By definition an ordinary prime number is a positive integer that cannot be expressed as a product
of two or more smaller factors. Its only divisors are 1 and itself
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.
The tetrahedron as a mathematical analytic machineErbol Digital
The document proposes using a tetrahedron as a mathematical model to study prime numbers and solve difficult problems in number theory. It describes the tetrahedron's geometric properties based on Euler's formula relating vertices, edges and faces. The model involves placing numbers on a virtual tetrahedron or designing one with spheres representing digits. This would allow creative study of properties like density and distribution of prime numbers, as well as problems like Riemann's hypothesis and integer factorization. The goal is to gain a unified understanding of mathematics through the tetrahedron model.
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.
1. This document discusses different perspectives on mathematics, including its history and nature. It explores whether math is discovered or invented, and how culture and different fields influence mathematical thought.
2. Key aspects of math discussed are its basis in axioms, deductive reasoning, and theorems. Different views are presented on whether mathematical truths are empirical, true by definition, or insights into reality.
3. The document prompts reflection on relationships between math and other domains like logic, religion, intuition, science, language, and beauty. It encourages examining how perception of math may differ depending on factors like one's background or profession.
This document discusses the prevalence and importance of mathematics in everyday life. It provides examples of how mathematics is used in areas like health, weather, transportation, society, and more. While some applications are directly observable, others involve more complex systems that are still being understood mathematically, like DNA. The document also discusses the historical foundations of mathematics over centuries, with concepts building upon each other like a pyramid, and provides a brief biography of the mathematician Aryabhata, who made important contributions in astronomy and mathematics.
The document discusses several famous mathematicians and their contributions. It mentions Srinivasa Ramanujan and his work in number theory. It also discusses C.R. Rao, founder of the Indian Statistical Institute, and Satyendranath Bose for his work in quantum mechanics and collaboration with Albert Einstein. The document then goes on to discuss topics in mathematics like the Golden Ratio, Fibonacci sequence, Euclidean geometry, chaos theory, and applications in architecture, topology, and numerology.
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.
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.
The tetrahedron as a mathematical analytic machineErbol Digital
The document proposes using a tetrahedron as a mathematical model to study prime numbers and solve difficult problems in number theory. It describes the tetrahedron's geometric properties based on Euler's formula relating vertices, edges and faces. The model involves placing numbers on a virtual tetrahedron or designing one with spheres representing digits. This would allow creative study of properties like density and distribution of prime numbers, as well as problems like Riemann's hypothesis and integer factorization. The goal is to gain a unified understanding of mathematics through the tetrahedron model.
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.
1. This document discusses different perspectives on mathematics, including its history and nature. It explores whether math is discovered or invented, and how culture and different fields influence mathematical thought.
2. Key aspects of math discussed are its basis in axioms, deductive reasoning, and theorems. Different views are presented on whether mathematical truths are empirical, true by definition, or insights into reality.
3. The document prompts reflection on relationships between math and other domains like logic, religion, intuition, science, language, and beauty. It encourages examining how perception of math may differ depending on factors like one's background or profession.
This document discusses the prevalence and importance of mathematics in everyday life. It provides examples of how mathematics is used in areas like health, weather, transportation, society, and more. While some applications are directly observable, others involve more complex systems that are still being understood mathematically, like DNA. The document also discusses the historical foundations of mathematics over centuries, with concepts building upon each other like a pyramid, and provides a brief biography of the mathematician Aryabhata, who made important contributions in astronomy and mathematics.
The document discusses several famous mathematicians and their contributions. It mentions Srinivasa Ramanujan and his work in number theory. It also discusses C.R. Rao, founder of the Indian Statistical Institute, and Satyendranath Bose for his work in quantum mechanics and collaboration with Albert Einstein. The document then goes on to discuss topics in mathematics like the Golden Ratio, Fibonacci sequence, Euclidean geometry, chaos theory, and applications in architecture, topology, and numerology.
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.
The document discusses the relationship between mathematics and the natural sciences. It notes that mathematics has been remarkably successful at describing natural phenomena, which is unexpected given that mathematics is a product of human thought while nature exists independently. The document raises questions about how the "laws of nature" can be exact copies of the patterns humans discover in their abstract systems of thought. It calls this alignment of the two fields the "unreasonable effectiveness of mathematics."
This document provides an overview of the history and development of mathematics. It discusses early contributions from ancient civilizations like Babylonians, Egyptians, Indians and Greeks. It then covers the major branches of mathematics like algebra, geometry, calculus and trigonometry. For each branch, it highlights some important mathematicians and their contributions throughout history that helped advance the field.
Mathematics is essential in daily life and has a long history of practical applications. It first arose from needs to count and measure, and early civilizations used math for tasks like construction and accounting. Over millennia, mathematical concepts and applications have expanded greatly. Today, areas like statistics, calculus, and other quantitative fields inform domains from politics to transportation to resource management. Many people misunderstand math as only involving formulas, but it really involves abstract problem-solving and modeling real-world situations. Core topics in daily use include commercial math, algebra, statistics, and financial calculations for tasks like budgeting and investing.
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.
Mathematics has been used since ancient times, first developing with counting. It is useful in many areas of modern life like business, cooking, and art. Mathematics is the science of shape, quantity, and arrangement, and was used by ancient Egyptians to build the pyramids using geometry and algebra. Percentages can be understood using currency denominations, and fractions can be seen by dividing fruits and vegetables. Geometry, arithmetic, and calculus are applied in fields like construction, markets, engineering, and physics. Mathematics underlies structures and is important for careers requiring university degrees.
Importance of mathematics in our daily lifeHarsh Rajput
The document discusses the history and origins of mathematics. It notes that mathematics originated from practical needs like measurement and counting, with early forms found on notched bones and cave walls. Over thousands of years, mathematics has developed from attempts to describe the natural world and arrive at logical truths. Today, mathematics is highly specialized but also applied in diverse fields from politics to traffic analysis. The document also provides examples of how concepts in commercial mathematics, algebra, statistics, geometry are useful in daily life.
