Syllabus for MA 723  section 1 , Spring 2001
1. Instructor: R. E. Hartwig
Office: Ha 217
Office Hours: MWF 12.30-1.30
Phone Number: 515-2385
E-mail address: hartwig @ math.ncsu.edu
 

Teaching Assistant:
Office:
Office Hours:
Phone Number:
E-mail address:


2. Goals and Objectives:  The main emphasis of this course will be on non-negative matrices and their applications tro Markov Chains,  Digraphs and Networks. We shall derive the necessary preliminary results on convergence, the Jordan form and functions of matrices. The concept of a generalized inverse will be introduced to streamline the notation.

3. Textbook: no textbook will be used. Notes may be handed out.

4. Topics and estimated days allocated to each topics:
1. Introduction and Classification of Markov Chains  (5 lec)t
2. Deflation, the Jacobi Form and Matrix Equations  (5 l ect)
3. Jordan Canonical Form and Convergence of Matrices (5 lect)
4. Function of Matrices (5 lect)
5. Gneralized Inverses, Group and Drazin inverses (5 lect)
6. Reducibiliy  and decomposability- Weak and Strong components. (5 lect)
7. Di-graphs, Boolean Matrices and Networks (5 lect)
8. Frobenius canonical form, The Perron Frobenius theory (5 lect)
9. Markov Chains: Ergodic, regular, Proper and Absorbing (5 lect)

5. Tentative schedule of reading assignments
Recommended reference books are:
(i)  Gantmacher vol 2, Matrix theory
(ii) Horn and Johnson, Matrix Analysis
(iii) Lancaster and Tismeneski,  Theory of Matrices
(iv)  Minc, Non-negative matrices
(v) Bapat, non negative matrices.

6. Tentative schedule of homework due dates, quizzes and tests
There will be
(i) Biweekly homework
(ii) Two in-class  tests approx Feb 14 and Mch 28
(iii) A comprehensive final exam.
 

7. Determination of grades: + and - system

Homework: 30%
Attendance:  Recommended
Tests:  40%
Final Exam: 30%
 
8. Policy on incomplete grades and late assignments:
A good reason must be given.
 

9. Policy on absences (excused and unexcused) and scheduling makeup work:
A good reason must be given

The attendance policy is consistent with the Academic Regulations which can be found at http://www2.ncsu.edu/unity/project/www/ncsu/provost/info/academic_regulations/attend/reg.htm (link)

In addition, the following clarifications are used in this course:

10. Course Prerequisites / Restrictive Statements:
MA 523 or MA 520 or equivalent
More information is available at : http://www2.acs.ncsu.edu/reg_records/crs_cat/MA.html (link)
 

In addition,the following clarifications are used in this course:

11. Academic Integrity Statement:
Students are expected to follow university guidelines available at http://www.ncsu.edu/provost/academic_regulations/integrity/reg.htm (link)

In addition, the following clarifications are used in this course:


12. NC State policy on working with students with disabilities:

Information can be found at http://www2.ncsu.edu/ncsu/stud_affairs/counseling_center/dss/ (link)

In addition, the following clarifications are used in this course:


13. Statement on laboratory safety or risk assumption in courses requiring physical activity or field trips:

None
14. Statement on "pass-through" charges e.g. , lane rental at bowling alley, field trip costs, etc.:
None
Further Information:
NCSU Academic Regulations can be found at http://www2.ncsu.edu/unity/project/www/ncsu/provost/info/academic_policies/  (link)