Course notes and worked problems for mathematics and statistics students.
For the sake of brevity, we will always represent this number 2.718281828459… by the letter e. Leonhard Euler
Sets and numbers, functions, polynomial and rational functions, trigonometry, exponentials and logarithms, differentiation and integration, then descriptive statistics and probability. Every tutorial-sheet question is worked in full.
Probability axioms, conditional probability and Bayes' theorem, counting techniques, random variables, and the standard discrete and continuous distributions.
Describing data, sampling distributions, estimation and confidence intervals, hypothesis testing and P-values, analysis of variance, and linear regression and correlation.
Distributions of functions of random variables and order statistics, estimation by moments, least squares and maximum likelihood, properties of estimators, and the theory of hypothesis testing.
In preparation — conic sections and polar coordinates, limits and continuity, the mean value theorems, series and curvature, techniques of integration, and vector analysis.
In preparation.
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