Mathematics
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Mathematics is the study of topics such as quantity, structure, space, and change. Mathematicians seek patterns and use them to formulate conjectures, which they then aim to prove or disprove through mathematical proof. When mathematical structures accurately model real phenomena, mathematics can provide insight and predictions about nature. Mathematics has developed through concepts like counting, calculation, measurement, and the study of shapes and motions, and is used throughout the world as an essential tool across many fields like science, engineering, medicine, and finance.
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Mathematics is the abstract study of topics such as quantity, structure, space and change. Mathematicians seek patterns and use them to formulate conjectures, which they then aim to prove or disprove through mathematical proof. Practical mathematics has been a human activity for as far back as written records exist, while rigorous arguments in mathematics first appeared in Greek mathematics. Today, mathematics is used throughout the world as an essential tool in many fields, and both pure and applied mathematics continue to develop and inspire new discoveries.
MatheMatics and Modern World
The document discusses several important mathematicians and their contributions throughout history:
- Leonhard Euler made significant advances in areas like calculus, trigonometry, and number theory. He introduced modern mathematical notation that is still used today.
- Carl Gauss was one of the greatest mathematicians, making influential discoveries in fields like algebra, geometry, statistics, and number theory. He laid the foundations of number theory, which computers rely on.
- John von Neumann designed the architecture underlying modern computers. The basic steps that allow computers to function were conceived by him.
- Benoit Mandelbrot discovered fractal geometry, which is fundamental to computer graphics and animation software. Fractals also have applications in technology like
Effective Computations and Foundations of Science
The problem of effective computation is discussed. Short historical analysis of this problem and basic ways of its development in culture and science, including computer science, are represented. Place the problem of the creation effective calculation in modern science is discussed. Necessity of creation “computation metascience” as system with variable hierarchy (open system) is observed. Polymetric analysis as example of this metascience is represented and discussed.
Philosophy of Mathematics
The document discusses different philosophical views on the foundations of mathematics. It covers the major schools of thought: logicism, which holds that mathematics can be reduced to logic; formalism, which views mathematics as the study of formal symbols and strings; intuitionism, which sees mathematics as mental constructions; and predicativism, which limits definitions to existing entities. The document also examines views from philosophers like Plato, Aristotle, Leibniz, Kant, Frege, Hilbert, Brouwer, and Gödel on topics like the nature of mathematical objects and truth. More recent perspectives discussed include structuralism, nominalism, fictionalism, and mathematical naturalism.
What is my favorite subject by abram villame
Mathematics is the abstract study of topics such as quantity, structure, space, and change. Mathematicians seek patterns and use them to formulate conjectures, which they then aim to prove or disprove through mathematical proof. When mathematical structures accurately model real phenomena, mathematics can provide insight and predictions about nature. Mathematics has developed from practical uses such as counting and measurement and now permeates fields like science, engineering, and finance through applications and inspires new areas of pure mathematics as well.
Mathematics applied in major fields of science and technology
This document discusses the history and importance of mathematics. It notes that mathematics has become essential in fields like robotics, space research, sports, biology, and information technology. It then discusses some key developments in mathematics throughout history, including how it became integrated into modern science in the 18th century. Several important mathematician's contributions to early computers are also outlined, such as Pascal's calculating machine and Babbage's Analytical Engine. The document ends by discussing ongoing research into modeling the human brain mathematically.
The search for certainty
1) In the 19th century, mathematics underwent significant changes with a new emphasis on rigor, structure, and abstract concepts.
2) This included the development of non-Euclidean geometry which showed that Euclid's parallel postulate is independent of the other postulates of geometry.
3) Algebra evolved from a focus on symbols and arithmetic to studying mathematical structures in more abstract ways, such as in Boolean and quaternion algebras.
The Comprehensive Guide on Branches of Mathematics
Are you struggling to get all the branches of mathematics? If yes then here is the best ever presentation that will help you to get all the branches of math. Here we have mentioned the basic mathematics branches to the advanced level.
Recommended
computer
Mathematics is the abstract study of topics such as quantity, structure, space and change. Mathematicians seek patterns and use them to formulate conjectures, which they then aim to prove or disprove through mathematical proof. Practical mathematics has been a human activity for as far back as written records exist, while rigorous arguments in mathematics first appeared in Greek mathematics. Today, mathematics is used throughout the world as an essential tool in many fields, and both pure and applied mathematics continue to develop and inspire new discoveries.
MatheMatics and Modern World
The document discusses several important mathematicians and their contributions throughout history:
- Leonhard Euler made significant advances in areas like calculus, trigonometry, and number theory. He introduced modern mathematical notation that is still used today.
- Carl Gauss was one of the greatest mathematicians, making influential discoveries in fields like algebra, geometry, statistics, and number theory. He laid the foundations of number theory, which computers rely on.
- John von Neumann designed the architecture underlying modern computers. The basic steps that allow computers to function were conceived by him.
- Benoit Mandelbrot discovered fractal geometry, which is fundamental to computer graphics and animation software. Fractals also have applications in technology like
Effective Computations and Foundations of Science
The problem of effective computation is discussed. Short historical analysis of this problem and basic ways of its development in culture and science, including computer science, are represented. Place the problem of the creation effective calculation in modern science is discussed. Necessity of creation “computation metascience” as system with variable hierarchy (open system) is observed. Polymetric analysis as example of this metascience is represented and discussed.
Philosophy of Mathematics
The document discusses different philosophical views on the foundations of mathematics. It covers the major schools of thought: logicism, which holds that mathematics can be reduced to logic; formalism, which views mathematics as the study of formal symbols and strings; intuitionism, which sees mathematics as mental constructions; and predicativism, which limits definitions to existing entities. The document also examines views from philosophers like Plato, Aristotle, Leibniz, Kant, Frege, Hilbert, Brouwer, and Gödel on topics like the nature of mathematical objects and truth. More recent perspectives discussed include structuralism, nominalism, fictionalism, and mathematical naturalism.
What is my favorite subject by abram villame
Mathematics is the abstract study of topics such as quantity, structure, space, and change. Mathematicians seek patterns and use them to formulate conjectures, which they then aim to prove or disprove through mathematical proof. When mathematical structures accurately model real phenomena, mathematics can provide insight and predictions about nature. Mathematics has developed from practical uses such as counting and measurement and now permeates fields like science, engineering, and finance through applications and inspires new areas of pure mathematics as well.
Mathematics applied in major fields of science and technology
This document discusses the history and importance of mathematics. It notes that mathematics has become essential in fields like robotics, space research, sports, biology, and information technology. It then discusses some key developments in mathematics throughout history, including how it became integrated into modern science in the 18th century. Several important mathematician's contributions to early computers are also outlined, such as Pascal's calculating machine and Babbage's Analytical Engine. The document ends by discussing ongoing research into modeling the human brain mathematically.
