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===== 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 [[courses:home:syhome|Symmetries and Idealizations]] and [[courses:home:vfhome|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 [[courses:home:emhome|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 [[http://www.math.oregonstate.edu/bridge|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 [[whitepapers:sequences:emsequence:start|ring sequence]] and the [[whitepapers:sequences:flux|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 [[courses:home:syhome|Static Vector Fields]], [[courses:home:oshome|Oscillations]] and [[courses:home:wvhome|Waves]] in their respective courses, orbital motion in [[courses:home:cfhome|Central Forces]], and special relativity in [[courses:home:rfhome|Reference Frames]].  The [[courses:home:cmhome|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

==== Thermodynamics ====


==== 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 [[courses:home:syhome|Symmetries and Vector Fields paradigms]], fourier series in [[courses:home:oshome|Oscillations]], (FIXME ask JT) separation of variables and boundary conditions in [[courses:home:wvhome|Waves]], and a first experience with special functions in [[courses:home:cfhome|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 [[courses:home:prhome|Preface]] immediately before [[courses:home:sphome|Spin and Quantum Measurements]] and partial derivatives in the [[courses:home:inhome|Interlude]] immediately before [[courses:home:eehome|Energy and Entropy]].

==== Computation ====

==== Optics ====