This paragraph by Ravi Vakil fully agrees with my experience:

Here's a phenomenon I was surprised to find: you'll go to talks, and hear various words, whose definitions you're not so sure about. At some point you'll be able to make a sentence using those words; you won't know what the words mean, but you'll know the sentence is correct. You'll also be able to ask a question using those words. You still won't know what the words mean, but you'll know the question is interesting, and you'll want to know the answer. Then later on, you'll learn what the words mean more precisely, and your sense of how they fit together will make that learning much easier. The reason for this phenomenon is that mathematics is so rich and infinite that it is impossible to learn it systematically, and if you wait to master one topic before moving on to the next, you'll never get anywhere. Instead, you'll have tendrils of knowledge extending far from your comfort zone. Then you can later backfill from these tendrils, and extend your comfort zone; this is much easier to do than learning "forwards". (Caution: this backfilling is necessary. There can be a temptation to learn lots of fancy words and to use them in fancy sentences without being able to say precisely what you mean. You should feel free to do that, but you should always feel a pang of guilt when you do.)

**Gathering time** It is extremely difficult to learn this material
alone. In order to give people a place and time to meet their fellow
students working on algebraic geometry, Tuesday afternoons in the tea room.
There is a schedule problem: based on class polling, most people become free after 4 PM, I will almost always need to leave by 5, and 4-5 is the colloquium.
I will come to the tea room between 4 and 5 unless I am going to the colloquium, but I hope that you will also be able to help each other.

**Webpage:** `http://www.math.lsa.umich.edu/~speyer/632`

**Textbooks:** *Algebraic Geometry*, by Robin Hartshorne. I
also strongly recommend Foundations of Algebraic Geometry by Ravi
Vakil.

**The Update:** A day by day summary of the course, written by the students and edited by me.

**Other valuable online sources:** Mel
Hochster's commutative algebra notes. The algebraic-geometry tag at mathoverflow
and math.stackexchange
(but see the homework policy below). Mark
Haiman's synopses of EGA, Ravi's notes and blog, the stacks project, the
algebraic geometry tag at nLab.

**Intended Level:** This is **not** a first course in algebraic
geometry. Many of you took Math 631 with me last term, and I am glad
to see you back. Whether through my course or another, you should
already have some geometric intuition for varieties before you work
with schemes.

The commutative algebra prerequisite will also be much more serious
this term. Last term, I made an effort to avoid significant use of
homological algebra, localization, completion or tensor products, and
it was often possible to do so by some clever planning. That is no
longer possible. You should have taken Math 614 or the equivalent
**before** taking this class.

**Anticipated topics** The primary goals of this construction are
schemes and sheaf cohomology — that is to say, Chapters 2 and 3
of Hartshorne. I hope to have time to say a bit about
*K _{0}*-theory, which is one of my favorite subjects, and
about algebraic de Rham theory. Ultimately, though, the two main
technical subjects are large enough that there will not be time for
another large topic.

Please read

Please read

In the week of

Please read

In

On

On

In the week of

In the final two weeks of class,

I don't intend for you to need to consult books and papers outside your notes. If you do consult such, you should be looking for better/other understanding of the definitions and concepts, not solutions to the problems.

You

Note: Last term, we had some trouble with conflicting edits to the Update file. Therefore, this term, start with the blank Template.tex, and I'll merge your LaTeX into Update.tex.

If you have forgetten when you are scheduled to write the update, you can check here.