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Applied Linear Algebra Course Overview

This document provides information about the Applied Linear Algebra course MAT-3004, including objectives, outcomes, modules, textbooks, and evaluation. The course aims to: 1) Present basic concepts of linear algebra and its applications to computer science and engineering. 2) Cover concepts of vector spaces, linear transformations, matrices, and inner product spaces. 3) Solve problems in cryptography, computer graphics, and transforms like wavelets. The course consists of 8 modules that cover topics such as systems of linear equations, vector spaces, linear transformations, inner product spaces, and their applications. Students will be evaluated through digital assignments, continuous assessments, and a final test.

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Saketh Sentinal
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272 views3 pages

Applied Linear Algebra Course Overview

This document provides information about the Applied Linear Algebra course MAT-3004, including objectives, outcomes, modules, textbooks, and evaluation. The course aims to: 1) Present basic concepts of linear algebra and its applications to computer science and engineering. 2) Cover concepts of vector spaces, linear transformations, matrices, and inner product spaces. 3) Solve problems in cryptography, computer graphics, and transforms like wavelets. The course consists of 8 modules that cover topics such as systems of linear equations, vector spaces, linear transformations, inner product spaces, and their applications. Students will be evaluated through digital assignments, continuous assessments, and a final test.

Uploaded by

Saketh Sentinal
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Course Code Applied Linear Algebra L T P J C

MAT-3004 3 2 0 0 4
Pre-requisite MAT2002 Applications of Differential and Syllabus Version
Difference Equations
1.0
Course Objectives (CoB):
[1] to give a presentation of basic concepts of linear algebra to illustrate its power and utility
through applications to computer science and Engineering.
[2] to give a presentation of concepts of vector space, linear transformations, matrices and
inner product space.
[3] to solve problems in cryptography, computer graphics and Transform like wavelets

Course Outcome (CO):


At the end of this course the students are expected to learn
[1] the abstract concepts (theory) of matrices which are the backbones of modern
engineering.
[2] how to solve the system of linear equations using decomposition methods, the basic
notion of Vector spaces
[3] how to transform the vectors using linear transform which is the basic idea required in
computer graphics and inner product spaces
[4] applications of inner product spaces, basic tools of cryptography
[5] Use of wavelet in image processing.

Student Learning Outcomes (SLO): 1,2,7


[1] Having an ability to apply knowledge of mathematics in Science and Engineering
[2] Having a clear understanding of the subject related concepts and of contemporary issues
[7] Having computational thinking

Module:1 System of Linear Equations: 6 hours CO: 1

Gaussian elimination and Gauss Jordan methods - Elementary matrices- permutation matrix
- inverse matrices - System of linear equations - - LU factorizations.

Module:2 Vector Spaces 6 hours CO: 2


n
The Euclidean space R and vector space- sub space –linear combination-span-linearly
dependent-independent- bases - dimensions-finite dimensional vector space.

Module:3 Subspace Properties: 6 hours CO: 2

Row and column spaces -Rank and nullity – Bases for subspace – invertibility- Application in
interpolation.
Module:4 Linear Transformations and applications: 7hours CO: 1, 2

Linear transformations – Basic properties-invertible linear transformation - matrices of


linear transformations - vector space of linear transformations – change of bases – similarity

Module:5 Inner Product Spaces: 6 hours CO: 3

Dot products and inner products – the lengths and angles of vectors – matrix
representations of inner products- Gram-Schmidt orthogonalization

Module:6 Applications of Inner Product Spaces: 6 hours CO: 3, 4


QR factorization- Projection - orthogonal projections – relations of fundamental subspaces –
Least Square solutions in Computer Codes

Module:7 Applications of Linear equations : 6hours CO: 4, 5

An Introduction to coding - Classical Cryptosystems –Plain Text, Cipher Text, Encryption,


Decryption and Introduction to Wavelets (only approximation of Wavelet from Raw data)

Module:8 Contemporary Issues: 2 hours CO: 3, 4, 5

Industry Expert Lecture

Total Lecture hours: 45 hours

Tutorial  A minimum of 10 problems to be worked 30 hours CO: 3, 4, 5


out by students in every Tutorial Class
 Another 5 problems per Tutorial Class to
be given as home work.
Text Book(s)
1. Jin Ho Kwak and Sungpyo Hong, Linear Algebra, Second edition, Springer(2004).
(Topics in the Chapters 1,3,4 &5)
2. Introductory Linear Algebra- An applied first course, 9th Edition Bernard Kolman and
David R. Hill Pearson Education, 2011.
Reference Books
1. Stephen Andrilli and David Hecker, Elementary Linear Algebra, 5th Edition,
Academic Press(2016)
2. Rudolf Lidl, Guter Pilz ‘Applied Abstract Algebra’, Second Edition, Springer 2004.
3. Howard Anton and Robert C Busby, Contemporary linear algebra, John Wiley
(2003).
4. Gilbert Strang, Introduction to Linear Algebra, 5th Edition, Wellesley- Cambridge
Press (2015).
Mode of Evaluation
Digital Assignments (Solutions by using soft skills), Continuous Assessments, Final
Assessment
Test
Recommended by Board of Studies 16.08.2017
Approved by Academic Council No. 47 Date 05.10.2017

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