- Algebraic Geometry (MWF 10)
- Commutative Algebra (MWF 12)
- Ramsey Theory (TR 9)
- Algebraic Topology (TRS (I know, right?! Saturday!) 11)
- Category Theory (TRS 12)
And there will be a sixth class, Quine Systems (MWF 9), that will start halfway through term when its lecturer returns from New Zealand. And a group (including me) of interested students is trying to convince the Quine Systems lecturer to offer a reading course in Set Theory, which the reader who is genuinely (!) interested in my life will recognize to be among my chief academic interests. This reading course could be next term (Lent), though.
Anywhom, here’s a quick bit about what these subjects are concerned with:
- AG is (roughly) the study of polynomials and the spaces on which they are zero.
- CA is the study of commutative rings: think the set of integers or the set of polynomials with coefficients in, say, the real numbers .
- As advertised by the course’s lecturer, RT is the study of searching for order in a lot of disorder. So far, that seems accurate. For instance (this is a theorem we’ve proved already): Suppose you have infinitely many strings, each of which is either blue or red. You take the positive integers and attach a string (either blue or red) between every pair of integers. Then there is a subset of the integers such that every string tied between two numbers in is the same color (either blue or red).
- AT is concerned with assigning invariants to topological spaces. The standard example is that the sphere is not ‘the same as’ a torus (doughnut with no filling) because the fundamental group of the torus is , whereas the fundamental group of the sphere is trivial.
- Mathematics is often concerned with studying objects (sets, groups, rings, topological spaces, affine varieties, etc.) and morphisms between them. Category theory emerges when one recognizes that the collection of all groups, for example, along with group homomorphisms between them, can be studied as a mathematical object (a category) in its own right.
- Quine Systems will discuss Quine‘s proposed foundations for set theory.
- Set theory is great. It’s the study of (among other things) infinite sets (of all sizes!) and their properties. Read the Wikipedia article on set theory for more information. Or, if you really want, I’ll tell you more.
Finally, here’s a brief overview of how Part III math(s) works. You attend some lecture courses during the Michaelmas (roughly Oct–Nov) and Lent (roughly mid-Feb–mid-March) terms, and in late May or early June you take exams over some of those courses. (You also have the option to substitute a long essay for an exam. This I will probably do. It’s a popular option.) After your exam is graded you get a Distinction, a Merit, a Pass, or a Fail. And that’s it.
I know this is really exciting for all of you! That’s all for now. Time for bed!
P.P.S. KT’s blog post should be really exciting tomorrow (today)!