A-level Further Maths: Advanced Topics
Develop advanced mathematical proficiency through comprehensive A-level topics, building essential foundations for success in university STEM programs.
Develop advanced mathematical proficiency through comprehensive A-level topics, building essential foundations for success in university STEM programs.
Dive deep into advanced A-level further mathematics with this comprehensive course from Imperial College London. Designed to enhance your problem-solving skills and mathematical fluency, this course covers crucial topics such as differential equations, complex numbers, curve sketching, and matrices. You'll develop the critical thinking and analytical skills necessary for success in A-level exams and undergraduate STEM degrees. Through eight intensive modules, you'll explore both theoretical concepts and practical applications, from solving first-order differential equations to understanding eigenvalues and eigenvectors. This course not only prepares you for exams but also provides a solid foundation for future studies in mathematics, engineering, and sciences.
4.8
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What you'll learn
Solve first-order differential equations using analytical and numerical methods
Understand and apply complex number theory, including nth roots of unity
Analyze and sketch curves using various coordinate systems and equations
Master advanced integration techniques, including improper integrals and reduction formulae
Apply integration to solve real-world problems involving areas, arc lengths, and surface areas
Solve second-order differential equations
Skills you'll gain
This course includes:
PreRecorded video
Graded assignments, exams
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Limited Access access
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There are 8 modules in this course
This course offers an in-depth exploration of advanced topics in A-level further mathematics, designed to prepare students for both exams and future STEM studies. It covers a wide range of crucial mathematical concepts, including first and second-order differential equations, complex numbers, curve properties, advanced integration techniques, vector products, and matrix operations. The course emphasizes not just theoretical understanding but also practical problem-solving skills, encouraging students to develop fluency, confidence, and deep reasoning abilities. Through eight comprehensive modules, students will learn to apply analytical and numerical methods to solve complex mathematical problems, understand the geometrical applications of complex numbers, master advanced integration techniques, and explore the properties of curves and vectors. The course also introduces students to eigenvalues and eigenvectors, providing a foundation for more advanced mathematical studies. Throughout, students are encouraged to think critically, construct mathematical arguments, and understand how these concepts fit into the broader mathematical landscape.
First Order Differential Equations
Module 1
Further Complex Numbers
Module 2
Properties of Curves
Module 3
Further Integration Methods
Module 4
Further Applications of Integration
Module 5
Second Order Differential Equations
Module 6
The Vector (cross) Product
Module 7
Matrices - Eigenvalues and Eigenvectors
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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4.8 course rating
5 ratings
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