MA283 Linear Algebra

Welcome to the homepage for Linear Algebra MA283.

This course will run over the 12 weeks of Semester 2 in the 2021-22 academic year, commencing on January 8. It is an introduction to the concepts, methods and applications of linear algebra, for students specializing in mathematics and related subject areas.

Content will be posted week by week at the links below.

Week 1Week 2Week 3Week 4
Week 5Week 6Week 7Week 8
Week 9Week 10Week 11Week 12

Lectures

Wednesday 1.00–1.45, G002 Áras Uí Cathail
Friday 11:00–11:45, D’Arcy Thompson lecture theatre

Lectures in the first week will be online (the first will be pre-recorded and the second will run via a Zoom meeting at 11). Lectures on campus will commence in Week 2, at the above venues. Video versions will continue to be posted, as I am sympathetic to the positions of students who cannot attend in person (either occasionally or consistently) in the current circumstances.

Tutorials

Tutorials commence in Week 3, at the following times and venues.

  • Monday 2.00 ENG 2033
  • Tuesday 11.00 AC202
  • Wednesday 12.00 McMunn Lecture Theatre

The module tutor is Victoria Sánchez Muňoz who is a research student in the School of Maths.

Syllabus Outline

This course is an introduction to Linear Algebra, which is the study of vector spaces. Vector spaces are algebraic structures (sets) whose elements can be added, subtracted or multiplied by scalars (numbers). The algebra of matrices is closely related to linear algebra, and provides a concrete framework and a comprehensive computational environment for studying the subject. Much of our work will be concerned with matrices and their properties, but we will also be interested in the wider context of abstract vector spaces.

The concepts and methods of Linear Algebra is absolutely pervasive and have fundamental importance in every area of the mathematical and statistical sciences. Matrix algebra is a powerful tool in the mathematical modelling of physical and dynamic processes in both discrete and continuous contexts. Because linear algebra is relatively well understood and particularly amenable to computational methods, it has huge importance in scientific computing as well as in numerical analysis and approximation theory. It is also indispensable in geometry, combinatorics, analysis and all areas of algebra.

Our syllabus will have four chapters.

  1. Preview: what is linear algebra about?
    Vector spaces, matrices, review of matrix algebra, systems of linear equations.
  2. Spanning sets, bases and dimension
    Linear independence, bases and dimension. The rank of a matrix. The kernel and image of a linear transformation. The Rank-Nullity Theorem.
  3. Linear Transformations, Eigenvectors and Similarity
    Choice of basis and change of basis. Diagonalizabilty. Eigenspaces.
  4. Orthogonality, inner products and projections
    Some additional useful structure in vector spaces

Course and Lecture Notes

The lecture notes form the main text for the course. They will be posted in instalments here as we proceed.

Chapter 1Section 1.1Section 1.2Section 1.3Section 1.4
Chapter 2Section 2.1Section 2.2Section 2.3
Chapter 3Section 3.1Section 3.2Section 3.3Section 3.4Section 3.5
Chapter 4Section 4.1

Assessment

Assessment of students’ learning in MA283 will consist of the following elements.

  • Four webwork homework assignments (30%)
  • Two-hour final exam in the summer exam session (70%)
  • Optional bonus: ten weekly challenges run via Blackboard (2% each, 20% total)
    Each challenge will ask students to provide an example of some object with specified properties. Submissions will be marked out of 10 points, with 5 for mathematical accuracy and 5 for creativity and quality of exposition.

As you can see, this adds up to more than 100%. Total scores that exceed 100% will be returned as 100%.