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Introduction to Generating Functions for A-Level Maths Students

Manchester Grammar School via FutureLearn

Description

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.

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.

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.

We will be using Wolfram Alpha in the course to do simple mathematical calculations (the free version is absolutely fine).

Tags
Economics

Syllabus

  • Introduction
    • Introduction to the course
    • Introduction to generating functions
    • Recurrence relations
  • Combinatorics and generating functions
    • Combinatorics overview
    • Building generating functions
    • Solving combinatorics problems
  • Probability and generating functions
    • Probability generating functions
    • Sums of random variables
    • Random walks (advanced)
    • Closing remarks

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Online Courses
FutureLearn

Introduction to Generating Functions for A-Level Maths Students

Manchester Grammar School
Start Learning Find study partner
Affiliate notice

  • Type
    Online Courses
  • Provider
    FutureLearn

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.

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.

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.

We will be using Wolfram Alpha in the course to do simple mathematical calculations (the free version is absolutely fine).

  • Introduction
    • Introduction to the course
    • Introduction to generating functions
    • Recurrence relations
  • Combinatorics and generating functions
    • Combinatorics overview
    • Building generating functions
    • Solving combinatorics problems
  • Probability and generating functions
    • Probability generating functions
    • Sums of random variables
    • Random walks (advanced)
    • Closing remarks

Tags

Economics

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