Course Design#
For most of you, 415 is an elective course that you are taking to learn more about how we use mathematical techniques in physics. As such, this course is designed under several different principles than a standard course. Below, I provide those principles and their rationale.
415 should help you learn the central tenets of modeling physical systems
The sheer volume of mathematical and computational physics knowledge out there is immense and impossible for any one person to learn. However, the central elements of making models, how to learn about specific techniques, and how to debug your approaches are things we can learn and employ broadly as well as to specific problems.
415 should be a celebration of your knowledge
For most of you, this course is part of your senior level coursework. What you have achieved in the last three to four years should be celebrated and enjoyed. This course will provide ample opportunities for you to share what things you know and what things you are learning with me and with each other.
415 should give you opportunities to engage in professional practice
As you start towards your professional career, it’s important to learn what professional scientists do. You have probably already begun this work in advanced lab and research projects that you have worked on. We will continue developing your professional skills in this course through the use of course projects.
415 will illustrate that we can learn from each other
Even though I’ve been learning physics for almost 20 years, I don’t know everything. I am excited to learn from you and I hope that you are excited to learn from me and each other.
Optional purchases:#
The core readings and work for this course will be this jupyterbook. I will find resources online, make my own, and provide as much organized free material as possible. If you want to have a textbook that helps you organize your readings, please obtain copies of:
Mary Boas, Mathematical Methods in the Physical Sciences (Wiley; 2005). This book is the definitive text on mathematical approaches, written by Dr. Boas originally in 1966! Any 3rd edition will be useful and I will put the section numbers from Boas in the online readings.
Mark Newman, Computational Physics (CreateSpace Independent Publishing Platform; 2012). This book is a great introduction to a variety of computational physics techniques, written by UMich professor Mark Newman for a computational physics course. I will put section numbers from Newman in the online readings.
Additional sources#
In addition, I will draw from the following books. I have copies of them if you want or need scans of sections. But they can found online in Google Books and other places as well. No need to purchase unless you want a copy for your personal library.
Mechanics#
Edwin Taylor, Mechanics
Jerry Marion and Stephen Thornton, Classical Dynamics of Particles and Systems
Charles Kittel, Walter D. Knight, Malvin A. Ruderman, A. Carl Helholtz, and Burton J. Moyer, Mechanics
Electromagnetism#
Edward Purcell, Electricity and Magnetism
David J. Grriffths, Introduction to Electromagnetism
Quantum Mechanics#
David McIntyre, Quantum Mechanics
David J. Griffiths, Introduction to Quantum Mechanics
Waves and Thermal Physics#
Frank S. Crawford, Waves
Charles Kittel, Thermal Physics
Ashley Carter, Classical and Statistical Thermodynamics
Daniel Schroeder, Thermal Physics
Additional Physics Topics#
Steven H. Strogatz, Nonlinear Dynamics and Chaos
B Lautrup, Physics of Continuous Matter
Frank L. Pedrotti and Leno S. Pedrotti, Introduction to Optics
Mathematics#
Susan M. Lea, Mathematics for Physicists
William E. Boyce and Richard C. DiPrima, Elementary Differential Equations
James Brown and Ruel Churchill, Complex Variables and Applications
Jerrold Marsden and Anthony Tromba, Vector Calculus
Sheldon Ross, A First Course in Probability
Presenting (Visual) Information#
Edward Tufte, The Visual Display of Quantitative information
Albert Cairo, The Truthful Art
Stephen E. Toulmin, The Uses of Argument
Course Activities#
“Readings”#
“Reading” is an essential part of 415! Reading the notes before class is very important. I use “reading” in quotes, because in our class this idea goes beyond just reading text and includes understanding figures and watching videos. These should help inform the basis of your understating that we will draw on in class to clarify your understanding and to help you make sense of the material. I will assume you have done the required readings in advance! It will make a huge difference if you spend the time and effort to carefully read and follow the resources posted. The calendar has the details on videos and readings that will be updated.
