## MA10209: Algebra 1A

[Page last updated: 20 April 2021]

Owning Department/School: Department of Mathematical Sciences
Credits: 6      [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Certificate (FHEQ level 4)
Period:
Semester 1
Assessment Summary: EX 100%
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites:
Aims: To provide a firm grounding in the fundamental objects of mathematics such as sets, functions, numbers, polynomials and matrices. To give an introduction to linear algebra in concrete terms.

Learning Outcomes: After taking this unit the students should be able to:
* Demonstrate understanding of the elementary concepts of geometry and algebra.
* Construct correct logical proofs of theorems about these concepts.
* Perform computations with numbers, polynomials and matrices, including the solution of systems of linear equations.
* Apply elementary abstract ideas in specific examples.

Skills: Numeracy T/F A
Problem Solving T/F A
Written and Spoken Communication F (in tutorials)

Content: Sets and functions: constructions and properties, cardinality.
Equivalence relations and partitions.
Permutations: cycle notation and sign, the symmetric group.
Numbers (natural, integer, rational, real, complex); algebraic properties as rings and fields.
Primes, factorisation and Euclid's algorithm;� modular arithmetic.
The complex plane: complex exponentials, roots of unity.
Polynomials: division with remainder, coprime polynomials
Matrices with real coefficients: matrix algebra, linear transformations, 2-by-2 and 3-by-3 determinants, geometric interpretation
Systems of linear equations: matrix representation, row operations and row echelon form

Programme availability:

#### MA10209 is Compulsory on the following programmes:

Department of Computer Science
• USCM-AFB20 : BSc(Hons) Computer Science and Mathematics (Year 1)
• USCM-AAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 1)
• USCM-AKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 1)
• USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 1)
• USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 1)
• USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 1)
Department of Economics
• UHES-AFB04 : BSc(Hons) Economics and Mathematics (Year 1)
• UHES-AAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 1)
• UHES-AKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 1)
• UHES-ACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 1)
Department of Mathematical Sciences
• USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 1)
• USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 1)
• USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 1)
• USMA-AFB13 : BSc(Hons) Mathematics (Year 1)
• USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 1)
• USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 1)
• USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 1)
• USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 1)
• USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 1)
• USMA-AFB20 : BSc(Hons) Mathematics, Statistics, and Data Science (Year 1)
• USMA-AAB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Study year abroad (Year 1)
• USMA-AKB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Industrial Placement (Year 1)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 1)
• USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 1)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 1)
Department of Physics
• USXX-AFB03 : BSc(Hons) Mathematics and Physics (Year 1)
• USXX-AAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 1)
• USXX-AKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 1)
• USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 1)
• USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 1)
• USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 1)

 Notes: This unit catalogue is applicable for the 2021/22 academic year only. Students continuing their studies into 2022/23 and beyond should not assume that this unit will be available in future years in the format displayed here for 2021/22. Programmes and units are subject to change in accordance with normal University procedures. Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.Find out more about these and other important University terms and conditions here.