Review Lecture Notes
Here is a summary of the topics discussed in the review lecture. This is a reasonably complete
facsimile of the lecture, though the coverage of particular topics within the course is obviously
considerably more extensive!
Generalized

Version 0.1b
Eduardo Martin-Martinez - Phys 434
Block 1
Review of the mathematical formalism of
Quantum Mechanics
1.1
1.1.1
Introduction to Hilbert spaces.
Dual vector space and Bra-Ket notation
Hilbert spaces and inner product
Definition (Vector space).

Math 225 - Practice Questions
September 20, 2016
The purpose of this document is to provide you with as many exercises as possible for you to
get some extra practice. More exercise can be found in the text for the course, as well as all over
the internet.

Math 225 - Assignment 1
Due September 28 at 4:30pm
1. This question is all about subspaces. For each question, justify your answer.
a b
(a) Is U =
M22 (R) : a + 2b c = 0 a subspace of M22 (R)?
c d
(b) Is U = cfw_p(x) P2 (C) : p (x) = 0 a subspace of P2 (

PHYS 474 (F 16) Assignment 1:
Galaxy Morphologies
Due Tue Sept 13 Sept, 2016 (at the beginning of class)
1. Warm-up: Grouping Galaxies Based on Appearance
Your first activity is to inspect a small set of galaxies, and to group them according to the
featur