JC1505: LINEAR ALGEBRA (2021-2022)

Last modified: 31 May 2022 13:05

Course Overview

Linear algebra is the study of linear equations and matrices. At a more abstract level, it concerns vector spaces and linear maps between them, and it is a central subject within mathematics. It provides foundations for almost all branches of mathematics and sciences in general. The techniques are used in engineering, physics, computer science, economics and others.

Course Details

Study Type	Undergraduate	Level	1
Term	Second Term	Credit Points	15 credits (7.5 ECTS credits)
Campus	Offshore	Sustained Study	No
Co-ordinators	Professor Benjamin Martin

What courses & programmes must have been taken before this course?

Any Undergraduate Programme (Studied)

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

Course Description

This course is an introduction to linear algebra over the real numbers and the complex numbers. It covers linear equations and matrices, vector spaces and linear maps, and eigenvectors and eigenvalues.

Syllabus

Solving a linear system. Elementary row operations, row echelon form, Gaussian algorithm for solving a linear system.
Vector spaces. Definition of a vector space over the real and complex numbers. Subspaces of a vector space, intersection and sum of subspaces. Span, spanning sets. Linear independence. Basis, dimension. Elementary results about bases and dimension. Change of basis matrix. The algebra of nxn-matrices.
Linear maps. Definition of a linear map between vector spaces. Kernel, image, injective, surjective linear maps. Matrix of a linear map. Rank of a matrix. Invertible matrices. Change of basis and the matrix of a linear map.
Determinants of matrices and linear transformations.
The various definitions of the determinant. Properties and methods of calculation. Finding the inverse of a matrix using cofactors.
Determinants of matrices and linear transformations.
Eigenvalues and eigenvectors of square matrices and of endomorphisms. Properties.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

More Information about Week Numbers

Details, including assessments, may be subject to change until 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

Summative Assessments

Homework Exercises

Assessment Type	Summative	Weighting	20
Assessment Weeks		Feedback Weeks		Look up Week Numbers
Feedback	Solutions provided

Learning Outcomes

Knowledge Level	Thinking Skill	Outcome
Conceptual	Analyse	Ability to prove elementary results about linear independence, basis and dimension
Conceptual	Understand	Ability to state and understand the main definitions and theorems of the course
Conceptual	Understand	Understand the connections among linear transformations, matrices and systems of linear equations
Factual	Understand	Understand the concepts of linear independence, basis and dimension
Factual	Understand	Ability to calculate rank, nullity and matrix inverses.
Factual	Understand	Ability to calculate matrix determinants
Factual	Understand	Understand the basic concepts of linear algebra, such as vector spaces and linear transformations
Factual	Understand	Understand the concepts of rank, nullity and invertibility of matrices and linear transformations
Procedural	Apply	Ability to calculate eigenvalues and eigenspaces and to diagonalize matrices
Procedural	Apply	Ability to row reduce matrices and solve systems of linear equations

Tutorial/Seminar Participation

Assessment Type	Summative	Weighting	10
Assessment Weeks		Feedback Weeks		Look up Week Numbers
Feedback	Discussion

Learning Outcomes

Knowledge Level	Thinking Skill	Outcome
Conceptual	Analyse	Ability to prove elementary results about linear independence, basis and dimension
Conceptual	Understand	Understand the connections among linear transformations, matrices and systems of linear equations
Conceptual	Understand	Ability to state and understand the main definitions and theorems of the course
Factual	Understand	Ability to calculate matrix determinants
Factual	Understand	Understand the basic concepts of linear algebra, such as vector spaces and linear transformations
Factual	Understand	Understand the concepts of rank, nullity and invertibility of matrices and linear transformations
Factual	Understand	Understand the concepts of linear independence, basis and dimension
Factual	Understand	Ability to calculate rank, nullity and matrix inverses.
Procedural	Apply	Ability to row reduce matrices and solve systems of linear equations
Procedural	Apply	Ability to calculate eigenvalues and eigenspaces and to diagonalize matrices

Exam

Assessment Type	Summative	Weighting	70
Assessment Weeks		Feedback Weeks		Look up Week Numbers
Feedback	Students to have opportunity to discuss script

Learning Outcomes

Knowledge Level	Thinking Skill	Outcome
Conceptual	Analyse	Ability to prove elementary results about linear independence, basis and dimension
Conceptual	Understand	Ability to state and understand the main definitions and theorems of the course
Conceptual	Understand	Understand the connections among linear transformations, matrices and systems of linear equations
Factual	Understand	Understand the concepts of linear independence, basis and dimension
Factual	Understand	Ability to calculate rank, nullity and matrix inverses.
Factual	Understand	Understand the basic concepts of linear algebra, such as vector spaces and linear transformations
Factual	Understand	Understand the concepts of rank, nullity and invertibility of matrices and linear transformations
Factual	Understand	Ability to calculate matrix determinants
Procedural	Apply	Ability to calculate eigenvalues and eigenspaces and to diagonalize matrices
Procedural	Apply	Ability to row reduce matrices and solve systems of linear equations

Formative Assessment

There are no assessments for this course.

Resit Assessments

Maximum of resit exam and resit exam with carried forward in-course assessment marks

Assessment Type	Summative	Weighting	100
Assessment Weeks		Feedback Weeks		Look up Week Numbers
Feedback

Learning Outcomes

Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator
Knowledge Level	Thinking Skill	Outcome

Course Learning Outcomes

Knowledge Level	Thinking Skill	Outcome
Factual	Understand	Understand the concepts of rank, nullity and invertibility of matrices and linear transformations
Factual	Understand	Understand the basic concepts of linear algebra, such as vector spaces and linear transformations
Factual	Understand	Understand the concepts of linear independence, basis and dimension
Procedural	Apply	Ability to row reduce matrices and solve systems of linear equations
Conceptual	Analyse	Ability to prove elementary results about linear independence, basis and dimension
Factual	Understand	Ability to calculate rank, nullity and matrix inverses.
Procedural	Apply	Ability to calculate eigenvalues and eigenspaces and to diagonalize matrices
Conceptual	Understand	Understand the connections among linear transformations, matrices and systems of linear equations
Conceptual	Understand	Ability to state and understand the main definitions and theorems of the course
Factual	Understand	Ability to calculate matrix determinants

JC1505: LINEAR ALGEBRA (2021-2022)

Course Overview

Course Details

What courses & programmes must have been taken before this course?

What other courses must be taken with this course?

What courses cannot be taken with this course?

Are there a limited number of places available?

Course Description

Contact Teaching Time

Teaching Breakdown

Summative Assessments

Homework Exercises

Learning Outcomes

Tutorial/Seminar Participation

Learning Outcomes

Exam

Learning Outcomes

Formative Assessment

Resit Assessments

Maximum of resit exam and resit exam with carried forward in-course assessment marks

Learning Outcomes

Course Learning Outcomes

Compatibility Mode