• 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
History of Mathematics
History of Mathematics

Common Core Skill Alignment
Common Core Skill Alignment

Int Alg Lecture Notes, Section 7.2
Int Alg Lecture Notes, Section 7.2

... Big Idea: Integer exponents represent repeated multiplication. As such, there are formulas for simplifying expressions with exponents whose basis lie in the concept of repeated multiplication or cancellation. These formulas extend to rational exponents (and real-valued exponents) as well. Big Skill: ...
Chapter 2 Lesson 1: Rational Numbers
Chapter 2 Lesson 1: Rational Numbers

full text (.pdf)
full text (.pdf)

Chapter 13
Chapter 13

DIFFERENTIABILITY OF A PATHOLOGICAL FUNCTION
DIFFERENTIABILITY OF A PATHOLOGICAL FUNCTION

Word - The Further Mathematics Support Programme
Word - The Further Mathematics Support Programme

CS243: Discrete Structures Mathematical Proof Techniques
CS243: Discrete Structures Mathematical Proof Techniques

Classical First-Order Logic Introduction
Classical First-Order Logic Introduction

Finite Calculus: A Tutorial - Purdue University :: Computer Science
Finite Calculus: A Tutorial - Purdue University :: Computer Science

Logarithms and Exponentials - Florida Tech Department of
Logarithms and Exponentials - Florida Tech Department of

Local deduction, deductive interpolation and amalgamation in
Local deduction, deductive interpolation and amalgamation in

count the number of legs and divide by 4
count the number of legs and divide by 4

PDF
PDF

SECTION 1-7 Radicals
SECTION 1-7 Radicals

Routines: Name-Collection Boxes
Routines: Name-Collection Boxes

Rosen 1pt5 p75. 21. Theorem: “If n is an integer and n + 5 is odd
Rosen 1pt5 p75. 21. Theorem: “If n is an integer and n + 5 is odd

An Overview of Intuitionistic and Linear Logic
An Overview of Intuitionistic and Linear Logic

PreCalculus Course # 1202340 Text: Advanced Mathematics By
PreCalculus Course # 1202340 Text: Advanced Mathematics By

1-3 - Mrs. Williams Math Class
1-3 - Mrs. Williams Math Class

Algebra I Part 1 - Educational Synthesis
Algebra I Part 1 - Educational Synthesis

... 2-5 Adding and Subtracting Rational Numbers After studying this lesson, you should be able to:  Add two or more rational numbers  Subtract rational numbers, and  Simplify expressions that contain rational numbers. Adding Numbers with the Same Sign The sum of numbers with the Same Sign is the sum ...
Number systems and sets - Cambridge University Press
Number systems and sets - Cambridge University Press

... To be able to identify sets of numbers including natural numbers, integers, rational numbers, irrational numbers, real numbers ...
Computers and Logic/Boolean Operators
Computers and Logic/Boolean Operators

to the PDF file
to the PDF file

< 1 ... 55 56 57 58 59 60 61 62 63 ... 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