This course teaches the fundamentals of scientific research. We approach the research process as a means of systematically reducing uncertainty and demonstrate how conducting a scientific investigation can be posed as an exercise in Bayesian uncertainty quantification. We begin by exploring the scientific landscape to understand the different types of research, where they are conducted, how they are supported, and why each of these types of research is important.
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We then formalize scientific inquiry and the scientific method and elaborate the research process and its scientific merits. Basic concepts in probability theory are introduced leading to a conceptually simple presentation of Bayes’ Rule. We then illustrate how Bayes’ Rule provides a mathematical framework for the research process. We place an emphasis on the role that research plays in our daily and professional lives and how research skills can help us think critically, whether you’re in a technical field or not. Exercises are designed to help you improve your research skills and think more scientifically.
Learners who are new to research fields or would like to improve their research skills in any field for career/professional or personal growth are encouraged to enroll. The course is taught at an introductory level such that, by the end of the course, you will be able to formulate a research hypothesis and devise a scientific research plan to test that hypothesis. To be successful in this course, you will need entrance-level college mathematics.
Syllabus
WEEK 1
Introduction to the Research Landscape
In this module, you will be introduced to the landscape of scientific research. Why do we perform research? Who conducts research and where do they conduct it? What different kinds of research are undertaken? Why are the various types of research important?
WEEK 2
Scientific Inquiry
In this module, you will be introduced to the fundamentals of scientific inquiry. What makes an investigation scientific? How do we tell the difference between a scientific and a non-scientific inquiry?
WEEK 3
Scientific Method & the Research Process
In this module, you will be introduced to the different methods of inquiry, most notably the scientific method. You will learn the terminology used in scientific inquiries and define hypotheses and theories. You will learn the steps of the research process and how the research process is scientific.
WEEK 4
Uncertainty & Probability
In this module, you will learn about the different types of uncertainty and how these uncertainties are modeled. You will learn some fundamentals in probability theory, specifically conditional probabilities and Bayes’ Rule, necessary to understand how uncertainty is modeled.
WEEK 5
Research as an Exercise in Uncertainty Quantification (UQ)
In this module, you will learn how the research process relates to uncertainty quantification. You will learn how to pose the research process through Bayesian hypothesis testing. You will learn how to develop a hypothesis and design a plan to test it using UQ methods.
