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

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 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.

Table of Contents

Part I: Teaching and Conducting Research

Teaching

Research and the Publication Process

Conferences and Collaborations

Transition to Reading and Writing Research Papers

Preparing Documents in Latex

Part II: Modern Applications in Industry

PageRank in GoogleSpectrum of the Google Matrix

Schrödinger Equation in Laser Technology

Stochastic Navier-Stokes Equation in Fluids

Biography

Parisa Fatheddin holds a Ph.D from University of Tennessee, Knoxville. She is currently a Senior Lecturer of Mathematics at Ohio State University, Marion. Her primary research area is in Stochastic Partial Differential Equations, in which she has contributed results published in Stochastic Analysis and Applications, Stochastic Processes and Applications, Journal of Applied Probability and Journal of Stochastic Analysis. She has completed Postdoctoral Fellowships at Air Force Institute of Technology and University of Pittsburgh.

這本富有洞察力的指南旨在幫助所有對數學教育和研究職業感興趣的人。作者的目標和本書的主題是幫助學生和其他人順利過渡成為數學教師和研究人員。

第一部分介紹了有關教學和進行研究的有用技巧。這本創新的書還提供了關於如何觀察和發展研究方法、進行研究和開始撰寫研究論文的策略。它還介紹了 LaTeX，這是最廣泛使用的數學排版和渲染計算機程序。

第二部分介紹了各個行業中的一些現代數學研究。其目的是讓讀者接觸現代應用，並幫助他/她熟悉研究論文以及如何閱讀和理解它們。

這本書是由一位年輕的教師和研究人員撰寫的，她也正在開始自己的職業生涯。大多數研究生，就像她一樣，沒有得到適當的過渡性研究介紹，也沒有在教學、參加會議和合作方面接受教導。這本書基於作者自己的觀察和她發現有效的技巧。

數學研究生和相關領域的人將找到幫助，幫助他們反思和推進他們的職業追求。指導教授和導師也可能在這裡找到有用的建議。

目錄

第一部分：教學和進行研究

教學

研究和出版過程

會議和合作

過渡到閱讀和撰寫研究論文

使用LaTeX準備文件

第二部分：行業中的現代應用

Google中的PageRank

Google矩陣的頻譜

激光技術中的薛定諾方程

流體中的隨機Navier-Stokes方程

簡歷

Parisa Fatheddin擁有田納西大學諾克斯維爾分校的博士學位。她目前是俄亥俄州立大學馬里昂分校的高級講師。她的主要研究領域是隨機偏微分方程，她在《隨機分析與應用》、《隨機過程與應用》、《應用概率學雜誌》和《隨機分析學雜誌》等期刊上發表了成果。她曾在空軍技術學院和匹茲堡大學完成博士後研究。

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.

Parisa Fatheddin是俄亥俄州立大學馬里昂分校的高級講師，她在那裡教授各種課程並從事數學研究。她的主要研究領域是隨機偏微分方程，在這方面她在隨機分析的知名期刊上發表了關於隨機納維爾-斯托克斯和薛定諤方程的研究成果。Fatheddin博士還積極從事應用領域的研究，如光學和網絡安全。作為美國空軍技術學院的訪問助理教授，她參與了一個光學實驗室並在《光學通訊》期刊上發表了她的研究成果。她還在匹茲堡大學擔任訪問職位，與流體力學領域的知名數學家合作並教授了許多課程。在網絡安全領域，Fatheddin博士為教科書《數學在網絡研究中的應用》撰寫了一章，解釋了使用微分方程模擬計算機病毒傳播的現代研究。Fatheddin博士已經教授了十年，並繼續幫助本科和研究生學生找到他們在學習數學方面的目標。