This insightful Guide is meant to serve any and all interested in pursuing a career in mathematics education and research. The authors goal and the books 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 authors own observations and on techniques she has found effective.
Mathematics graduate students and those in related fields will find assistance to help them reflect on and advance their career pursuits. Advisors and mentors might also find useful suggestions here.
| Preface |
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ix | |
| Biography |
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xi | |
| Introduction |
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xiii | |
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Part I Teaching and Conducting Research |
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1 | (80) |
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3 | (14) |
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2 Research and the Publication Process |
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17 | (12) |
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3 Conferences and Collaborations |
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29 | (12) |
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4 Transition to Reading and Writing Research Papers |
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41 | (10) |
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4.1 Common words and Expressions for a Mathematics Research Paper |
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48 | (3) |
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5 Preparing Documents in Latex |
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51 | (30) |
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51 | (4) |
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5.2 Typing the Main Content |
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55 | (11) |
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66 | (1) |
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67 | (3) |
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70 | (2) |
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5.6 Beamer for Presentations |
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72 | (9) |
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Part II Modern Applications in Industry |
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81 | (126) |
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6 Schrodinger Equation in Laser Technology |
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83 | (46) |
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6.1 Schrodinger Equation Modeling Laser Propagation |
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87 | (11) |
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98 | (19) |
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117 | (6) |
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123 | (6) |
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129 | (32) |
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7.1 Spectrum of the Google Matrix |
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131 | (6) |
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7.2 Computing the PageRank |
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137 | (10) |
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7.3 Improving the PageRank |
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147 | (7) |
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154 | (7) |
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7.4.1 Stochastic Processes |
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154 | (1) |
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7.4.2 Markov Process and Markov Chain |
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155 | (1) |
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7.4.3 Properties of Markov Chains |
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155 | (1) |
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7.4.4 Types of Markov Chains |
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156 | (1) |
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7.4.5 Computing the Transition Probabilities |
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157 | (1) |
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7.4.6 Stationary Probability Distribution |
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158 | (3) |
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8 Stochastic Navier-Stokes Equations in Fluids |
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161 | (46) |
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8.1 Stochastic Navier Stokes Equation |
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168 | (12) |
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180 | (11) |
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8.3 Large Deviations for Stochastic Navier Stokes Equation |
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191 | (10) |
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201 | (6) |
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8.4.1 Brownian Motion, Levy Process and Random Walk |
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201 | (1) |
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8.4.2 Applications of large deviations |
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202 | (5) |
| Index |
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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.
