The MIF Conjecture
The MIF Tree of Knowledge
This will become the central map of the website. Every topic will eventually connect to videos, notes, examples, worksheets, quizzes and future courses. The aim is to show maths as one connected subject, not a pile of random chapters.
GCSE Foundation Maths
The starting point for students who want to build confidence from the ground up.
Number sense
Understanding numbers before jumping into methods.
Open chapterFour operations
Adding, subtracting, multiplying and dividing properly.
Open chapterDecimals
Understanding place value and decimal operations.
Open chapterFractions
Building confidence with fractions from the beginning.
Open chapterRatio
Sharing, comparing and scaling quantities.
Open chapterPercentages
Percentages as a natural extension of fractions and decimals.
Open chapterBasic algebra
The beginning of using letters and structure in maths.
Open chapterFoundation geometry
Angles, shapes, perimeter, area and basic geometry ideas.
Open chapterGCSE Higher Maths
For students moving into higher GCSE topics and deeper problem-solving.
Advanced algebra
Expanding, factorising and manipulating expressions more confidently.
Open chapterQuadratics
Solving and understanding quadratic expressions, equations and graphs.
Open chapterGraphs
Connecting algebra, coordinates and visual patterns.
Open chapterCircle theorems
Understanding angle rules inside circles.
Open chapterTrigonometry
Using triangles, ratios and angles to solve problems.
Open chapterVectors
Representing movement and direction with mathematical structure.
Open chapterProbability
Understanding chance, outcomes and probability rules.
Open chapterStatistics
Working with data, averages, charts and interpretation.
Open chapterGCSE Further Maths
Focused on AQA Level 2 Certificate Further Maths and GCSE Further Maths support.
Proof
Learning how to explain why something is always true.
Open chapterFunctions
Understanding inputs, outputs, mappings and notation.
Open chapterMatrices introduction
A first look at matrix operations and transformations.
Open chapterHarder trigonometry
Moving beyond basic SOHCAHTOA into deeper trig problems.
Open chapterCoordinate geometry
Lines, gradients, equations and geometry on the coordinate plane.
Open chapterAdvanced graphs
Quadratic, cubic, reciprocal and other graph types.
Open chapterIntroduction to differentiation
The first idea of gradients changing along a curve.
Open chapterAS-Level Maths
The first step after GCSE, mainly following Edexcel AS-Level Maths structure.
Algebra and functions
Building fluency with expressions, equations and functions.
Open chapterCoordinate geometry
Using algebra to understand lines and curves.
Open chapterTrigonometry
Extending trigonometry into A-Level methods and identities.
Open chapterDifferentiation
Understanding gradients, rates of change and curves.
Open chapterIntegration
The reverse process of differentiation and area under curves.
Open chapterMechanics
Forces, motion and modelling physical situations.
Open chapterStatistics
Data, distributions and probability models.
Open chapterA-Level Maths
The full Edexcel A-Level Maths route, building from AS into the harder second-year content.
Pure maths
The main algebra, functions, calculus and proof-based content.
Open chapterSequences and series
Understanding patterns, sums and long-term behaviour.
Open chapterAdvanced calculus
Harder differentiation and integration methods.
Open chapterExponentials and logarithms
Growth, decay and inverse relationships.
Open chapterTrigonometry
Identities, equations, graphs and modelling.
Open chapterMechanics
Modelling motion, forces and physical systems.
Open chapterStatistics and modelling
Using probability and data to model real situations.
Open chapterAS-Level Further Maths
A step above AS Maths, introducing deeper Further Maths ideas before the full A-Level Further Maths route.
Complex numbers
Working with numbers beyond the real number line.
Open chapterMatrices
Using arrays of numbers to represent transformations and systems.
Open chapterProof
Explaining mathematical truth with structure.
Open chapterFurther algebra
Deeper manipulation, equations and problem solving.
Open chapterFurther calculus
More advanced differentiation and integration ideas.
Open chapterFurther mechanics, statistics or decision maths
Applied Further Maths options to be added later.
Open chapterA-Level Further Maths
The deeper school-level maths route for students preparing for maths-heavy degrees.
Further pure maths
Advanced pure maths beyond standard A-Level.
Open chapterComplex numbers
Using complex numbers in deeper algebra and geometry.
Open chapterMatrices and transformations
Understanding linear transformations through matrices.
Open chapterDifferential equations
Equations involving rates of change and unknown functions.
Open chapterPolar coordinates
Representing curves using distance and angle.
Open chapterHyperbolic functions
Functions connected to exponentials and advanced calculus.
Open chapterAdvanced applied maths
Further mechanics, statistics or decision content.
Open chapterPre-University Maths
A bridge from school maths to university-style mathematics, especially for technical degrees.
Algebra fluency
Getting fast and confident with algebraic manipulation.
Open chapterProof foundations
Learning how university-style maths explains itself.
Open chapterLinear algebra basics
Vectors, matrices and systems before university.
Open chapterCalculus fluency
Becoming comfortable with differentiation and integration.
Open chapterMathematical modelling
Turning situations into mathematical structures.
Open chapterProblem-solving habits
Building the habits needed for technical subjects.
Open chapterUniversity Courses
Future university-level maths, engineering maths, linear algebra, calculus and modelling.
Engineering mathematics
Core maths used in engineering degrees.
Open courseLinear algebra
Vectors, matrices, spaces and transformations.
Open courseCalculus
Single and multivariable calculus for university study.
Open courseDifferential equations
Modelling change through equations involving derivatives.
Open courseNumerical methods
Approximation methods used when exact answers are hard.
Open courseDiscrete maths
Logic, counting, graphs, algorithms and structures.
Open courseMathematical modelling
Using maths to represent real systems.
Open course