# MAT5939-03 ACM Computing Seminar – Fall 2016

## Course Information (syllabus)

 Time & Place: Monday 6:45PM - 8:00PM, LOV 102 Instructor: Matt Hancock Office Hours: Tues 12-2, Thurs 2-4, 409 B MCH Email: mhancock@math.fsu.edu

## Assignments

Week Assignment
1 <2016-08-29 Mon> Install gcc / g++; write and compile "hello world".
2 <2016-09-12 Mon> Compute the value of the truncated sum,
$$s_N := \sum_{n=1}^N \frac{1}{n^2}$$
and the absolute error,
$$a_N := \vert{}\frac{\pi^2}{6} - s_N\vert{}$$
while $$a_N > 10^{-5}$$. For each iteration, print
$$N$$, $$s_N$$, $$a_N$$
if $$N$$ is a multiple of $$100$$.
3 <2016-09-19 Mon> The files, x.txt, and y.txt contain 101 sampled
points. The x values are not sampled equidistantly.
Write functions to read both files, and approximate
the definite integral of the sampled function over
the values given, using the trapezoidal rule.
implementation files
4 <2016-09-26 Mon> Add a member function, norm, to the vector class
discussed in the C++ guide. The function should
have the signature:

double norm(double p);

and should implement the vector p-norm. The function
would be then called like:

x.norm(1.53);

where x is a vector object. Write a test script
that loops through values of p=1, 1.1, ..., 1.9, 2
and for each value of p, prints the average p-norm
of 100 vectors of length 10 whose components are
uniform random on [0,1] (see the C++ guide section
on generating random numbers).
5 <2016-10-03 Mon> Extend the vector class given in the guide, by
adding functions dot, operator+, operator-,
and operator==. Implement these as friend
functions.

dot should implement the inner product between
two vectors, x and y, while operator+ and
operator- should implement component-wise addition
and subtraction.

The behavior of operator== should be
such that x==y returns true for vectors if
abs(x[i]-y[i]) < 1e-10
for all the components of the vectors, x and y.
7 <2016-10-17 Mon> Write a squarematrix class that inherits from the
matrix template class. The constructor should only
accept a single argument to create the matrix, rather
than two like the normal matrix class.

Add a member function, unique to the squarematrix
class, that computes the matrix determinant
recursively using the Laplace expansion. Test your
algorithm on square matrices, $$A \in R^{n \times n}$$,
where $$A_{ij} = ni + j$$, where $$i=0,\ldots,n-1$$ and
$$j=0,\ldots,n-1$$ for $$n=2,3,\ldots,100$$.