# Math 337: Linear AlgebraFall 2018 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.

Course-Section and Instructors

Course-Section Instructor
Math 337-007 Professor P. Milojevic
Math 337-009 Professor J. H. Ro
Math 337-013 Professor P. Milojevic
Math 337-017 Professor P. Petropoulos
Math 337-029 Professor S. Afkhami
Math 337-101 Professor E. Ammicht

Office Hours for All Math Instructors: Fall 2018 Office Hours and Emails

Required Textbook:

 Title Linear Algebra and its Applications Author Lay Edition 5th Publisher Pearson ISBN # 978-0321982384

University-wide Withdrawal Date:The last day to withdraw with a w is Monday, November 12, 2018. It will be strictly enforced.

## Course Goals

### Course Objectives

• Learn about matrices, determinants, applications to solving linear system of equations, matrix factorization, eigenvalues and eigenvectors, Gram-Schmidt process.
• Cover relevant applications in economics, science and engineering to illustrate the utility of learning these topics.
• Use mathematical software, in problem solving, to allow the solution of more complex problems and provide visualization of the same.

### Course Outcomes

• Prepare students for further study in theoretical courses such as differential and difference equations and least squares analyses.
• To enable students to use linear algebra use for numerical solvability of many problems.
• Students are prepared for applying linear algebra to many practical applications in fields like economics, computer science, physics, engineering, archeology, demography, relativity, etc.

## 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:

 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 October 10, 2018 Common Midterm Exam II November 14, 2018 Final Exam Period December 15 - 21, 2018

The time of the midterm exams is 4:15-5:40 pm for daytime students and 5:45-7:10 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.

Math Tutoring Center: Located in the Central King Building, Lower Level, Rm. G11 (See: Fall 2018 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 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: Fall 2018 Academic Calendar, Registrar)

Date Day Event
September 4, 2018 T First Day of Classes
September 10, 2018 M Last Day to Add/Drop Classes
November 12, 2018 M Last Day to Withdraw
November 20, 2018 T Thursday Classes Meet
November 21, 2018 W Friday Classes Meet
November 22 - 25, 2018 R - Su Thanksgiving Recess
December 12, 2018 W Last Day of Classes
December 13 & 14, 2018 R & F Reading Days
December 15 - 21, 2018 Sa - F 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 - OCTOBER 10, 2018
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 - NOVEMBER 14, 2018
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 Gram-Schmidt Procedure 6.4: 1,4,8,9,12
Inner Product Spaces 6.7: 1,2,4,6,8
Diagonalization of Symmetric Matrices 7.1: 1-10,14,17,22,26
Exam Review

# MATLAB Projects for M337: Linear Algebra, Fall 2018

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.

Lower Triangular Matrices October 29, 2018 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.