Theory of Knowledge - mathematics philosophiesplangdale
This document discusses different philosophical views of mathematics:
- Formalism views mathematics as true or false based only on definitions, but this cannot explain unproven conjectures.
- Platonism sees mathematical truths existing independently and discovered through reason, but new geometries challenged this.
- Empiricism holds mathematics is generalized from experience, but math has greater certainty than science.
Godel's incompleteness theorems showed that for any axiom system, there are true statements not provable within the system, implying mathematics involves more than just applying rules to axioms. Whether mathematics is discovered or created is debated, with some arguing both discovery and creation are involved.
* There are 6 guests besides Alice who will sit in the chairs around the table
* The first chair can be filled by any of the 6 guests.
* Once the first chair is filled, the second chair can be filled by any of the remaining 5 guests.
* Continuing in this way, the number of ways to seat the guests is 6 * 5 * 4 * 3 * 2 * 1 = 720
Since they change seating every half hour and there are 720 possible seatings, it will take 720 / 2 = 360 hours or 15 days for every possible seating to occur.
This document is the preface to the textbook "Elementary Number Theory and its Applications" by Kenneth H. Rosen. The preface provides an overview of the book's content, intended audience, and how it can be used. It integrates traditional number theory topics with applications to computer science, cryptography, and algorithms. The preface describes each chapter's content and recommends which sections are core material and which are optional. It also discusses problem sets, computer projects, and unsolved problems covered in the book.
Rosen - Elementary number theory and its applications.pdfSahat Hutajulu
This textbook introduces elementary number theory and its applications. It covers topics such as divisibility, representations of integers, prime numbers, greatest common divisors, congruences, multiplicative functions, and applications to cryptography. The book is suitable for undergraduate number theory courses and provides traditional topics as well as applications relevant to computer science, such as cryptography. It aims to integrate important applications of elementary number theory with traditional topics.
A Study On The Development And Application Of Number Theory In Engineering FieldKim Daniels
This document discusses the development and applications of number theory in engineering. It begins with a brief history of number theory, from its origins in ancient Greece to the modern classifications of elementary, analytic, algebraic, geometric, and computational number theory. It then discusses some key applications of number theory in engineering, including cryptography, using Fibonacci sequences in architecture and engineering design, computer animation through linear transformations, and modeling processes through Fibonacci series. The document aims to explore how number theory has influenced technology and applications in fields like computing, cryptography, physics, and more.
Application of First Order Linear Equation Market Balanceijtsrd
If we consider economic variables as a continuous function of time, then we will encounter with relations which we have to use differential equations to solve them. If we consider the collection of relations of economic variables that are matched in accordance with the conditions, this collection of relations is called an economic model. models are two types, fixed models and variable models, and fixed models are related to equilibrium. In these models, the variables are independent of time, and when it comes to equilibrium, it does not change anymore, for example, if p is supposed the price of a commodity that the function of p is the amount of demand d and supply s in a fixed period, thenwe have that The above links are a fixed system of economic model.If the price of many goods is focused, this price is constantly in changing. Sometimes it can be considered a continuous function of time, and the balance of demand and supply is also a continuous function of time, in this case, moreover the demand is a function of its price, it is the function of price changes as well, because if the price is predicted to be added or reduced in the future, it will be effective in terms of supply and demand therefore, the demand and supply equation is as follow The above is a fixed model. The purpose of this study is to study the importance of the differential equation and its use in economics.As the result of this article I found that the relationship of differential equations with economics has been mostly closed and expanded, and solution of many issues in economics depends on formation and solving of differential equations. Abdul Tamimahadi "Application of First- Order Linear Equation Market Balance" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd25305.pdfPaper URL: https://www.ijtsrd.com/mathemetics/other/25305/application-of-first--order-linear-equation-market-balance/abdul-tamimahadi
John Stillwell-Numerele reale-An Introduction to Set Theory and Analysis ( PD...LobontGheorghe
This document provides context about the book "The Real Numbers: An Introduction to Set Theory and Analysis" by John Stillwell. It discusses how typical real analysis courses fail to properly define or address the foundations of the real number system. The book aims to fill this gap by constructing the real numbers rigorously while also making the material accessible through historical context, examples, and explanatory remarks. It argues that analysis is fundamentally based on studying sets, particularly uncountable sets like the real numbers and countable ordinals, and their relationship is central to the continuum problem.
An Introduction to the Analysis of Algorithms (2nd_Edition_Robert_Sedgewick,_...Saqib Raza
The preface honors the late co-author Philippe Flajolet and dedicates the second edition to his memory. It recounts Sedgewick's eulogy for Flajolet, praising his brilliance, creativity, generosity and the impact he had on many lives through his collaborations. The second edition aims to teach future generations and continue building upon Flajolet's mathematical legacy.
This document summarizes interactions between computational complexity theory and several fields of mathematics. It discusses the computational complexity of primality testing in number theory, point-line incidences in combinatorial geometry, the Kadison-Singer problem in operator theory, and generation problems in group theory. For each area, it provides background, describes important problems and results, and notes connections to algorithms and complexity theory.
Lecture 1 Slides -Introduction to algorithms.pdfRanvinuHewage
- The document discusses reasons for studying algorithms and their broad impacts.
- Key reasons include solving hard problems, intellectual stimulation, becoming a proficient programmer, unlocking secrets of life and the universe, and fun.
- Algorithms have roots in ancient times but new opportunities in the modern era with computers and large data. They allow addressing problems that could not otherwise be solved.
This document is a student manual that introduces arithmetic and algebra. It covers basic topics like the fundamental arithmetic operations, number sets such as natural numbers, integers, rational numbers, and real numbers. It also discusses operations and properties for these number sets like the addition, subtraction, multiplication and division of integers. The manual is intended to provide students with the necessary tools and practice problems to develop skills in solving mathematical problems and reasoning logically. It aims to lay the foundation for more advanced mathematics courses.
