Data Mining
Originally, data mining was a statisticians term for overusing data to draw invalid
inferences.
A famous example - David Rhine, a parapsychologist at Duke in the 1950s tested
students for extrasensory perception by asking them to guess 10 card

ISC 5315
Applied Computational Science I
Lab # 7 : Runge-Kutta Methods for Systems of IVPs
April 9
Due: April 23, 2015
Goals.
In this lab we want to write library routines for RK methods of order one through
ve for a system of IVPs. Recall that a RK metho

ACS I - Problem Set # 5
Approximation Theory
Due: Friday, 3/20
1. Suppose we want to nd a Hermite interpolating polynomial which interpolates not just the function values
but also the derivatives at the points. In this case we are given triples of data (x

ACS I - Problem Set # 2
Problems # 4,5,7 are to be turned in
1.
Let
Due: Tuesday, 2/3
4 1
1 2
A=
2 0
2 1
2
2
0
1
3 2
2 1
B=
4
1
1
4
a. Use Householder matrices to nd a tridiagonal matrix which is similar to A. Verify that your matrices
are similar by usi

ACS I - Problem Set # 3
All problems are to be turned in
Due: Tuesday, 2/17
1. Consider the general iterative method xk = P xk1 + c for the system Ax = b. Let ek be the error at
the kth step, i.e., ek = x xk . For simplicity assume that we are solving a 2

Lab # 4 - ACS I
Goals. For homework you have written codes for evaluating a Lagrange interpolating polynomial which
you can use for this lab. In the rst exercise you are asked to provide code for a piecewise linear interpolant
and in the next two exercise

ACS I - Problem Set # 1
Problems # 2 ,4,5,8 are to be turned in
Due: Thursday, 1/22
1. a. First determine if each of the sets is a vector space when the standard operations of addition and
scalar multiplication are used. If the space is nite dimensional d

Introduction to Dierential Equations
Dierential equations arise in many disciplines such as engineering,
mathematics, sciences (e.g., physical, chemical and biological) as well
as economics. These dierential equations often result from modeling
some pheno

Introduction to Boundary Value Problems
When we studied IVPs we saw that we were given the initial value
of a function and a dierential equation which governed its behavior
for subsequent times. Now we consider a dierent type of problem
which we call a bo

Linear Least Squares
Suppose we are given a set of data points cfw_(xi, fi), i = 1, . . . , n. These
could be measurements from an experiment or obtained simply by evaluating
a function at some points. One approach to approximating this data is to
interp

Interpolation & Polynomial Approximation
The next problem we want to investigate is the problem of nding a simple
function such as a polynomial, trigonometric function or rational function
which approximates either a discrete set of (n + 1) data points
(

Numerical Quadrature
When you took calculus, you quickly discovered that integration is much
more dicult than dierentiation. In fact, the majority of integrals can not
be integrated analytically. For example, integrals such as
b
b
sin x dx
a
2
ex dx
2
a

Iterative Methods for Solving Ax = b
A good (free) online source for iterative methods for solving Ax = b is given in
the description of a set of iterative solvers called templates found at netlib:
http : /www.netlib.org/linalg/html templates/Templates.ht

The QR Decomposition
We have seen one major decomposition of a matrix which is A = LU (and its
variants) or more generally PA = LU for a permutation matrix P. This was
valid for a square matrix and aided us in solving the linear system Ax = b.
The QR de

Clustering
What do we mean by clustering?
Clustering strives to identify groups/clusters of objects that behave similarly
or show similar characteristics. In common terms it is also called look-a-like
groups.
Similarity is often quantied through the use

Approximation Theory
Function approximation is the task of constructing, for a given function, a simpler
function so that the dierence between the two functions is small and to then
provide a quantiable estimate for the size of the dierence.
Why would one

Homework # 4 - Sample Midterm Exam
ACS I, Spring 2015
PART I - Short Answers (1 point each) (You do not have to show any work)
1.
Let A be a real nn matrix. Then A is orthogonal if
.
and its eigenvalues
2. Let A be a real m n matrix. Then the range of A i

ISC 5315
Applied Computational Science
Lab # 5 : Quadrature
March 19, March 26
Due: April 2, 2015
Goals.
In practice, when we approximate an integral we often have an idea about the
required degree of accuracy but have no idea about the number of points n

ISC 5315
Applied Computational Science
Lab # 6 : Modeling the Harvesting of Cod
April 2
Due: April 13
NOTE: This lab must be done with a compiled language such as C, Fortran, Python, etc.
However, you can use Matlab to generate your plots.
Introduction.
W

Data Mining
Data mining emerged in the 1980s when the amount of data generated and
stored became overwhelming.
Data mining is strongly inuenced by other disciplines such as mathematics,
statistics, articial intelligence, data visualization, etc.
One of

ACS I
Data Mining
Homework # 5
Due: Friday, 2/18/11
1. Consider the set of training data shown in the table below for a binary classication
problem (Here + or -). Note that for each record there are three attributes, two of
which are binary and one which

Lab # 2
Using Library Routines to Solve Linear Systems
Goals: Oftentimes we are working on a project which requires using standard library
routines. It is useful to gain experience with using these routines because usually they
have been optimized and, in

Lab # 3 - ACS I
DATA COMPRESSION in IMAGE PROCESSING using SVD
Goals.
The goal of this lab is to demonstrate how the SVD can be used
to remove redundancies in data; in this example we will be compressing image
data. We will see that for a matrix of rank r

Using the Lab
http:/people.sc.fsu.edu/jburkardt/isc/week01/
lecture 02.pdf
.
ISC3313:
Introduction to Scientic Computing with C+
Summer Semester 2011
.
John Burkardt
Department of Scientic Computing
Florida State University
Last Modied: 09 May 2011
s
C
ci

Part II - Random Processes
Goals for this unit:
Give overview of concepts from discrete probability
Give analogous concepts from continuous probability
See how the Monte Carlo method can be viewed as sampling technique
See how Matlab can help us to si

ACS I
Linear Algebra
Homework # 3
1. Short proofs.
a. A symmetric matrix has real eigenvalues. Use this fact to show that a symmetric
positive denite matrix has positive eigenvalues, i.e., i > 0 for all i.
b. Show how the SVD of an m n matrix A with n lin

ACS I
Linear Algebra
Homework # 4
Due: Monday, 2/14
1. SOR Algorithm Write a code to implement the component form of the SOR method
for a symmetric positive denite matrix. As a stopping criteria use
xk+1 xk
xk+1 2
or a maximum number of steps of
Ax = b.
4

Numerical Linear Algebra
The two principal problems in linear algebra are:
Linear system
Given an n n matrix A and an n-vector b, determine x I n such that
R
Ax = b
Eigenvalue problem
Given an n n matrix A, nd a scalar (an
eigenvalue) and a nonzero vector

The QR Decomposition
We have seen our rst decomposition of a matrix, A = LU (and its variants).
This was valid for a square matrix and aided us in solving the linear system
Ax = b.
The QR decomposition is valid for rectangular matrices as well square on