KL4002 - Linear Algebra and Geometry

What will I learn on this module?

The module is designed to introduce you to the concepts, definitions and methods linear algebra, coordinate transformations and geometry of curves and surfaces.

Outline Syllabus:

1. Sets, Rings, Groups (basic definitions)
2. Vector Spaces
3. Linear maps (basis expansions, rank, kernel)
4. Matrices (determinants, systems of linear equations, eigenvalues and eigenvectors, similarity transformations)
5. Quadratic forms
6. Euclidean vector spaces
7. Affine spaces
8. Projective spaces
9. Conics
10. Curves in the plane (length of a curve and natural parametrisation, tangent vector, normal vector and curvature)
11. Quadrics
12. Surfaces.

How will I learn on this module?

You will learn through a combination of lectures and exercise sessions. Lectures give a formal introduction to theoretical aspects of linear algebra and geometry. You will attend exercise classes throughout the academic year, during which you will work through problems to develop your knowledge and skills, with the support of the tutor.

Assessment is by a mid semester multiple-choice test and a formal examination at the end of semester. Both assessments aim at testing your knowledge of the discipline along with your problem-solving abilities.

You will receive both written and oral feedback as well as formative feedback throughout the course, in particular during the exercise classes.

Independent study is supported by further technology-enhanced resources provided via the e-learning portal.

How will I be supported academically on this module?

Lectures and exercise classes will be the main point of academic contact, providing you with a formal teaching environment for core learning. In particular, exercise classes will provide you with opportunities for critical enquiry and exchanges. Outside formal scheduled teaching, you will be able to contact the module team (module tutor, year tutor, programme leader) either via email or the open door policy operated throughout the programme. Further academic support will be provided through technology-enhanced resources via the e-learning portal. You will also have the opportunity to give your feedback formally through periodic staff-student committees and directly to the module tutor at the end of the semester.

What will I be expected to read on this module?

All modules at Northumbria include a range of reading materials that students are expected to engage with. The reading list for this module can be found at: http://readinglists.northumbria.ac.uk
(Reading List service online guide for academic staff this containing contact details for the Reading List team – http://library.northumbria.ac.uk/readinglists)

What will I be expected to achieve?

Knowledge & Understanding:
1. Construct mathematical arguments involving linear algebra (KU1).

2. To apply methods of geometry of vector spaces, curves and surfaces (KU1).

Intellectual / Professional skills & abilities:

3. Construct rigorous mathematical arguments, prove propositions and theorems using the modern language of linear algebra and geometry (IPSA1).

4. Select and apply appropriate methods and techniques to solve standard linear algebra and geometry problems (IPSA2).

Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity) (PVA):
5. Demonstrate the ability of learning new concepts; present clear and logical arguments; work independently and manage time effectively.

How will I be assessed?

1. Coursework (component 1)– (20%) – 1, 3, 5
2. Examination (component 2) – (80%) – 1, 2, 3, 4, 5

You will be prepared for the summative assessment in each semester via dedicated exercise sessions including exam type questions, the discussion of previous exam papers and mock exam papers. Different solutions strategies and approaches to the exam and optimal time management will also be discussed.

1. Exercise classes – 1, 2, 3, 4

Feedback will take several forms, including verbal feedback during exercise classes; individual verbal and written comments on both examinations will be delivered during dedicated classes and via eLP.





Module abstract

Linear Algebra and Geometry will provide you with the necessary mathematical tools needed to formulate a variety of applied problems in the modern language of linear maps and vector spaces. You will enhance your abstraction skills and learn techniques to describe high dimensional structures. You will learn, using rigorous mathematical reasoning, to translate your intuition into specific mathematical objects such as vectors, matrices and systems of algebraic equations. The module will underpin your further studies of a range of pure and applied mathematics subjects.
The module consists of combination of lectures and exercise classes. During the lectures you will be introduced to the language of vector spaces and linear transformations using definitions, fundamental propositions, theorems and techniques that will allow you to manipulate and study complex algebraic and geometric structures in suitable coordinate systems. Exercise classes will enable you to apply these techniques and appreciate the abstract power of algebra of vector spaces, geometry of curves and surfaces, and their intrinsic beauty. You will be assessed by two formal examinations designed to put forward your new skills and techniques. You will receive constructive feedback during exercise classes throughout the year, and the eLearning Portal will serve as a point of contact, information and discussion with the Tutor.
Concepts and techniques you will learn in this module will constitute a solid foundation for your further studies, enhance your abstract thinking, sharpen your analytical mindset and nurture your effective problem-solving transferrable skills, enhancing your employability on the longer term.

Course info

UCAS Code G100

Credits 20

Level of Study Undergraduate

Mode of Study 3 years Full Time or 4 years with a placement (sandwich)/study abroad

Department Mathematics, Physics and Electrical Engineering

Location City Campus, Northumbria University

City Newcastle

Start September 2024 or September 2025

Fee Information

Module Information

All information is accurate at the time of sharing. 

Full time Courses are primarily delivered via on-campus face to face learning but could include elements of online learning. Most courses run as planned and as promoted on our website and via our marketing materials, but if there are any substantial changes (as determined by the Competition and Markets Authority) to a course or there is the potential that course may be withdrawn, we will notify all affected applicants as soon as possible with advice and guidance regarding their options. It is also important to be aware that optional modules listed on course pages may be subject to change depending on uptake numbers each year.  

Contact time is subject to increase or decrease in line with possible restrictions imposed by the government or the University in the interest of maintaining the health and safety and wellbeing of students, staff, and visitors if this is deemed necessary in future.


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