Math 453: High-Performance Numerical Computing
Spring 2019 Course Syllabus
NJIT Academic Integrity Code: All Students should be aware that the Department of Mathematical Sciences takes the University Code on Academic Integrity at NJIT very seriously and enforces it strictly. This means that there must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or any form of cheating in quizzes and exams. Under the University Code on Academic Integrity, students are obligated to report any such activities to the Instructor.
Course Information
Course Description: This course covers state-of-the-art numerical algorithms for solving large scale problems accurately and efficiently. Topics include iterative methods for linear systems and eigenvalue computations, introduction to parallel programs and parallel numerical algorithms, and spectral methods. An instructor selected advanced topic will be included in the course.
Number of Credits: 3
Prerequisites: MATH 391 with a grade of C or better and MATH 440 with a grade of C or better.
Course-Section and Instructors
Course-Section |
Instructor |
Math 453-002 |
Professor S. Afkhami |
Office Hours for All Math Instructors: Spring 2019 Office Hours and Emails
References:
- Using MPI: Portable Parallel Programming with the Message-Passing Interface by W. Gropp, E. Lusk, and A. Skellum, MIT Press.
- Numerical Analysis of Spectral Methods: Theory and Applications by D. Gottlieb and S. Orszag, SIAM.
- Numerical Linear Algebra by L. N. Trefethen and D. Bau, SIAM.
- Spectral Methods in Matlab by L. N. Trefethen, SIAM.
University-wide Withdrawal Date: The last day to withdraw with a W is Monday, April 8, 2019. It will be strictly enforced.
Policies
DMS Course Policies: All DMS students must familiarize themselves with, and adhere to, the Department of Mathematical Sciences Course Policies, in addition to official university-wide policies. DMS takes these policies very seriously and enforces them strictly.
Grading Policy: The final grade in this course will be determined as follows:
Homework |
50% |
Midterm Exam |
25% |
Final Exam |
25% |
Attendance Policy: Attendance at all classes will be recorded and is mandatory. Please make sure you read and fully understand the Math Department’s Attendance Policy. This policy will be strictly enforced.
Cellular Phones: All cellular phones and other electronic devices must be switched off during all class times.
Additional Resources
Math Tutoring Center: Located in the Central King Building, Lower Level, Rm. G11 (See: Spring 2019 Hours)
Further Assistance: For further questions, students should contact their instructor. All instructors have regular office hours during the week. These office hours are listed on the Math Department's webpage for Instructor Office Hours and Emails.
All students must familiarize themselves with and adhere to the Department of Mathematical Sciences Course Policies, in addition to official university-wide policies. The Department of Mathematical Sciences takes these policies very seriously and enforces them strictly.
Accommodation of Disabilities: Disability Support Services (DSS) offers long term and temporary accommodations for undergraduate, graduate and visiting students at NJIT.
If you are in need of accommodations due to a disability please contact Chantonette Lyles, Associate Director of Disability Support Services at 973-596-5417 or via email at lyles@njit.edu. The office is located in Fenster Hall Room 260. A Letter of Accommodation Eligibility from the Disability Support Services office authorizing your accommodations will be required.
For further information regarding self identification, the submission of medical documentation and additional support services provided please visit the Disability Support Services (DSS) website at:
Important Dates (See: Spring 2019 Academic Calendar, Registrar)
Date |
Day |
Event |
January 22, 2019 |
T |
First Day of Classes |
February 1, 2019 |
F |
Last Day to Add/Drop Classes |
March 17 - 24, 2019 |
Su - Su |
Spring Recess - No Classes, NJIT Open |
April 8, 2019 |
M |
Last Day to Withdraw |
April 19, 2019 |
F |
Good Friday - No Classes, NJIT Closed |
May 7, 2019 |
T |
Friday Classes Meet/ Last Day of Classes |
May 8 & 9, 2019 |
W & R |
Reading Days |
May 10 - 16, 2019 |
F - R |
Final Exam Period |
Course Outline
Weekly Schedule (Approximate)
Week # |
Topic |
Week 1 |
Introduction to high-performance computing |
Week 2 |
Introduction to parallel computing, speedup, efficiency, cost optimality |
Week 3 |
Introduction to Open MP |
Week 4 |
Parallel matrix and vector operations |
Week 5 |
Sparse matrices |
Week 6 |
Iterative methods, Jacobi, Gauss-Seidel |
Week 7 |
Parellelizable methods for large linear systems, GMRES |
Week 8 |
Midterm exam / Preconditioning techniques, multicoloring |
Week 9 |
Conjugate Gradient |
Week 10 |
Spectral methods I: Introduction to FFT |
Week 11 |
Spectral methods II: Interpolation, integration and differentiation, boundary value problems. |
Week 12 |
Spectral methods III: Boundary values problems for PDE, Chebychev methods |
Week 13 |
Other applications of spectral methods |
Week 14 |
Instructor selected advanced topic |
Week 15 |
Final exam |
Updated by Professor S. Afkhami - 1/21/2019
Department of Mathematical Sciences Course Syllabus, Spring 2019