Module Code - Title:

MB4002 - ALGEBRA 2

Year Last Offered:

2025/6

Hours Per Week:

Lecture

2

Lab

0

Tutorial

1

Other

0

Private

7

Credits

6

Grading Type:

N

Prerequisite Modules:

MB4001

Rationale and Purpose of the Module:

To promote an understanding of basic algebraic concepts of discrete mathematics. To examine the use of transformations in geometry. To apply discrete mathematics in the solution of various applied problems.

Syllabus:

Mathematical logic: statements, sentences, truth tables, quantifiers, proof; Sets: notation, definition, set operations; Relations: equivalence relation, partitions, congruence; Mappings: injective, surjective, bijective maps, composition, inverse; Mappings in the plane: projections, transformations; Matrix representation; Algebra of sets: De Morgan's law, principle of duality; simple applications to switching theory.

Learning Outcomes:

Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)

At the end of this module students should be able to: -demonstrate the use of logical thinking -analyse and use the main methods of logical reasoning in mathematics -describe and explain basic concepts of algebra including sets, set operations, relations, equivalence relations, partitions, congruence of integers, maps, injective, surjective and bijective maps, maps in the plane -explain the use logic and algebra in selected applications -show an increased facility in manipulating algebraic expressions.

Affective (Attitudes and Values)

None

Psychomotor (Physical Skills)

None

How the Module will be Taught and what will be the Learning Experiences of the Students:

Normal lecture and tutorial mode of delivery. Examples should be kept simple and with applications where appropriate.

Research Findings Incorporated in to the Syllabus (If Relevant):

Prime Texts:

Gerstein, Larry J. (1987) mathematics and algebraic structures. , W.H. Freeman and Company.

Other Relevant Texts:

Denvir, Tim, (1986) An introduction to discrete mathematics for software engineering. , Macmillan.

Finkbeiner, Daniel T., and Lindstrom, Wendell D. (1987) A primer of discrete mathematics. , W.H. Freeman

Programme(s) in which this Module is Offered:

Semester(s) Module is Offered:

Module Leader:

niamh.omeara@ul.ie