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...

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

by Justin Petrillo | Math Lecture

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...

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

by Justin Petrillo | Math Lecture

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

by Justin Petrillo | Math Lecture

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

by Justin Petrillo | Math Lecture

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

by Justin Petrillo | Math Lecture

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...

## A Tutorial in Data Science: Lecture 8 – The Functional Theory of Communication in Stochastic Processes

by Justin Petrillo | Math Lecture

From Laplace's Calculus of Probability (Lecture 3), a finite difference equation explains probabilistically how a game evolves over discrete time, defining thus a stochastic process and specifically a Markov Chain where there is finite recursion or limited historical dependence. While one can...

## A Tutorial in Data Science: Lecture 9 – The Functional Theory of Communication in Dynamic Systems

by Justin Petrillo | Math Lecture

We consider thus the functional notion of communication within the theory of dynamic systems, where the finite difference equation, or flow of a differential equation, is iterated upon as a function. Within this framework, there is a true underlying deterministic system which can be explained by a...