SYLLABUS

ALGEBRA AND ANALYTICAL GEOMETRY I

Four credits

COURSE OBJECTIVES

To introduce the students to the fundamental concepts of matrices, systems of linear equations, vector spaces and linear maps.

PREREQUISITES

- None.

DETAILED COURSE OUTLINE

1. Matrices and system of linear equations

1.1. Complex number

1.2. Polynomials over number fields

1.3. Matrix operations

1.4. Elementary transformations. Rank of a matrix

1.5. Invertible matrix

1.6. System of linear equations

1.7. Gauss’s method

2. Determinant

2.1. Permutations

2.2. Determinant

2.3. Basic properties of determinants

2.4. Cramer’s method

3. Vector spaces

3.1. Definitions and properties

3.2. Subspace

3.3. Linear dependence and linear independence

3.4. Basis and dimension

3.5. Direct sum

3.6. Coordinates

3.7. Root space

3.8. Row space of a matrix

4. Linear maps

4.1. Definitions and properties

4.2. Kernel and Image

4.3. Factor space

4.4. Matrix representation of a linear map

4.5. Dual space

COURSE MATERIALS

1. Bui Xuan Hai et al., Linear Algebra, The VNU of Ho Chi Minh City Publishing House, 2002.

2. Ngo Viet Trung, Linear Algebra, The HaNoi National University Publishing House, 2001.