### Linear Algebra (MATH-5125)

Introduction

Linear algebra is the study of vector spaces and linear transformations. The main objective of this course is to help students learn in rigorous manner, the tools and methods essential for studying the solution spaces of problems in mathematics, engineering, the natural sciences, and social sciences and develop mathematical skills needed to apply these to the problems arising within their field of study; and to various real-world problems.

Prerequisite

To succeed in this course you will need to be comfortable with vectors, matrices, and n-dimensional coordinate systems.

Learning Outcomes

At the end of this course the student will be able to:

• Solve linear systems of equations
• Comprehend vector spaces, subspaces and inner product spaces
• Understand fundamental properties of matrices including determinants, inverse matrices, matrix factorizations, eigenvalues, orthogonality and diagonalization
• Have an insight into the applicability of linear algebra
• Critically analyze and construct mathematical arguments that relate to the study of introductory linear algebra.

Contents

1. subspaces
2. Bases
3. Dimension of vector spaces
4.  Quotient spaces
5. Change of bases
6. LInear Transformation and matrices
7. inner product spaces
8. eigen values and eigen vectors
9. Gramm Schmidt Process, Orthogonal and Orthonormal matrices
10. Dual Spaces

Textbook(s)

•  Introduction to Linear Algebra by Gilbert Strang, Wellesley Cambridge Press; 4th Edition (February 10, 2009).

Reference Material

1.   Elementary Linear Algebra with Applications by Bernard Kolman, David Hill, 9th Edition, Prentice Hall PTR, 2007.
2.  Linear Algebra And Its Applications by Gilbert Strang, Strang, Brett Coonley, Andrew Bulman-Fleming, 4th Edition, 2005.
3. Elementary Linear Algebra: Applications Version by Howard Anton, Chris Rorres, 9th Edition, Wiley, 2005.
4. Linear Algebra and Its Applications by David C. Lay, 2nd Edition, Addison-Wesley, 2000.
5. Linear Algebra by Harold M. Edwards, Birkhäuser; 1st Edition, 2004.
6. Linear Algebra: A Modern Introduction by David Poole by Brooks Cole, 3rd Edition.

Suggested Books

• Linear Algebra by David Cherney, Tom Denton, Rohit Thomas and Andrew Waldron.
•  Linear Algebra and Its Applications by David C Lay and Steven R Lay.
• Schaum’s Outline of Theory and Problem of Linear Algebra. Seymour Lipschutz. Mc-Graw Hill.

ASSESSMENT CRITERIA

Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)

Mid-Term Exam:  30

Final-Term Exam: 50

### Key Dates and Time of Class Meeting

Wednesday                                                                    09:00 am - 10:00 am

Thursday                                                                       09:00 am - 10:00 am

Friday                                                                            09:00 am- 10:00 am

Commencement of Classes                                                   Feb 22, 2021

Mid Term Examination                                                            December 19-23, 2021

Final Term Examination                                                          June  21-25, 2021

Declaration of Result                                                              July 02, 2021