A Mathematically Sound Introduction to Relativity for Math, Physics and Astronomy Majors

3. Course Content

The course addresses three general topics (see Figure 4): differential geometry, special relativity, and general relativity.

Topics covered in differential geometry are:

Notice that some standard topics from differential geometry (such as differentiable forms) are omitted. We concentrate on topics which we will need in the development of general relativity.

Topics covered in special relativity include:

Classical examples are presented such as the detection of pions at Earth's surface and "putting a 10m pole in a 5m barn."

Topics covered in general relativity include:

Though the motivation for Einstein's choice for the field equations is weak, the remaining topics are well motivated and the solutions are mathematically sound (though approximations are sometimes necessary). In my opinion, the major accomplishment of the general relativity topics is to explain exactly what Einstein's field equations are (namely, 16 second order PDE's in 16 unknown functions) and what it means to "solve" them (which is explicitly illustrated in the Schwarzschild solution).

Figure 4. Click here for a copy of the syllabus.


Go to Section 4.