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PURCHASE COMPREHENSIVE DEGREE LEVEL PURE MATHS, A'LEVEL STATISTICS AND PROBABILITY LECTURES




Statistics and Probability theory finally explained..

Pure Maths Lectures include a description of the Development of Number theory and Analysis, with basic Set and Function theory explained.

Linear algebra lectures include Suffix notation, summation convention and their use in Matrix algebra.

Any extra theory provided on request.

Email or Skype chat discussion about Lectures available, before or after purchase.



PURE MATHS SAMPLES PROBABILITY AND STATISTICS LECTURES IN PDF FORM
Covering all or most of any A'level Syllabus.
All Numbers are Interesting.
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PROBABILITY LECTURE COURSE [69pages]

Introduction to Probability: Pdf, Cdf. Skew and Kurtosis. Expectation algebra. Binomial. Poisson. Normal. Central Limit theorem.
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Purchase : 45.00 GBP

Relations (Equivalence classes. Partial Ordering.....) [8pages] 4.00 GBP
STATISTICS LECTURE [46pages]:

Sampling. Estimators. Maximum Likelihood Estimator. Hypothesis testing. Regression.
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Purchase : 40.00 GBP

Supremum (and infimum) [8pages] 4.00 GBP
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DEGREE LEVEL PURE MATHS LECTURES PURCHASE LECTURES IN PDF FORM
NUMBERS AND SETS Course: 3 Lectures. plus Questions and Solutions:

1. Lecture 1 [40pages]: An Introduction to Number systems and Logic, Set theory, The Natural Numbers and Euclid, Primes, Proof of the infinity of Primes.
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2. Lecture 2 [39pges]: Functions, Relations, Ordering, Indicator Functions.
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3. Lecture 3 [52pages]. Permutations and Combinations. The Binomial theorem. Induction. The Well-Ordering principle. Proof that "All Numbers are Interesting".
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Select Numbers and Sets Lecture
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'.
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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.
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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..
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Select Analysis Lecture
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.
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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.
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3. Lecture 3 [37pages] : Vector Spaces over the Complex numbers. Complex scalar product. 'Gram-Schmidt'. Eigenvectors and eigenvalues. 'CAYLEY HAMILTON'. Diagonalization.
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Select Linear Algebra Lecture
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.
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2. Lecture 2 [60pages] : Isometry and Matrix groups. The Dihedral group. Cyclic groups. Direct products. Finitely generated Abelian groups. Coset groups.
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