3. Lecture 3 [52pages]. Permutations and Combinations. The Binomial theorem. Induction. The Well-Ordering principle. Proof that "All Numbers are Interesting". Request contents page or Sample
ANALYSIS Course: 3 LECTURES. Plus Questions and Solutions
1. Lecture 1 [45pages] : Develpment of Number Systems. Discovery of the Reals and Irrationals, incluidng 'Dedekind cuts'. Supremum and Infimum. Series. Limits. 'Bolzano-Weierstarss'. Request contents page or Sample
2. Lecture 2 [44pages] : Continuity, (epsilon and delta). The Fundamental Axiom. The Axiom of Archimedes. Countability and
'Cantor's Diagonal argument'. Convergence of Sums. Cauchy sequences. Request contents page or Sample
3. Lecture 3 [40pages] Uniform convergence, and the MONSTER Weierstrass function. The Intermediate Value theorem. The Riemann Integral.
The Fundamental theorem of calculus. Leibniz. Power series.. Request contents page or Sample
LINEAR ALGEBRA COURSE: 3 LECTURES.
1. Lecture 1 [71 pages] : Vector Spaces and Subspaces. Spanning and Linear independence. Bases and Dimension. Scalar product and 'Cauchy Schwarz'.
Intersection and sum of Subspaces. Linear maps. Rank-Nullity. Composition of maps. Request contents page or Sample
2. Lecture 2-MATRICES [66pages] : Suffix Notation explained. Orthonormality. Matrices as linear maps. Change of basis. Orthogonal matrices. Determinants and linear equations. Kramer's Solution. Request contents page or Sample
3. Lecture 3 [37pages] : Vector Spaces over the Complex numbers. Complex scalar product. 'Gram-Schmidt'. Eigenvectors and eigenvalues. 'CAYLEY HAMILTON'. Diagonalization. Request contents page or Sample
GROUP THEORY: 2 LECTURES Plus Questions and Solutions.
1. Lecture 1 [46pages] : Group definitions and Subgroups. Finite groups. The group Zn. Lagrange. Permutation groups. Isomorphism. Request contents page or Sample
2. Lecture 2 [60pages] : Isometry and Matrix groups. The Dihedral group. Cyclic groups. Direct products. Finitely generated Abelian groups. Coset groups. Request contents page or Sample
PURCHASE COMPREHENSIVE DEGREE LEVEL PURE MATHS, A'LEVEL STATISTICS AND PROBABILITY LECTURES