Data is the new oil! Modern analytical methods are a decisive success factor for service-oriented business models in IoT and Industry 4.0. A new white paper explains the state of the art and shows what latest methods can achieve in practice
The Design and Analysis of Computer Algorithms [Aho, Hopcroft & Ullman 1974-0...YanNaingSoe33
This document provides an introduction and overview of the book "The Design and Analysis of Computer Algorithms" by Aho, Hopcroft, and Ullman. It discusses the scope and intended use of the book. The book begins by introducing several models of computation and a programming language to analyze algorithms. It then covers fundamental algorithm design techniques and applies them to problems in sorting, searching, graph algorithms, and computational complexity. The goal is to teach the unifying principles of algorithm design and analysis.
A Modern Introduction To Probability And Statistics Understanding Why And How...Todd Turner
This document is the preface to the book "A Modern Introduction to Probability and Statistics" by F.M. Dekking, C. Kraaikamp, H.P. Lopuhaä, and L.E. Meester. It introduces the topics covered in the book, which include the basics of probability theory and statistics. The book is aimed at undergraduate engineering students and contains examples from real-life situations. It is designed to be used for a one-semester course.
This document provides an overview of formal methods for software engineering. It begins with an introduction to formal methods, including the use of mathematically rigorous techniques to specify, design, and verify software systems. Notations for formal methods include first-order logic and set theory. Tools can be used for specification and verification. Verification tools may prove properties like the absence of race conditions. Formal methods can provide high confidence that software meets critical requirements by proving properties will "always" or "never" hold. The document discusses the history of logic and mathematical reasoning leading to formal methods. It also outlines limitations of formal methods established by Gödel's incompleteness theorems and the halting problem.
The document discusses the relationship between mathematics and the natural sciences. It notes that mathematics has been remarkably successful at describing natural phenomena, which is unexpected given that mathematics is a product of human thought while nature exists independently. The document raises questions about how the "laws of nature" can be exact copies of the patterns humans discover in their abstract systems of thought. It calls this alignment of the two fields the "unreasonable effectiveness of mathematics."
This document provides an overview of the history and development of mathematics. It discusses early contributions from ancient civilizations like Babylonians, Egyptians, Indians and Greeks. It then covers the major branches of mathematics like algebra, geometry, calculus and trigonometry. For each branch, it highlights some important mathematicians and their contributions throughout history that helped advance the field.
Mathematics is essential in daily life and has a long history of practical applications. It first arose from needs to count and measure, and early civilizations used math for tasks like construction and accounting. Over millennia, mathematical concepts and applications have expanded greatly. Today, areas like statistics, calculus, and other quantitative fields inform domains from politics to transportation to resource management. Many people misunderstand math as only involving formulas, but it really involves abstract problem-solving and modeling real-world situations. Core topics in daily use include commercial math, algebra, statistics, and financial calculations for tasks like budgeting and investing.
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.
Mathematics has been used since ancient times, first developing with counting. It is useful in many areas of modern life like business, cooking, and art. Mathematics is the science of shape, quantity, and arrangement, and was used by ancient Egyptians to build the pyramids using geometry and algebra. Percentages can be understood using currency denominations, and fractions can be seen by dividing fruits and vegetables. Geometry, arithmetic, and calculus are applied in fields like construction, markets, engineering, and physics. Mathematics underlies structures and is important for careers requiring university degrees.
Importance of mathematics in our daily lifeHarsh Rajput
The document discusses the history and origins of mathematics. It notes that mathematics originated from practical needs like measurement and counting, with early forms found on notched bones and cave walls. Over thousands of years, mathematics has developed from attempts to describe the natural world and arrive at logical truths. Today, mathematics is highly specialized but also applied in diverse fields from politics to traffic analysis. The document also provides examples of how concepts in commercial mathematics, algebra, statistics, geometry are useful in daily life.
Theory of Knowledge - mathematics philosophiesplangdale
This document discusses different philosophical views of mathematics:
- Formalism views mathematics as true or false based only on definitions, but this cannot explain unproven conjectures.
- Platonism sees mathematical truths existing independently and discovered through reason, but new geometries challenged this.
- Empiricism holds mathematics is generalized from experience, but math has greater certainty than science.
Godel's incompleteness theorems showed that for any axiom system, there are true statements not provable within the system, implying mathematics involves more than just applying rules to axioms. Whether mathematics is discovered or created is debated, with some arguing both discovery and creation are involved.
* There are 6 guests besides Alice who will sit in the chairs around the table
* The first chair can be filled by any of the 6 guests.
* Once the first chair is filled, the second chair can be filled by any of the remaining 5 guests.
* Continuing in this way, the number of ways to seat the guests is 6 * 5 * 4 * 3 * 2 * 1 = 720
Since they change seating every half hour and there are 720 possible seatings, it will take 720 / 2 = 360 hours or 15 days for every possible seating to occur.
This document is the preface to the textbook "Elementary Number Theory and its Applications" by Kenneth H. Rosen. The preface provides an overview of the book's content, intended audience, and how it can be used. It integrates traditional number theory topics with applications to computer science, cryptography, and algorithms. The preface describes each chapter's content and recommends which sections are core material and which are optional. It also discusses problem sets, computer projects, and unsolved problems covered in the book.
Rosen - Elementary number theory and its applications.pdfSahat Hutajulu
This textbook introduces elementary number theory and its applications. It covers topics such as divisibility, representations of integers, prime numbers, greatest common divisors, congruences, multiplicative functions, and applications to cryptography. The book is suitable for undergraduate number theory courses and provides traditional topics as well as applications relevant to computer science, such as cryptography. It aims to integrate important applications of elementary number theory with traditional topics.
