Math Physics III

This website served the Spring 2008 term of Math Physics III. The course has completed, and the site is now closed. Feel free to browse through the site if you wish, but I don't guarantee all the links still work.

Today continues work on the take-home final exam. Your exams are due Friday.

Today we will look at Bell's Inequality and the EPR experiment. As we will see, symmetry tells us some very interesting things about the nature of quantum reality.

Quantum mechanics can also be represented as information, but not in terms of bits. Instead we must use a quantum bit, or q-bit. We will see how this concept leads us to quantum phenomena such as entanglement.

Today we will look at how physics can be represented as information, specifically strings of bits. This will lead us to quantum physics, where we will need to approach things a little differently.

The fifth homework is posted, and you can find it here. It is due Monday the 12th of May.

Today we will see how the Dirac algebra can be used to derive the Dirac equation. From there we will discuss certain aspects of electrons.

Today we will look at how spin plays a role in quantum mechanics.

Today we will see how geometric algebra handles rotations. This will lead us to the concept of spinors.

Today we will look at another way of looking at vectors, known as geometric algebra. We will introduce the Clifford product which will allow us to have a vector group product. As we will see, this has some interesting consequences.

The fourth homework is posted, and you can find it here. It is due Monday the 28th of April. Note: If you downloaded the homework Thursday evening, there were a couple of minor errors. The corrected version is now posted.

Today we will see how Maxwell's equations can be written as a pair of tensor equations. We will also see how the electromagnetic field can be expressed as a rank-two tensor.

Today we will look at the property of Four-Vectors, and see how they are related to conserved quantities.

Today we will look at how the direct product can be used to generate higher-order tensors. We will look at some examples of rank 2 tensors.

Today we will see how tensors are defined by the rotation group. We will see that scalars and vectors are special cases of tensors.

Today we will continue our discussion of Lie matrix groups. We will look at the general properties of rotation groups SO(n). We will also look at the Lorentz group, and see how special relativity can be seen as a group symmetry.

Today we will look at Lie groups. Although there are Lie groups which cannot be expressed as matrices, most Lie groups we use in physics can be expressed as matrix groups. We will look at some of their general properties.

The third homework is posted, and you can find it here. It is due Monday the 7th of April.

Today we will look at how subgroups and groups can relate to each other. We will also look at the general form of the direct product, by which we can construct larger groups from smaller ones.

Today we will return to the topic of subsets. We will see how subsets can be decomposed via cosets. This will tell us something about groups of prime order. It will also give us a clue as to how we can generate larger groups from smaller ones.

Today we will discuss equivalence relations, which is a generalization of isomorphism and homomorphism. We will then talk about another equivalence relation, known as conjugacy.

The second homework is posted, and you can find it here. It is due Wednesday the 26th.

Today we will look at how to map one set to another. We will apply this concept to groups, which will lead us to the concept of isomorphisms and homomorphisms.

The first homework is posted, and you can find it here. It is due a week from today.

Today we will look at finite groups of various order. We will look at their abstract forms as well as some realizations. We will look at group tables as a representation of a group's structure, and look at some of the general types of groups, such as Abelian vs. non-Abelian groups. We will also introduce groups of infinite order.

Today's lecture will start with a general introduction to the course. We will go over the syllabus and related items. We will also review some of the basic concepts from last term.

We will then begin the course with a discussion of symmetry. As we will see, symmetry is central to science in general, and physics in particular. The mathematical formalism of symmetry is group theory, so we will discuss what constitutes a group.

Welcome to the website for Math Physics III. Here is where you will find copies of the syllabus, schedules for the lectures and workshops, and any other useful information.