Links:
Khan Academy - online academy with videos
WolframAlpha - calculations online
statistika.bg - statistics basic concepts with videos
btu.bg - statistics basic concepts
matematika.bg - basic concepts with examples
More:
YouTube channel - 3Blue1Brown
Interesting Jupyter Notebooks
- scientific method introduction;
- solving linear equations and systems (the “slow” way);
- trigonometry. Right triangle, unit circle, functions and graphs, identities;
- high-School geometry, intro to computational geometry.
=> Basic concepts
=> Exercise
- functions (in maths and programming);
- polynomials – idea, representation, operations;
- complex numbers, geometric intuition;
- euler's formula;
- fundamental theorem of algebra.
=> Basic concepts
=> Exercise
- matrices. Operations with matrices;
- vectors and vector spaces. Basis, change of basis;
- inverse matrix;
- determinant, oriented area and volume.
=> Basic concepts
=> Exercise
- limits;
- derivatives – intuition, slope of a function at a point;
- table derivatives;
- rules for calculating derivatives;
- higher-order derivatives;
- riemann sums and integrals. Intuition, oriented area;
- fundamental theorem of calculus;
- extension of calculus to many dimensions – intuition.
=> Basic concepts
=> Exercise
- random variables;
- probability. Definitions: frequency, chance of happening next time;
- events and algebra of events;
- combinatoric rules;
- probability mass function, probability density function, cumulative distribution function;
- central limit theorem.
=> Basic concepts
=> Exercise
- definition. Descriptive and inferential statistics;
- sample and population. Sampling rules;
- moments of distributions;
- covariance and correlation;
- anscombe's quartet;
- simpson's paradox.
=> Basic concepts
=> Exercise
- confidence intervals, confidence level, alpha parameter;
- null and alternate hypothesis
- z-test, t-test, chi-squared;
- ANOVA;
- p-value;
- p-value misconceptions.
=> Basic concepts
=> Exercise
online viewer of Jupyter Notebooks: https://gke.mybinder.org