• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
Blue Book - Tucson Unified School District
Blue Book - Tucson Unified School District

... determine domains, to which an argument applies, listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. High school students can apply the mathematics they know to solve problems arising in everyday life, society, and the ...
Consecutive Sums - Implementing the Mathematical Practice
Consecutive Sums - Implementing the Mathematical Practice

KnotandTonk 1 Preliminaries
KnotandTonk 1 Preliminaries

Chapter 5 - Stanford Lagunita
Chapter 5 - Stanford Lagunita

Sets - ncert
Sets - ncert

Indirect Proofs - Stanford University
Indirect Proofs - Stanford University

Algebra 2 Curriculum - Poudre School District
Algebra 2 Curriculum - Poudre School District

lecture notes on mathematical induction
lecture notes on mathematical induction

STANDARDS FOR MATHEMATICS High School Algebra 1
STANDARDS FOR MATHEMATICS High School Algebra 1

Equivalence of the information structure with unawareness to the
Equivalence of the information structure with unawareness to the

Logic in the Finite - CIS @ UPenn
Logic in the Finite - CIS @ UPenn

Formale Methoden der Softwaretechnik Formal methods of software
Formale Methoden der Softwaretechnik Formal methods of software

... The problem with this proof is step 8. In this step we have used step 3, a step that occurs within an earlier subproof. But it turns out that this sort of justification—one that reaches back inside a subproof that has already ended—is not legitimate. To understand why it’s not legitimate, we need to ...
The Continuum Hypothesis H. Vic Dannon  September 2007
The Continuum Hypothesis H. Vic Dannon September 2007

On Triangular and Trapezoidal Numbers
On Triangular and Trapezoidal Numbers

TUSD`s Mathematics Curriculum - Algebra 1
TUSD`s Mathematics Curriculum - Algebra 1

... determine domains to which an argument applies, listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. High school students can apply the mathematics they know to solve problems arising in everyday life, society, and the ...
P 5. #1.1 Proof. n N - Department of Mathematics
P 5. #1.1 Proof. n N - Department of Mathematics

Discrete mathematics and algebra
Discrete mathematics and algebra

Order of Operations
Order of Operations

Contents - Maths, NUS
Contents - Maths, NUS

english,
english,

Standard: 2: Patterns, Functions, and Algebraic Structures
Standard: 2: Patterns, Functions, and Algebraic Structures

... The simplification of algebraic expressions and solving equations are tools used to solve problems in science. Scientists represent relationships between variables by developing a formula and using values obtained from experimental measurements and algebraic manipulation to determine values of quant ...
Full text
Full text

... numbers. Of course, the triangular numbers themselves are the binomial coefficients appearing in the second column of Pascal's triangle, so that, by mathematical induction or by applying known properties of binomial coefficients, we can sum the triangular numbers: ...
(pdf)
(pdf)

... encode sentences as numbers, so that Peano Arithmetic, being a theory of numbers, may indirectly talk about its own sentences. These issues are sidestepped in a theory of sets such as ZFC, because virtually any mathematical object, including systems of sentences, can already be thought of as sets, s ...
Some transcendence results from a harmless irrationality theorem
Some transcendence results from a harmless irrationality theorem

Differentiation and Integration
Differentiation and Integration

< 1 ... 23 24 25 26 27 28 29 30 31 ... 187 >

Foundations of mathematics

Foundations of mathematics is the study of the logical and philosophical basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be quite vague. Foundations of mathematics can be conceived as the study of the basic mathematical concepts (number, geometrical figure, set, function, etc.) and how they form hierarchies of more complex structures and concepts, especially the fundamentally important structures that form the language of mathematics (formulas, theories and their models giving a meaning to formulas, definitions, proofs, algorithms, etc.) also called metamathematical concepts, with an eye to the philosophical aspects and the unity of mathematics. The search for foundations of mathematics is a central question of the philosophy of mathematics; the abstract nature of mathematical objects presents special philosophical challenges.The foundations of mathematics as a whole does not aim to contain the foundations of every mathematical topic.Generally, the foundations of a field of study refers to a more-or-less systematic analysis of its most basic or fundamental concepts, its conceptual unity and its natural ordering or hierarchy of concepts, which may help to connect it with the rest of human knowledge. The development, emergence and clarification of the foundations can come late in the history of a field, and may not be viewed by everyone as its most interesting part.Mathematics always played a special role in scientific thought, serving since ancient times as a model of truth and rigor for rational inquiry, and giving tools or even a foundation for other sciences (especially physics). Mathematics' many developments towards higher abstractions in the 19th century brought new challenges and paradoxes, urging for a deeper and more systematic examination of the nature and criteria of mathematical truth, as well as a unification of the diverse branches of mathematics into a coherent whole.The systematic search for the foundations of mathematics started at the end of the 19th century and formed a new mathematical discipline called mathematical logic, with strong links to theoretical computer science.It went through a series of crises with paradoxical results, until the discoveries stabilized during the 20th century as a large and coherent body of mathematical knowledge with several aspects or components (set theory, model theory, proof theory, etc.), whose detailed properties and possible variants are still an active research field.Its high level of technical sophistication inspired many philosophers to conjecture that it can serve as a model or pattern for the foundations of other sciences.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report