Our focus in Maths this camp will be Combinatorics. How many ways can words be created from a set of letters? How many ways are there to shuffle a pack of cards and in how many cases can a card player be dealt a strong hand? These types of questions are not only important in playing and in gambling but also in cryptography where we want to hide a secret behind countless possibilities. Modern physics provides an even more significant role to this topic. It turns out that a particle can be better described by considering all the possible states it could be in rather than choosing a particular state.
Thus Combinatorics is essential in probability, cryptography, statistics, statistical thermodynamics and quantum-mechanics but also has its own beauty and all the wonderful questions that relate to it.
During this camp pupils will learn how to collect cases in a clever order, how to make a tree diagram and use lexicographic ordering. Children will study how to create formulae based on experience and data and how to find analogous problems and use an earlier result when tackling a new question. Pupils may even have to set up recursions to handle complex tasks and will definitely meet Pascal’s triangle and will discover and apply the secrets of it.
Combinatorics opens the world: instead of sticking to one single result students are challenged to find all possibilities. A useful skill in life.
Our online camp format provides four one hour lessons each day, two in Programming and two in Maths, each one being relative to the age, experience and knowledge of the camp participant.
In Maths by year groups, participants will study:
Years 3-6
Pupils will learn to enumerate all possible cases in a systematic way using lists, tables and graphs. By noticing some patterns in the process and in the arising lists, they will find potential shortcuts that lead to basic combinatorial formulas. Recognizing the situations for direct application of these formulas in various contexts will help deeper understanding of the main ideas of combinatorics.
Years 7-9
Problems and variations: how to plan, how to structure your work to cover all possibilities. From special to general: making a formula. Number of orderings with conditions.
Different questions with the same answers - what is the underlying mathematical essence? Go deep to get high. Deductive and Inductive formulae.
Years 10-12
Pascal’s triangle, its variations and tricky applications. Permutations, Combinations and Variations. When deductive formulas are hard to find; how to find and handle recursions.
In Programming, depending on your child’s age and experience in coding they may study coding as follows:
- Coding Club (Scratch), Years 3 to 5 most children in this age group will already be familiar with Scratch, however instead of teaching them the programming environment we go further and, using games as a learning tool, aim to teach them the major programming constructions and how to compose effective algorithms.
- Algorithmical Drawing (Java based), Years 5 to 7 the beauty of the Object Oriented way of thinking in programming begins with our Java classes. Pupils start with the basics and move on to development patterns, animations and applications.
- Processing Programming (Java based), Years 6 to 10 pupils learn to program using a Java-based language, building dynamic, visual and interactive applications.
- Python Programming, Years 6 to 13 as well as being an ‘industrial strength’ programming language, popular in web development, data analysis and machine learning, Python is also an ideal teaching tool. Pupils learn algorithm construction, syntax, the theory and practice of coding as well as Python itself.
Format and fees for the senior online camp:
- class sizes are six pupils or fewer of similar age and ability
- each day runs for six hours with four one hour classes and strategic breaks from the screen between them
- class times are: 10.00-11.00, 11.30-12.30, 13.30-14.30, 15.00-16.00
- all classes are interactive, using Zoom, with pupils solving problems with the teacher and with each other
- pupils must have a PC or laptop (Windows or Mac OS) with a camera and mic and a stable internet connection.
- fees are £550 for five days. Bookings of fewer days are not possible for this camp
Places are limited, please register your interest HERE.
