Undergraduate Course: Linear Algebra 2 (MATH08080)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 8 (Year 2 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 20 |
ECTS Credits | 10 |
| Summary | This is a course on the theoretical concepts of linear algebra. Students will develop strategies for making the computations of Linear Algebra 1 apply to vectors in general finite-dimensional vector spaces, broadening their knowledge of the subject and enhancing their ability to apply techniques of abstraction and generalization to mathematical problems. |
| Course description |
This is a second course in linear algebra, following on from Linear Algebra 1. It builds upon the concrete examples and applications in the first course to extend linear algebra to general, finite dimensional vector spaces. This will further develop and reinforce the ideas of abstraction and rigorous proof developed in Introduction to Mathematics at University.
Alongside knowledge of linear algebra, this course will provide students with training in generalization and abstraction, which are two key skills required in future courses in pure mathematics.
A representative outline of the course is: Euclidean spaces; Inner products; Bases; Dual spaces; Eigenvalues and eigenvectors; Diagonalizability over C.
Summary of student experience: you will learn to extend the explicit examples of vectors and matrices studied in Linear Algebra I to more general, finite-dimensional vector spaces. You will be trained in the required methods of abstraction and generalization, which are key skills that every mathematician requires. You will use the proof-writing skills you have developed in prerequisite courses to abstract concepts, whilst also learning how to apply some of the techniques developed in the course to examples of vector spaces and linear operators. Alongside the key skills developed, the mathematics you learn here is crucial for many areas of pure and applied maths, including analysis in several variables, mathematical physics, and applied analysis
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Information for Visiting Students
| Pre-requisites | Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling. |
| High Demand Course? |
Yes |
Course Delivery Information
| Not being delivered |
Learning Outcomes
On completion of this course, the student will be able to:
- Determine, given a collection of vectors in a vector space: whether that collection is linearly independent, the dimension of the span, the angle between the vectors with respect to given inner product.
- Determine the matrix of a linear map relative to chosen bases, and how that matrix will change if the bases are changed.
- Find the eigenvalues and eigenvectors of a linear operator, and determine whether that operator is diagonalizable.
- Demonstrate understanding of the conceptual underpinning of material they have already seen at computation level, and re-interpret the computations in the new light of these concepts.
- Apply the proof-writing ability developed in previous courses to abstract concepts, including being able to generalize to previously unseen settings.
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Reading List
Nicolson, Linear Algebra with Applications
Strang, Introduction to Linear Algebra |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | Linear Algebra,Vector Spaces,Linear transformations |
Contacts
| Course organiser | |
Course secretary | |
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