The search for certainty
1) In the 19th century, mathematics underwent significant changes with a new emphasis on rigor, structure, and abstract concepts.
2) This included the development of non-Euclidean geometry which showed that Euclid's parallel postulate is independent of the other postulates of geometry.
3) Algebra evolved from a focus on symbols and arithmetic to studying mathematical structures in more abstract ways, such as in Boolean and quaternion algebras.
The Comprehensive Guide on Branches of Mathematics
Are you struggling to get all the branches of mathematics? If yes then here is the best ever presentation that will help you to get all the branches of math. Here we have mentioned the basic mathematics branches to the advanced level.
Euclid the mathematician
Euclid was a Greek mathematician born around 300 BC in Alexandria, Egypt. He is best known for his work Elements, which laid out the principles of geometry and remains influential to this day. Little is known about Euclid's life directly, as historical references to him are few. Elements presented geometric concepts and results established by earlier mathematicians in a single, logically coherent framework, and introduced rigorous proof-based reasoning that is still used in mathematics. Euclid is also attributed with several other works dealing with geometry and related topics, though some attributions are uncertain.
Mathematicians
This document provides biographies of several famous 18th-19th century mathematicians including Leonhard Euler, Gabriel Cramer, Thomas Simpson, Jean Le Rond d'Alembert, Joseph Louis Lagrange, Pierre-Simon Laplace, Gaspard Monge, Adrien-Marie Legendre, Jean Baptiste Joseph Fourier, Johann Carl Friedrich Gauss, and Augustin Louis Cauchy. It discusses their major contributions and achievements in fields such as calculus, geometry, number theory, algebra, and analysis, and how they helped advance mathematics as a modern science.
Geometry
Geometry is the study of shapes and configurations in mathematical contexts. It focuses on properties that remain invariant under symmetries, like those of flat space studied in Euclidean geometry or multi-dimensional spaces examined in Riemannian geometry. Geometry has many branches including differential geometry, algebraic geometry, semi-Riemannian geometry, and symplectic geometry, each generalizing geometric concepts in important ways like informing Einstein's theory of relativity or underpinning modern theoretical physics.
Eykleidis
Euclid was a Greek mathematician from Alexandria who lived during the reign of Ptolemy I between 323-283 BC. He is often referred to as the "Father of Geometry" and wrote influential works on geometry, perspective, number theory and other areas of mathematics. His most famous work is the Elements, which deduced geometric principles from a small set of axioms and served as the main geometry textbook used for over 2000 years. The Elements also explored the parallel postulate and properties of parallel lines.
Branches of mathematics
Mathematics can be divided into several branches that each focus on different areas of study. Some of the main branches include arithmetic, algebra, mathematical analysis, combinatorics, and geometry/topology. Arithmetic is the oldest branch and focuses on numbers and basic operations like addition and multiplication. Algebra studies the properties of numbers and methods for solving equations. Mathematical analysis examines continuous change through calculus, limits, and functions. Combinatorics analyzes discrete collections of objects and their relationships. Geometry and topology use spatial relationships and properties of shapes.
contribution of mathematicians.pdf
1) Aryabhata was a 5th century Indian mathematician who made several important contributions including developing a place-value decimal system, computing π to four decimal places, and formulating algebraic formulae.
2) Carl Friedrich Gauss was an influential 19th century German mathematician and scientist who made seminal contributions across many areas of mathematics and science, including constructing a 17-sided polygon, developing complex numbers, discovering the Gaussian distribution, and conducting pioneering work in geometry, algebra, statistics, and astronomy.
3) Both Aryabhata and Gauss were pioneering mathematicians who made enduring contributions that expanded the boundaries of mathematics and influenced many subsequent scientists and mathematicians.
Application of Mathematics
This was an Inter Collegiate and a State Level Contest named SIGMA '08. Won a special prize for this paper. This research emphasized on how simple concepts of Mathematics helps into constructing complex mathematical models for space programming and their individual importance in real time applications.
Some Interesting Facts, Myths and History of Mathematics
This paper deals with primary concepts and fallacies of mathematics which many a times students and even teachers ignore. Also this paper comprises of history of mathematical symbols, notations and methods of calculating time. I have also included some ancient techniques of solving mathematical real time problems. This paper is a confluence of various traditional mathematical techniques and their implementation in modern mathematics.
Math's project, winter break
Thales was a Greek philosopher, mathematician and scientist considered the first of the Seven Sages of Greece. He founded the Ionian school of philosophy in Miletus and is credited with introducing abstract geometry. Thales traveled to Egypt where he learned mathematical innovations from Egyptian priests and brought this knowledge back to Greece. He made early contributions to geometry, including determining the height of pyramids and using triangles to calculate ship distances from shore. Thales is also credited with five theorems of geometry and the first known proof, proving that any angle inscribed in a semicircle is a right angle.
euclid
Euclid was a Greek mathematician from Alexandria, Egypt who lived from the mid-4th century BC to the mid-3rd century BC. He is considered the "Father of Geometry" and is best known for writing Elements, one of the most influential works in the history of mathematics. Elements deduced the principles of Euclidean geometry from a small set of axioms and served as the main geometry textbook for over 2000 years. Euclid made important contributions to mathematics, including the fields of perspective, conic sections, spherical geometry, number theory, and rigor.
8 Great mathematicians and their inventions
The role mathematics has played in changing the world has been very much underplayed. This slide was made with intention to show the inventions of some of the greatest mathematicians who have graced the surface of this Earth
Top 10 mathematicians
Pythagoras of Samos was a Greek mathematician considered one of the first great mathematicians. He founded the Pythagorean cult which studied and advanced mathematics. He is commonly credited with the Pythagorean theorem in trigonometry, though some credit his students or earlier Indian mathematicians. Nonetheless, the theorem plays a large role in modern measurements and technology. Pythagoras could be called the founding father of modern mathematics.
Wonders in maths
Mathematics guides all sciences and social sciences by providing principles and models. During the 19th century, mathematics was seen as abstract but it is now widely applied across many fields from engineering to genetics due to developments in applied mathematics spurred by World War 2 and Sputnik. Modern technologies like CAT scanners and economic models all depend on sophisticated mathematical foundations. Engineering in particular utilizes differential equations, geometry, and other areas of mathematics.
Euclid's geometry presentation 2007
Euclid, often called the "Father of Geometry", was a Greek mathematician from Alexandria who wrote the influential textbook Elements. In Elements, Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. His work served as the main geometry textbook from its publication until the late 19th century. Euclid also wrote works on other areas of mathematics including perspective, conic sections, spherical geometry, number theory and rigor.
