subject-mathematics-gutenberg

Introduction

This is a Distant Reader "study carrel", a set of structured data intended to help the student, researcher, or scholar use & understand a corpus.

This study carrel was created on 2021-06-06 by Eric Morgan <emorgan@nd.edu>. The carrel was created using the Distant Reader gutenberg process, and the input was the result of a query applied to a local mirror of Project Gutenberg -- facet_subject:"Mathematics". Then, for future reference, the results were saved to a Zip file complete with rudimentary bibliographics. The name of the file is input-file.zip. The Zip file was then unpacked and the contents saved to a cache as well as a directory of plain text files. All of the analysis -- "reading" -- has been done against these plain text files. For example, a short narrative report has been created. This Web page is a more verbose version of that report.

All study carrels are self-contained -- no Internet connection is necessary to use them. Download this carrel for offline reading. The carrel is made up of many subdirectories and data files. The manifest describes each one in greater detail.

Size

There are 13 item(s) in this carrel, and this carrel is 264,034 words long. Each item in your study carrel is, on average, 33,004 words long. If you dig deeper, then you might want to save yourself some time by reading a shorter item. On the other hand, if your desire is for more detail, then you might consider reading a longer item. The following charts illustrate the overall size of the carrel.

Readability

On a scale from 0 to 100, where 0 is very difficult and 100 is very easy, the documents have an average readability score of 93. Consequently, if you want to read something more simplistic, then consider a document with a higher score. If you want something more specialized, then consider something with a lower score. The following charts illustrate the overall readability of the carrel.

Word Frequencies

By merely counting & tabulating the frequency of individual words or phrases, you can begin to get an understanding of the carrel's "aboutness". Excluding "stop words", some of the more frequent words include:

will, one, digits, us, two, may, first, shall, space, must, number, without, know, say, science, therefore, law, point, true, even, see, make, time, another, since, fact, different, principle, now, theory, certain, made, always, mathematical, geometry, necessary, definition, laws, new, just, motion, still, way, body, bodies, yet, well, second, great, velocity

Using the three most frequent words, the three files containing all of those words the most are The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method, Five of Maxwell''s Papers, and The Second Story of Meno A Continuation of Socrates'' Dialogue with Meno in Which the Boy Proves Root 2 is Irrational.

The most frequent two-word phrases (bigrams) include:

let us, one another, muscular sensations, three dimensions, mathematical physics, milky way, physical continuum, series sigma, whole number, whole numbers, straight line, great number, teach us, euclidean geometry, two points, shall see, give us, will never, teaches us, mathematical continuum, enable us, tell us, visual space, instant alpha, geometric space, shall call, instant beta, enables us, differential equations, one hand, scientific fact, carried along, mathematical reasoning, relative motion, real mass, one may, relative position, two series, will always, cathode rays, least action, one will, square root, mechanical explanation, physical sciences, negative electrons, kinetic theory, absolute space, shall say, absolute velocity

And the three file that use all of the three most frequent phrases are The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method Five of Maxwell''s Papers, and The Second Story of Meno A Continuation of Socrates'' Dialogue with Meno in Which the Boy Proves Root 2 is Irrational.

While often deemed superficial or sophomoric, rudimentary frequencies and their associated "word clouds" can be quite insightful:

Keywords

Sets of keywords -- statistically significant words -- can be enumerated by comparing the relative frequency of words with the number of times the words appear in an entire corpus. Some of the most statistically significant keywords in the carrel include:

science, number, body, university, theory, space, socrates, sigma, scientific, russell, riemann, point, poincaré, physics, newton, meno, maxwell, man, lorentz, lobachevski, law, hilbert, geometry, experiment, euclidean, euclid, digit, definition, couturat, constant, chapter, bonnell

And now word clouds really begin to shine:

Topic Modeling

Topic modeling is another popular approach to connoting the aboutness of a corpus. If the study carrel could be summed up in a single word, then that word might be digits, and The Way To Geometry is most about that word.

