During the MAT program in addition to our teaching internship, we take six courses at Duke in the academic field that we will be teaching.  Four of these courses must be at the graduate student level (200 or above).  The courses that I have taken (and am currently taking) are as follows:

 The following is an analysis of three of these courses:

Physics 222S:

General Relativity

Course Description:

This course was intended for graduate students and advanced undergraduates as an introduction and survey of Einstein's theory of General Relativity.  The main objective of the course was to give us a basic understanding and intuition for the ideas of General Relativity.  Topics covered included: shortfalls of Newtonian theory and history of general relativity, theory of special relativity (including time dilation, length contraction, changes in mass and Doppler shift), manifolds, theory of general relativity, gravitational lensing and other cosmological consequences of general relativity.

Summary of Work Completed:

• 2 problem sets: one covering special relativity; one covering general relativity
  
• final research project and presentation on an application of general relativity of our choice.  I chose to do a survey of cosmological distance measures with a focus on how to convey the concepts involved to a high school general physics class.
  

Personal and Academic Benefits of the Course:

One of the reasons I love physics so much is that it constantly takes my breath away with the majesty it reveals about our universe.  Studies of astronomy, astrophysics, and particle physics bring huge personal rewards for me.  In addition, the study of general relativity is foundational to understand current research in astrophysics and cosmology as well as to understand the difficulties of combining the theories of relativity and quantum mechanics.  Academically this course has enabled me to understand and enjoy many further topics in physics and to understand the underpinnings of current developments in the field.

Course's Contribution to Teaching:

While high school physics courses generally do not cover general relativity in any depth, an AP physics course should cover the basics of special relativity and modern physics.  While these topics can be studied without any specific knowledge of general relativity, such knowledge enhances and enriches the understanding of special relativity.  This course not only gave me a wonderful background on understanding the historical underpinnings and need for a theory beyond Newtonian theory, but also helped to have a more intuitive understanding of and ability to work with the complex ideas of special relativity.  The framework built by general relativity is fundamental to understanding any current studies of cosmology. 

Stats 213 :

Intro to Statistics

Course Description:

This course was intended for graduate students in science who would be doing research and needed a foundation of statistics to interpret the quantitative results of their work.  We covered the foundational topics of introductory statistics including: probability; statistical representations; probability densities; families of distributions; joint, conditional and marginal probabilities; dependence and independence; likelihood functions; Bayesian inference; hypothesis testing; and special distributions (multinomial, chi-squared, poisson, uniform, gamma, beta, tau).

Summary of Work Completed:

• weekly problem sets based on material covered in class
  
• occasional in-class quizzes based on material covered in class
  

Personal and Academic Benefits of the Course:

Since so much of science and applied mathematics research is based in statistics, understanding the basics of statistics is critical to understanding much of the current world of science and math.  Taking this course has made me feel much more confident in understanding such topics and in understanding the mathematical field of probability and statistics.

Course's Contribution to Teaching:

Since I did not take statistics as an undergraduate, I felt uncomfortable going into teaching mathematics without some knowledge in that area.  This course provided a great survey of the general methods of statistics and the applications to real problems and research.  Having taken this course makes me feel fairly confident in teaching statistics to high school students, making the material accessible and applicable.  In addition, the some of the methods and theory of statistics is very helpful in grading and evaluating student progress and effectiveness of teaching methods.

 

Physics 055:

Astronomy

Course Description:

This course was intended for undergraduate students and to be accessible to non-physics majors.  Thus topics were covered with an emphasis on understanding the general principles, but not all of the mathematical details.  Topics included: observing the sky, history of astronomy, key physical underpinnings of the universe, lives of stars, death of stars (white dwarfs, neutron stars, black holes), galaxies and galactic evolution, dark matter, the big bang, relativity, and our solar system (planets, the sun, Earth).

Summary of Work Completed:

• Weekly homework assignments based on class lectures and readings.  These assignments included working problems as well as researching current topics and areas of research in astronomy.
  
• Three observation sessions including summary of what was seen and research on those astronomical objects.
  
• Quizzes (approximately bi-weekly)
  
• Mid-term and Final exams

Personal and Academic Benefits of the Course:

Having already completed my undergraduate degree in physics, this course did not present a huge challenge conceptually.  It did, however, challenge me to take a step back from the details of all of the various branches of physics and to see how they all combine and work together to describe the amazing systems that comprise our universe.  In addition to recapturing the beauty of the cosmos revealed in physics, this course offered a wonderful hands-on experience in the observation sessions.  We learned how to set-up and to operate the telescopes, to find certain stars, planets, constellations, and other celestial objects, and to more fully understand the changes in the sky on a nightly and yearly basis.  These observation sessions made the course come even more personally alive for me.

Course's Contribution to Teaching:

Precisely because this course focused on physics and astronomy without delving into too much mathematical rigor, I think that it will be a huge help to me as I enter the classroom as a high-school physics teacher.  Since I love astronomy and astrophysics so much, I hope that I have the chance to teach a course on astronomy and cover these very topics with my own students.  I was impressed with the teaching methods used in this class to force us to interact with the subject material and to make it accessible to students who did not have an enormous mathematics background.  I am sure that I will use many of these techniques in my classroom, especially if I teach astronomy.