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  6. MA2004: SETS AND ALGEBRAIC STRUCTURES

MA2004: SETS AND ALGEBRAIC STRUCTURES (2014-2015)

Last modified: 28 Jun 2018 10:27


Course Overview

The importance of introducing the study of sets into mathematics was recognised  in the late 19th century by Georg Cantor, who was the first to discover the existence of the “infinity of infinities”. Following that and some further remarkable achievements, “Set Theory" became a vibrant subject, and is regarded as the very foundation of mathematics. The course will start with an introduction to the language of set theory, and some of the basics of the subject. Having set the foundations, the course will then proceed with its main bulk consisting of an introduction to a variety of algebraic topics.





Course Details

Study Type Undergraduate Level 2
Term First Term Credit Points 15 credits (7.5 ECTS credits)
Campus None. Sustained Study No
Co-ordinators
  • Professor Ran Levi

What courses & programmes must have been taken before this course?

None.

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

No

Course Description

This course provides an introduction to algebraic structures and elementary number theory.

The course includes a discussion of:

  • Sets (notation, functions, injections, surjections, bijections)
  • Countability of the rational numbers and uncountability of the real numbers
  • The integers and factorisation
  • Prime numbers, Euclidean algorithm, uniqueness of factorisation
  • The integers modulo n
  • Equivalence relations
  • Permutations
  • Group axioms
  • The symmetric group
  • Lagrange's Theorem
  • Fermat's Little Theorem
  • Definition of commutative ring and of a field with examples, especially polynomial rings
  • Vector spaces and linear transformations.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

More Information about Week Numbers


Details, including assessments, may be subject to change until 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

Summative Assessments

1st Attempt: 1 two-hour written examination (80%); in-course assessment (20%).

Resit: 1 two-hour written examination paper, maximum resit (100%) and resit (80%) with in-course assessment (20%).

Formative Assessment

Informal assessment of weekly homework through discussions in tutorials.

Feedback

In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact Course Coordinator for feedback on the final examination.

Course Learning Outcomes

None.
 

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