Accessibility statement

# Foundations & Calculus - MAT00012C

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• Department: Mathematics
• Credit value: 20 credits
• Credit level: C
• Academic year of delivery: 2024-25
• See module specification for other years: 2023-24

## Module summary

The basic tools necessary to study higher level mathematics will be developed including basic set theory, complex numbers, limits, vectors, the derivative and the integral. Students will develop their understanding through lectures, self study, small group teaching and computer labs.

## Related modules

Post-requisite modules:

• Multivariable Calculus & Matrices
• Introduction to Applied Maths

## Module will run

Occurrence Teaching period
A Semester 1 2024-25

## Module aims

The basic tools necessary to study higher level mathematics will be developed including basic set theory, complex numbers, limits, vectors, the derivative and the integral. Students will develop their understanding through lectures, self study, small group teaching and computer labs

## Module learning outcomes

By the end of the module, students should be able to:

1. prove basic results about sets and functions;

2. use the core tools of mathematics, such as derivatives, integrals, vectors and complex numbers to perform calculations and solve problems;

3. prove rigorous statements and solve problems about limits, including their relation to derivatives and integrals;

4. use a Computer Algebra System to answer suitable questions about the topics of this module.

## Module content

• Set theory, functions (careful definition of a function), notation, cartesian products of sets, elementary functions (trigonometric, hyperbolic)

• Complex numbers

• Limits (using epsilon-delta methods) and continuity

• Differentiability

• Vectors and parametric curves

• Integration

• First order ODEs

## Indicative assessment

Closed/in-person Exam (Centrally scheduled) 70
Essay/coursework 20
Essay/coursework 10

### Special assessment rules

None

If a student has a failing module mark, only failed components need be reassessed.

NB the 10% written coursework is merged with the exam, so if a student fails the module they resit the exam for 80%. If they have passed the 20% computer-based coursework they may keep that mark, or they may choose to resit it.

Note:

Due to the pedagogical desire to provide speedy feedback in seminars, extensions to the written coursework and computer exercises are not possible.

To mitigate for exceptional circumstances, the written coursework grade will be the best 4 out of the 5 assignments. If more than one assignment is affected by exceptional circumstances, an ECA claim must be submitted (with evidence).

Similarly, the computational grade will be the best 2 out of the 3 exercises. If more than one exercise is affected by exceptional circumstances, an ECA claim must be submitted (with evidence).

For extreme exceptional circumstances cases, the 10% coursework component can be discounted, with the exam mark making up 80% of the module

### Indicative reassessment

Closed/in-person Exam (Centrally scheduled) 80
Essay/coursework 20

## Module feedback

Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.