Euclid
Euclid was a Greek mathematician from Alexandria known as the "Father of Geometry". His influential work Elements deduced the principles of Euclidean geometry from a small set of axioms. It served as the main textbook for teaching mathematics for over 2000 years. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and rigor. He established an innovative deductive system in geometry based on definitions, axioms, and theorems and used it to prove various geometric results, such as how to construct a regular dodecahedron.
Geometry
1. Euclid's Elements/Postulates - Euclid wrote a text titled 'Elements' in 300 BC which presented geometry through a small set of statements called postulates that are accepted as true. He was able to derive much of planar geometry from just five postulates, including the parallel postulate which caused much debate.
2. Euclid's Contribution to Geometry - Euclid is considered the "Father of Geometry" for his work Elements, which introduced deductive reasoning to mathematics. Elements influenced the development of the subject through its logical presentation of geometry from definitions and postulates.
3. Similar Triangles - Triangles are similar if they have the same shape but not necessarily the same
Yash group Maths PPT for class IX
Geometry is a branch of mathematics concerned with shapes, sizes, positions, and properties of space. It arose independently in early cultures and emerged in ancient Greece where Euclid formalized it in his influential Elements text around 300 BC. Elements defined geometry axiomatically and influenced mathematics for centuries. It included proofs of theorems like two triangles being congruent if they share two equal angles and one equal side. Euclid's work defined much of the rules and language of geometry still used today.
Famous mathematicians
This document provides biographical information on several famous mathematicians and physicists:
- Ada Lovelace was an English mathematician in the 1800s considered the first computer programmer for writing instructions for Charles Babbage's proposed mechanical computer.
- Fibonacci introduced the Fibonacci sequence and popularized the Hindu-Arabic numeral system in Western Europe.
- Georg Cantor invented set theory and established that there are different levels of infinity. His work faced resistance from contemporaries.
- Emmy Noether made fundamental contributions to abstract algebra and theoretical physics through her development of ring and field theory.
- John Forbes Nash Jr. made pioneering contributions to game theory and differential geometry and won the Nobel Prize in Economics. He struggled with schizophrenia.
Mathematics
This document provides an overview of the history of mathematics, outlining some of the key developments in different time periods and civilizations. It discusses the origins and early developments of mathematics in ancient Babylon, Egypt, India, Greece, and beyond. Some of the important concepts covered include early algebra and geometry developed by civilizations like the Babylonians, as well as later advances in areas like calculus, trigonometry, and abstract algebra made from the 16th century onward by mathematicians such as Newton, Leibniz, Descartes, and others. It also profiles several influential mathematicians and their contributions to fields like algebra, geometry, and number theory.
Its all about history of math
The document provides a summary of the history of Greek mathematics from Thales in the 6th century BC to the collapse of the University of Alexandria in the 5th century AD. It discusses how Thales founded the Ionian school of mathematics and influenced Pythagoras. It then outlines the development of Greek mathematics through figures like Euclid and Archimedes, and the establishment and destruction of the University of Alexandria, which marked the end of the peak of Greek mathematical achievements.
Postgraduate module theory 2013- lectures
This document outlines the syllabus for a postgraduate course on module theory taught during the second semester of the 2013-2014 academic year. The syllabus covers fundamental concepts in module theory over 10 weeks, including definitions of modules and submodules, direct sums, homomorphisms, free and finitely presented modules, simple and semisimple modules, injective modules, tensor products, and character modules. References for additional reading are provided.
Generalization of p injective rings and projective modules
This academic article discusses the generalization of p-injective rings and projective modules. It begins with definitions of terms like p-injective modules and epp-rings (rings where every projective module is p-injective). It presents properties of p-injective modules and proves conditions under which a module is p-injective. It also proves properties of epp-rings, including a theorem showing when a ring is a right epp-ring. Examples of epp-rings and rings that are left but not right epp are also given. The article concludes with a proposition about rings that are Morita equivalent.
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Euclid the mathematician
Euclid was a Greek mathematician born around 300 BC in Alexandria, Egypt. He is best known for his work Elements, which laid out the principles of geometry and remains influential to this day. Little is known about Euclid's life directly, as historical references to him are few. Elements presented geometric concepts and results established by earlier mathematicians in a single, logically coherent framework, and introduced rigorous proof-based reasoning that is still used in mathematics. Euclid is also attributed with several other works dealing with geometry and related topics, though some attributions are uncertain.
Mathematicians
This document provides biographies of several famous 18th-19th century mathematicians including Leonhard Euler, Gabriel Cramer, Thomas Simpson, Jean Le Rond d'Alembert, Joseph Louis Lagrange, Pierre-Simon Laplace, Gaspard Monge, Adrien-Marie Legendre, Jean Baptiste Joseph Fourier, Johann Carl Friedrich Gauss, and Augustin Louis Cauchy. It discusses their major contributions and achievements in fields such as calculus, geometry, number theory, algebra, and analysis, and how they helped advance mathematics as a modern science.
Geometry
Geometry is the study of shapes and configurations in mathematical contexts. It focuses on properties that remain invariant under symmetries, like those of flat space studied in Euclidean geometry or multi-dimensional spaces examined in Riemannian geometry. Geometry has many branches including differential geometry, algebraic geometry, semi-Riemannian geometry, and symplectic geometry, each generalizing geometric concepts in important ways like informing Einstein's theory of relativity or underpinning modern theoretical physics.
Eykleidis
Euclid was a Greek mathematician from Alexandria who lived during the reign of Ptolemy I between 323-283 BC. He is often referred to as the "Father of Geometry" and wrote influential works on geometry, perspective, number theory and other areas of mathematics. His most famous work is the Elements, which deduced geometric principles from a small set of axioms and served as the main geometry textbook used for over 2000 years. The Elements also explored the parallel postulate and properties of parallel lines.
Branches of mathematics
Mathematics can be divided into several branches that each focus on different areas of study. Some of the main branches include arithmetic, algebra, mathematical analysis, combinatorics, and geometry/topology. Arithmetic is the oldest branch and focuses on numbers and basic operations like addition and multiplication. Algebra studies the properties of numbers and methods for solving equations. Mathematical analysis examines continuous change through calculus, limits, and functions. Combinatorics analyzes discrete collections of objects and their relationships. Geometry and topology use spatial relationships and properties of shapes.
contribution of mathematicians.pdf
1) Aryabhata was a 5th century Indian mathematician who made several important contributions including developing a place-value decimal system, computing π to four decimal places, and formulating algebraic formulae.
