Brokk Toggerson

Welcome to Physics 131!

Let me start off by recognizing that you are not physics majors and that you may even have some trepidation about the subject. That being said, why are you being required to take this course? The first common answer you might get from your advisors is something to the effect of, “Well, physics is the underpinning of all the other sciences. Thus, it is important to understand physics.” While this statement is true, I feel that it leaves out so much! My primary goal is to hopefully help you discover that physics is not only a “set of facts I need to master to graduate,” but also a beautiful way of thinking different from your major disciplines. Just like any other diverse way of thinking, the physics approach combined with knowledge and skills from your home disciplines can help you see the world in a different light and give you new perspectives on some of the most important problems in our world today.

Course Goals – What do I hope you will remember five-years from now

I know that five years from now most of you will have probably forgotten the exact details of how to calculate the net resistance from air or water on a moving object (unless you work with such ideas every day in your careers!).


However, there are certain things that I hope you will remember from this class when you are in your careers or wherever else you will be in five years:

  1. Physics is NOT list of equations – The goal of physics is to figure out the rules by which the Universe plays: to really understand how it works. This effort has, over time, led to the key discovery that, perhaps counter to our intuition, there are actually very few of these rules that govern the operation of everything we see around us from atoms to galaxies. Consequently, physics has developed a quest to describe as many different diverse phenomena with as few rules as possible.
  2. Math is one of many languages we can use to describe the world as well as express the ideas of science in general and physics in particular – To help learn the physics concepts described above, we will first explore them in our “native languages” of words and pictures. Only after mastering these ideas will we translate them into mathematics. No one actually knows why the rules of the Universe can be represented mathematically! All we know is that it works. One of the most important things, I think, you can learn in this class is how to take a situation or physical law and describe it mathematically. While what you have learned in your math courses will serve as a critical foundation, we will be using mathematics in a bit of a different way than you do in math class. I like to say that “math courses teach you the grammar of the mathematical language. In this class, on the other hand, we will add vocabulary.”

    “Now mathematics is both a body of truth and a special language, a language more carefully defined and more highly abstracted than our ordinary medium of thought and expression. Also it differs from ordinary languages in this important particular: it is subject to rules of manipulation. Once a statement is cast into mathematical form it may be manipulated in accordance with these rules and every configuration of the symbols will represent facts in harmony with and dependent on those contained in the original statement. Now this comes very close to what we conceive the action of the brain structures to be in performing intellectual acts with the symbols of ordinary language. In a sense, therefore, the mathematician has been able to perfect a device through which a part of the labor of logical thought is carried on outside the central nervous system with only that supervision which is requisite to manipulate the symbols in accordance with the rules.”

    – Horatio Burt Williams (1927) Mathematics and the Biological Sciences, Bulletin of the American Mathematical Society 33(3): 273–94.


  3. In addition to describing how the world works, physics also has a very discipline specific way of applying that understanding and modeling the world – Ultimately the approach is to “start simple and add complexity as you need it: focus on what you know to be true and then reason, doing one thing at a time, from there.” This philosophy may seem simple, but it can take some practice to learn how to implement effectively. Moreover, the concept of “starting simple and add complexity as you need it” can be quite different from the approach used in other sciences. For example, in biology, this approach is less effective as there are many different factors all interacting the ignorance of any of which can cause your results to be completely wrong. In physics, by contrast, even a simple analysis ignoring most of the details can provide excellent insight and even an answer that may be good enough.
  4. Confidence with not knowing – In this course, you will be analyzing new situations. You will NOT know all the steps at first glance. This may be a new, and stressful experience for you. These feelings are okay! Through this course, I want you to gain comfort with making mistakes and taking wrong turns, gaining confidence that you can figure it out.
  5. Becoming a better learner through learning how to learn (including from failure) – Developing confidence and mastering the physics method of understanding/modeling the world requires both a growth mindset and practice. Not just any practice, but intentional practice where you actively think about the concepts, your application of them, and any mistakes you may make. As physics is a discipline with which many of you are less familiar, it makes a good place to learn and practice these skills which will make you a better learner throughout the remainder of your college career and the rest of your life. You will fail at things in this class your first time through: that is not just okay it is expected! As long as you learn from your mistakes and improve you will be fine.
  6. Solving real, interesting problems requires computers – most problems of actual interest are too complex to solve with just pencil-and-paper. You must use computers. Throughout this class we will gain familiarity with using computers for scientific analyses. You will be analyzing data with computers in the lab and using physics to write simulations of real-world situations.
  7. If it was ever true, in today’s world the idea of a “solo scientific genius working alone” is a myth – Modern science is done in teams and the work of a team is almost always better than the work of any of the members individually.

Spreadsheets and Computers

One of the goals for this class (#6 specifically!) is to learn how to use computers to help you analyze physical situations. All work in today’s world (scientific, health-based, and otherwise!) is done with the aid of computers – a trend which is only going to accelerate with the development of artificial intelligence. If you cannot compute, you will be replaced either by a computer or by someone who can.

To this end, you will be using computers throughout this course in various ways. In particular, we will focus on using spreadsheet programs to do calculations, analyze data, and perform simulations. In order to make things consistent for everyone in the class, I will be using Google sheets, but you are free to Excel or Numbers as you like.

To help you become more familiar with this software, we will be using it for everything, including as your calculator in this class. This includes on exams: you will be using a spreadsheet as your calculator. To help you get acquainted there are a few sections in the next part about orienting you to spreadsheets. If you are familiar with this software, feel free to skip it.

The Philosophy Behind the Preparation

To help you on your journey, we have compiled this book specifically for you the University of Massachusetts, Amherst Physics 131 student. The selection of topics included in this book and the order in which they are presented will exactly match our class. While the structure of the course is detailed elsewhere (like your syllabus) the basic structure of the course is that it has five units reflected here.


In line with the goals of this course, I really want you to see physics as an effort to explain how the world works, NOT as an equation sheet. As such, the physics is almost exclusively focused on concepts. You will be expected to learn what the different concepts represent in pictures and words and may need to do some basic reasoning with these concepts in a way that does not require mathematics in the traditional sense. One of the things we will then focus on in class is the translation of these physics concepts in to mathematical statements.

Math and Chemistry

In addition to introduction to the physics concepts, you will also be expected to review some ideas from math and chemistry as we go. These topics will require you to use and manipulate equations. However, this material should be review for most of you. If, however, you have not seen the material for a while, or it has been a long time, we will provide resources. The most basic fundamentals will be provided within each unit while some extensive additional resources can be found in the appendices.

We hope you enjoy this book. If you have any feedback, please contact us at

Brokk Toggerson, Ph.D.


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