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7/29/2020

Course Outline for Academic Council Approval

MAT204 Linear Algebra Course Outline for Academic Council Approval Faculty Name(s)

Gaurav Goswami

School

School of Engineering and Applied Science

Credits

3

Prerequisite

MAT100 Calculus and Differential Equations Calculus and Linear Algebra. It is expected that the students have already taken a very introductory course on Linear Algebra which introduces the basic concepts (e.g. vector spaces, linear independence, basis, dimensions, inner products, linear transformation, matrices as representations of linear transformations, rank of a matrix, solution of linear systems, eigenvalues, eigenvectors, diagonalization etc).

Antirequisite

None

Course Description

The course includes the study of vectors in the space, systems of linear equations, matrices, determinants, vectors, vector spaces, linear transformations, inner products, eigenvalues and eigenvectors, singular values, principle components, quadratic forms. It is specically meant for students planning to specialise in Computer Science and related disciplines.

Course Objectives

Learn basic linear algebraic techniques and utilize them for modeling and solving engineering problems.

Learning Outcomes

Student will be able to model a problem as a linear system and with appropriate linear algebraic concept will be able to propose a solution.

Pedagogy

Lecturing, problem solving.

Expectation From Students

Attend all sessions, solve all assignments and contribute to group assignments.

Assessment/Evaluation

Contact

[email protected]

End Semester Examination: Online Exam [20%] Other Components: Quiz [15%], Assignment [10%], Project [35%] Mid Semester Examination: Online Exam [20%]

Attendance Policy

As per Ahmedabad University Policy

Project / Assignment Details

The project (and associated) viva component will be based on applications of the concepts introduced in the course to some problems in Computer Science.

https://auris.ahduni.edu.in/core-emli/code/faculty-dashboard/proposed_course_v1.php

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Course Material

Course Outline for Academic Council Approval

Text Book: Linear algebra and its applications, Lay, David C, 3rd edition Edition, Pearson Education India, ISBN: 978-8177583335, Year: 2002 Linear Algebra and Its Applications, Strang Gilbert, 4 edition Edition, CENGAGE LEARNING , ISBN: 978-8131501726, Year: 2005 Coding The Matrix: : Linear Algebra Through Applications to Computer Science, Philip N. Klein, 1st edition Edition, Lightning Source Inc, ISBN: 978-0615880990, Year: 2011 Reference Book: Linear Algebra Done Right, Sheldon Axler, 2nd Edition, Springer Linear Algebra and Learning from Data , Gilbert Strang, 1st Edition, Wellesley-Cambridge Press;

Additional Information

The class will be divided into 2 sections. Both sections will have common two theory sessions each week. In addition, there will be 1.5 hours of tutorial for each section to be held separately.

https://auris.ahduni.edu.in/core-emli/code/faculty-dashboard/proposed_course_v1.php

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Course Outline for Academic Council Approval

Session Plan SESSION NO.

TOPIC TITLE

TOPIC & SUBTOPIC DETAILS

READINGS,CASES,ETC.

1

Why Linear Algebra for Computer Science?

Various ways Linear Algebra is useful in Computer Science

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2

Solution of linear systems: a quick reminder

The four fundamental subspaces

Chapter 2 of Strang, chapter 7 of Klein

3

Solution of linear systems: a quick reminder

Applications to various engineering problems

Chapter 2 of Strang, examples from chapter 7 of Klein

4

Solution of linear systems: numerical aspects

Numerical matrix inversion and numerical solution of linear system of equations

Chapter 2 of Strang, examples from chapter 7 of Klein

5

Vector spaces: a quick reminder

Vector spaces, subspaces, linear independence, basis, dimensions,

Strang chapter 1 and 2; chapter 3, 5 and 6 of Klein; chapter 4 of Lay et al

6

Vector spaces: a few applications

linear transformations and how matrices represent linear transformations

Examples from chapter 4, 5 and 6 of Klein

7

Inner products: a quick reminder

An application oriented approach to inner products

Strang chapter 3, chapter 8 of Klein

8

Least squares

Optimisation problems, least square minimisation; applications

Strang chapter 3

https://auris.ahduni.edu.in/core-emli/code/faculty-dashboard/proposed_course_v1.php

ACTIVITIES

IMPORTANT DATES

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Course Outline for Academic Council Approval

9

Orthogonalisation

Gramm-Schmidt orthogonalisation

Strang chapter 3, chapter 9 of Klein

10

Fast Fourier Transforms

FFTs and their applications

Strang chapter 3, chapter 10 of Klein

11

A few more applications

Difference equations, Markov chains, computer graphics

David Lay, chapter 2 and 4

12

Eigenvalues and eigenvectors

Introduction

Chapter 5 of Strang, chapter 12 of Klein

13

Matrix diagonalisation

Basic results and applications; similarity transformations

Strang chapter 5

14

Applications of eigenvalues and eigenvectors

PCA, shear stresses.

chapter 12 of Klein

15

MIDTERM EXAM

-

-

16

Positive denite matrices

Denition, maxima and minima of functions of several variables, saddle point;

Strang chapter 6

17

Applications of positive denite matrices

Cholesky decomposition, singular value decomposition, image processing, PCA and least squares reloaded

Strang chapter 6

18

Quadratic forms

Strand chapter 6, Lay quadratic forms, conics, conicoids, chapter 7 multivariate data and applications

https://auris.ahduni.edu.in/core-emli/code/faculty-dashboard/proposed_course_v1.php

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Course Outline for Academic Council Approval

19

Determinants

Introduction, properties, volumes, applications

Strang chapter 4

20

Linear programming

Simplex method and applications

Lay chapter 9

21

Markov chains and their applications

Random process, Markov processes, Markov Chain Monte Carlo, Page ranks etc;

Lay chapter 10

22

Markov chains and their applications

Practise with Markov models

Lay chapter 10

23

Other applications

Comparing voting records using dot-product, error correcting codes, perspective rectication

Klein: relevant sections.

24

Introduction to machine learning

Data, supervised learning, optimization, more applications

Strang (2019: Learning from data): relevant sections; section 8.4 of Klein

25

Introduction to machine learning

Practise with ML concepts

Strang (2019: Learning from data): relevant sections

26

Introduction to Machine learning

Neural networks and deep learning

Strang (2019: Learning from data): relevant sections

27

Quantum mechanics, quantum information and computation

Shannon information; principles of QM, information, computation;

John Preskill's lecture notes

28

Reection and Review

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-

29

Quiet Reading

-

-

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Course Outline for Academic Council Approval

End-semester examination

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https://auris.ahduni.edu.in/core-emli/code/faculty-dashboard/proposed_course_v1.php

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