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MATH20300

Academic Year 2026/2027

Linear Algebra 2 for the Mathematical Sciences (MATH20300)

Subject:
Mathematics
College:
Science
School:
Mathematics & Statistics
Level:
2 (Intermediate)
Credits:
5
Module Coordinator:
Professor Gary McGuire
Trimester:
Autumn
Mode of Delivery:
On Campus
Internship Module:
No
How will I be graded?
Letter grades

Curricular information is subject to change.

This is a second university course in Linear Algebra, delving deeper into the concepts of this beautiful subject.
The successful student will gain a solid understanding of the theoretical aspects of linear algebra as well as the ability to carry out practical computations, and the ability to apply concepts and techniques to unseen problems.

The topics discussed will include:
Vector spaces over a field - axiomatic definition, span, linear independence, bases, dimension, sum, direct sum;
Linear maps - definition, rank-nullity, matrix of a linear map, change of basis, column and row rank;
Eigen theory - eigenvalues, eigenvectors, eigenspaces and diagonalization of linear maps, real symmetric matrices;
Inner product spaces, Gram-Schmidt procedure.

About this Module

Learning Outcomes:

Upon successful achievement of the learning outcomes the student will be able to:

Prove elementary facts and identities related to the axioms of a vector space.
State and unpack the fundamental definitions of linear algebra.
State and prove the key theorems in the subject.
Determine whether or not given sets of vectors form a vector subspace.
Compute the span of a set of vectors.
Decide if a set of vectors are linearly independent or not.
Calculate the basis and dimension of a vector space.
Apply the Rank-Nullity theorem.
Find the image and nullspace of a linear transformation along with their bases.
Calculate the change of basis matrix.
Calculate the eigenvalues, eigenvectors, and eigenspaces of a linear transformation.
Determine when a linear transformation is diagonalizable and when it is not.
Prove facts about inner product spaces.
Apply known results to unseen problems and applications.

The United Nations identified seventeen Sustainable Development Goals (SDGs) as core to the 2030 Agenda for Sustainable Development, and UCD contributes in general to SDG 4 Quality Education. Further SDGs explored within this module if relevant are listed below. A scale of 1 - 5 indicates the extent to which the SDG is covered.


 

Student Effort Hours:
Student Effort Type Hours
Autonomous Student Learning

51
Lectures

23
Tutorial

12
Online Learning

24
Total

110

Approaches to Teaching and Learning:
 I won't ask you to purchase any textbooks for this course but it might be helpful to have a copy of "Linear Algebra Done Right" by Sheldon Axler which is legally available at https://linear.axler.net/

Requirements, Exclusions and Recommendations
Learning Requirements:

A good first year knowledge of undergraduate linear algebra will be assumed, such as that given in MATH10340, or its equivalent from other universities.


Module Requisites and Incompatibles
Pre-requisite:
MATH10340 - Linear Algebra 1 (MPS)

Incompatibles:
MATH20030 - Linear Algebra 2 (Sci)., MST20050 - Linear Algebra II


 

Assessment Strategy
Description Timing Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Quizzes/Short Exercises: Worksheets in tutorial to be worked on in groups Week 2, Week 3, Week 4, Week 5, Week 6, Week 7, Week 8, Week 9, Week 10, Week 11, Week 12 Standard conversion grade scale 40% No
10
 No
Exam (In-person): Mid trimester examination. No remediation. Week 7 Standard conversion grade scale 40% No
20
 No
Exam (In-person): Final examination held at the end of the trimester End of trimester
Duration:
2 hr(s)
 Standard conversion grade scale 40% No
70
 No

As part of UCD's student support, under the Additional Consideration policy, extensions may be available for the following assessments in the module: Assignment (including essay/poster), Portfolio, Reflective Assignment, Report(s), and Individual Project.


Carry forward of passed components
No
 

Resit In Terminal Exam
Spring Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 

Feedback Strategy/Strategies

• Feedback individually to students, on an activity or draft prior to summative assessment
• Group/class feedback, post-assessment
• Peer review activities
• Self-assessment activities

How will my Feedback be Delivered?

An important part of this module is self-directed learning and knowing when a submission is good enough to meet the module's learning outcomes. Therefore you will spend time in tutorials on problems and solutions.

Name Role
Arani Paul Tutor

Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
Autumn Lecture Offering 1 Week(s) - Autumn: All Weeks Tues 10:00 - 10:50
Autumn Lecture Offering 1 Week(s) - Autumn: All Weeks Wed 09:00 - 09:50
Autumn Tutorial Offering 1 Week(s) - Autumn: All Weeks Mon 14:00 - 14:50
Autumn Tutorial Offering 3 Week(s) - Autumn: All Weeks Tues 12:00 - 12:50
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