** Course outline:**
Unlike Riemannian geometry, whose purpose is to classify Riemannian metrics
(according to Felix Klein's "Erlangen program" of characterizing various
geometries), symplectic geometry should not be viewed as yet another branch.
It is rather a language, or a common landscape for classical mechanics,
quantization, PDEs, representations of Lie groups, and probably much else.
As any language, it is elegant and powerful but not particularly deep.
In the contrary,
symplectic *topology* is a deep theory studying intricate rigidity
properties of phase spaces of Hamiltonian mechanics. It is not our goal to
sink into symplectic topology, but time permitting, we'll have an informal
primer of it as well.

For the most of the course, we will loosely follow the article
* Symplectic Geometry* by Vladimir Arnold and myself,
found on pages 1--135 in the aforementioned
volume * Dynamical Systems IV*. Officially it is a survey paper, and as
such is not required to contain proofs. In reality the exposition of all the
essential material was organized as if a detailed textbook was first
written, and then all trivial proofs removed and left as exercises to the
reader, while all non-trivial ones left as outlines. This makes the text
suitable for a graduate-level course, and testing this
conjecture is a part of the plan.

** HW1, due Th, Sep. 2:** Read 1.1-2.1, 2.5, 4.1-4.4 in Ch.1.
Solve: 1 and 3 from
the (ever growing) list of excercises.

** HW2, due Th, Sep. 9:** Read 4.5, 3.1 in Ch. 1, and 1.1, 1.3 in Ch. 2.
Solve: 10 and 13.

** HW3, due Th, Sep. 16:** Read 1.5, Section 2, and 3.1 in Ch. 2. Solve: 20, 23.

** HW4, due Th, Sep. 23:** 3.2-3,4 from Ch. 2, and the excerpt from Weinstein's paper. Solve: 24, 26.

** HW5, due Th, Sep. 30:** Read 4.1-4.2 from Ch. 2. Solve: 30, 31.

** HW6, due Th, Oct. 7:** Read Ch. 3 Section 1 (Variational principles).
Solve 33,34.

** HW7, due Th, Oct. 14:** Read 1.4-1.5, 2.1-2.4 from Ch. 3. Solve: 37, 39.

** HW8, due Th, Oct. 21:** Read: the same. Solve: 49, 50.

** HW9, due Th, Oct. 28:** Read: Read Section 3 (Hamiltonian systems with
symmetries) from Chapter 3. Solve: 51, 52.

** HW10, due Th, Nov. 4:** Read: the same, especially 3.8. Solve: 53, 55.

** HW11, due Th, Nov. 11:** Read: Chapter 4, Section 1. Solve: 56, 57.

** HW12, due Th, Nov. 18:** Read the rest of Chapter 4. Solve: 58, 61.

** HW13, due Tu, Nov. 23:** Due to Thanksgiving, and cancelled Nov. 18
lecture, let's skip this week's homework; but I recommend reading pp. 148--154
(from Kirillov's paper on Geometric Quantization).

** HW14, due Th, Dec. 2:** Read pages 38-42 (as well as 2.4 of Chapter 4).
Solve 64 and 66.

An excerpt from A. Weinstein's