A Study On The Development And Application Of Number Theory In Engineering FieldKim Daniels
This document discusses the development and applications of number theory in engineering. It begins with a brief history of number theory, from its origins in ancient Greece to the modern classifications of elementary, analytic, algebraic, geometric, and computational number theory. It then discusses some key applications of number theory in engineering, including cryptography, using Fibonacci sequences in architecture and engineering design, computer animation through linear transformations, and modeling processes through Fibonacci series. The document aims to explore how number theory has influenced technology and applications in fields like computing, cryptography, physics, and more.
Application of First Order Linear Equation Market Balanceijtsrd
If we consider economic variables as a continuous function of time, then we will encounter with relations which we have to use differential equations to solve them. If we consider the collection of relations of economic variables that are matched in accordance with the conditions, this collection of relations is called an economic model. models are two types, fixed models and variable models, and fixed models are related to equilibrium. In these models, the variables are independent of time, and when it comes to equilibrium, it does not change anymore, for example, if p is supposed the price of a commodity that the function of p is the amount of demand d and supply s in a fixed period, thenwe have that The above links are a fixed system of economic model.If the price of many goods is focused, this price is constantly in changing. Sometimes it can be considered a continuous function of time, and the balance of demand and supply is also a continuous function of time, in this case, moreover the demand is a function of its price, it is the function of price changes as well, because if the price is predicted to be added or reduced in the future, it will be effective in terms of supply and demand therefore, the demand and supply equation is as follow The above is a fixed model. The purpose of this study is to study the importance of the differential equation and its use in economics.As the result of this article I found that the relationship of differential equations with economics has been mostly closed and expanded, and solution of many issues in economics depends on formation and solving of differential equations. Abdul Tamimahadi "Application of First- Order Linear Equation Market Balance" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd25305.pdfPaper URL: https://www.ijtsrd.com/mathemetics/other/25305/application-of-first--order-linear-equation-market-balance/abdul-tamimahadi
John Stillwell-Numerele reale-An Introduction to Set Theory and Analysis ( PD...LobontGheorghe
This document provides context about the book "The Real Numbers: An Introduction to Set Theory and Analysis" by John Stillwell. It discusses how typical real analysis courses fail to properly define or address the foundations of the real number system. The book aims to fill this gap by constructing the real numbers rigorously while also making the material accessible through historical context, examples, and explanatory remarks. It argues that analysis is fundamentally based on studying sets, particularly uncountable sets like the real numbers and countable ordinals, and their relationship is central to the continuum problem.
An Introduction to the Analysis of Algorithms (2nd_Edition_Robert_Sedgewick,_...Saqib Raza
The preface honors the late co-author Philippe Flajolet and dedicates the second edition to his memory. It recounts Sedgewick's eulogy for Flajolet, praising his brilliance, creativity, generosity and the impact he had on many lives through his collaborations. The second edition aims to teach future generations and continue building upon Flajolet's mathematical legacy.
This document summarizes interactions between computational complexity theory and several fields of mathematics. It discusses the computational complexity of primality testing in number theory, point-line incidences in combinatorial geometry, the Kadison-Singer problem in operator theory, and generation problems in group theory. For each area, it provides background, describes important problems and results, and notes connections to algorithms and complexity theory.
Lecture 1 Slides -Introduction to algorithms.pdfRanvinuHewage
- The document discusses reasons for studying algorithms and their broad impacts.
- Key reasons include solving hard problems, intellectual stimulation, becoming a proficient programmer, unlocking secrets of life and the universe, and fun.
- Algorithms have roots in ancient times but new opportunities in the modern era with computers and large data. They allow addressing problems that could not otherwise be solved.
This document is a student manual that introduces arithmetic and algebra. It covers basic topics like the fundamental arithmetic operations, number sets such as natural numbers, integers, rational numbers, and real numbers. It also discusses operations and properties for these number sets like the addition, subtraction, multiplication and division of integers. The manual is intended to provide students with the necessary tools and practice problems to develop skills in solving mathematical problems and reasoning logically. It aims to lay the foundation for more advanced mathematics courses.
Data is the new oil! Modern analytical methods are a decisive success factor for service-oriented business models in IoT and Industry 4.0. A new white paper explains the state of the art and shows what latest methods can achieve in practice
The Design and Analysis of Computer Algorithms [Aho, Hopcroft & Ullman 1974-0...YanNaingSoe33
This document provides an introduction and overview of the book "The Design and Analysis of Computer Algorithms" by Aho, Hopcroft, and Ullman. It discusses the scope and intended use of the book. The book begins by introducing several models of computation and a programming language to analyze algorithms. It then covers fundamental algorithm design techniques and applies them to problems in sorting, searching, graph algorithms, and computational complexity. The goal is to teach the unifying principles of algorithm design and analysis.
A Modern Introduction To Probability And Statistics Understanding Why And How...Todd Turner
This document is the preface to the book "A Modern Introduction to Probability and Statistics" by F.M. Dekking, C. Kraaikamp, H.P. Lopuhaä, and L.E. Meester. It introduces the topics covered in the book, which include the basics of probability theory and statistics. The book is aimed at undergraduate engineering students and contains examples from real-life situations. It is designed to be used for a one-semester course.
This document provides an overview of formal methods for software engineering. It begins with an introduction to formal methods, including the use of mathematically rigorous techniques to specify, design, and verify software systems. Notations for formal methods include first-order logic and set theory. Tools can be used for specification and verification. Verification tools may prove properties like the absence of race conditions. Formal methods can provide high confidence that software meets critical requirements by proving properties will "always" or "never" hold. The document discusses the history of logic and mathematical reasoning leading to formal methods. It also outlines limitations of formal methods established by Gödel's incompleteness theorems and the halting problem.
This document contains a syllabus for the subject "Design and Analysis of Algorithms". It discusses the following key points:
- The objectives of the course are to learn algorithm analysis techniques, become familiar with different algorithm design techniques, and understand the limitations of algorithm power.
