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MA24G-Elementary Algebra

Module Provider: Mathematics
Number of credits: 20 [10ECTS credits]
Level: I (Intermediate)
Terms in which taught: Autumn, Spring and Summer
Module Convenor: Dr GD Williams
Pre-requisites: MA11B MA11C
Co-requisites:
Modules excluded: MA113MA11D
Module version for: 2008/9

Email: g.d.williams@reading.ac.uk

Aims:
To introduce, by considering problems in which they are required, the main ideas of set theory, functions and the "language" of mathematics.
To introduce the idea of developing an area of mathematics from axioms, and illustrate this by developing suitable algebraic structures and deriving their properties.

Assessable learning outcomes:
By the end of the module students are expected to be able to:

  • carry out simple instructions involving sets;
  • manipulate the concept of function;
  • identify groups and rings and prove simple properties of groups;
  • recognise and use equivalence relations.

    Additional outcomes:
    At the end of the course students will have acquired some skill in logical reasoning.

    Outline content:
    After an introduction to ideas about sets, functions and binary operations, the course studies the properties of the mathematical structures known as groups and rings, i.e., sets in which an operation of multiplication, or two operations of addition and multiplication, behave in accordance with certain basic axioms. This provides both an understanding of the common properties of many different kinds of mathematical objects which can be added or multiplied and insight into the differences between them.

    Brief description of teaching and learning methods:
    Lectures supported by practical classes

    Contact hours:

      Autumn Spring Summer
    Lectures 20 20 4
    Tutorials/seminars      
    Practicals 9  9  4 
    Other contact (eg study visits)      
    Total hours 29  29  8 
    Number of essays or assignments 9  9   
    Other (eg major seminar paper)      

    Assessment:
    Coursework
    One piece of assessed work in each of the Christmas and Easter vacations
    Relative percentage of coursework :20
    Examinations
    A three hour exam. This contributes 80 % of the overall assessment.
    Requirements for a pass
    A mark of 40% overall.
    Reassessment arrangements
    Re-examination in August/September only.

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