2) Carl Friedrich Gauss was an influential 19th century German mathematician and scientist who made seminal contributions across many areas of mathematics and science, including constructing a 17-sided polygon, developing complex numbers, discovering the Gaussian distribution, and conducting pioneering work in geometry, algebra, statistics, and astronomy.
3) Both Aryabhata and Gauss were pioneering mathematicians who made enduring contributions that expanded the boundaries of mathematics and influenced many subsequent scientists and mathematicians.
Application of Mathematics
This was an Inter Collegiate and a State Level Contest named SIGMA '08. Won a special prize for this paper. This research emphasized on how simple concepts of Mathematics helps into constructing complex mathematical models for space programming and their individual importance in real time applications.
Some Interesting Facts, Myths and History of Mathematics
This paper deals with primary concepts and fallacies of mathematics which many a times students and even teachers ignore. Also this paper comprises of history of mathematical symbols, notations and methods of calculating time. I have also included some ancient techniques of solving mathematical real time problems. This paper is a confluence of various traditional mathematical techniques and their implementation in modern mathematics.
Math's project, winter break
Thales was a Greek philosopher, mathematician and scientist considered the first of the Seven Sages of Greece. He founded the Ionian school of philosophy in Miletus and is credited with introducing abstract geometry. Thales traveled to Egypt where he learned mathematical innovations from Egyptian priests and brought this knowledge back to Greece. He made early contributions to geometry, including determining the height of pyramids and using triangles to calculate ship distances from shore. Thales is also credited with five theorems of geometry and the first known proof, proving that any angle inscribed in a semicircle is a right angle.
euclid
Euclid was a Greek mathematician from Alexandria, Egypt who lived from the mid-4th century BC to the mid-3rd century BC. He is considered the "Father of Geometry" and is best known for writing Elements, one of the most influential works in the history of mathematics. Elements deduced the principles of Euclidean geometry from a small set of axioms and served as the main geometry textbook for over 2000 years. Euclid made important contributions to mathematics, including the fields of perspective, conic sections, spherical geometry, number theory, and rigor.
8 Great mathematicians and their inventions
The role mathematics has played in changing the world has been very much underplayed. This slide was made with intention to show the inventions of some of the greatest mathematicians who have graced the surface of this Earth
Top 10 mathematicians
Pythagoras of Samos was a Greek mathematician considered one of the first great mathematicians. He founded the Pythagorean cult which studied and advanced mathematics. He is commonly credited with the Pythagorean theorem in trigonometry, though some credit his students or earlier Indian mathematicians. Nonetheless, the theorem plays a large role in modern measurements and technology. Pythagoras could be called the founding father of modern mathematics.
Wonders in maths
Mathematics guides all sciences and social sciences by providing principles and models. During the 19th century, mathematics was seen as abstract but it is now widely applied across many fields from engineering to genetics due to developments in applied mathematics spurred by World War 2 and Sputnik. Modern technologies like CAT scanners and economic models all depend on sophisticated mathematical foundations. Engineering in particular utilizes differential equations, geometry, and other areas of mathematics.
Euclid's geometry presentation 2007
Euclid, often called the "Father of Geometry", was a Greek mathematician from Alexandria who wrote the influential textbook Elements. In Elements, Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. His work served as the main geometry textbook from its publication until the late 19th century. Euclid also wrote works on other areas of mathematics including perspective, conic sections, spherical geometry, number theory and rigor.
Euclid
Euclid was a Greek mathematician from Alexandria known as the "Father of Geometry". His influential work Elements deduced the principles of Euclidean geometry from a small set of axioms. It served as the main textbook for teaching mathematics for over 2000 years. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and rigor. He established an innovative deductive system in geometry based on definitions, axioms, and theorems and used it to prove various geometric results, such as how to construct a regular dodecahedron.
Geometry
1. Euclid's Elements/Postulates - Euclid wrote a text titled 'Elements' in 300 BC which presented geometry through a small set of statements called postulates that are accepted as true. He was able to derive much of planar geometry from just five postulates, including the parallel postulate which caused much debate.
2. Euclid's Contribution to Geometry - Euclid is considered the "Father of Geometry" for his work Elements, which introduced deductive reasoning to mathematics. Elements influenced the development of the subject through its logical presentation of geometry from definitions and postulates.
3. Similar Triangles - Triangles are similar if they have the same shape but not necessarily the same
Yash group Maths PPT for class IX
Geometry is a branch of mathematics concerned with shapes, sizes, positions, and properties of space. It arose independently in early cultures and emerged in ancient Greece where Euclid formalized it in his influential Elements text around 300 BC. Elements defined geometry axiomatically and influenced mathematics for centuries. It included proofs of theorems like two triangles being congruent if they share two equal angles and one equal side. Euclid's work defined much of the rules and language of geometry still used today.
Famous mathematicians
This document provides biographical information on several famous mathematicians and physicists:
- Ada Lovelace was an English mathematician in the 1800s considered the first computer programmer for writing instructions for Charles Babbage's proposed mechanical computer.
- Fibonacci introduced the Fibonacci sequence and popularized the Hindu-Arabic numeral system in Western Europe.
- Georg Cantor invented set theory and established that there are different levels of infinity. His work faced resistance from contemporaries.
- Emmy Noether made fundamental contributions to abstract algebra and theoretical physics through her development of ring and field theory.
- John Forbes Nash Jr. made pioneering contributions to game theory and differential geometry and won the Nobel Prize in Economics. He struggled with schizophrenia.
Mathematics
This document provides an overview of the history of mathematics, outlining some of the key developments in different time periods and civilizations. It discusses the origins and early developments of mathematics in ancient Babylon, Egypt, India, Greece, and beyond. Some of the important concepts covered include early algebra and geometry developed by civilizations like the Babylonians, as well as later advances in areas like calculus, trigonometry, and abstract algebra made from the 16th century onward by mathematicians such as Newton, Leibniz, Descartes, and others. It also profiles several influential mathematicians and their contributions to fields like algebra, geometry, and number theory.
Its all about history of math
The document provides a summary of the history of Greek mathematics from Thales in the 6th century BC to the collapse of the University of Alexandria in the 5th century AD. It discusses how Thales founded the Ionian school of mathematics and influenced Pythagoras. It then outlines the development of Greek mathematics through figures like Euclid and Archimedes, and the establishment and destruction of the University of Alexandria, which marked the end of the peak of Greek mathematical achievements.