If the study carrel could be summed up in three words ("topics") then those words and their significantly associated titles include:

1. shall - The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method
2. digits - The Fibonacci Number Series
3. compute - The Number "e"

If the study carrel could be summed up in five topics, and each topic were each denoted with three words, then those topics and their most significantly associated files would be:

1. shall, space, know - The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method
2. digits, constant, 25 - The Fibonacci Number Series
3. socrates, boy, meno - The Golden Mean
4. invert, compute, seconds - The Number "e"
5. sea, illustrations, heavy - The First 498 Bernoulli Numbers

Moreover, the totality of the study carrel's aboutness, can be visualized with the following pie chart:

Noun & Verbs

Through an analysis of your study carrel's parts-of-speech, you are able to answer question beyonds aboutness. For example, a list of the most frequent nouns helps you answer what questions; "What is discussed in this collection?":

digits, space, number, law, point, science, time, fact, principle, laws, definition, theory, body, motion, bodies, way, geometry, velocity, series, action, question, nature, example, light, sensations, nothing, object, numbers, world, dimensions, experiment, points, phenomena, facts, one, day, case, energy, experience, part, force, mass, hypothesis, position, order, mind, continuum, system, others, principles

An enumeration of the verbs helps you learn what actions take place in a text or what the things in the text do. Very frequently, the most common lemmatized verbs are "be", "have", and "do"; the more interesting verbs usually occur further down the list of frequencies:

is, be, have, are, has, was, do, been, know, say, were, see, make, had, does, made, said, give, suppose, take, think, called, being, find, let, given, speak, seems, call, according, become, seen, put, come, having, go, found, mean, seem, understand, remain, led, remains, wish, show, am, represent, known, regarded, believe

Proper Nouns

An extraction of proper nouns helps you determine the names of people and places in your study carrel.

_, b, a, c, s, sigma, m., meno, newton, socrates, maxwell, m, t, science, lorentz, chapter, u, +, russell, d, euclid, poincaré, riemann, hilbert, n, lobachevski, x, physics, couturat, ampère, mathematical, q, retina, leroy, p, iv, ii, iii, hertz, helmholtz, space, fresnel, e, geometry, v, university, sciences, physical, milky, ab

An analysis of personal pronouns enables you to answer at least two questions: 1) "What, if any, is the overall gender of my study carrel?", and 2) "To what degree are the texts in my study carrel self-centered versus inclusive?"

it, we, i, they, us, our, them, their, he, its, you, his, my, itself, me, themselves, one, him, ourselves, myself, himself, your, her, ours, she, oneself, herself, theirs, yours, ''s, yourself, u, p_2, ourself, mine, hitherto

Below are words cloud of your study carrel's proper & personal pronouns.

Adjectives & Verbs

Learning about a corpus's adjectives and adverbs helps you answer how questions: "How are things described and how are things done?" An analysis of adjectives and adverbs also points to a corpus's overall sentiment. "In general, is my study carrel positive or negative?"

same, other, true, first, different, certain, necessary, new, mathematical, great, such, second, many, more, possible, least, simple, physical, scientific, little, absolute, general, euclidean, whole, relative, constant, real, particular, able, equal, experimental, small, -, initial, impossible, non, muscular, ordinary, good, common, continuous, natural, only, odd, straight, several, external, capable, analogous, own

not, only, so, then, more, very, therefore, even, now, thus, always, just, still, as, most, no, yet, first, never, well, here, longer, also, too, however, less, far, up, often, much, already, again, perhaps, out, long, finally, rather, consequently, all, alone, back, once, there, on, precisely, simply, evidently, else, almost, indeed

Next steps

There is much more to a study carrel than the things outlined above. Use this page's menubar to navigate and explore in more detail. There you will find additional features & functions including: ngrams, parts-of-speech, grammars, named entities, topic modeling, a simple search interface, etc.

Again, study carrels are self-contained. Download this carrel for offline viewing and use.

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