MATH 527

**Meeting times**: TTh
9:30 - 10:45 AM at **LeConte**** (LC)
303B**.

**Instructor**: Dr**. Peter G. Binev**

http://www.math.sc.edu/~binev/

e-mail: binev@math.sc.edu

phones: 576-6269 (at LC
425) *or*
576-6304 (at SUM
206H)

**Office hours**: TTh 11:00
- 12:00 AM at LeConte 425 or by appointment.

**Credits:
**3

**Cross-listed
Course: **CSCE
561

**Prerequisites**: MATH 242 or
MATH 520

**Learning
Outcomes**:
Upon the successful completion of this course students will be able to:

· read, interpret,
and use vocabulary, symbolism, and basic definitions from Numerical Analysis;

·
use
facts, formulas, and techniques learned in this course to apply algorithms and
theorems to find numerical solutions and bounds on their errors to various
types of problems including root finding, polynomial and spline
approximation, numerical differentiation and integration, numerical solutions
of ODEs.

**Attendance**: Regular class attendance is
important. A grade penalty will be applied to any student missing five or more
classes (10%) during the semester. The "10 percent rule" stated above
applies to both excused and unexcused absences. Students who anticipate
potential excessive absences due to participation in permissible events as
described in the USC Academic Bulletins (http://www.sc.edu/bulletin/ugrad/acadregs.html#class
atten.) should receive prior approval from the
instructor to potentially avoid such penalty.

**Cell Phones**: All cell phones ** must
be turned off** during the class.

**Homework
and Quizzes**:
A few homework problems will be assigned each class. Be sure to solve and write
these problems before the next class. The homework will be discussed in class. Some
solutions will be collected and graded. There will be a few quizzes (announced
in advance) on problems similar to ones from the homework. The homework
grade will be based on student’s participation in the discussions and the
grades on the quizzes and the collected homework problems.

**Projects**:** **Every student has to choose a project
motivated by the computational or theoretical problems discussed in the course.
The projects should be submitted on or before **April 17, 2012**. The instructor will suggest several possible themes
for the projects in the length of the course. The projects for the undergraduate
students should prepare a 2-page description of a numerical method with a
presentation one of the following subjects:

· computational realization of
the method in Matlab or other programming language;

· theoretical considerations
of the error estimation and the stability of the method;

· analysis of the
computational flow of the algorithm and discussion of a realization on a
multiprocessor platform.

The
graduate students should submit a 5-page research paper that addresses all
three issues about the method in consideration.

**Midterm Exams**: There will be a midterm exam
in a form of a test. The tentative dates of the exam are **February 9 **and **March 20**.
The problems on the test will be similar to the ones from the homework and the
discussions in class.

**Final Exam**: The final exam in a form of a
test will take place on **Saturday, April 28
at 2:00 PM**.

**Graduate
Students**:** **The graduate students attending the
class will be given some additional problems on the exams. They should also
prepare a 10-minute oral presentation based on their projects during the class
on **April 19, 2012**.

**Grading for Undergraduates**: The final
grade will be determined from the homework grade (30%), the midterm exams (15%+15%=30%),
the project (10%), and the final (30%).

**Grading for Graduate Students**: The final
grade will be determined from the homework grade (20%), the midterm exams (15%+15%=30%),
the project (20%), and the final (30%).

**Academic
Dishonesty: **Cheating
and plagiarism will not be allowed. The University of South Carolina has clearly
articulated its policy governing academic integrity and students are encouraged
to carefully review the policy (http://www.housing.sc.edu/academicintegrity/policy.html)
on the Honor Code in the Carolina Community.

**ADA**:
If you have special needs as addressed by the Americans with Disabilities Act
and need any assistance, please notify the instructor immediately.

**Web
Materials**:
The authors of the textbook maintain a webpage http://rene.ma.utexas.edu/CNA/NMC6/.
In particular, they make available free software codes on the variety of
programming languages under the link *Sample
Codes*.

**Important
Dates**:

January 13 – Last day to drop without **W**

February 9 – Midterm Exam 1

February 27 – Last day to drop without **WF**

March 4-11 – Spring Break

March 20 – Midterm Exam 2

April 17 – Deadline to submit the projects

April 19 – Graduate students’ presentations

April 28 – Final Exam at 2:00 PM