Topic 1: Proof by mathematical Induction


































































Summation notation or Sigma Notation



























































Why we need proof by mathematical induction



























































Proof by Mathematical Induction: Mathematical Dominoes



























































Proof by induction partial sums worked examples



























































Proof by Induction Divisibility proofs







Topic 2: Vectors and Matrices


































































Dominance Matrices from start to finish



























































Dominance Matrices as a mathematical model



























































Matrix Multiplication and Addition in Excel for Dominance Matrices



























































Markov Chains & Matrices: Part 1



























































Markov Chains Worked examples



























































Matrix Multiplication and Matrix Powers in Excel



























































Matrix Calculations on the TI-84 plus



























































Leslie Matrices for population age distribution modelling



























































Leslie Matrices – What's really going on? (downloadable excel file in description)



























































15 Vector Questions you should know how to do by the end of year 11



























































An Introduction to vectors in 3 dimensions



























































Converting 3D Vectors between Cartesian and Polar forms



























































Scalar or Dot Product in 3 Dimensions



























































Vector Functions Introduction and converting vector functions to cartesian functions



























































Converting Vector Equations to Cartesian Equations using trigonometric Identities



























































Vector equations and finding collision points



























































Vector Equations of Lines



























































Converting Vector equations to cartesian form and parametric equations



























































Parallel and perpendicular vector equations



























































Calculating distance from a point to a vector equation of a line



























































Vectors: Line of intersection & the angle between two planes



























































The Vector Product (Cross Product)



























































Vector Equation of a plane fully explained and shown graphically



























































Finding equations of planes: Three worked examples



























































Vectors: Calculating the distance from a point to a plane or a plane to a plane



























































Vectors Intersection points between lines and planes and the angle between a line and a plane



























































Vector Calculations & 3D Graphing on the Casio FX CG50AU



























































Intersections of 3D Lines, Skew Lines and angles between lines



























































Equation of spheres in cartesian and vector form



























































The geometric interpretation of systems of linear equations in 2 & 3 dimensions



























































Using Matrix Algebra to find an intersection point of 3 planes



























































Solving Simultaneous Equations on the Casio FX CG50AU



























































Gaussian elimination part 1



























































Guassian Elimination Part 2 Systems with lines as solutions



























































Gaussian Elimination on the Casio FX CG50AU



























































Gaussian Elimination part 3: systems resulting in No Solution


