Combinatorics This lesson covers the topics of combinatorics (combinations, permutations with and without repetitions, circular and constrained permutations). It will equip you with all the necessary theoretical knowledge on the topic, and show how it is applied in standardized test problems....

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## A Tutorial in Data Science: Lecture 1 – The Foundations of Data Science

Data Science is the study of the datum, which is the Being of a being in its there-being. The datum of a being is its having been measured, and thus observed in one of its states. The science of data is thus how to interrogate data such as to reveal the being that has been measured, and thus the...

## A Tutorial in Data Science: Lecture 2 – The Hermeneutic Nature of Scientific Data

The question of science itself has never been its particular object of inquiry but the existential nature, in its possibility and thereby the nature of its actuality. Science is power, and thus abstracts itself as the desired meta-good, although it is always itself about particularities as an...

## A Tutorial in Data Science: Lecture 3 – Laplace’s Analytical Theory of Probability

This lecture serves as a philosophically informed mathematical introduction to the ideas and notation of probability theory from its most important historical theorist. It is part of an ongoing contemporary formal reconstruction of Laplace's Calculus of Probability from his english-translated...

## A Tutorial in Data Science: Lecture 4 – Statistical Inference by Systems of Conditions

We consider here how to estimate a parameter to a distribution given a sample space of observations. It is important to recognize that the testing of any hypothesis relies upon assumptions, which may be further explicated as obtaining validity based upon the further assumptions. The system of...

## A Tutorial in Data Science: Lecture 5 – Generating Distributions by Spectral Analysis

When two states, i.e. possibly measured outcomes, of the stochastic sampling process of the underlying statistical object communicate, there is a probability of one occurring after the other, perhaps within the internal time (i.e. indexical ordering) of the measurement process, $t \in \pi=(1,...

## A Tutorial in Data Science: Lecture 6 – Exploratory Data Analysis

The Issue of The Datum Data, as finite, can never be merely fit without presupposition. The theory of the data, as what it is, is the presupposition that discloses the data in the first place through the act of measurement. As independent and identical (i.i.d.) measurements, there is not...

## A Tutorial in Data Science: Lecture 7 – The Elements of Fourier Analysis

Fourier Analysis is the decomposition of any square-integrable functions into an infinite series of trigonometric functions. Here we show that the trigonometric polynomial functions are dense in the space of periodic continuous functions, and thus can be used as good approximations. This implies...