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.
Author(s): Parisa Fatheddin
Publisher: CRC Press/Chapman & Hall
Year: 2022
Language: English
Pages: 222
City: Boca Raton
Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface
Biography
Introduction
Part I Teaching and Conducting Research
1. Teaching
2. Research and the Publication Process
3. Conferences and Collaborations
4. Transition to Reading andWriting Research Papers
4.1 Common words and Expressions for a Mathematics Research Paper
5. Preparing Documents in Latex
5.1 The Beginning Code
5.2 Typing the Main Content
5.3 Inserting Pictures
5.4 References
5.5 Dissertations
5.6 Beamer for Presentations
Part II Modern Applications in Industry
6. Schrödinger Equation in Laser Technology
6.1 Schrödinger Equation Modeling Laser Propagation
6.2 Optimal Control
6.3 Phase Screens
6.4 Appendix
7. PageRank in Google
7.1 Spectrum of the Google Matrix
7.2 Computing the PageRank
7.3 Improving the PageRank
7.4 Appendix
7.4.1 Stochastic Processes
7.4.2 Markov Process and Markov Chain
7.4.3 Properties of Markov Chains
7.4.4 Types of Markov Chains
7.4.5 Computing the Transition Probabilities
7.4.6 Stationary Probability Distribution
8. Stochastic Navier-Stokes Equations in Fluids
8.1 Stochastic Navier Stokes Equation
8.2 Large Deviations
8.3 Large Deviations for Stochastic Navier Stokes Equation
8.4 Appendix
8.4.1 Brownian Motion, Lévy Process and RandomWalk
8.4.2 Applications of large deviations
Index
