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 ContentsPart I: Teaching and Conducting ResearchTeachingResearch and the Publication ProcessConferences and CollaborationsTransition to Reading and Writing Research PapersPreparing Documents in LatexPart II: Modern Applications in IndustryPageRank in GoogleSpectrum of the Google MatrixSchrödinger Equation in Laser Technology

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