Math 337: Linear Algebra
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: Matrices, determinants, systems of linear equations, vector spaces, linear transformations, eigenvalues, eigenvectors, and related topics.
Number of Credits: 3
Prerequisites: MATH 112 with a grade of C or better or MATH 133 with a grade of C or better.
CourseSection and Instructors
CourseSection 
Instructor 
Math 337002 
Professor K. Sullivan 
Math 337004 
Professor P. Milojevic 
Math 337008 
Professor K. Sullivan 
Math 337010 
Professor P. Milojevic 
Math 337014 
Professor J. Ratnaswamy 
Math 337018 
Professor J. H. Ro 
Math 337030 
Professor N. Tsipenyuk 
Math 337102 
Professor J. H. Ro 
Office Hours for All Math Instructors: Spring 2019 Office Hours and Emails
Required Textbook:
Title 
Linear Algebra and its Applications 
Author 
Lay 
Edition 
5th 
Publisher 
Pearson 
ISBN # 
9780321982384 
Universitywide 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 universitywide policies. DMS takes these policies very seriously and enforces them strictly.
Grading Policy: The final grade in this course will be determined as follows:
Quizzes and Projects 
25% 
Common Midterm Exam I 
20% 
Common Midterm Exam II 
20% 
Final Exam 
35% 
Your final letter grade will be based on the following tentative curve.
A 
90  100 
C 
60  69 
B+ 
85  89 
D 
50  59 
B 
75  84 
F 
0  49 
C+ 
70  74 


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. Absences from class will inhibit your ability to fully participate in class discussions and problem solving sessions. Tardiness to class is very disruptive to the instructor and students and will not be tolerated. Students might be withdrawn from the class or receive an "F" because of absences.
MATLAB: MATLAB is a mathematical software program that is used throughout the science and engineering curricula. Several MATLAB assignments will be given out. These assignments have been designed to help you learn how to use this software in order to visualize many of the concepts taught in class.
Projects: It is vital that you complete the required assignments by the specified dates.
Quiz Policy: A short quiz based on the homework problems will be given weekly.
Exams: There will be two common midterm exams held during the semester and one comprehensive common final exam. Exams are held on the following days:
Common Midterm Exam I 
February 27, 2019 
Common Midterm Exam II 
April 17, 2019 
Final Exam Period 
May 10  16, 2019 
The time of the midterm exams is 4:155:40 pm for daytime students and 5:457:10 pm for evening students. The final exam will test your knowledge of all the course material taught in the entire course. Make sure you read and fully understand the Math Department's Examination Policy. This policy will be strictly enforced.
Makeup Exam Policy: To properly report your absence from a midterm or final exam, please review and follow the required steps under the DMS Examination Policy found here:
Cellular Phones: All cellular phones and other electronic devices must be switched off and put away during all class times.
Additional Resources
Math Tutoring Center: Located in the Central King Building, Lower Level, Rm. G11 (See: Spring 2019 Hours)
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 9735965417 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
*Application Sections in Red
Week 
Subjects 
Section and Recommended Exercises 
1 
Systems of Linear Equations 
1.1: 2, 4, 10, 15, 18, 24, 29 

Row Reduction and Echelon Form 
1.2: 2, 4, 8, 11, 13, 18, 20 

Vector equations 
1.3: 2, 5, 9, 11, 13, 17, 24 
2 
Matrix Equations 
1.4: 2,4,5,9,17 

Solutions of Linear Systems 
1.5: 1,4,6,8,11,15,23 
3 
Application to Chemistry (brief) 
1.6: 7,9 

Linear Independence 
1.7: 1,4,6,7,14,16,31 

Linear Transformations 
1.8: 2,4,7,9,13,15 
4 
Matrix form of Linear Transformations 
1.9: 5,7,10,15,18,22 

Matrix Operations 
2.1: 4,7,9,16,23 

Inverse of a Matrix 
2.2: 3,6,9,26,29,32 
5 
Invertible Matrices 
2.3: 2,6,9,11,13,14,41 

LU Factorization 
2.5: 2,4,5,8,11,15,17 
6 
Exam Review 

Common Midterm #1 Wednesday  FEBRUARY 27, 2019


Application to Computer Graphics (brief) 
2.7: 1,2,5 

Introduction to Determinants 
3.1: 3,8,9,12,22,24,25,28 
7 
Properties of Determinants 
3.2: 1,4,6,9,21,22,25,26 

Cramer's Rule 
3.3: 2,5,8,11,16 

Vector Spaces and Subspaces 
4.1: 8,24,30,38 
8 
Null Spaces and Columns Spaces 
4.2: 2,4,14,20,24 

Linear Maps 
4.3: 4,5,10,14,15,21 

Dimension of a Vector space 
4.5: 2,4,6,9,13,15,18 
9 
Rank 
4.6: 1,2,5,9,13,17,18 

Application to Markov Chains (Brief) 
4.9: 2,4,6, 8,10 
10 
Eigenvalues and Eigenvectors 
5.1: 3,7,9,13,15,17,20 

The Characteristic Equation 
5.2: 4,7,9,13,15,16,20,21 
11 
Exam Review 

Common Midterm #2 Wednesday  APRIL 17, 2019


Diagonalization 
5.3: 2,4,6,7,8,12,17,21 

Complex Eigenvalues 
5.5: 4,5,13,14 
12 
Inner Product, Length, and Orthogonality 
6.1: 1,8,10,12,14,15,16,20 

Orthogonal Sets 
6.2: 1,4,8,12,16,1720,23 

Orthogonal Projections 
6.3: 2,4,6,8,10,12,14,16 
13 
The GramSchmidt Procedure 
6.4: 1,4,8,9,12 

Inner Product Spaces 
6.7: 1,2,4,6,8 

Diagonalization of Symmetric Matrices 
7.1: 110,14,17,22,26 
14 
Quadratic Forms 
7.2: 2,5,7,10,13,21 

Exam Review 

MATLAB Projects for M337:
Linear Algebra, Spring 2019
Visit the textbook website for supplementary materials including a guide to getting started with Matlab. For additional help, the math department has Matlab TA’s. Click for locations and times when they are available.
The first thing you need to do is to install the LayData toolbox on the computer where you will be using it. Here are the steps. I will assume that you have Matlab installed or are using Matlab on a campus PC.
 Download the LayData Toolbox.
 Uncompress the file and move the unzipped directory to the location on your computer where you want it.
 Add the toolbox to the Matlab search path. To do this run Matlab, and at the >> prompt, type pathtool to bring up the path management window. Click Add Folder, and select the folder containing the toolbox. Be sure to save it.
Subject 
Week Due 
Notes 
Getting Started with MATLAB 
February 4, 2019 
Section 14: Some recent versions of Matlab use New > Script instead of New > Mfile. Do install the Laydata programs and set the path as described in section 16 for next assignment.
DO NOT HAND IN. 
Practice Row Operations and Reduced Echelon form and ref 
February 18, 2019 
Note that there are two separate short assignments here. 
Lower Triangular Matrices 
March 11, 2019 
Problem (1c) and (2b) ask you to prove a result about lower triangular matrices. If you have trouble doing this in general, try it first with \(2\times2\) lower triangular matrices, then \(3\times3\) until you see the pattern. For general Matrices, try using the \(\Sigma\) notation for the \((i,j)\) entry of a matrix product. 
Using backslash to solve Ax=b 
March 25, 2019 

LU Factorization 
April 15, 2019 

Updated by Professor P. Milojevic  1/15/2019
Department of Mathematical Sciences Course Syllabus, Spring 2019