# Mathematics II Syllabus: B.Sc. CSIT 2nd Semester (2080)

Mathematics II Syllabus: CSIT 2nd Semester Syllabus 2080. It Covers Linear algebra & Equation, Vector, eigenvalues, matrix, Group, Ring and Field.

## Mathematics II Syllabus

General Information

Course B.SC. CSIT
Course Title Mathematics II
Course No MTH168
Nature of the course Theory + Lab
Semester II (Second)
Full Marks 60 + 20 + 20
Pass Marks 24 + 8 + 8
Credit Hrs. 3

CHAPTER LIST: Mathematics II

S.N. Chapter Time
Unit 1 Linear Equations in Linear Algebra 5 Hrs
Unit 2 Transformation 4 Hrs
Unit 3 Matrix Algebra 5 Hrs
Unit 4 Determinants 4 Hrs
Unit 5 Vector Spaces 5 Hrs
Unit 6 Vector Space Continued 4 Hrs
Unit 7 Eigenvalues and Eigen Vectors 5 Hrs
Unit 8 Orthogonality and Least Squares 5 Hrs
Unit 9 Groups and Subgroups 5 Hrs
Unit 10 Rings and Fields 4 Hrs

Course Description: The course contains concepts and techniques of linear algebra. The course topics include systems of linear equations, determinants, vectors and vector spaces, eigen values and eigenvectors, and singular value decomposition of a matrix.

Course Objectives: The main objective of the course is to make familiarize with the concepts and techniques of linear algebra, solve system of linear equation with Gauss-Jordon method, to impart knowledge of vector space and subspace, eigenvalues and eigenvectors of a matrix and get the idea of diagonalization of a matrix, linear programming, Group, Ring, and Field.

## Course Contents:

### Unit 1: Linear Equations in Linear Algebra

(5 Hrs.)

System of linear equations, Row reduction and Echelon forms, Vector equations, The matrix equations Ax = b, Applications of linear system, Linear independence

### Unit 2:Transformation

(4 Hrs.)

Introduction to linear transformations, the matrix of a linear Transformation, Linear models in business, science, and engineering

### Unit 3: Matrix Algebra

(5 Hrs)

Matrix operations, The inverse of a matrix, Characterizations of invertible matrices, Partitioned matrices, Matrix factorization, The Leontief input output model, Subspace of Rn, Dimension and rank

### Unit 4: Determinants

(4 Hrs.)

Introduction, Properties, Cramer’s rule, Volume and linear transformations

### Unit 5: Vector Spaces

(5 Hrs.)

Vector spaces and subspaces, Null spaces, Column spaces, and Linear transformations, Linearly independent sets: Bases, Coordinate systems

### Unit 6: Vector Space Continued

(4 Hrs.)

Dimension of vector space and Rank, Change of basis, Applications to difference equations, Applications to Markov Chains

### Unit 7: Eigenvalues and Eigen Vectors

(5 Hrs.)

Eigenvectors and Eigenvalues, The characteristic equations, Diagonalization, Eigenvectors and linear transformations, Complex eigenvalues, Discrete dynamical systems, Applications to differential equations

### Unit 8: Orthogonality and Least Squares

(5 Hrs.)

Inner product, Length, and orthogonality, Orthogonal sets, Orthogonal projections, The Gram- Schmidt process, Least squares problems, Application to linear models, Inner product spaces, Applications of inner product spaces

### Unit 9: Groups and Subgroups

(5 Hrs.)

Binary Operations, Groups, Subgroups, Cyclic Groups

### Unit 10: Rings and Fields

(4 Hrs.)

Rings and Fields, Integral domains

## Mathematics II Books

### Text Books:

1. Linear Algebra and Its Applications, David C. Lay, 4th Edition, Pearson Addison Wesley.

2. Linear Algebra and Its Applications, Gilbert Strang, 4th Edition, Addison, CENGAGE Learning.

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