# MATH10340 Linear Algebra in the Mathematical and Physical Sciences

## Academic Year 2023/2024

Students will cover mathematical topics and concepts essential to the study of the Mathematical and Physical Sciences. Topics covered include: (1) a review of complex numbers - their fundamental arithmetic, Euler's formula and roots of unity; (2) matrices - sums, products and transposes, determinants of (n x n)-matrices, their computation for small n, and the adjugate method of finding inverses; (3) solutions of systems of linear equations by Gaussian elimination, connections between matrices and linear systems, and elementary matrices and their effects on determinants; (4) vectors in n-dimensional real and complex space, scalar products, angles between vectors, the Cauchy-Schwarz inequality, orthogonal projections, vector products and lines and planes in 3-space; (5) eigenvalues and eigenvectors of (n x n)-matrices, and their computation for small n; (6) linear spaces and bases - examples of linear spaces from previous chapters, linearly independent and spanning sets, bases and dimension, eigenspaces and orthonormal bases. Examples and applications of these topics in the Mathematical and Physical Sciences will be presented throughout the module.

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Curricular information is subject to change

Learning Outcomes:

On successful completion of this module, the student is expected to (1) demonstrate a solid understanding of the theoretical aspects of the topics covered in the module, and (2) be able to carry out any computations associated with the concepts presented in the module (including, but not limited to, finding determinants and inverses of (3 x 3)-matrices, solving systems of linear equations, or finding the eigenvalues and eigenvectors (3 x 3)-matrices).

Student Effort Hours:
Student Effort Type Hours
Lectures

36

Tutorial

10

Specified Learning Activities

24

Autonomous Student Learning

40

Total

110

Approaches to Teaching and Learning:
Lectures, tutorials, enquiry and problem-based learning.
Requirements, Exclusions and Recommendations
Learning Recommendations:

Minimum of Least Leaving Certificate H4 (or equivalent)

Module Requisites and Incompatibles
Incompatibles:
ECON10030 - Intro Quantitative Economics, MATH10030 - Maths for Business, MATH10050 - Linear Algebra & Geom, MATH10090 - Matrices & Vectors, MATH10120 - Linear Algebra Apps to Econ, MATH10200 - Matrix Algebra, MATH10260 - Linear Algebra for Engineers, MATH10270 - Linear Algebra in the Math Sci, MATH10280 - Linear Algebra in the Phys.Sci, MATH10290 - Linear Algebra for Science, MATH10390 - Linear Algebra (Online), MST10030 - Linear Algebra I

Assessment Strategy
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Continuous Assessment: Tutorial quizzes fortnightly Throughout the Trimester n/a Not yet recorded No

15

No
Continuous Assessment: Webwork online problem sets Throughout the Trimester n/a Other No

15

No
Examination: Final examination 2 hour End of Trimester Exam No Not yet recorded No

70

No

Carry forward of passed components
No

Resit In Terminal Exam
Autumn Yes - 2 Hour