Cyber Research, explaining modern research that use differential equations to model the spread of computer virus. Dr. Fatheddin has taught for ten years and continues to help undergraduate and graduate students find their purpose in studying Mathematics.

Part I: Teaching and Conducting Research. 1. Teaching. 2. Research and the Publication Process. 3. Conferences and Collaborations. 4. Transition to Reading and Writing Research Papers. 5. Preparing Documents in Latex. Part II: Modern Applications in Industry. 6. PageRank in Google. Spectrum of the Google Matrix. Computing the PageRank. Improving the PageRank. Appendix. 7. Schrodinger Equation in Laser Technology. Schrodinger Equation Modeling Laser Propagation. Optimal Control. Phase Screens. Appendix. 8. Stochastic Navier-Stokes Equation in Fluids. Stochastic Navier-Stokes Equation. Large Deviations. Large Deviations for Stochastic Navier-Stokes Equation. Appendix.