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Some Interesting Facts, Myths and History of Mathematics
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Postgraduate module theory 2013- lectures
This document outlines the syllabus for a postgraduate course on module theory taught during the second semester of the 2013-2014 academic year. The syllabus covers fundamental concepts in module theory over 10 weeks, including definitions of modules and submodules, direct sums, homomorphisms, free and finitely presented modules, simple and semisimple modules, injective modules, tensor products, and character modules. References for additional reading are provided.
Generalization of p injective rings and projective modules
This academic article discusses the generalization of p-injective rings and projective modules. It begins with definitions of terms like p-injective modules and epp-rings (rings where every projective module is p-injective). It presents properties of p-injective modules and proves conditions under which a module is p-injective. It also proves properties of epp-rings, including a theorem showing when a ring is a right epp-ring. Examples of epp-rings and rings that are left but not right epp are also given. The article concludes with a proposition about rings that are Morita equivalent.
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Similar to Mathematics
Science and contribution of mathematics in its development
Mathematics is the science of logical reasoning that has its development linked to research, interest in discovering the new and investigate highly complex situations. The escalation of Mathematics began in ancient times when it was aroused the interest by the calculations and numbers according to the need of man to relate the natural events to their daily lives. Today, Mathematics is the most important science of the modern world because it is present in all scientific areas.
maths project
This document provides information about various topics in mathematics including the invention of mathematics, algorithms, logarithms, and arithmetic progressions. It discusses how mathematics developed from counting and measurement in early civilizations. Algorithms are defined as well-defined procedures for solving problems, and logarithms are introduced as a way to simplify calculations by relating exponential functions. Arithmetic progressions follow a constant difference between consecutive terms of a sequence. The document also provides details on the development of algorithms, logarithms, and arithmetic as branches of mathematics.
2P-MAT02 HANDOUTS.docx
This document provides an overview of the history and evolution of mathematics education. It discusses how mathematics has transitioned from being studied primarily for philosophical purposes to becoming a central part of the core curriculum in modern developed countries. Key developments include the establishment of mathematics as an independent field of research in the 20th century and the creation of organizations like ICMI that have helped standardize mathematics education globally through frameworks like the Common Core standards in the US. The document also outlines typical mathematics content covered at different grade levels and in post-secondary education, as well as objectives of mathematics education that have varied across time and place.
The Oldest Branch of Mathematics.pdf
Mathematics, often referred to as the universal language of the universe, has a rich and diverse history that spans millennia.
nas23-vardi.pptx
This document discusses the history of mathematical reasoning and efforts to automate it. It covers topics like logic and proofs introduced by Aristotle and Leibniz's dream of a universal mathematical language. Later, issues around set theory and paradoxes emerged, challenging foundations. Hilbert proposed formalizing mathematics to establish its consistency, but Gödel and Turing showed its incompleteness and undecidability. Modern automated reasoning tools like SAT solvers have made huge advances, solving problems with millions of variables, but challenges remain around fully automating mathematical reasoning.
Harsh math ppt number system
This document provides an overview of different number systems and concepts in mathematics related to numbers. It defines real numbers, rational numbers, integers, whole numbers, and natural numbers. It discusses that rational numbers can be divided into integers, whole numbers, and natural numbers. Irrational numbers are also introduced. Important mathematicians who contributed to the study and understanding of numbers are referenced, including Pythagoras, Archimedes, Aryabhatta, Dedekind, Cantor, Babylonians, and Euclid.
Nature, characteristics and definition of maths
This document discusses various views of mathematics, including student, parent, and teacher views. It also covers the nature, characteristics, development, and applications of mathematics. Some key points include:
- Mathematics involves finding and studying patterns, and can be seen as a language, way of thinking, and problem solving approach.
- It has developed over time from ancient subjects like geometry to a more modern field incorporating diverse areas.
- Major subfields include algebra, analysis, applied math, with connections to many other domains. Real-world applications span fields like imaging, cryptography, simulation, and bioinformatics.
Maths in daily life
For over 2000 years, mathematics has evolved from practical applications to a field of rigorous inquiry and back again. Early civilizations developed basic arithmetic and geometry to solve practical problems. The Greeks were first to study mathematics with a philosophical spirit, seeking inherent truths. Their work in geometry, algebra, and other areas remains valid today. Over centuries, mathematics spread across cultures through trade, exploration, and scholarship. It has grown increasingly specialized while also finding new applications, aided by computers. Today, mathematics is more valuable than ever as a way of understanding both natural and human systems through abstraction and modeling.
Top 10 indian mathematician
contain the information of all famous mathematicians of india who had put his value able efforts in the invention of maths to bring it to advance level.
slides contains the picture of mathematician with the full description about him and their contribution in the field of maths.
One’s own work
Mathematics appears to be both discovered and invented. While mathematical concepts like shapes, sizes and quantities have always existed in nature and been waiting to be discovered, many mathematical tools, systems and theories have been invented by humans over centuries to help develop mathematics as a formal science. Key inventions include numerical systems, abstraction of concepts, and tools like the abacus, while mathematical objects and patterns in nature have been discovered through observation and study. Overall, mathematics has advanced through both the discovery of principles present in the universe and the invention of tools and ideas to formally express and apply these principles.
computers in education mathematics
The document provides definitions and overviews of various topics in mathematics, including:
- Slope intercept form and the definition of slope and y-intercept of a line
- Quadratic equations and their standard form
- The Pythagorean theorem and how to use it to find the lengths of sides of a right triangle
- The order of operations using the acronym PEMDAS
- What algebra and its uses in representing unknown values and proving properties
- Euclidean geometry and its origins from Euclid's Elements textbook
- Trigonometry and its uses in studying triangles and relationships between side lengths and angles
- Calculus and its two main branches of differential and integral calculus
- Probability theory and its uses
history of mathematics by pavansai
Mathematics is the study of relationships among quantities, magnitudes, and properties, as well as logical operations to deduce unknowns. Historically, it was regarded as the science of quantity in fields like geometry, arithmetic, and algebra. The history of mathematics is nearly as old as humanity itself and has evolved from simple counting and measurement to the complex discipline we know today. Ancient civilizations developed practical mathematics for tasks like trade, construction, and tracking seasons, which required numeration systems, arithmetic techniques, and measurement strategies.
The Importance of Math and 10 Greatest Msthemeticians.
explaining how important the math is and the top 10 mathematicians that have contributed so many in mathematics.
What impact did Pythagoras have on EuclidSolutionPythagorasP.pdf
What impact did Pythagoras have on Euclid?
Solution
Pythagoras
Probably the most famous name during the development of Greek geometry is Pythagoras, even
if only for the famous law concerning right angled triangles. This mathematician lived in a secret
society which took on a semi-religious mission. From this, the Pythagoreans developed a number
of ideas and began to develop trigonometry. The Pythagoreans added a few new axioms to the
store of geometrical knowledge.