- The syllabus is divided into 5 units which cover topics like introduction to algorithms, brute force and divide-and-conquer techniques, dynamic programming and greedy algorithms, iterative improvement methods, and coping with limitations of algorithmic power.
- Examples of algorithms discussed include merge sort, quicksort, binary search, matrix multiplication, knapsack problem, shortest paths, minimum spanning trees, and NP-complete problems.
- References
This document provides an overview of automated theorem proving. It discusses:
1) The history and background of automated theorem proving, from Hobbes and Leibniz proposing algorithmic logic to modern computer-based approaches.
2) The theoretical limitations of automated reasoning due to results like Godel's incompleteness theorems, but also practical applications like verifying mathematics and computer systems.
3) How automated reasoning involves expressing statements formally and then manipulating those expressions algorithmically, as anticipated by Leibniz centuries ago.
Calculus is used extensively in software engineering and related fields for several purposes:
1) In computer graphics, calculus is used to simulate light bouncing and rendering objects smoothly as well as powering physics engines.
2) In programming language design and semantics, calculus provides a functional predicate calculus to support formal reasoning about programs.
3) Calculus allows the creation of mathematical models to arrive at optimal solutions and is used in many areas of physics that relate to software such as motion, heat, and dynamics.
4) Fields like signal analysis, scientific computing, financial modeling, and robotics also employ calculus for tasks like examining functions, simulating systems, and modeling optimization.
Unit I of the syllabus covers propositional logic and counting theory. It introduces concepts such as propositions, logical connectives like conjunction, disjunction, negation, implication and biconditional. It discusses how to represent compound statements using these connectives and their truth tables. The unit also covers topics like predicate logic, methods of proof, mathematical induction and fundamental counting principles like permutations and combinations. It aims to provide the logical foundations for discrete mathematics concepts that will be useful in computer science and information technology.
The importance of_numbers_and_the_need_to_study_prmohamed abdalla
This document discusses the importance and history of studying prime numbers. It begins with definitions of prime and composite numbers. It then discusses the historical interest in numbers across ancient cultures and the development of place-value systems. The document outlines Euclid's proof that there are an infinite number of primes. It also discusses some open questions in prime number theory, like Riemann's hypothesis. The goal is to spark more interest in number theory among young mathematicians by highlighting its rich history and some of the enduring puzzles that remain.
This document provides a summary of Valeria de Paiva's background and research interests related to proofs, logic, and programming languages. It discusses her education in mathematics in Brazil and the UK. It then outlines some of her research exploring connections between category theory, proof theory, type theory, and programming through the Curry-Howard correspondence. This includes work on dialectica categories as a model of intuitionistic linear logic. The document promotes an interdisciplinary approach and highlights opportunities at the intersection of logic, computing, linguistics and categories.
Pronunciamiento de Mujeres en defensa de la Ley 348Erbol Digital
El diputado “arcista” Rolando Cuéllar ha presentado una denuncia formal ante la Fiscalía contra Evo Morales, por el delito de legitimación de ganancias ilícitas, para que explique el financiamiento de sus vuelos privados que realiza incluso a nivel internacional.
Denuncia del diputado Arce contra el hijo del presidente de BoliviaErbol Digital
El diputado del ala “evista”, Héctor Arce Rodríguez, denunció este martes que Luis Marcelo Arce Mosqueira, hijo del presidente Luis Arce, ha entablado contactos con empresas internacionales para incurrir en un “negociado”, “lobby” y esquema de corrupción relacionado a la explotación del litio boliviano.
Carta de Elvira Parra, detenida siete años por caso FondiocErbol Digital
Tras siete años de encarcelamiento y un repentino traslado a la cárcel de Palmasola, la exdirectora del Fondo Indígena, Elvira Parra, expresó su desesperación por la situación que atraviesa en tribunales, con múltiples procesos en varios departamentos y que la mantiene alejada de su familia.
En una sentencia de 75 páginas, el Tribunal de Sentencia Anticorrupción Primero de La Paz expuso los argumentos por los cuales condenó a la cárcel a la expresidenta Jeanine Añez y a exjefes militares y de la Policía en el caso denominado “Golpe de Estado II”.
Decreto contra las cláusulas abusivas en venta de inmueblesErbol Digital
El Gobierno emitió el Decreto Supremo 4732, mediante el cual se establece un mecanismo para evitar prácticas y cláusulas abusivas en los contratos de venta futura, venta con reserva de propiedad u otras modalidades, de bienes inmuebles.
DOCUMENTO DE ANÁLISIS DE LA CONFLICTIVIDAD SOCIAL EN BOLIVIA N°1Erbol Digital
Un análisis de la conflictividad de Bolivia, realizado por la Fundación UNIR, identificó que entre noviembre de 2021 y marzo de 2022, los conflictos por temas económicos fueron los más significativos que se reportaron en el país.
Renuncia la vocal del TSE, María Angélica RuizErbol Digital
María Angélica Ruiz renunció al cargo de vocal del Tribunal Supremo Electoral (TSE), entidad en la que estuvo desde finales de 2019 y administró las elecciones de 2020 y 2021.
Trayectoria de los 16 postulantes finalistas para Defensor 2022Erbol Digital
La Iniciativa Ciudadana de Monitoreo a la Justicia sistematizó los perfiles de los 16 candidatos a Defensor del Pueblo que siguen en carrera, después de la revisión de méritos por parte de la Comisión Mixta de Constitución.
Convocatoria a taller en tráfico de fauna silvestre y madera para comunicadoresErbol Digital
La problemática del tráfico de fauna silvestre y madera necesita ser
abordada con información clara, pertinente y adecuada.
Postúlate al taller virtual dirigido a comunicadores y comunicadoras de los municipios de Pando, Beni, Santa Cruz y norte de La Paz, que organiza @Erbol y la #AlianzaFaunaYBosques, una acción
regional de WCS y WWF, financiada por la Unión Europea.
