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Foundations & Calculus - MAT00012C

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  • Department: Mathematics
  • Module co-ordinator: Dr. Simon Eveson
  • Credit value: 20 credits
  • Credit level: C
  • Academic year of delivery: 2023-24
    • See module specification for other years: 2024-25

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 2023-24

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

  • Sequences and series of real numbers

  • First order ODEs

Assessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Foundations & Calculus		 2 hours 70
Essay/coursework
Foundations & Calculus - Computational Exercises		 N/A 20
Essay/coursework
Foundations & Calculus - Written Coursework		 N/A 10

Special assessment rules

None

Additional assessment information

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

Reassessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Foundations & Calculus		 2 hours 80
Essay/coursework
Foundations & Calculus		 N/A 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.

Indicative reading

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


The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.