Weekly Questions: To encourage and reward you for keeping up with the “readings”, there will be weekly questions about the readings posted for you to respond to. These are not meant to test your knowledge, but rather to focus your “reading” towards what you understand, and what you don’t yet understand. I will ask you about those things weekly and use that information to tailor in-class activities based on what I am hearing is confusing, unclear, or challenging. These questions are only graded for completion, but I do want your honest attempt.
Class Meetings#
Classroom Etiquette: Please silence your electronic devices when entering the classroom. I don’t mind you using them (in fact, see below, we will use them). But, sometimes, they can very distracting to your neighbors, so use your judgement. I appreciate that you might have questions or comments about things in class. We are going to be having short lectures combined with longer project work in class. So you will have plenty of time to catch up with social media and the news.
If you and/or your group mates are confused, just raise your hand and ask questions. If you are confused, you are likely not the only one and it’s better to chat about it, then move on. Questions are always good, and are strongly encouraged! The only way we learn is to question what we know and how we know it.
Computing Devices: Please bring some sort of computing device to class everyday. You might be researching information online, reviewing work you have done, or actively building models of systems together. This device can be a computer, a tablet, or a phone. You can also partner up with folks because we will use them in groups. If you need a computing device brought to class for you or your group mates to use, let me know. I will organize for some small collection of laptops if we need it.
In-Class: We will have some short lectures about topics or concepts; some of those will be in-the-moment as needed. The idea is that you are developing a basic understanding through readings and videos, practicing using those new ideas with me and with your classmates in class, and then applying what you are learning to new ideas. So, we will also use a variety of in-class activities that help you construct an understanding of a particular topic or concept. These will not be collected or graded, but we will discuss the solutions in class. I will not post solutions for these activities as we have no exams or quizzes.
“Homework”#
Worked Problems: We will spend much of our time learning specific techniques and approaches to use withh many different kinds of problems and models. Your “weekly” homework will be to select a particular example where the method or model applies, and work that problem yourself. You will need to explain your approach and findings on paper or in a notebook. You will turn in seven of eight of these worked problems. I will not post solutions for these problems as we have no exams or quizzes.
Projects#
In-class Projects: The class is designed to support your independent research into ideas that you are excited about. So in-class projects are meant to equip you with the knowledge and practice to learn new things for your projects. These in-class projects will be short demonstrations of models that you complete in groups. We will circulate around the room and check on you and your group’s progress and understanding. At the end of the class period, we will share the results of the in-class project and discuss any sticking points. These in-class activities will not be graded, but they will be essential for your out-of-class projects.
Out-of-class Projects: For this class, we anticipate 6 projects to be turned in roughly every 2-3 weeks, with a weeklong turn-in window (see calendar). Except for the first project, up to 3 of these projects can be completed as partner projects. Partner projects are subject to a different grading rubric that evaluates collaborative efforts and increases the expectation for other areas compared to an individual project. A preliminary rubric appears here, but we will define these collectively after the first project.
These projects will take the form a computational essay, which provides documentation and rationale for the exploration that you are completing. We will model a computational essay project in our first project and we will reflect on the rubric after it, and make changes collectively as a class to it.
I strongly encourage collaboration, an essential skill in science and engineering (and highly valued by employers!) Social interactions are critical to scientists’ success – most good ideas grow out of discussions with colleagues, and essentially all physicists work as part of a group. Find partners and work together. However, it is also important that you OWN the material. I strongly suggest you start working by yourself (and that means really making an extended effort on every activity). Then work with a group, and finally, finish up on your own – write up your own work, in your own way. There will also be time for peer discussion during classes – as you work together, try to help your partners get over confusions, listen to them, ask each other questions, critique, teach each other. You will learn a lot this way! For all assignments, the work you turn in must in the end be your own: in your own words, reflecting your own understanding. (If, at any time, for any reason, you feel disadvantaged or isolated, contact me and I can discretely try to help arrange study groups.)
Help Session#
Help sessions/office hours are to facilitate your learning. We encourage attendance - plan on working in small groups, our role will be as learning coaches. The sessions are concept and project-centric, but we will not be explicitly telling anyone how to do your project (how would that help you learn?) I strongly encourage you to start all projects on your own. If you come to help sessions “cold”, the value of the project to you will be greatly reduced.