Informe de la Iglesia sobre los hechos de 2019Erbol Digital
La Iglesia Católica emitió este martes una Memoria de su labor de pacificación en los hechos de 2019, en la cual reveló que en los diálogos de noviembre Adriana Salvatierra se había negado a asumir la Presidencia del Estado ante el vacío de poder que se había generado por las dimisiones de Evo Morales y Álvaro García Linera.
Carta al Ministro de Justicia de organizaciones de la sociedad civilErbol Digital
Mediante una carta pública, varias organizaciones, medios de comunicación, redes y activistas exhortaron al ministro de Justicia, Iván Lima, a que se integre a la sociedad civil en el proceso de elaboración y análisis del anteproyecto de Ley de Acceso a la Información Pública.
Precios en clínicas privadas por COVID en BoliviaErbol Digital
El Gobierno, mediante el Ministerio de Salud, emitió una resolución mediante la cual se establecen los precios que deben cobrar los centros de salud del sector privado para laboratorios y servicios contra la COVID-19.
Lista de precios de medicamentos en Bolivia.Erbol Digital
La pandemia de COVID-19 ha tenido un impacto significativo en la economía mundial. Muchos países experimentaron fuertes caídas en el PIB y aumentos en el desempleo en 2020. A medida que se implementan las vacunas, se espera que la actividad económica se recupere en 2021 a medida que disminuya la propagación del virus.
Pronunciamiento de organizaciones en respaldo a Fundación TierraErbol Digital
Sesenta organizaciones de la sociedad civil emitieron en pronunciamiento, mediante el cual respaldan a la Fundación Tierra, después de que su Director, Gonzalo Colque, fue demandando por difamación y calumnias por parte del exministro de Economía, Branko Marinkovic.
El Conteo Rápido de la alianza Tu Voto Cuenta asigna al candidato del Movimiento al Socialismo, Luis Arce, un 53,0% de los votos lo que le daría una victoria en primera vuelta frente al candidato de Comunidad Ciudadana, Carlos Mesa, que alcanza un 30,8%.
Datos por departamento (Tu Voto Cuenta-octubre)Erbol Digital
La encuesta Tu Voto Cuenta de octubre señala que el MAS lleva la delantera en cuatro departamentos, al igual que Comunidad Ciudadana, mientras que Creemos gana sólo en Santa Cruz.
Ficha técnica encuesta Tu Voto Cuenta (octubre 2020)Erbol Digital
Este documento presenta los resultados de la segunda encuesta de intención de voto realizada en Bolivia por una alianza de 27 instituciones. La encuesta entrevistó a 1,500 personas entre el 2 y 5 de octubre en 234 municipios de los 9 departamentos del país. El sondeo tuvo un tamaño de muestra de 15,537 encuestas y cubrió 487 asientos electorales y 1,058 recintos electorales. El documento describe el método de muestreo utilizado y proporciona detalles sobre la distribución de la muestra por departamento
Dictamen de la Procuraduría en caso respiradoresErbol Digital
La Procuraduría General del Estado (PGE) emitió su dictamen 001/2020 donde halla participación criminal de trece personas en el proceso de compra bajo la modalidad de contratación directa de 170 ventiladores pulmonares de origen español.
UiPath Test Automation using UiPath Test Suite series, part 6DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 6. In this session, we will cover Test Automation with generative AI and Open AI.
UiPath Test Automation with generative AI and Open AI webinar offers an in-depth exploration of leveraging cutting-edge technologies for test automation within the UiPath platform. Attendees will delve into the integration of generative AI, a test automation solution, with Open AI advanced natural language processing capabilities.
Throughout the session, participants will discover how this synergy empowers testers to automate repetitive tasks, enhance testing accuracy, and expedite the software testing life cycle. Topics covered include the seamless integration process, practical use cases, and the benefits of harnessing AI-driven automation for UiPath testing initiatives. By attending this webinar, testers, and automation professionals can gain valuable insights into harnessing the power of AI to optimize their test automation workflows within the UiPath ecosystem, ultimately driving efficiency and quality in software development processes.
What will you get from this session?
1. Insights into integrating generative AI.
2. Understanding how this integration enhances test automation within the UiPath platform
3. Practical demonstrations
4. Exploration of real-world use cases illustrating the benefits of AI-driven test automation for UiPath
Topics covered:
What is generative AI
Test Automation with generative AI and Open AI.
UiPath integration with generative AI
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Communications Mining Series - Zero to Hero - Session 1DianaGray10
This session provides introduction to UiPath Communication Mining, importance and platform overview. You will acquire a good understand of the phases in Communication Mining as we go over the platform with you. Topics covered:
• Communication Mining Overview
• Why is it important?
• How can it help today’s business and the benefits
• Phases in Communication Mining
• Demo on Platform overview
• Q/A
Full-RAG: A modern architecture for hyper-personalizationZilliz
Mike Del Balso, CEO & Co-Founder at Tecton, presents "Full RAG," a novel approach to AI recommendation systems, aiming to push beyond the limitations of traditional models through a deep integration of contextual insights and real-time data, leveraging the Retrieval-Augmented Generation architecture. This talk will outline Full RAG's potential to significantly enhance personalization, address engineering challenges such as data management and model training, and introduce data enrichment with reranking as a key solution. Attendees will gain crucial insights into the importance of hyperpersonalization in AI, the capabilities of Full RAG for advanced personalization, and strategies for managing complex data integrations for deploying cutting-edge AI solutions.
Best 20 SEO Techniques To Improve Website Visibility In SERPPixlogix Infotech
Boost your website's visibility with proven SEO techniques! Our latest blog dives into essential strategies to enhance your online presence, increase traffic, and rank higher on search engines. From keyword optimization to quality content creation, learn how to make your site stand out in the crowded digital landscape. Discover actionable tips and expert insights to elevate your SEO game.
Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...SOFTTECHHUB
The choice of an operating system plays a pivotal role in shaping our computing experience. For decades, Microsoft's Windows has dominated the market, offering a familiar and widely adopted platform for personal and professional use. However, as technological advancements continue to push the boundaries of innovation, alternative operating systems have emerged, challenging the status quo and offering users a fresh perspective on computing.
One such alternative that has garnered significant attention and acclaim is Nitrux Linux 3.5.0, a sleek, powerful, and user-friendly Linux distribution that promises to redefine the way we interact with our devices. With its focus on performance, security, and customization, Nitrux Linux presents a compelling case for those seeking to break free from the constraints of proprietary software and embrace the freedom and flexibility of open-source computing.
For the full video of this presentation, please visit: https://www.edge-ai-vision.com/2024/06/building-and-scaling-ai-applications-with-the-nx-ai-manager-a-presentation-from-network-optix/
Robin van Emden, Senior Director of Data Science at Network Optix, presents the “Building and Scaling AI Applications with the Nx AI Manager,” tutorial at the May 2024 Embedded Vision Summit.
In this presentation, van Emden covers the basics of scaling edge AI solutions using the Nx tool kit. He emphasizes the process of developing AI models and deploying them globally. He also showcases the conversion of AI models and the creation of effective edge AI pipelines, with a focus on pre-processing, model conversion, selecting the appropriate inference engine for the target hardware and post-processing.
van Emden shows how Nx can simplify the developer’s life and facilitate a rapid transition from concept to production-ready applications.He provides valuable insights into developing scalable and efficient edge AI solutions, with a strong focus on practical implementation.
Cosa hanno in comune un mattoncino Lego e la backdoor XZ?Speck&Tech
ABSTRACT: A prima vista, un mattoncino Lego e la backdoor XZ potrebbero avere in comune il fatto di essere entrambi blocchi di costruzione, o dipendenze di progetti creativi e software. La realtà è che un mattoncino Lego e il caso della backdoor XZ hanno molto di più di tutto ciò in comune.
Partecipate alla presentazione per immergervi in una storia di interoperabilità, standard e formati aperti, per poi discutere del ruolo importante che i contributori hanno in una comunità open source sostenibile.
BIO: Sostenitrice del software libero e dei formati standard e aperti. È stata un membro attivo dei progetti Fedora e openSUSE e ha co-fondato l'Associazione LibreItalia dove è stata coinvolta in diversi eventi, migrazioni e formazione relativi a LibreOffice. In precedenza ha lavorato a migrazioni e corsi di formazione su LibreOffice per diverse amministrazioni pubbliche e privati. Da gennaio 2020 lavora in SUSE come Software Release Engineer per Uyuni e SUSE Manager e quando non segue la sua passione per i computer e per Geeko coltiva la sua curiosità per l'astronomia (da cui deriva il suo nickname deneb_alpha).
GraphRAG for Life Science to increase LLM accuracyTomaz Bratanic
GraphRAG for life science domain, where you retriever information from biomedical knowledge graphs using LLMs to increase the accuracy and performance of generated answers
Unlocking Productivity: Leveraging the Potential of Copilot in Microsoft 365, a presentation by Christoforos Vlachos, Senior Solutions Manager – Modern Workplace, Uni Systems
Pushing the limits of ePRTC: 100ns holdover for 100 daysAdtran
At WSTS 2024, Alon Stern explored the topic of parametric holdover and explained how recent research findings can be implemented in real-world PNT networks to achieve 100 nanoseconds of accuracy for up to 100 days.
Infrastructure Challenges in Scaling RAG with Custom AI modelsZilliz
Building Retrieval-Augmented Generation (RAG) systems with open-source and custom AI models is a complex task. This talk explores the challenges in productionizing RAG systems, including retrieval performance, response synthesis, and evaluation. We’ll discuss how to leverage open-source models like text embeddings, language models, and custom fine-tuned models to enhance RAG performance. Additionally, we’ll cover how BentoML can help orchestrate and scale these AI components efficiently, ensuring seamless deployment and management of RAG systems in the cloud.
GraphSummit Singapore | The Future of Agility: Supercharging Digital Transfor...Neo4j
Leonard Jayamohan, Partner & Generative AI Lead, Deloitte
This keynote will reveal how Deloitte leverages Neo4j’s graph power for groundbreaking digital twin solutions, achieving a staggering 100x performance boost. Discover the essential role knowledge graphs play in successful generative AI implementations. Plus, get an exclusive look at an innovative Neo4j + Generative AI solution Deloitte is developing in-house.
TrustArc Webinar - 2024 Global Privacy SurveyTrustArc
How does your privacy program stack up against your peers? What challenges are privacy teams tackling and prioritizing in 2024?
In the fifth annual Global Privacy Benchmarks Survey, we asked over 1,800 global privacy professionals and business executives to share their perspectives on the current state of privacy inside and outside of their organizations. This year’s report focused on emerging areas of importance for privacy and compliance professionals, including considerations and implications of Artificial Intelligence (AI) technologies, building brand trust, and different approaches for achieving higher privacy competence scores.
See how organizational priorities and strategic approaches to data security and privacy are evolving around the globe.
This webinar will review:
- The top 10 privacy insights from the fifth annual Global Privacy Benchmarks Survey
- The top challenges for privacy leaders, practitioners, and organizations in 2024
- Key themes to consider in developing and maintaining your privacy program
AI 101: An Introduction to the Basics and Impact of Artificial IntelligenceIndexBug
Imagine a world where machines not only perform tasks but also learn, adapt, and make decisions. This is the promise of Artificial Intelligence (AI), a technology that's not just enhancing our lives but revolutionizing entire industries.
