Preparing for Further Study in Mathematics

Examine key mathematical concepts and theory in preparation for a maths degree

When considering a mathematics degree, people often have little idea how the subject develops from school to university and its use in professional contexts.

On this six-week course from Manchester Grammar School, you’ll be introduced to mathematical ideas you may encounter as an undergraduate, gaining an overview of higher level maths.

Explore concepts of advanced mathematics, from number theory to non Euclidean geometry

Advanced maths can open doors to many careers, including finance, engineering, and computer science.

On this course, you’ll examine advanced mathematical theory, including computability and metric spaces, and expand your understanding of mathematical analysis.

Using a case study to demonstrate your understanding of advanced maths, you’ll put your learning into practice and prove you have the necessary skills to take the next steps in your mathematical studies.

Learn how to explain complex theories, using proof of contradiction, induction, and contrapositive

In maths, proof is a series of logical steps used to verify, or disprove, a mathematical argument.

Through group discussion and a range of examples, you’ll examine the surprisingly complex nature of providing absolute proof in a mathematical context, learning how proof can be subjective.

Investigate the history of mathematics

You’ll gain a critical view of how maths has developed from ancient civilisations to modern mathematics, being able to explain key moments in mathematical development.

Using this knowledge, you’ll be able to explain the evolution of mathematical thinking and discuss the potential future of maths and its applications.

By the end of this course, you’ll understand some complex theories and concepts of advanced maths, as well as their applications in a variety of contexts.

This course is designed for those considering an undergraduate degree in mathematics. It’s also suitable for anyone interested in situating mathematics into a historical and cultural framework.

• Introduction
• What is Mathematics?
• Age-appropriate Mathematics
• Numbers and Notation
• Historical Context - Modern Maths starts in 1687?
• Classical Mathematics
• Newton, Leibnitz and Calculus
• Modern Mathematics
• Proof
• The History of proof
• Some methods of proof
• What makes a proof good, or bad?
• Topics in Maths 1
• Analysis
• Group Theory
• Number Theory
• Topics in Maths 2
• Computability
• Metric Spaces
• Non-Euclidean Geometry
• Some Real Mathematics
• Some Real Problems
• Further Resources
• Thank You