Applied Linear Algebra

Math 4350-001

Due F 1/23
Problem 2.1.
Problem 2.2.
Problem 2.4. First find an $x$ of odd length with $xxx$ prime. Then either find an $x$ of even length with $xxx$ prime or prove that no such $x$ exists.
Problem 2.6. You may assume that $f$ is an increasing function of $n$ if that is of any use to you.
Due F 1/30
Problem 3.2.
Problem 3.4.
Problem 3.7.
Problem 3.8.
Problem 3.9.
Due M 2/9
Problem 4.7.
Problem 4.8.
Problem 4.9.
Problem 4.10.
Due W 2/18
Last update on 2015-02-11 at 11:40am.
Due W 3/4
Last update on 2015-03-04 at 4:00pm. This now contains solutions to the last two problems.
Redo the midterm (correctly this time). You will present this corrected version to me in my office. Sign up for a time slot in class. When you come to my office bring both the original and the corrected versions with you.
Due M 4/20
For each part of this problem construct a circuit for the given transform using only the Hadamard gate $H$, controlled-$R_k$ for various $k$, and swap gates. Recall that $R_k=\begin{pmatrix} 1 & 0 \\ 0 & \exp(2 \pi i\; 2^{-k})\; \end{pmatrix}$
1. The quantum Fourier transform on four bits.
2. The inverse quantum Fourier transform on four bits.
Due F 5/1
Last update on 2015-05-04 at 1:32pm.