This paper is an introduction to the fundamental ideas and techniques of linear algebra and the application of these ideas to computer science and the sciences.
The principal aim of this paper is for students to develop a working knowledge of
the central ideas of linear algebra: vector spaces, linear transformations, orthogonality,
eigenvalues and eigenvectors, the spectral theorem and the applications of these ideas
in science, computer science and engineering.
In particular, the paper introduces students to one of the major themes of modern mathematics: classification of structures and objects. Using linear algebra as a model, the paper investigates techniques that allow you to tell when two apparently different objects can be treated as if they were the same.
|Paper title||Linear Algebra|
|Teaching period||Second Semester|
|Domestic Tuition Fees (NZD)||$868.95|
|International Tuition Fees (NZD)||$3,656.70|
- MATH 170
- MATH 242, MATH 341
- Schedule C
- Arts and Music, Science
- MATH 202 is compulsory for the Mathematics major and is of particular relevance, also, for students majoring in Statistics, Computer Science and Physics.
- More information link
- View more information about MATH 202
- Teaching staff
- To be advised.
- Paper Structure
- Main topics:
- One-to-one and onto functions
- Basic group theory (definition, subgroups, group homomorphisms and isomorphisms)
- Vector spaces over the real and complex numbers (mainly finite-dimensional)
- Linear transformations and their properties, kernel and range, examples involving Euclidean spaces, spaces of polynomials, spaces of continuous functions
- Linear combinations, linear independence and spans, bases, dimension, standard bases, extending bases of subspaces, coordinate vectors and isomorphisms, rank-nullity theorem
- Representation of linear transformations by matrices
- Diagonalisation, eigenvalues and eigenvectors
- Inner products, orthogonality, orthogonal projections, Cauchy-Schwartz inequality, inner-product norm, orthonormal bases, Gram-Schmidt process, orthogonal complements, minimisation problems
- the spectral theorem for matrices, singular-value decomposition of a matrix
- Text books are not required for this paper.
- Course outline
- View course outline for MATH 202
- Graduate Attributes Emphasised
- Critical thinking.
View more information about Otago's graduate attributes.
- Learning Outcomes
- To develop a working knowledge of the central ideas of linear algebra:
- Vector spaces
- Linear transformations
- Eigenvalues and eigenvectors
- The spectral theorem