AI 101: An Introduction to the Basics and Impact of Artificial Intelligence
The Aguilar-Acha prime numbers
1. Research and Development in Mathematics
THE AGUILAR-ACHA
PRIME NUMBERS
By: Ramón Aguilar Achá (*)
INTRODUCTION
By definition an ordinary prime number is a positive integer that cannot be expressed as a product
of two or more smaller factors. Its only divisors are 1 and itself The set or succession of primes is
infinite and apparently does not follow any role, order or simple law. So the enigma and problem is
such that the model, density, structure and distribution of the absolute prime numbers continue to
be extremely complicated, as well as the factorisation problem and the so called Riemann's
hypothesis. Those are the great problems and challenges in number theory; still open to the study
and research throughout the world.
BACKGROUND
Historically, a legion of professional and amateur mathematicians had put their best efforts to
unveil intuitive1y or formally any method to solve these and other problems, within the framework
of the decimal or ordinary system of numeration. Thousands of conjectures, hypotheses and
theorems have been formulated, beginning with the most simple and incredible, up to the most
complicated and even curious. Many have been proved, but the great majority not yet. They are in
that respect known as the Fermaf s primes, the Mersenne' s primes, the Sophie Germain' s
primes, the Factorial primes, the Twin primes, etc. We have also asked ourselves, How do you
find the giant primes?, what is the formula?, Is there any efficient algorithm? How many primes are
there up to any ? How do you identify methodically, systematically and mathematically the
primes of pseudo-primes? Which are the roles and operators for those and other goals? How can
you partition them for an efficient grid processing?
THE AGUILAR-ACHA'S PRIME NUMBERS
Our creative and unpublished research about the primes is based on the study and investigation
of the inner properties and relations of the numbers themselves. So, that applying the deductive
inductive method and the systematic and abstract reasoning of the mathematical logic, we could
discover and prove a set of theorems, departing from 2,3,5, 7, ...n... , which let us close a
finished, logic and structured theory about the prime numbers. Following that innovative idea we
have to generate what we call the Aguilar - Acha' s prime numbers. A special class of absolute
primes endowed with some characteristic and unique properties, which allow us to formalize the
generation of all the primes in a strict and logical manner.
So, avoiding to give technical details, such as formulas and algorithms in this scientific article
whose purpose is most of all to divulge the discovery following a remarkable and fully proved
2. pattern we define as Aguilar Acha's primes, (¿Aguilar Acha's pseudoprimes?) for example the five
following absolute prime numbers:
a) 83206188165605210378137
b) 1265387069261248073095693911931899040830517
c) 44619154012697354916874972804312121957361090119
d) 450094620862682215953169056804394023557088230914503061621591
e) 51887711213803354677207493948038953621564859177886491154411636348879189189752059388157
f) 55258396954645311201303802735233011443775848174791602706756357221469136208017678018537
24599722008379503935030673596961
g) 12631855271974763766014762391931165315340616789985950504573100701508179434833834506490
56736088894387159830628853856984823048678494977827531984433414007724685048764627198804
23217636990756716352258790755189082669228490128194881646186775811709865934885290861311
71
h) 18481401679431183493463074635310948111614108150080607991616342671121104921110793364064
28050406940594411474056093076827834106111321336711273506107136804391582051212606406278
37240610441661388127708162826241360887081150412068372181380618608108643613804081093388
07949305061206767856405069394803487808194083735107208121063627806108097911940836730782
93828028543083722107806138137793606177339442077937808769180610837081208111076143112138
7878372388350648781206194794308351169509151087019238811231678116899187
i) 1246478061171112107435108374350822201394671270621298050945337351107788162858479
1673616921337511940867461868880692515883710412827517358806546528124534728255840
7887189255376270716584844717445413535544881810736282553634807181872081019191920
9918080808188188188107210108929191082897989080808911191833718355128891825537313
6928082712827370691717189389119191163610617080858192883691691717293552826537189
7452820191827907071718102919191082807171881717291919181090977207119287571717171
7272871729281270451162645137161346152626404535873883712726471626263658728173863
6273555562626116363715372893065545543593642926494717346307846412718103926448816
5046264471827098305584071825628188340717356281883554528261428173552819725638918
3018216347192874455372554585068626404371908912821634444292195872826461626543793
9882890909065453672537105148684628891405462776441770444413890919841126586453830
6121437125128115372105121049406559317875871851099385238686869587813859658365818
5484549510437136614447195652515856873628252173678377
CONCLUSION
It is an extraordinary and outstanding discovery of . With it, it has been unveiled an
important set of mathematical relations that rule the Law of the Primes, based on our formulated
and proved theorems, which have been rigorously proved by other national and international
mathematicians.
APPLICATIONS
It has been said that they are surprising discoveries, which perhaps have been neglected by other
mathematicians, because they are no other thing that numerical and recurrent patterns of new
3. order and style, from which we extract a kind of recipes or new operational algorithms in
acceptable and competitive timing; which can be programmed more efficiently via
supercomputers. With that in mind - since the required numbers are quite long - you end up
requiring the most potent tools and batteries of processing power, to generate the prime numbers
as big as-desired, including those that are truly world records of different types for a variety of
industrial, technical and technological uses, as well as for theoretical and applied scientific ends.
FUTURE VISION
It is necessary to fully generalize this theory discovering and proving some other theorems
unifying in the process the theory of numbers with the algebraic theory of numbers, the analyt:ic
theory of numbers and the algebraic geometry, which will be undoubtedly a landmark in the
advancement of its ruling law, and máybe the solution of important problems as the so called
strong and weak Goldbach' s Conjectures, or the Riemann' s Hypothesis, the most important of
the contemporary mathematical problems.
Additional information:
Telf: (591-2) 2-485559
Email: raguilar18@gmail.com
(All worldwide rights reserved La Paz, Apri16, 2004).
Note: It is permitted the use of this material, mentioning to the discoverer-author, especially with
educational and scientific ends.
First 990 prime numbers ( 36 Kb ) ( 10 Kb )
4. Index Reseña Historica Marco Legal PLANCITI Indicadores
Agenda Becas-Convocatorias Noticias CyT Sitios de interés Enlaces