Student Records
Programme & Unit Catalogues

## MA10209: Algebra 1A

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%
Assessment Detail:
• Examination (EX 100%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: While taking this module you must take MA10207 . You must have A level Mathematics Grade A, or equivalent in order to take this unit.
Description: Aims:
To provide a firm grounding in the fundamental objects of mathematics such as sets and functions, numbers, polynomials and matrices. To give a first taste of the axiomatic method, via group theory.

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, using techniques such as contradiction and induction.
* State and prove fundamental results of group theory.
* Apply 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. Direct and inverse image. Equivalence relations.
Numbers (natural, integer, rational, real, complex).
Arithmetic and prime factorisation. Euclid's algorithm.
Polynomials: division with remainder. Modular arithmetic.
Groups, rings and fields (definitions and examples).
Arithmetic of matrices, 2x2 & 3x3 determinants.
Linear, affine & Euclidean transformations of R^2 & R^3, area/volume interpretation of determinants.
Geometry of the complex plane.
Axiomatic development of group theory.
Subgroups, homomorphisms, kernel and image. Isomorphism.
Order of an element and of a group; cyclic groups.
Permutations: cycle notation, sign of a permutation.
Actions, orbits, stabilizers and Cayley's theorem.
Cosets, Lagrange's theorem and applications.
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-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)
• 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-AFB05 : BSc(Hons) Statistics (Year 1)
• USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 1)
• USMA-AKB06 : BSc(Hons) Statistics 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 2017/18 academic year only. Students continuing their studies into 2018/19 and beyond should not assume that this unit will be available in future years in the format displayed here for 2017/18. 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. Undergraduates: Find out more about these and other important University terms and conditions here. Postgraduates: Find out more about these and other important University terms and conditions here.