Unified Validator Framework for the Collatz Conjecture: Logical, Spectral, and Cryptographic Resolution Protocols

Authors: Forrest M. Anderson, Forrest

Subject Terms: Collatz Conjecture, 3x+1 Problem, Syracuse Problem, Paul Erdős, John Horton Conway, Kurt Gödel, Alan Turing, Stephen Wolfram, Terence Tao, Yuri Matiyasevich, Gregory Chaitin, Harvey Friedman, Scott Aaronson, Proof Complexity, Natural Proofs Barrier, Razborov-Rudich Natural Proofs, P vs NP, Spectral Complexity, Spectral Complexity Operator, Spectral Operator Framework, Meta-mathematics, Arithmetic Dynamics, Discrete Dynamical Systems, Symbolic Dynamics, Integer Sequences, Recursive Functions, Halting Problem, Turing Machines, Turing Complete, Undecidability, Computability, Algorithmic Information Theory, Kolmogorov Complexity, Digital Arithmetic, Mathematical Logic, Formal Logic, Peano Arithmetic, ZFC, Logical Independence, Gödel Incompleteness Theorems, Incompleteness Theorems, Bounded Computation, Complexity Theory, Computational Complexity, Theoretical Computer Science, Discrete Math, Open Problems in Mathematics, Automated Theorem Proving, Formal Proof Systems, Mathematical Induction, Chaos in Arithmetic, Foundations of Mathematics, Arithmetic Functions, Special Sequences, Elementary Number Theory, Number Theory, Models of Computation, Logic in Computer Science, Dynamical Systems, Proof Theory, Decision Problems, Algorithmic Complexity, Computational Models

An Introduction to Number Theory

Authors: Veerman, J. J. P.

Source: PDXOpen: Open Educational Resources

Subject Terms: Number theory -- Study and teaching (Higher), Arithmetic -- Foundations, Diophantine equations, Prime numbers, Continued fractions, Additive functions, Modular arithmetic, Number Theory

File Description: application/pdf

Relation: https://pdxscholar.library.pdx.edu/pdxopen/34; https://pdxscholar.library.pdx.edu/context/pdxopen/article/1039/viewcontent/0_mainfile_03_2021.pdf

Availability: https://pdxscholar.library.pdx.edu/pdxopen/34
https://doi.org/10.15760/pdxopen-37
https://pdxscholar.library.pdx.edu/context/pdxopen/article/1039/viewcontent/0_mainfile_03_2021.pdf

Routledge philosophy guidebook to Frege on sense and reference
Frege on sense and reference

Authors: Textor, Markus

Subject Terms: Logic, Arithmetic -- Foundations

Subject Person: Frege, Gottlob 1848-1925. Uber Sinn und Bedeutung

Στοιχεία Αριθμητικής / υπό του Κυρίου Βουρδώνος, Ιππέως της Βασιλικής Τάξεως, του Τάγματος της Τιμής, Επιθεωρητού της Ακαδημίας των Παρισίων, Δόκτορος των Επιστημών, κ. τ. λ., μεταφρασθέντα εκ του Γαλλικού εκ της τρίτης αυτών εκδόσεως υπό του Δόκτορος Ιωάννου Καρανδηνού Κεφαλληνός, Εφόρου της Ιονίου Ακαδημίας, Δεκάνου της Σχολής της Φιλοσοφίας, και Προφέσσορος των Μαθηματικών Επιστημών

Authors: Bourdon, Louis Pierre Marie 1779-1854.

Subject Terms: Arithmetic -- Early works to 1900, Arithmetic -- Foundations, Mathematics -- Early works to 1800

File Description: 560 σ

Relation: http://catalog.lib.aegean.gr/webopac/FullBB.csp?WebAction=ShowFullBB&EncodedRequest=*A8*E4*C7*F8*D0*AE*CC*5C*F5*21*28C*15*F2*29*18&Profile=Default&OpacLanguage=gre&NumberToRetrieve=50&StartValue=3&WebPageNr=1&SearchTerm1=1828.1.68057&SearchT1=&Index1=Titlenew&SearchMethod=Find_1&ItemNr=3; http://hdl.handle.net/11610/16658

Availability: http://hdl.handle.net/11610/16658
http://catalog.lib.aegean.gr/webopac/FullBB.csp?WebAction=ShowFullBB&EncodedRequest=*A8*E4*C7*F8*D0*AE*CC*5C*F5*21*28C*15*F2*29*18&Profile=Default&OpacLanguage=gre&NumberToRetrieve=50&StartValue=3&WebPageNr=1&SearchTerm1=1828.1.68057&SearchT1=&Index1=Titlenew&SearchMethod=Find_1&ItemNr=3

The secret lives of numbers: numerals and their peculiarities in mathematics and beyond/ Alfred S. Posamentier.

Authors: Posamentier Alfred S.

Source: EN05CEBSCO05C2919

Subject Terms: Number concept, Numerals, Arithmetic -- Foundations

Relation: http://dspace.kpfu.ru/xmlui/bitstream/net/178975/-1/3303439.pdf; https://dspace.kpfu.ru/xmlui/handle/net/178975

Availability: https://dspace.kpfu.ru/xmlui/handle/net/178975

Die Grundlagen der Arithmetik Eine logische mathematische Untersuchung über den Begriff der Zahl

Authors: Frege, Gottlob, Frege, G. (Gottlob), Frege, Friedrich Gottlob, Frege, Friedrich Ludwig Gottlob

Subject Terms: Number concept, Arithmetic -- Foundations

Availability: https://www.gutenberg.org/ebooks/48312/

Strong Foundations in Early Mathematics

Authors: Lorna Earle, Sam Parkes

Resource Type: eBook.

