# Summer schools 2023

Will run any time from the end of May to the start of the next academic year (roughly an 11 week period), allowing you to keep your maths skills fresh learning some new and useful things for future maths studies. All courses are delivered online which means more screen time but hopefully worth it for you to get a head start in the next school year.

## STEP etc intended for H/AH

**Open ended (finish at your discretion)**- Working through STEP preparation materials
- Increase your knowledge of advanced school maths
- Improve your reasoning skills

## Progression to SQA Advanced Higher AH

**Open ended (finish at your discretion)**- Topics covered include
- A grade Higher questions
- Further techniques of differentiation and integration
- Vectors

- Preparation for 6th year and 1st year of University courses

## Progression to SQA Higher H

**Open ended (finish at your discretion)**- Topics covered
- Straight line
- Introduction to Calculus
- Extending National 5 Trigonometry

- Ensures that you are ready for SQA Higher
- Please read my How to get an A

## Improve your trigonometry ALL

Intended for those moving up to SQA Higher from N5, or from SQA Higher to Advanced Higher. Trig is tricky but like most maths will yield to practice.

**3 weeks**- Topics covered
- Period and Amplitude N5 to H
- Graphs — using Desmos N5 to H
- Radian measure N5 to H
- 2 triangles N5 to H
- Exact values N5 to H
- CAST diagrams N5 to H
- Addition formulae N5 to H
- Wave function N5 to H
- Trig identities
- Further trig ratios H to AH
- Trig and calculus H to AH
- Inverse trig functions H to AH

## Number theory and Proof AH

Intended for those interested in getting ahead of the curve when moving up to SQA Advanced Higher from SQA Higher. These topics will be new to you. Number theory however is usually considered to be one of the most inherently interesting parts of maths since it deals with the properties of familiar mathematical objects ie whole numbers.

**6 weeks**- Topics covered
- Number theory
- Divisibility
- Primes
- Division
- The Euclidean algorithm
- Number bases

- Proof
- Truth tables
- Necessary and sufficient conditions
- Direct Proof
- Indirect Proof
- Proof by induction

## Probability / mathematical statistics AH

If you are interested in entering a field like, for just one example, machine learning, then data science will be important to you. The sooner you start learning the better, and you have to start somewhere.

**8 weeks**- Topics include
- Probability
- Elementary probability
- Solving probability problems
- Laws of probability

- Statistical distributions
- Probability distributions
- Binomial distribution
- Binomial cumulative distribution function
- Modelling real problems

- Probability

## Mechanics, an introduction AH

Preparation for AH Mathematics of Mechanics

**6 weeks**- Topics covered
- Mathematical models in mechanics
- Displacement, velocity and acceleration
- Force and Newton’s laws

## Algebra and geometry ALL

A general maths course introducing the language of maths (sets) and intended to improve your reasoning skills

**8 weeks**- Topics covered
- Introduction to Sets
- What is a set?
- Sets of sets
- Combining sets

- Geometry of the triangle
- 4 centres
- The Euler line — the one topic in school maths that is a real gem of mathematics

- Introduction to Sets

## Group Theory, an introduction AH

Structure in maths, so on the abstract side

**6 weeks**- Topics covered
- Examples of groups
- Binary operations
- Definition of a group
- Further examples and exercises

## Mathematics as part of a liberal arts education ALL

This course may include any, or all, of the following topics:

**4 weeks**- Readings and discussions on the history, philosophy and culture of mathematics and maths education
- What are numbers?
- What is mathematics?
- Sets, mappings, invariants
- Platonism, formalism, constructivism
- How to account for the “unreasonable effectiveness of mathematics”
- Fibonacci sequence
- Art of maths, and maths in art
- Why study maths? See “Give him threepence, since he must make gain out of what he learns.”

## Numeracy ALL

Intended for adult learners to help them improve their numeracy and confidence in working with numbers

**6 weeks**- Topics covered
- Fractions
- Percentages
- Introductory Statistics
- Calculators
- Any topic that you want help with