Group Size
Approx 15 hours
Skill Level
100 euro

Course Description

This PRELIMINARY UNIT is also made available as a free sample stand-alone distance learning course!

Please complete the application form if you wish to get access to this free course.

Who is this course for ?

This course unit is aimed at students studying, or about to study mathematics or physics at A-level or International Baccalaureate Diploma and other pre-university courses. This is the preliminary unit for the course: A Hitchhiker's Guide To Infinity and covers technical mathematical prerequisites and concepts in sequences and the theory of geometric series.

Be prepared

To get the most out of the material in this unit, students are highly recommended to carefully study these preliminary topics and practical examples, as well as undertake all the set exercises which review key concepts that underpin the theory for later topics on the main course units. The complete course consists of this preliminary unit and the four main units:

  • UNIT 1: Paradoxes of Infinity 
  • UNIT 2: Big Numbers 
  • UNIT 3: How big is Infinity ?
  • UNIT 4: The infinite in Geometry.

The complete course uses a variety of intuitive visual proofs, interspersed with a tantalising sprinkling of mathematical analysis and technology to examine the beautiful and contradictory world of “the infinite” from a variety of perspectives. In highlighting key developments in the history of mathematics, the course exposes the student to the branches of analysis, number theory, transfinite numbers, set theory, infinitesimal calculus and fractals.

This distance learning course is structured around a very specific hierarchy of concepts through which the student is guided. Individual learning steps are accordingly broken down into bite-sized chunks that are linked to particular sub-topics. The sub-topics are grouped into sections, and these sections are in turn amalgamated into full tutorial units. To ease the transition into the main body of the material, students are guided through a carefully designed set of pre-requisite theory, examples and exercises.  

However, the material is designed to stretch all students. For example, optional ‘higher-level’activities are included for the especially gifted or motivated student.

Course Content

This course preliminary unit is broken down into three sections:

SECTION 1: Mathematical Sequences Review

SECTION 2: Introduction to Geometric Series

SECTION 3: Sigma Notation

which should be studied in this order.

It will be important for you to understand the subtle, but precise, use of notation, that will be introduced in this unit. So take your time. The supporting exercises and Progress Checks will give you plenty of opportunities to check your understanding and are designed to guide you through a carefully selected set of examples, pre-requisite theory and application of concepts.

We wish you every success. Enjoy your course!


Ian Tame
Senior Tutor

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