MA204-5-AU-CO:
Abstract Algebra
2018/19
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Undergraduate: Level 5
Current
Thursday 04 October 2018
Friday 14 December 2018
15
17 April 2019
Requisites for this module
MA114
(none)
MA201
(none)
MA301
BSC G100 Mathematics,
BSC G102 Mathematics (Including Year Abroad),
BSC G103 Mathematics (Including Placement Year),
BSC G104 Mathematics (Including Foundation Year)
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.
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.
• 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
This module will run in alternate years (first year 2018/19).
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.
This module does not appear to have a published bibliography.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Coursework |
Homework 1 |
|
|
| Coursework |
Homework 2 |
|
|
| Exam |
Main exam: 120 minutes during Summer (Main Period)
|
Exam format definitions
- Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
- In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
- In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
- In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary,
for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.
Your department will provide further guidance before your exams.
Overall assessment
Reassessment
Module supervisor and teaching staff
Prof Gerald Williams, email: gerald.williams@essex.ac.uk.
Dr Gerald Williams, email gwill@essex.ac.uk
MIss Claire Watts, Department Manager, email cmwatts@essex.ac.uk
Yes
No
No
No external examiner information available for this module.
Available via Moodle
Of 33 hours, 31 (93.9%) hours available to students:
2 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
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The University will endeavour to keep such changes to a minimum, and will also keep students informed appropriately by updating our programme specifications and module directory.
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