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E-grāmata: Teaching and Research in Mathematics: A Guide with Applications to Industry

(Ohio State University, Marion)
  • Formāts: 222 pages
  • Izdošanas datums: 26-Aug-2022
  • Izdevniecība: Chapman & Hall/CRC
  • Valoda: eng
  • ISBN-13: 9781000604672
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  • Formāts: 222 pages
  • Izdošanas datums: 26-Aug-2022
  • Izdevniecība: Chapman & Hall/CRC
  • Valoda: eng
  • ISBN-13: 9781000604672
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"This insightful Guide is meant to serve any and all interested in pursuing a career in mathematics education and research. The author's goal and the book's theme is to help students and others make a smooth transition to teachers and researchers of mathematics. Part I presents helpful techniques on teaching and conducting research. This innovative book also offers strategies on how to observe from and develop research methods, carry out research, and begin writing research papers. It includes an introduction to LaTeX, the most widely used mathematics typesetting and rendering computer program. Part II introduces some modern research in mathematics in various industries. The aim in is to expose the reader to modern applications and help him/her become acquainted with research papers and how to read and understand them. Authored by a young teacher and researcher, also beginning her career, this book is written by and for young mathematicians. Most graduate students as she experienced, are not given a proper transitory introduction to research and are not taught the "how" in teaching, attending conferences and collaborating. The book is based on the author's own observations and on techniques she has found effective. Mathematics graduate students and thosein related fields will find assistance to help them reflect on and advance their career pursuits. Advisors and mentors might also find useful suggestions here"--

The author's goal is to help the transition from graduate studies and make it less diffcult and time-consuming. Part I covers techniques on teaching and conducting research and in Part II, the author has introduced some modern research in mathematics in various industries.
Preface ix
Biography xi
Introduction xiii
Part I Teaching and Conducting Research
1(80)
1 Teaching
3(14)
2 Research and the Publication Process
17(12)
3 Conferences and Collaborations
29(12)
4 Transition to Reading and Writing Research Papers
41(10)
4.1 Common words and Expressions for a Mathematics Research Paper
48(3)
5 Preparing Documents in Latex
51(30)
5.1 The Beginning Code
51(4)
5.2 Typing the Main Content
55(11)
5.3 Inserting Pictures
66(1)
5.4 References
67(3)
5.5 Dissertations
70(2)
5.6 Beamer for Presentations
72(9)
Part II Modern Applications in Industry
81(126)
6 Schrodinger Equation in Laser Technology
83(46)
6.1 Schrodinger Equation Modeling Laser Propagation
87(11)
6.2 Optimal Control
98(19)
6.3 Phase Screens
117(6)
6.4 Appendix
123(6)
7 PageRank in Google
129(32)
7.1 Spectrum of the Google Matrix
131(6)
7.2 Computing the PageRank
137(10)
7.3 Improving the PageRank
147(7)
7.4 Appendix
154(7)
7.4.1 Stochastic Processes
154(1)
7.4.2 Markov Process and Markov Chain
155(1)
7.4.3 Properties of Markov Chains
155(1)
7.4.4 Types of Markov Chains
156(1)
7.4.5 Computing the Transition Probabilities
157(1)
7.4.6 Stationary Probability Distribution
158(3)
8 Stochastic Navier-Stokes Equations in Fluids
161(46)
8.1 Stochastic Navier Stokes Equation
168(12)
8.2 Large Deviations
180(11)
8.3 Large Deviations for Stochastic Navier Stokes Equation
191(10)
8.4 Appendix
201(6)
8.4.1 Brownian Motion, Levy Process and Random Walk
201(1)
8.4.2 Applications of large deviations
202(5)
Index 207
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.