- Department: Mathematics
- Credit value: 20 credits
- Credit level: C
- Academic year of delivery: 2024-25
- See module specification for other years: 2023-24
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.
Post-requisite modules:
Occurrence | Teaching period |
---|---|
A | Semester 1 2024-25 |
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
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.
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
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 70 |
Essay/coursework | 30 |
None
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
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 70 |
Essay/coursework | 30 |
Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
The lectures will be supplemented by a free open source textbook that will be used to support the lectures and computer sessions using a symbolic algebra package which will give students the tools to carry out calculations and also to self-check results.
There are many excellent textbooks. For calculus, this course will be based around
https://lyryx.com/calculus-early-transcendentals/
which is a free open source calculus textbook