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Algebra - MAT00010C

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  • Department: Mathematics
  • Module co-ordinator: Dr. Jason Levesley
  • Credit value: 20 credits
  • Credit level: C
  • Academic year of delivery: 2021-22
    • See module specification for other years: 2022-23

Module will run

Occurrence Teaching period
A Autumn Term 2021-22 to Summer Term 2021-22

Module aims

The first years of all mathematics programmes are designed to give students a thorough grounding in a wide spectrum of mathematical ideas, techniques and tools in order to equip them for the later stages of their course. During first year, as well as consolidating, broadening and extending core material from pre-University study, we initiate a cultural transition to the rigorous development of mathematics which is characteristic at University. Students will develop both their knowledge of mathematics as a subject and their reasoning and communication skills, through lectures, tutorials, seminars, guided self-study, independent learning and project work. This development is addressed in all of our first year modules, although different modules have a different emphasis.

In addition to the above broad aims of the first year, this module focusses on specific areas of Pure mathematics, including vectors, complex numbers, matrices and linear equations.

Module learning outcomes

Subject content

  • Vectors in 2 and 3 dimensions: definition; manipulation (algebra); dot and cross products; vector equations of lines and planes.

  • Complex numbers and their algebra: their origin as solutions to real quadratic equations; geometric representation and polar form; De Moivre’s theorem and roots; curves and regions in the plane described using complex numbers; roots of real polynomials occur in conjugate pairs.

  • Integers and congruences: common divisors, highest common factors, Euclid’s algorithm, primes and factorisation.

  • Real and complex polynomials; factorising, remainder theorem, long division, highest common factors and Euclid’s algorithm.

  • Introduction to matrices and their algebra: (addition, multiplication, inverse, transpose); determinants.

  • Systems of linear equations: solution by reduction to echelon form; rank of a matrix; application to finding inverses of matrices. Applications to solving systems of linear ODEs.

  • Linear transformations in 2 and 3 dimensions: actions on coordinates and basis vectors; eigenvectors and eigenvalues; diagonalisation in 2 and 3 dimensions.


Academic and graduate skills

  • Academic skills: the application of rigorous mathematical techniques and ideas to the development of mathematics;the power of abstraction as a way of solving many similar problems at the same time;the development and consolidation of essential skills which a mathematician needs in their toolkit and needs to be able to use without pausing for thought.

  • Many of the techniques and ideas developed in this module are ones which graduates employed as mathematicians and in other numerate professions will use from day to day in their work. On top of this, students, through lectures, examples, classes, will develop their ability to assimilate, process and engage with new material quickly and efficiently.


Task Length % of module mark
Online Exam - 24 hrs (Centrally scheduled)
Algebra - Competency exam
8 hours 0
Online Exam -less than 24hrs (Centrally scheduled)
2.5 hours 100

Special assessment rules


Additional assessment information

Competency exam is pass/fail and must be passed to pass the module, although multiple attempts will be allowed.  Since a proper grasp of the material in this module is essential for success in any of our programmes involving it, the module is non-compensatable. 5% of the final exam mark comes from a coursework mark, calculated by taking the average over the best n-1 out of n assignments. 


Task Length % of module mark
Online Exam - 24 hrs (Centrally scheduled)
Algebra - Competency exam
8 hours 0
Online Exam -less than 24hrs (Centrally scheduled)
2.5 hours 100

Module feedback

Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

Indicative reading

Martin Liebeck, A Concise Introduction to Pure Mathematics. ISBN 1584885475


G H Hardy, A Course in Pure Mathematics (10th edition). ISBN 1603860495

[A “classic” text, first published in 1952, covering both Algebra and Calculus. Suitable for students who wish to be stretched.]

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.