1)The sum of the internal angles of a triangle equals two right angles 180*.
2)The sum of the external angles of a triangle equals four right angles 360*
3)The sum of the interior angles of any polygon equals 2n-4 right angles, where n is the number
of sides.
4)The sum of the exterior angles of a polygon equals four right angles, however many sides.
5)The three polygons, the triangle, hexagon, and square completely fill the space around a point
on a plane - six triangles, four squares and three hexagons. In other words, you can tile an area
with these three shapes, without leaving gaps or having overlaps.
6)For a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of
the other two sides.
Most of these rules are instantly familiar to most students, as basic principles of geometry and
trigonometry. One of his pupils, Hippocrates, took the development of geometry further. He was
the first to start using geometrical techniques in other areas of maths, such as solving quadratic
equations, and he even began to study the process of integration. He solved the problem of
Squaring a Lune and showed that the ratio of the areas of two circles equalled the ratio between
the squares of the radii of the circles.
Euclid
Alongside Pythagoras, Euclid is a very famous name in the history of Greek geometry. He
gathered the work of all of the earlier mathematicians and created his landmark work, \'The
Elements,\' surely one of the most published books of all time. In this work, Euclid set out the
approach for geometry and pure mathematics generally, proposing that all mathematical
statements should be proved through reasoning and that no empirical measurements were
needed. This idea of proof still dominates pure mathematics in the modern world.
The reason that Euclid was so influential is that his work is more than just an explanation of
geometry or even of mathematics. The way in which he used logic and demanded proof for every
theorem shaped the ideas of western philosophers right up until the present day. Great
philosopher mathematicians such as Descartes and Newton presented their philosophical works
using Euclid\'s structure and format, moving from simple first principles to complicated
concepts. Abraham Lincoln was a fan, and the US Declaration of Independence used Euclid\'s
axiomatic system.
Apart from the Elements, Euclid also wrote works about astronomy, mirrors, optics, perspective
and music theory, although many of his works are lost to posterity. Certainl.
Línea del tiempo
This document presents a timeline that outlines the key problems in the foundations of mathematics throughout history. It begins in ancient Greece where problems arose regarding the existence of irrational numbers. In the 17th-18th centuries, calculus and analytic geometry developed rapidly but lacked rigor. In the 19th century, mathematicians like Gauss formalized analysis and constructed the real numbers. In the 20th century, paradoxes emerged which led to different philosophical schools like logicism, intuitionism and formalism to interpret and resolve the paradoxes.
Math is the mother of all Science
This document provides an introduction to a presentation on mathematics. It lists the names of five presenters and then provides three paragraphs explaining what mathematics is, why it is called the "mother of all sciences", and how mathematics is the foundation of other subjects. It includes brief quotes from scientists about the importance and role of mathematics in understanding the universe and reality.
7 contributionsof indian mathematicians to mathematics
This document provides an overview of the history of mathematics, beginning with ancient Indian mathematicians like Aryabhata, Brahmagupta, Mahavira, and Varahamihira who made early contributions to algebra, trigonometry, and calculus. It then discusses Greek mathematicians such as Euclid, Pythagoras, and Archimedes and their foundational work in geometry and number theory. The document highlights seminal European mathematicians like Euler, Gauss, Riemann, Hilbert and their advances in areas like analysis, algebra, geometry and topology. It concludes that the collective contributions of these mathematicians established the foundations of modern mathematics.
The History and Evolution of the Concept of Infinity
This document provides a detailed overview of the history and evolution of the concept of infinity in mathematics. It discusses how early Greek mathematicians like Euclid, Archimedes, and Eudoxus began the formal study of infinity and developed key concepts like π and methods like exhaustion. Later mathematicians like Euler, Gauss, and Cantor made major contributions, with Cantor developing set theory and the distinction between different types of infinities. The document also examines how infinity relates to fields like astronomy, art, and philosophy. It discusses open problems and paradoxes involving infinity that remain unsolved.
Mathematics in Ancient Greece
The document provides an overview of mathematics in ancient Greece, covering important Greek mathematicians and their contributions. It discusses Thales of Miletus, who made early advances in geometry. It also covers Pythagoras and the Pythagorean school, whose discoveries included relationships between musical intervals and ratios. Euclid is discussed for writing the influential Elements, compiling earlier work. Archimedes made advances in areas and used a method of exhaustion to calculate pi. The document provides context on Plato, Aristotle, and others who helped develop mathematics.
maths
Mathematics has been an important part of the human search for understanding for over two thousand years. Mathematical discoveries have come from attempts to describe the natural world and from logical reasoning. In recent centuries, mathematics has also been successfully applied to other human endeavors such as politics, archaeology, traffic analysis, and sustainable forestry management. Today, mathematical thinking is more valuable than ever before and is an essential part of a liberal education.
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Science and contribution of mathematics in its development
Science and contribution of mathematics in its development
The Importance of Math and 10 Greatest Msthemeticians.
The Importance of Math and 10 Greatest Msthemeticians.
What impact did Pythagoras have on EuclidSolutionPythagorasP.pdf
What impact did Pythagoras have on EuclidSolutionPythagorasP.pdf
7 contributionsof indian mathematicians to mathematics
7 contributionsof indian mathematicians to mathematics
The History and Evolution of the Concept of Infinity
The History and Evolution of the Concept of Infinity
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Concept of self reflection and peer evaluation
This document discusses self-reflection and peer evaluation in education. Self-reflection is introspection where students examine their own values, viewpoints, communication styles, and experiences. Peer evaluation involves students providing feedback on each other's work and contributions. Some advantages are that it encourages student involvement, responsibility, and judgment skills. However, it also increases the lecturer's workload and students may feel unequipped to do evaluations.
Correlation of mathematics
This document discusses the correlation of mathematics with various domains:
1) Mathematics is correlated with life activities through concepts like percentages, interest rates, and ratios that are useful in everyday life.
2) Different branches of mathematics like arithmetic, algebra, geometry are interrelated through concepts like functions and mathematical structures.
3) Topics within the same branch of mathematics are also correlated, for example concepts in algebra relate to equations, and areas of shapes relate in geometry.
4) Mathematics is also correlated with other subjects like physical sciences through expression of laws as mathematical equations, with biology through use of higher math methods, and with engineering as mathematics forms the basis of engineering courses.
Leonardo fibonacci
Leonardo Fibonacci was an Italian mathematician who introduced the Hindu-Arabic decimal number system to Europe in 1202 with his book Liber Abaci. This system uses 10 symbols (0-9) in a positional notation, which was a significant improvement over the cumbersome Roman numeral system. Fibonacci's book helped popularize this new method of calculation in Europe and launched the modern use of the decimal number system. Fibonacci is also known for the Fibonacci sequence found in nature and described in Liber Abaci, where each number is the sum of the previous two.
