# Department of Mathematics and Computer Studies

## Undergraduate Courses — Outline Module Content

### First Year B.A. — Autumn

**MH4731** — Elementary Number Theory
⇒ Full Syllabus

Representation of numbers, mathematical induction, divisibility, prime numbers, Euclid's Algorithm, congruences.

### First Year B.A. — Spring

**MH4722** — Introduction to Geometry
⇒ Full Syllabus

Angle, distance, length, area, coordinates, lines, triangles and circles, geometric constructions, congruence and similarity.

### Second Year B.A. — Autumn

**MH4713** — Linear Algebra
⇒ Full Syllabus

Vectors and vector spaces, inner products, matrices, linear equations, linear mappings, linear transformations.

**MH4763** — Calculus I: Differentiation
⇒ Full Syllabus

Functions, slope, Newton quotient, derivative, limits, differentiation rules, trigonometric functions, logarithms, exponential functions, continuous functions, completeness of the real numbers, Intermediate Value Theorem, inverse functions and their derivatives.

### Second Year B.Ed. (Arts Elective) — Autumn

**MH4753** — Numbers
⇒ Full Syllabus

The number system hierarchy, key algebraic properties of addition and multiplication, integers, divisibility, elementary number theory, rational and irrational numbers, place value, other number bases.

### Second Year B.A. — Spring

**MH4724** — Introduction to Statistics
⇒ Full Syllabus

Description of sample data; graphical representation, mean and standard deviation, probability theory, random variables, sampling theory, estimation, hypothesis testing, correlation and regression, testing methods.

**MH4764** — Calculus II: Integration
⇒ Full Syllabus

Maxima and minima, Rolle's Theorem, Mean Value Theorem, antiderivatives, Riemann sums, definite integrals, Fundamental Theorem of Calculus, Taylor's Formula.

### Third Year B.A. — Autumn and Spring

**OC4310** and **OC4320** — Off Campus Programme

B.A. students follow the Off Campus Programme for both semesters of the third year. This is comprised of international study placement and / or relevant work placement. Mathematics students, who wish to study abroad, are advised by department staff on the availability of appropriate courses. Guidance is also provided for those who wish to use the opportunity to begin research work for final year projects in Mathematics.

### Third Year B.Ed. (Arts Elective) — Autumn

**MH4715** — Measure
⇒ Full Syllabus

Limits of sequences and series; functions; sketching graphs; limits of functions; rate of change; derivatives of functions; measure of area and volume; integration; Fundamental Theorem of Calculus.

### Third Year B.Ed. (Arts Elective) — Spring

**MH4736** — Statistics
⇒ Full Syllabus

Description of sample data; probability theory; random variables; probability distributions; sampling theory; hypothesis testing; correlation and regression; testing methods.

### Fourth Year B.A. — Autumn

**MH4749** — Geometry
⇒ Full Syllabus

angle, distance, length, area; coordinates; geometric constructions; symmetry; vectors and dot product; non-euclidean geometry.

**MH4718** — Numerical Methods and Computing
⇒ Full Syllabus

Number representation, Introduction to Maple, error analysis, non-linear algebraic equations, iteration, numerical integration, polynomial interpolation, numerical differentiation, systems of linear equations, ordinary differential equations.

**MH4747** — Final Year Project Option

An opportunity for personal work / study, with limited supervision, on an approved mathematical topic or computing assignment of special interest to the student; an opportunity to develop research and presentation skills and / or computing expertise.

### Fourth Year B.A. — Spring

**MH4724** — Introduction to Statistics
⇒ Full Syllabus

Description of sample data, probability theory, random variables, probability distributions, sampling theory, estimation, hypothesis testing, correlation and regression, testing methods.

**MH4728** — Abstract Algebra
⇒ Full Syllabus

Groups, subgroups, Lagrange's theorem. Binary codes. Conjugacy, normal subgroups, permutation groups. Rings, subrings. Integral domains, congruences. Fields.

**MH4748** — Final Year Project Option

An opportunity for personal work / study, with limited supervision, on an approved mathematical topic or computing assignment of special interest to the student; an opportunity to develop research and presentation skills and / or computing expertise.

### Fourth Year B.Ed. (Arts Elective) — Spring

**MH4758** — Geometry
⇒ Full Syllabus

lines, angles, circles, area, geometric constructions, transformations, congruence, similarity, triangles, polygons, special points in triangles, Non-Euclidean geometry.

**MH4768** — Mathematical Problem Solving
⇒ Full Syllabus

Techniques of mathematical problem solving, problem solving as a tool of mathematics instruction, solving problems, how to write a solution or a proof.