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MATH202 Linear Algebra

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
Paper code MATH202
Subject Mathematics
EFTS 0.1500
Points 18 points
Teaching period Second Semester
Domestic Tuition Fees (NZD) $851.85
International Tuition Fees (NZD) $3,585.00

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Prerequisite
MATH 170
Restriction
MATH 242, MATH 341
Schedule C
Arts and Music, Science
Eligibility
MATH 202 is compulsory for the Mathematics major and is of particular relevance, also, for students majoring in Statistics, Computer Science and Physics.
Contact
david.bryant@otago.ac.nz
Teaching staff
Dr Lisa Clark and Prof Astrid an Huef
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
Textbooks
Text books are not required for this paper.
Linear Algebra Outline Notes can be purchased.
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
  • Orthogonality
  • Eigenvalues and eigenvectors
  • The spectral theorem
And the applications of these ideas in science, computer science and engineering.

^ Top of page

Timetable

Second Semester

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
Other

Lecture

Stream Days Times Weeks
Attend
L1 Monday 09:00-09:50 28-34, 36-41
Wednesday 09:00-09:50 28-34, 36-41
Friday 09:00-09:50 28-34, 36-41

Tutorial

Stream Days Times Weeks
Attend one stream from
T1 Monday 14:00-14:50 29-34, 36-41
T2 Tuesday 11:00-11:50 29-34, 36-41
T3 Wednesday 14:00-14:50 29-34, 36-41

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
Paper code MATH202
Subject Mathematics
EFTS 0.1500
Points 18 points
Teaching period Second Semester
Domestic Tuition Fees Tuition Fees for 2018 have not yet been set
International Tuition Fees Tuition Fees for international students are elsewhere on this website.

^ Top of page

Prerequisite
MATH 170
Restriction
MATH 242, MATH 341
Schedule C
Arts and Music, Science
Eligibility
MATH 202 is compulsory for the Mathematics major and is of particular relevance, also, for students majoring in Statistics, Computer Science and Physics.
Contact
david.bryant@otago.ac.nz
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
Textbooks
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
  • Orthogonality
  • Eigenvalues and eigenvectors
  • The spectral theorem
And the applications of these ideas in science, computer science and engineering.

^ Top of page

Timetable

Second Semester

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
Other

Lecture

Stream Days Times Weeks
Attend
L1 Monday 09:00-09:50 28-34, 36-41
Wednesday 09:00-09:50 28-34, 36-41
Friday 09:00-09:50 28-34, 36-41

Tutorial

Stream Days Times Weeks
Attend one stream from
T1 Monday 14:00-14:50 29-34, 36-41
T2 Tuesday 11:00-11:50 29-34, 36-41
T3 Wednesday 14:00-14:50 29-34, 36-41