Online assignmentvdcv
This document discusses learning management systems (LMS) and how they can be used in education. An LMS is a software application that can be used to create and deliver course content, monitor student participation, and assess student performance. It allows instructors to manage training programs remotely and provides interactive features for students. Common components of an LMS include tools for class registration, content uploading and management, remote course delivery, calendars, student interaction, assessments, and reporting. LMS provides benefits like efficient content reuse, customizable delivery options, and lower costs through economies of scale. The document also examines how electronic resources influence classrooms and the types of online and offline resources available to teachers through library access.
Lesson transcript
The document is a lesson transcript for a mathematics class on right angles and circles. It discusses how if the endpoints of a diameter of a circle are joined to any other point on the circle, the angle formed is a right angle. It provides definitions, facts, and concepts to the students. The lesson involves drawing circles and diameters, forming triangles, and proving that the angles are right angles. Students are asked to apply the concept to determine if angles in other drawings are right angles.
Area ratio
The document discusses calculating the ratio of the areas of two triangles. It first draws a perpendicular from the point A to the base BC of the triangles. It then states that the area of triangle ABD is 1/2 times the height h times the length BD, and the area of triangle ACD is 1/2 times the height h times the length CD. Finally, it concludes that the ratio of the two areas is equal to the ratio of the lengths BD and CD.
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The debris of the ‘last major merger’ is dynamically young
The Milky Way’s (MW) inner stellar halo contains an [Fe/H]-rich component with highly eccentric orbits, often referred to as the
‘last major merger.’ Hypotheses for the origin of this component include Gaia-Sausage/Enceladus (GSE), where the progenitor
collided with the MW proto-disc 8–11 Gyr ago, and the Virgo Radial Merger (VRM), where the progenitor collided with the
MW disc within the last 3 Gyr. These two scenarios make different predictions about observable structure in local phase space,
because the morphology of debris depends on how long it has had to phase mix. The recently identified phase-space folds in Gaia
DR3 have positive caustic velocities, making them fundamentally different than the phase-mixed chevrons found in simulations
at late times. Roughly 20 per cent of the stars in the prograde local stellar halo are associated with the observed caustics. Based
on a simple phase-mixing model, the observed number of caustics are consistent with a merger that occurred 1–2 Gyr ago.
We also compare the observed phase-space distribution to FIRE-2 Latte simulations of GSE-like mergers, using a quantitative
measurement of phase mixing (2D causticality). The observed local phase-space distribution best matches the simulated data
1–2 Gyr after collision, and certainly not later than 3 Gyr. This is further evidence that the progenitor of the ‘last major merger’
did not collide with the MW proto-disc at early times, as is thought for the GSE, but instead collided with the MW disc within
the last few Gyr, consistent with the body of work surrounding the VRM.
Micronuclei test.M.sc.zoology.fisheries.
Current Ms word generated power point presentation covers major details about the micronuclei test. It's significance and assays to conduct it. It is used to detect the micronuclei formation inside the cells of nearly every multicellular organism. It's formation takes place during chromosomal sepration at metaphase.
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The use of Nauplii and metanauplii artemia in aquaculture (brine shrimp).pptx
Although Artemia has been known to man for centuries, its use as a food for the culture of larval organisms apparently began only in the 1930s, when several investigators found that it made an excellent food for newly hatched fish larvae (Litvinenko et al., 2023). As aquaculture developed in the 1960s and ‘70s, the use of Artemia also became more widespread, due both to its convenience and to its nutritional value for larval organisms (Arenas-Pardo et al., 2024). The fact that Artemia dormant cysts can be stored for long periods in cans, and then used as an off-the-shelf food requiring only 24 h of incubation makes them the most convenient, least labor-intensive, live food available for aquaculture (Sorgeloos & Roubach, 2021). The nutritional value of Artemia, especially for marine organisms, is not constant, but varies both geographically and temporally. During the last decade, however, both the causes of Artemia nutritional variability and methods to improve poorquality Artemia have been identified (Loufi et al., 2024).
Brine shrimp (Artemia spp.) are used in marine aquaculture worldwide. Annually, more than 2,000 metric tons of dry cysts are used for cultivation of fish, crustacean, and shellfish larva. Brine shrimp are important to aquaculture because newly hatched brine shrimp nauplii (larvae) provide a food source for many fish fry (Mozanzadeh et al., 2021). Culture and harvesting of brine shrimp eggs represents another aspect of the aquaculture industry. Nauplii and metanauplii of Artemia, commonly known as brine shrimp, play a crucial role in aquaculture due to their nutritional value and suitability as live feed for many aquatic species, particularly in larval stages (Sorgeloos & Roubach, 2021).
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Slides from talk:
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https://ashpc.eu/
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With increasing population, people need to rely on packaged food stuffs. Packaging of food materials requires the preservation of food. There are various methods for the treatment of food to preserve them and irradiation treatment of food is one of them. It is the most common and the most harmless method for the food preservation as it does not alter the necessary micronutrients of food materials. Although irradiated food doesn’t cause any harm to the human health but still the quality assessment of food is required to provide consumers with necessary information about the food. ESR spectroscopy is the most sophisticated way to investigate the quality of the food and the free radicals induced during the processing of the food. ESR spin trapping technique is useful for the detection of highly unstable radicals in the food. The antioxidant capability of liquid food and beverages in mainly performed by spin trapping technique.
Bob Reedy - Nitrate in Texas Groundwater.pdf
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The binding of cosmological structures by massless topological defects
Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field
equations sourced by a topological defect, i.e. a singularity of a very specific form, the result is a localized gravitational
field capable of driving flat rotation (i.e. Keplerian circular orbits at a constant speed for all radii) of test masses on a thin
spherical shell without any underlying mass. Moreover, a large-scale structure which exploits this solution by assembling
concentrically a number of such topological defects can establish a flat stellar or galactic rotation curve, and can also deflect
light in the same manner as an equipotential (isothermal) sphere. Thus, the need for dark matter or modified gravity theory is
mitigated, at least in part.
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Classification
Metal ion ion indicators
Masking and demasking reagents
Estimation of Magnisium sulphate
Calcium gluconate
Complexometric Titration/ chelatometry titration/chelating titration, introduction, Types-
1.Direct Titration
2.Back Titration
3.Replacement Titration
4.Indirect Titration
Masking agent, Demasking agents
formation of complex
comparition between masking and demasking agents,
Indicators/Metal ion indicators/ Metallochromic indicators/pM indicators,
Visual Technique,PM indicators (metallochromic), Indicators of pH, Redox Indicators
Instrumental Techniques-Photometry
Potentiometry
Miscellaneous methods.
