Advanced A-Level Math: Matrices to Complex Numbers
Master key A-Level Further Mathematics topics, from 3x3 matrices to complex numbers, preparing for STEM degrees.
Master key A-Level Further Mathematics topics, from 3x3 matrices to complex numbers, preparing for STEM degrees.
Delve into advanced A-Level Further Mathematics with this comprehensive course from Imperial College London. Covering crucial topics like 3x3 matrices, mathematical induction, advanced calculus, Maclaurin series, complex numbers, and polar coordinates, this course enhances your mathematical fluency and problem-solving skills. Through eight modules, you'll develop a deep understanding of complex mathematical concepts, learn to construct rigorous proofs, and apply your knowledge to solve challenging problems. Designed to align with various A-level specifications, this course prepares you for success in your exams and lays a strong foundation for undergraduate STEM degrees.
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What you'll learn
Master the determinant and inverse operations for 3x3 matrices
Apply mathematical induction to prove series, divisibility, and matrix results
Utilize advanced differentiation and integration techniques for complex functions
Calculate volumes of revolution and function means using integration methods
Develop and manipulate Maclaurin series for various functions
Apply De Moivre's Theorem to solve complex number problems
Skills you'll gain
This course includes:
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Graded assignments, exams
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Limited Access access
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There are 8 modules in this course
This advanced course in A-Level Further Mathematics covers a wide range of topics essential for students preparing for their A-level exams and future STEM degrees. The course is structured into eight comprehensive modules, each focusing on key areas of advanced mathematics. Students will explore 3x3 matrices, including determinants and inverses, and their applications in three-dimensional transformations. The course delves into mathematical induction, teaching students how to construct rigorous proofs for series, divisibility, and matrix results. Advanced calculus methods are covered, including complex differentiation and integration techniques, along with their real-world applications such as calculating volumes of revolution. The course also introduces students to Maclaurin series, De Moivre's Theorem for complex numbers, polar coordinates, and hyperbolic functions. Throughout the course, emphasis is placed on developing critical thinking, problem-solving skills, and the ability to construct mathematical arguments. This course is designed to deepen students' understanding of how these advanced mathematical concepts interconnect and apply to various fields of study.
Matrices - The determinant and inverse of a 3 x 3 matrix
Module 1
Mathematical induction
Module 2
Further differentiation and integration
Module 3
Applications of Integration
Module 4
An Introduction to Maclaurin series
Module 5
Complex Numbers: De Moivre's Theorem and exponential form
Module 6
An introduction to polar coordinates
Module 7
Hyperbolic functions
Module 8
Fee Structure
Instructors
8 Courses
Mathematics Education and Outreach Expert at Imperial College London
Philip Ramsden serves as Director of Cross-Curricular Mathematics Education and Principal Teaching Fellow at Imperial College London, where he has made significant contributions to mathematics education and outreach since 1993. His teaching spans multiple departments including Mathematics, Physics, and Aeronautics, while leading major initiatives in widening participation and mathematics education. He directs the mAths programme, an extensive outreach initiative targeting Year 12 and 13 students from underrepresented backgrounds pursuing A grades at A-level, and coordinates the monthly "Maths Circle" masterclasses in partnership with the Royal Institution
8 Courses
Mathematics Education and Problem-Solving Expert at MEI
Phil Chaffé serves as a national coordinator for the Advanced Mathematics Support Programme, a UK government-funded initiative promoting post-16 mathematics education, bringing extensive experience from his previous roles in schools and universities. His current work focuses on coordinating projects across England that prepare students for advanced study at top universities, with particular emphasis on developing problem-solving skills necessary for university admissions examinations. As a respected figure in mathematics education, he has gained recognition for his engaging presentations on diverse topics including evolutionary biology mathematics, music mathematics, and recursive universe concepts, making complex mathematical ideas accessible to students. His expertise spans both theoretical mathematics and its practical applications, demonstrated through his work in developing enrichment programs and delivering masterclasses that bridge the gap between secondary education and university-level mathematics. His contributions to mathematics education extend beyond traditional classroom teaching to include innovative approaches that inspire students to explore advanced mathematical concepts and their real-world applications.
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