
Course Description  CMSC/AMSC 660, Fall 2012


Overview

This course is an introduction to fundamential techniques in scientific
computation, including
numerical linear algebra,
solution algorithms for nonlinear systems of equations,
optimization,
numerical solution of ordinary differential equations,
and
Monte Carlo simulation.
For each topic, there will be material on theory, computation and
software development.
Students are expected to have an undergraduatelevel knowledge of numerical
analysis, including linear equations, nonlinear equations, integration and
interpolation.
Programming assignments will be in Matlab.


Outline of Topics Covered

 Introduction, Computer Arithmetic and Errors
 Course survey
 Machine arithmetic
 Error analysis
 Stability and conditioning
 Matrix Factorizations
 Matrix manipulation
 Matrix decompositions and their uses:
LU and QR factorizations, eigendecompositions
singular value decomposition, updating decompositions,
software issues
 Nonlinear Systems
 Newton's method and variants
 Continuation
 Globally convergent methods
 Optimization
 Unconstrained optimization:
line searches and trust regions, Newtonlike methods, conjugate gradients
 Constrained optimization
barrier method, reducedvariable methods,
simulated annealing, the Metropolis algorithm
 Ordinary Differential Equations
 Numerical solution of initial value problems
 Differentialalgebraic equations
 Boundary value problems
 MonteCarlo Simulations
 Basic statistics: random variables, pseudorandom numbers
 Mean, variance, central limit theorem
 Basic MonteCarlo simulation
 MonteCarlo integration, convergence
 MonteCarlo optimization, convergence
 Variance reduction, stratified sampling, importance sampling

Recommended Text

Dianne P. O'Leary,
Scientific Computing with Case Studies,
SIAM Press, 2009.
The book can be ordered directly from SIAM (the Society of Industrial and
Applied Mathematics), see
http://www.ecsecurehost.com/SIAM/OT109.html
The list price of the book is $95, but SIAM members pay $66.50, a 30% discount.
University of Maryland students can get
free membership in SIAM,
since UMD is an Academic Member of SIAM.
There are many other benefits to membership in SIAM.
However, if you prefer not to join, SIAM also offers a 20% discount to
students. Contact the instructor for information on obtaining the
student discount.
Information about MATLAB can be found at:
http://www.mathworks.com/academia/student_center/tutorials/launchpad.html
Search "Matlab tutorial" for other sources.
For Matlab and computer access on campus: see
http://www.oit.umd.edu/as/cl/


Grading

Grades will be determined as follows:
 46 homework assignments: 40%
 Inclass midterm examination: 25%
 Final project: 35%
Assignments should be handed in at the beginning of class (9:30 AM)
on the due date.
Late assignments will be accepted within 48 hours of the due date and
not later.
The value of late assignments will decrease according to the following
rule:
 within 24 (weekday) hours after the due date: 85% of the original
value
 within 48 (weekday) hours after the due date: 70% of the original
value
No makeups will be given for the midterm exam.
If the exam is missed and a valid medical excuse is provided,
then grading will be determined by increasing the
weights of the final exam and homework.
The final grade will be on a curve. A grade of A is guaranteed with
an average of 90% or better, a grade of B with 80% or better, etc.
Plagiarism:
You are welcome to discuss assignments in a general way among yourselves,
but you may not use other students' written work or programs.
Use of external references for your work should be cited.
Clear similarities between your work and others will result in a grade
reduction for all parties.
Flagrant violations will be referred to appropriate university authorities.
UMCP Code of Academic Integrity

 