Complex titration with EDTA.
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Travis Hills of Minnesota developed a method to convert waste into high-value dry fertilizer, significantly enriching soil quality. By providing farmers with a valuable resource derived from waste, Travis Hills helps enhance farm profitability while promoting environmental stewardship. Travis Hills' sustainable practices lead to cost savings and increased revenue for farmers by improving resource efficiency and reducing waste.
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...
Context. With a mass exceeding several 104 M⊙ and a rich and dense population of massive stars, supermassive young star clusters
represent the most massive star-forming environment that is dominated by the feedback from massive stars and gravitational interactions
among stars.
Aims. In this paper we present the Extended Westerlund 1 and 2 Open Clusters Survey (EWOCS) project, which aims to investigate
the influence of the starburst environment on the formation of stars and planets, and on the evolution of both low and high mass stars.
The primary targets of this project are Westerlund 1 and 2, the closest supermassive star clusters to the Sun.
Methods. The project is based primarily on recent observations conducted with the Chandra and JWST observatories. Specifically,
the Chandra survey of Westerlund 1 consists of 36 new ACIS-I observations, nearly co-pointed, for a total exposure time of 1 Msec.
Additionally, we included 8 archival Chandra/ACIS-S observations. This paper presents the resulting catalog of X-ray sources within
and around Westerlund 1. Sources were detected by combining various existing methods, and photon extraction and source validation
were carried out using the ACIS-Extract software.
Results. The EWOCS X-ray catalog comprises 5963 validated sources out of the 9420 initially provided to ACIS-Extract, reaching a
photon flux threshold of approximately 2 × 10−8 photons cm−2
s
−1
. The X-ray sources exhibit a highly concentrated spatial distribution,
with 1075 sources located within the central 1 arcmin. We have successfully detected X-ray emissions from 126 out of the 166 known
massive stars of the cluster, and we have collected over 71 000 photons from the magnetar CXO J164710.20-455217.
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Thematic analysis in qualitative research is a time-consuming and systematic task, typically done using teams. Team members must ground their activities on common understandings of the major concepts underlying the thematic analysis, and define criteria for its development. However, conceptual misunderstandings, equivocations, and lack of adherence to criteria are challenges to the quality and speed of this process. Given the distributed and uncertain nature of this process, we wondered if the tasks in thematic analysis could be supported by readily available artificial intelligence chatbots. Our early efforts point to potential benefits: not just saving time in the coding process but better adherence to criteria and grounding, by increasing triangulation between humans and artificial intelligence. This tutorial will provide a description and demonstration of the process we followed, as two academic researchers, to develop a custom ChatGPT to assist with qualitative coding in the thematic data analysis process of immersive learning accounts in a survey of the academic literature: QUAL-E Immersive Learning Thematic Analysis Helper. In the hands-on time, participants will try out QUAL-E and develop their ideas for their own qualitative coding ChatGPT. Participants that have the paid ChatGPT Plus subscription can create a draft of their assistants. The organizers will provide course materials and slide deck that participants will be able to utilize to continue development of their custom GPT. The paid subscription to ChatGPT Plus is not required to participate in this workshop, just for trying out personal GPTs during it.
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Current descriptions of immersive learning cases are often difficult or impossible to compare. This is due to a myriad of different options on what details to include, which aspects are relevant, and on the descriptive approaches employed. Also, these aspects often combine very specific details with more general guidelines or indicate intents and rationales without clarifying their implementation. In this paper we provide a method to describe immersive learning cases that is structured to enable comparisons, yet flexible enough to allow researchers and practitioners to decide which aspects to include. This method leverages a taxonomy that classifies educational aspects at three levels (uses, practices, and strategies) and then utilizes two frameworks, the Immersive Learning Brain and the Immersion Cube, to enable a structured description and interpretation of immersive learning cases. The method is then demonstrated on a published immersive learning case on training for wind turbine maintenance using virtual reality. Applying the method results in a structured artifact, the Immersive Learning Case Sheet, that tags the case with its proximal uses, practices, and strategies, and refines the free text case description to ensure that matching details are included. This contribution is thus a case description method in support of future comparative research of immersive learning cases. We then discuss how the resulting description and interpretation can be leveraged to change immersion learning cases, by enriching them (considering low-effort changes or additions) or innovating (exploring more challenging avenues of transformation). The method holds significant promise to support better-grounded research in immersive learning.
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3D Particle-In-Cell (PIC) algorithm,
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Applied Science: Thermodynamics, Laws & Methodology.pdf
When I was asked to give a companion lecture in support of ‘The Philosophy of Science’ (https://shorturl.at/4pUXz) I decided not to walk through the detail of the many methodologies in order of use. Instead, I chose to employ a long standing, and ongoing, scientific development as an exemplar. And so, I chose the ever evolving story of Thermodynamics as a scientific investigation at its best.
Conducted over a period of >200 years, Thermodynamics R&D, and application, benefitted from the highest levels of professionalism, collaboration, and technical thoroughness. New layers of application, methodology, and practice were made possible by the progressive advance of technology. In turn, this has seen measurement and modelling accuracy continually improved at a micro and macro level.
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The debris of the ‘last major merger’ is dynamically young
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The binding of cosmological structures by massless topological defects
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Sharlene Leurig - Enabling Onsite Water Use with Net Zero Water
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Compexometric titration/Chelatorphy titration/chelating titration
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Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...
Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...
Authoring a personal GPT for your research and practice: How we created the Q...
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Describing and Interpreting an Immersive Learning Case with the Immersion Cub...
Describing and Interpreting an Immersive Learning Case with the Immersion Cub...
3D Hybrid PIC simulation of the plasma expansion (ISSS-14)
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Applied Science: Thermodynamics, Laws & Methodology.pdf
Applied Science: Thermodynamics, Laws & Methodology.pdf
aziz sancar nobel prize winner: from mardin to nobel
aziz sancar nobel prize winner: from mardin to nobel
Mathematics
- 1. MATHEMATICS Mathematics is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Piano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day. Galileo (1564–1642) said, "The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth." Carl Friedrich Gauss (1777–1855) referred to mathematics as "the Queen of the Sciences". Benjamin Peirce (1809–1880) called mathematics "the science that draws necessary conclusions”. David Hilbert said of mathematics: "We are not
- 2. speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise." Albert Einstein (1879–1955) stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." French mathematician Claire Violin states "There is creative drive in mathematics; it's all about movement trying to express itself." Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries, which has led to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered.