Foundations & Calculus - MAT00012C
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 2025-26 |
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:
-
prove basic results about sets and functions;
-
use the core tools of mathematics, such as derivatives, integrals, vectors and complex numbers to perform calculations and solve problems;
-
prove rigorous statements and solve problems about limits, including their relation to derivatives and integrals;
-
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
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 70 |
| Essay/coursework | 30 |
Special assessment rules
None
Additional assessment information
If a student has a failing module mark, only failed components need be reassessed.
Note:
The assessed coursework component mark will be calculated from a written coureswork and computer exercises, weighted 2:1 respectively.
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
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 70 |
| Essay/coursework | 30 |
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.
Indicative reading
The majority of the course is based on parts of the following book:
Thomas' Calculus: Early Transcendentals, 15th edition in SI Units
https://www.pearson.com/en-gb/subject-catalog/p/thomas-calculus-early-transcendentals/P200000010771/9781292745817
All students on the module will have free access to an electronic version of this book through the VLE page.