Advanced Algebra and Probability

Course Length: Full academic year (30 weeks)
This Year's ScheduleClick here to view

Aims of the Course

This course on Advanced Algebra and Probability is aimed at high-school students who have already shown strength and aptitude for mathematics, or who want a course that's out of the ordinary.  For UK students, that may be someone who's studying A-levels already, or who has finished a GCSE-level exam and waiting to start a higher course.  For US students, it's likely that they've completed Algebra 2 and are shoring up their transcript for a competitive college. 

The motivation for putting Algebra and Probability together in a single course is that they provide the foundations for data science.  These areas of mathematics are becoming increasingly important when studying mathematics in college and also for many technology jobs.  They are also beautiful and challenging in their own right.

Homework Expectations

In algebra, the emphasis is on matrices and their applications.  I don't expect any previous familiarity with matrices, but students should be familiar with solving a pair of linear equations in two unknowns and also with quadratic equations.

In probability, the emphasis will be on foundations and applications. We shall look at common pitfalls when working with probabilities, and the importance of notions such as conditional probability.  There is no previous experience with probability assumed, and I also avoid topics that require any knowledge of calculus.

All the course material will be contained in the webinars.  There is no specific text that I follow for algebra.  For the sections on probability, I follow roughly the early chapters of Introduction to Probability (2nd edition) by Joseph Blitzstein and Jessica Hwang, published by CRC Press (2019).  It is not necessary to have a copy of the book, but if you do wish to have one, it is available as a download at or in hardcopy from the usual channels.

How It Supports Your Child's Education

For UK students and other students wishing to take UK-style exams, while the course does not lead directly to a specific IGCSE/GCSE qualification, the Advanced Algebra and Probability course is covering topics and skills that are relevant to any ambitious mathematician and those aiming for STEM fields.

For US students, this course can fulfil a high school credit in Advanced Mathematics.

Who Teaches Advanced Algebra and Probability?

Dr Robert Leese has taught mathematics at one of the most prestigious universities in the world for over 25 years, and is CTO in a systems engineering company. He sees a role for himself in conveying mathematics as a set of analytical skills instead of a collection of facts and formulae that few students know what to do with. He's the father of four children whom he has homeschooled for over a decade, and is an avid collector and repairer of antique fountain pens.
See all courses taught by Robert