## Features of the Paradigms Curriculum

Listed below are some unique features of the Paradigms curriculum which could be used at other institutions without the major reordering of content into paradigms and capstones.

### Electromagnetism

The two electromagnetism paradigms are Symmetries and Idealizations and Static Vector Fields. These two short courses cover roughly chapters 1, 2, and 5 of Griffiths Introduction to Electromagnetism, although in a somewhat different order. (More advanced content is covered in the E & M Capstone.) These courses also cover a review of vector calculus and the gravitational analogue to electrostatics. Special features include:

• Review of vector calculus is integrated into the physics content in a fluid way.
• Vector calculus is unified by using $d\vec r$ as the central geometric concept. More information about this approach can be found at the Vector Calculus Bridge Project.
• Integration is thought of as chopping space into many pieces and adding (accumulation) those pieces.
• Integration is unified as measureing change.
• Sequences of activities are designed to help students build confidence in their ability to break a complicated problem up into smaller pieces. (See, for example, the ring sequence and the flux sequence.)
• Students build a deep understanding of electrostatic potentials before they study electrostatic fields (in reverse order from the typical lower-division experience).
• Emphasis is place on careful symmetry arguments for Gauss's and Ampère's Laws.

### Classical Mechanics

Classical mechanics is the subdiscipline of physics that has been most distributed throughout the rest of the curriculum. You will find classical mechanics content distributed through most of the paradigms: gravitational fields in Static Vector Fields, Oscillations and Waves in their respective courses, orbital motion in Central Forces, and special relativity in Reference Frames. The Capstone in Classical Mechanics covers more advanced topics such as rocket motion, Lagrangians, and Hamiltonians.

### Quantum Mechanics

• Spins first
• Multiple representations
• Building blocks first
• Postulates first in an applied setting
• Linear algebra preface

### Mathematical Methods

There are two approaches to teaching mathematical methods in physics: one is to integrate the methods in with the physics and the other is to teach it as a separate course. The Paradigms course structure allows us to take both approaches in a more integrated fashion. Some content is integrated into particular paradigms: you will find vector calculus content in the Symmetries and Vector Fields paradigms, fourier series in Oscillations, ( ask JT) separation of variables and boundary conditions in Waves, and a first experience with special functions in Central Forces. In two cases, we have found that this approach is not sufficient to get students up to speed with the needed mathematics, so we teach a separate 7-contact-hour unit in a just-in-time fashion before the relevant physics. You will find linear algebra and bra-ket notation in the Preface immediately before Spin and Quantum Measurements and partial derivatives in the Interlude immediately before Energy and Entropy.

### Optics

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