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Module Code - Title:

MB4001 - ALGEBRA 1

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:

Rationale and Purpose of the Module:

To promote understanding of the number systems and their properties. To develop an understanding of the fundamental concepts of Linear Algebra. To promote proficiency in selected techniques and applications.

Syllabus:

Number: basic number concepts, laws, equations;Number systems: extensions from N to Z, Z to Q and Q to R, complex numbers C;Elementary number theory: Peano's axioms, mathematical induction, binomial coefficients, fundamental theorem of arithmetic; Equations: linear, quadratic, polynomial equations, solution by graphical and numerical methods; Matrices: matrix algebra, applications.

Learning Outcomes:

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

At the end of this module students should be able to: -describe and explain the various number systems commonly used in mathematics -demonstrate the use of elementary number theory -show a facility in manipulating algebraic expressions -show a facility in solving polynomial equations -use the fundamental ideas of linear algebra -manipulate matrices and determinants and apply them to the solution of linear systems -use standard proof techniques in number theory including proof by contradiction and mathematical induction.

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 used should be appropraite and relevant as far as practicable.

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

Prime Texts:

Hunter, J., Blackburn, W.T., Monk, D., and Donald, D (1983) Algebra and number systems. , Blackie and Chambers.

Other Relevant Texts:

Stewart, Ian, and Tall, David (1979) The foundations of mathematics , Oxford University Press.
James, D.J.G. (ed.) (1977) Polymaths Books A and C , Stanley Thornes

Programme(s) in which this Module is Offered:

Semester(s) Module is Offered:

Module Leader:

niamh.omeara@ul.ie