Parent Programme

Bachelor of Science in Computing (Level 7 NFQ)

NFQ Levil & Reference

Level 6 / Ref: M1.8

Duration

12 Weeks X 3 Hours per week

MODULE TITLE

Mathematics for IT 1

STAGE

Year 1

Module Credit Units

ECTS: 5

The Mathematics for IT 1 enables the learner to develop and foster their problem-solving skills using mathematics. This module ensures the learner sees mathematics as an integral part of their studies and necessary as part of successful progression both horizontally and vertically within the programme.

**Mathematics for IT**

**Matrices**:

- Introduction to matrices and the order of matrices
- Types of (square) matrices: symmetric, diagonal, identity
- Adding, subtracting and multiplying matrices
- Transpose of a matrix
- The determinant and inverse of 2 x 2 and 3 x 3 matrices

**Relations:**

- (Binary) relations (as a set of ordered pairs), digraphs
- Reflexive, symmetric, antisymmetric, transitive, and closures
- Equivalence relations, equivalence classes, partitions

**Functions:**

- Introduction to (finite discrete) functions as a special case of relations
- Domain, codomain, image (range)
- Expressing a function as a mapping diagram and in “domain-codomain-rule" notation
- Types of functions: injective, surjective, bijective
- Inverse of a function, domain restriction
- Composition of functions
- Exploring some non-finite and continuous functions (e.g. linear on an interval or the Reals, modulo)

**Trigonometry:**

- Degrees and Radians
- Pythagoras' theorem
- Trigonometric ratios: sin, cos and tan, and the inverses of these
- Sine rule and cosine rule
- Compound angle formula

**Algebra:**

- Factorization and roots, solving quadratics and cubics
- Solving simultaneous equations
- Solving inequalities which involve intersections/unions, quadratics, absolute values

**Coordinate Geometry:**

- Points as ordered pairs and expressed on the Cartesian plane
- Distance between two points, slope
- Equation of a line, and construction of such from two points or the slope and a point or y-intercept, calculating a y value from an x value or an x value from a y value
- Perpendicular and parallel lines
- 3-dimensional Cartesian coordinate system

Upon successful completion of this module, the learner should be able to:

MIMLO1

Use matrix operations on matrices of various orders.

MIMLO2

Produce digraphs of relations and functions of their various types.

MIMLO3

Solve trigonometric problems using Pythagoras' theorem and the sine, cosine and tangent ratios and rules.

MIMLO4

Solve algebraic problems involving simultaneous equations and inequalities.

MIMLOs

Assessment

Percentage

1, 2, 3, 4

Continuous Assessment (In-class written text)

Total 100%

Final Examination (Proctored written Exam)

All Assessments

Where the combined marks of the assessment and examination do not reach the pass mark the learner will be required to repeat the element of assessment that they failed. Reassessment materials will be published on Moodle after the Examination Board Meeting and will be aligned to the MIMLOs and learners will be capped at 40% unless there are personal mitigating circumstances.

**This Mathematics for IT module will ensure learners meet the following objectives:**

- Understand matrices, including their order, types, and operations.
- Explore binary relations and their properties.
- Investigate equivalence relations and partitions.
- Comprehend (discrete) functions, their types, and function composition.
- Gain proficiency in trigonometric concepts and formulas.
- Develop proficiency in algebraic techniques and solving equations.
- Explore coordinate geometry, including the Cartesian plane and equations of lines.

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