**P****urpose and Aims of Courses**

Our Mathematics courses aim to motivate and challenge learners by enabling them to select and apply mathematical techniques in a variety of mathematical and real-life situations. Mathematics develops skills in manipulation of abstract terms in order to solve problems and to generalise. It allows learners to interpret, communicate and manage information in mathematical form, skills which are vital to scientific and technological research and development.

Mathematics is the only universal language, a beautiful, rigorous and creative subject in its own right. It is a subject which is at the forefront of the greatest issues facing the world today and current scientific developments.

Mathematics as a skill is in high demand by employers and Higher Education establishments alike. Many former pupils have gone on to study Mathematics at college and University alongside Economics, Statistics, Finance, Actuarial Science and Engineering.

- develop confidence in the subject and a positive attitude towards further study in mathematics and the use of mathematics in employment
- deliver in-depth study of mathematical concepts and the ways in which mathematics describes our world
- allow learners to interpret, communicate and manage information in mathematical form; skills which are vital to scientific and technological research and development
- deepen the learner’s skills in using mathematical language and exploring advanced mathematical ideas

The pace of the course is much more intense than at National 5. Pupils are encouraged to discuss and investigate new topics and to take responsibility for their learning using a variety of resources. ICT is used in lessons to encourage active learning. Pupils have the opportunity to develop their mathematical communication skills, and to work in groups to achieve their potential, using a variety of cooperative learning and formative assessment approaches.

All resources for this course are found in the Mathematics O365 area. Learners are issued with notes booklets to structure and support their learning journey.

Mathematics helps us make sense of the world around us. It is the study of relationships, patterns, proofs and the properties of numbers. Mathematics takes a reasoned approach to thinking and is characterised by order and the use of carefully designed terms and processes. Mathematics can be used to model real-life situations and can equip us with the skills we need to interpret and analyse information, simplify and solve problems, assess risk and make informed decisions. Mathematics at Advanced Higher provides the foundation for many developments in the sciences and in technology as well as having its own intrinsic value.

Advanced Higher Mathematics develops and expands a range of mathematical skills. It allows the learner to develop further skills in calculus and algebra. Areas such as number theory (which helps keep the internet secure), complex numbers (the uses of which are ubiquitous, ranging from the solution of equations to the description of electronic circuits) and matrices (used in game theory and economics) are introduced. The learner’s mathematical thinking will also benefit from examples of rigorous proof.

The syllabus is designed to build upon and extend students’ mathematical learning in the areas of algebra, geometry and calculus. The three units are progressive and continue the development from Higher level.

Learners will have daily homework and formal homework tasks to complete. This will build their confidence and skills progressively.

We are keen to support learners whenever possible and welcome all feedback.

- You learn to communicate and manage information in mathematical form, skills which are vital to scientific research and development.
- You develop operational skills in numeracy, algebra, geometry, trigonometry and statistics.
- You learn to solve problems in a variety of mathematical and real-life situations in an engaging and enjoyable way.

**Mathematics in S5-S6**** **

**You will enjoy this subject if:**** **

*You like understanding how the world around us is understood and shaped by mathematics.**You enjoy number and developing your mathematical skills to cope with increasingly complex ideas and problems.**You like to communicate in a concise and logical way.*

*‘My love for maths is like x approaching a vertical asymptote – the limit does not exist.’*

Joanna Littlefield 6Cr

**Influential Mathematicians**

**Leonhard Euler** is regarded as being one of the most prolific Mathematicians ever to have lived and is thought to be the only Mathematician to have two constants named after him (including the Euler constant which you will come to know and love if you study Higher Mathematics). Euler’s contributions to mathematics include very early work in the field of Graph Theory (The famous Seven Bridges of Konigsberg problem), various contributions to number theory and giving us the Euler identity , widely regarded as the most beautiful equation in Mathematics (as it involves the five most important numbers).

**Hannah Fry** is an English Mathematician who has won awards for her work in engaging the public in mathematics. Much of her research concerns using mathematics to understand and explain human behaviour and relationships. Her written works include “The Mathematics of Love: Patterns, Proofs and the Search for the Ultimate Equation” and “The Indisputable Existence of Santa Claus”. Hannah is a regular contributor to the YouTube Channel “Numberphile” and I would encourage you to watch some of her videos!

**Maryam Mirzakhani** was a mathematician and a professor of mathematics at Stanford University. She was the first woman and first Iranian to win the Fields Medal. The citation for her award recognised her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces.

**John Napier**, a Scottish mathematician and theological writer who originated the concept of logarithms as a mathematical device to aid in calculations. You will study logarithms in Higher and Advanced Higher Mathematics.