# Learning Aims

The physics department has developed six learning aims for the physics major:

- Students will develop a solid understanding of the fundamental principles of physics,
including:
- a firm conceptual grasp of the central principles of physics,
- an ability to work with the concepts mathematically, and
- a functional understanding of how these ideas play out in the real world.

- Student will develop a flexible and creative problem-solving ability.
- Students will develop an integrated understanding of the unity of physics.
- Students will develop their ability to communicate ideas of science.
- Students will develop a functional understanding of symbolic and numerical computation
- Students will develop an expertise in experimental methodologies

## More Detailed Discussion

The learning goals of the majors curriculum in the physics department can be discussed in a variety of ways, including content areas, skills and abilities, types and levels of understanding, and so on. The below will address all of these categories and attempt to delineate with some specificity what we are trying to accomplish.

## Content areas

At the simplest level, we have a list the topics that are covered somewhere in the majors curriculum. Broadly speaking, the central topics match the required courses: classical dynamics, thermal physics, quantum physics, electricity & magnetism, and experimental methods. A more highly-specified list of essential topics for each course is provided in the appendix. We can then state our learning goal in a straightforward manner: physics majors will have a good understanding of the topics included in this list. This, however, begs the question of what we mean by understanding, so we now pass on to a discussion of that question.

## Levels of understanding

There are at least three ways in which students should understand the material in the physics majors program. One level of understanding is conceptual [What does it mean to say that an electric field exists at a point? What effect does a force exerted normal to a particle’s velocity have? What accounts for the intensity variations in a wave interference pattern?]. Students should be able to visualize and verbalize the relevant physics in a system. In addition to conceptual understanding, students should also have a mathematical understanding [What are the equations governing a physical system, and how are these equations solved? What are the formal mathematical definitions of the relevant concepts? How does the general mathematical structure of a theory express itself in a particular physical system?]. Mathematics is the natural language for much of physics, and students should be adept at its use. Lastly, students should have a functional understanding of the material in the majors program [How do the concepts and formal structure of a physical theory play out in the real world? What approximations need to be imposed to calculate realistic results? What experiments and observations make us believe that our understanding is correct?] The laboratory component of the curriculum is important in achieving this level of understanding, but it also needs to be reinforced throughout the entire sequence of courses.

## Problem-solving ability

The ability to analyze and solve novel problems is central to the education of physics students. Cultivation of such problem-solving ability extends through all parts of our curriculum, both lecture and laboratory components. Many different skills contribute to this overall ability: determining the most important factors in a problem; breaking the difficult problem into simpler sub-problems; formulating appropriate approximations to a attack an otherwise insoluble problem; recognizing the similarity between an unsolved problem and a previous problem with a known solution; ability to formulate a mathematical model of system; ability to make order-of-magnitude estimates of needed quantities; ability to troubleshoot a system and test proposed methods of solution; checking proposed solutions by examining appropriate limiting cases; and so on. These abilities cannot be taught directly but rather must be acquired by practice and by example—in other words, by solving very many problems of different types and difficulty levels. Such practice is exactly what we require in virtually every course in our curriculum. National survey statistics from people with undergraduate physics degrees working in a wide variety of employment settings virtually always show that problem-solving ability is considered to be the most valuable thing that a student learns in a physics program. It is a central learning goal in our curriculum.

## Integrated understanding

One of the great beauties of physics, as an intellectual discipline, is the underlying unity of knowledge that it suggests. An extremely wide variety of phenomena can be explained with the use of only a small number of fundamental principles, and these principles themselves form a coherent set which summarize much of our understanding of the physical world. The fragmentation of physics into research sub-disciplines, along with the fragmentation of the curriculum into discrete courses with delimited subject matter in each one, tends to obscure and disguise this underlying unity. One of the learning goals of our overall curriculum, rather than any single particular course, is for the students to recognize the profound connections between material learned piecemeal in the individual courses and hence to acquire an integrated understanding of physics that cuts across sub-areas and to recognize the fundamental unity of the discipline as a whole.

## Ability to communicate

Consistent with the Jesuit intellectual tradition and the liberal arts context of our program, an important learning goal of our curriculum is that students be able to communicate their understanding of physics effectively both in a written format and in verbal presentations. Although much of physics is mathematical and numerical in character, the mathematics and numbers must eventually be communicated in some form in order to be effective, and the conceptual understanding that is part of our learning goals also requires clear written and verbal formulation. Although upper-division lecture courses occasionally include assigned papers on some specific topic, the majority of the written material and verbal presentations are associated with extended projects and laboratory work.

## Symbolic manipulation

Many of the central results of physics are in the form of mathematical equations, and facility in the manipulation of mathematical symbols is necessary to succeed in physics. Such manipulation includes basic algebra, differential and integral calculus, graphical techniques, and so on. In the last decade or so, powerful computer algorithms have been developed that perform much of this mathematical symbol manipulation automatically. Using computer software packages of this sort allows us to assign much more extensive and difficult (and interesting!) tasks than would have been possible in the past. At the same time, this software eliminates the need to master some of these skills “by hand” and thus creates dangers as well as opportunities, pedagogically speaking. It is a learning goal of our curriculum that our students be able to employ mathematical symbolic manipulation methods appropriately and skillfully in their physics work, using both their own brains and computer software tools as the situation calls for.

## Experimental methodologies

In addition to an understanding of presently-known results, our students should also know the methods by which new knowledge is acquired and evaluated. Thus, along with a deeper understanding pf physical principles, the laboratory component of our curriculum should also impart methodological knowledge and skills. For example, an understanding of how to use basic scientific equipment (multimeters, oscilloscopes, power supplies, and so on) and an understanding of experimental uncertainty analysis are both learning goals of our curriculum.