MA204-5-SP-CO:
Abstract Algebra

The details
2019/20
Mathematical Sciences
Colchester Campus
Spring
Undergraduate: Level 5
Current
Monday 13 January 2020
Friday 20 March 2020
15
01 October 2019

 

Requisites for this module
(none)
(none)
MA201
(none)

 

MA301

Key module for

BSC G100 Mathematics,
BSC G102 Mathematics (Including Year Abroad),
BSC G103 Mathematics (Including Placement Year),
BSC G104 Mathematics (Including Foundation Year)

Module description

The module introduces the key abstract algebraic objects of groups, rings and fields and develops their fundamental theory. The theory will be illustrated and made concrete through numerous examples in settings that students will already have encountered.

Aims

To introduce basic principles of abstract algebraic structures and to teach how an extensive and important theory can be developed by logical deductions from a small number of axioms.

Learning Outcomes

On completion of the course, students should
* Know and understand the formal definitions for Groups, Rings, and Fields
* be able to produce simple proofs based on the algebraic axioms
* Be familiar with standard examples of these algebras, including the Symmetric Group, Modular Arithmetic, finite abelian groups, Polynomial and Matrix Rings, and examples of finite fields.
* Be familiar with the notions of subalgebras as they apply to Groups, Rings, and Fields
* Understand the notion of isomorphism and homomorphism of these algebra types


Syllabus

Groups: Binary operations, groups, subgroups, cyclic groups, direct products, groups of permutations, cosets, Lagrange's theorem; Isomorphisms and homomorphisms of groups

Rings, Fields, zero divisors and integral domains, subrings, ideals. Direct products, homomorphisms, Isomorphisms. The Ring of integers modulo n, polynomial rings, the Euclidean algorithm.

Module aims

To introduce basic principles of abstract algebraic structures and to teach how an extensive and important theory can be developed by logical deductions from a small number of axioms.

Module learning outcomes

• Know and understand the formal definitions for Groups, Rings, and Fields
• be able to produce simple proofs based on the algebraic axioms
• Be familiar with standard examples of these algebras, including the Symmetric Group, Modular Arithmetic, finite abelian groups, Polynomial and Matrix Rings, and examples of finite fields.
• Be familiar with the notions of subalgebras as they apply to Groups, Rings, and Fields
• Understand the notion of isomorphism and homomorphism of these algebra types

Module information

No additional information available.

Learning and teaching methods

25 lectures and 5 classes (5 lectures, 1 class every fortnight), and 3 revision lectures. This information can be found on the timetable and module directory.

Bibliography

  • Fraleigh, John B. (©2014) A first course in abstract algebra: Pearson.

The above list is indicative of the essential reading for the course. The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students. Further reading can be obtained from this module's reading list.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Weighting
Coursework Homework 1 14/02/2020 50%
Coursework Homework 2 20/03/2020 50%
Exam 120 minutes during Summer (Main Period) (Main)

Overall assessment

Coursework Exam
20% 80%

Reassessment

Coursework Exam
0% 100%
Module supervisor and teaching staff
Dr Gerald Williams, email gwill@essex.ac.uk
Professor Gerald Williams (gerald.williams@essex.ac.uk)

 

Availability
Yes
No
No

External examiner

No external examiner information available for this module.
Resources
Available via Moodle
Of 33 hours, 33 (100%) hours available to students:
0 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).

 

Further information
Mathematical Sciences

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