Introduction to Generating Functions for A-Level Maths Students (FutureLearn)

Learn the fundamentals of generating functions and experience studying maths at a university level. Discover what it’s like to study mathematics at University. This three-week course from Manchester Grammar School will give you an opportunity to study a university-level topic in-depth. As an A-level mathematics student, you’ll be able to further your learning through the study of generating functions and obtain a sense of what it’s like to study maths at university.

Enroll in course

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Explore the capabilities of generating functions as a problem-solving tool

Generating functions is a powerful mathematical tool that can be applied to solve problems in many different contexts.

On this course, you’ll be introduced to generating functions and its applications in mathematics. In the first week of the course, you’ll define generating functions and work with various mathematical problems to understand the types of problems generating functions can solve.

Learn how to use generating functions for probability distributions and more

This course will cover roughly one topic per week and is structured to provide you with an in-depth understanding of how to build generating functions for a wide range of mathematical problems.

You’ll learn how to derive the nth term for a selection of recurrence relations, solve combinatorial problems, work with standard probability distributions, and more, all using generating functions.

Decide your academic trajectory with help from an expert educator

The lead educator on this course is an experienced A-Level teacher who has studied generating functions at a high level during his own undergraduate and postgraduate studies.

With the insight and expertise of your lead educator, you will have an understanding of what it means to study maths at a higher level, and be better equipped to make a decision in pursuing maths at university.

Syllabus

Week 1: Introduction

Week 2: Combinatorics and generating functions

Week 3: Probability and generating functions

What will you achieve?

By the end of the course, you‘ll be able to...

- Explain what generating functions are and why they are useful

- Apply generating functions to find the nth term for sequences defined using recurrence relations

- Solve combinatorics problems

- Apply generating functions in the context of combinatorics

- Apply generating functions in the context of probability distributions
Who is the course for?

This course is designed for A-Level mathematics students who are considering applying to study mathematics at university, but anyone with an interest in mathematics is welcome to join the course.