Subjects: Mathematics--Study and teaching (Early childhood, Arithmetic--Foundations

Categories: EDUCATION / Schools / Levels / Early Childhood (incl. Preschool & Kindergarten), EDUCATION / General, EDUCATION / Schools / Levels / Elementary, EDUCATION / Teacher Training & Certification

Discutindo os conceitos de multiplicação e exponencial ; A discussion on the concepts of multiplication and exponential

Authors: Pillati, Jâmia Jurich

Contributors: Probst, Roy Wilhelm, orcid:0000-0003-3282-6096, http://lattes.cnpq.br/8875516070185483, Bernardes, Mateus, orcid:0000-0003-3366-122X, http://lattes.cnpq.br/5327544341228659, Figueiredo, Elisandra Bar de, orcid:0000-0003-2101-4009, http://lattes.cnpq.br/6886923319101401, Bobko, Nara, orcid:0000-0003-2534-7572, http://lattes.cnpq.br/8431211659310477

Subject Terms: Multiplicação, Matemática - Ensino e estudo, Livros didáticos, Ensino - Metodologia, Adição, Aritmética - Fundamentos, Estudantes do ensino fundamental, Multiplication, Mathematics - Study and teaching, Textbooks, Teaching - Methodology, Addition, Arithmetic - Foundations, School children, CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA, Matemática

File Description: application/pdf

Relation: http://repositorio.utfpr.edu.br/jspui/handle/1/24693

Availability: http://repositorio.utfpr.edu.br/jspui/handle/1/24693

The Logic of Number

Authors: Neil Tennant

Resource Type: eBook.

Subjects: Arithmetic--Foundations, Logic

Categories: PHILOSOPHY / Logic, PHILOSOPHY / Metaphysics

Secret Lives of Numbers : Numerals and Their Peculiarities in Mathematics and Beyond

Authors: Alfred S. Posamentier

Resource Type: eBook.

Subjects: Arithmetic--Foundations, Numerals, Number concept

Categories: MATHEMATICS / Number Theory, MATHEMATICS / Counting & Numeration, MATHEMATICS / History & Philosophy

Architecture of Mathematics

Authors: Simon Serovajsky

Resource Type: eBook.

Subjects: Logic, Symbolic and mathematical, Arithmetic--Foundations, Mathematics--Philosophy

Categories: MATHEMATICS / General, MATHEMATICS / Logic, MATHEMATICS / Set Theory, MATHEMATICS / Functional Analysis

Aritmetinių vaizdinių formavimo IV–V klasėse taikant virtualiuosius mokymo(si) objektus teorinis pagrindimas

Authors: Šalkuvienė, Orinta

Source: Jaunųjų mokslininkų darbai, ISSN 1648-8776, 2013, [Nr.] 1(39), p. 70-75
Jaunųjų mokslininkų darbai., Šiauliai : Šiaulių universiteto leidykla, 2013, Nr. 1, p. 70-75.

Subject Terms: Aritmetika--Pagrindai, Matematika, arithmetic operations, arithmetic images, virtual teaching and learning objects, Arithmetic--Foundations, Virtuali realybė ir mokymas, Mathematics

File Description: application/pdf

Access URL: http://vddb.laba.lt/fedora/get/LT-eLABa-0001:J.04~2013~ISSN_1648-8776.N_1_39.PG_70-75/DS.002.0.01.ARTIC
https://repository.vu.lt/VU:ELABAPDB6097384&prefLang=en_US

Неразрешимост на първата теорема за непълнотата. Гьоделова и Хилбертова математика

Subject Terms: Gödel, Hilbert, incompleteness theorems, liar paradox, completeness and compactness theorems, Peano arithmetic, foundations of mathematics, Gödel and non-Gödel (Hilbert) mathematics

File Description: application/pdf

Access URL: https://philpapers.org/rec/PEN-21

Essays on Frege's Basic Laws of Arithmetic

Authors: Philip A. Ebert, Marcus Rossberg

Resource Type: eBook.

Subjects: Arithmetic--Foundations, Arithemetic--Philosophy, Logic, Symbolic and mathematical

Categories: MATHEMATICS / Essays, MATHEMATICS / Arithmetic

Juliette Kennedy and Roman Kossak eds. Set Theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies.

Source: Philosophia Mathematica. Jun2012, Vol. 20 Issue 2, p272-273. 2p.

Reviews & Products: SET Theory, Arithmetic & Foundations of Mathematics: Theorems, Philosophies (Book)

People: KENNEDY, Juliette, KOSSAK, Roman

Set Theory: The Structure of Arithmetic

Authors: Norman T. Hamilton, Joseph Landin

Resource Type: eBook.

Subjects: Set theory, Arithmetic--Foundations

Categories: MATHEMATICS / Set Theory

The Real Number System in an Algebraic Setting

Authors: J. B. Roberts

Resource Type: eBook.

Subjects: Number theory, Arithmetic--Foundations, Numbers, Real

Categories: MATHEMATICS / Algebra / Intermediate

Gottlob Frege: Foundations of Arithmetic : (Longman Library of Primary Sources in Philosophy)

Authors: Gottlob Frege

Resource Type: eBook.

Subjects: Arithmetic--Foundations, Number concept, Logic, Symbolic and mathematical

Categories: PHILOSOPHY / General, PHILOSOPHY / Logic, PHILOSOPHY / Reference

Metamathematics of First-Order Arithmetic

Authors: Petr Hájek, Pavel Pudlák

Resource Type: eBook.

Subjects: Arithmetic--Foundations

Categories: MATHEMATICS / Logic

Numbers and numerals: a story book for young and old

Authors: Smith, David Eugene, 1860-1944

Contributors: Ginsburg, Jekuthiel, 1889-1957

Subject Terms: Number concept, Numerals, Arithmetic -- Foundations