What was Galois’ contribution to the theory of algebraic equations a.pdf
•
0 likes•3 views
What was Galois’ contribution to the theory of algebraic equations and what were some of the reasons why it was so remarkable? Solution Tangent equation passing through (1,1) is Galois achieved proof by looking at whether or not the “permutation group” of its roots (now known as its Galois group) had a certain structure. He was the first to use the term “group” in its modern mathematical sense of a group of permutations (foreshadowing the modern field of group theory), and his fertile approach, now known as Galois theory, was adapted by later mathematicians to many other fields of mathematics besides the theory of equations. He studied Legendre\'s Géométrie and the treatises of Lagrange. In April 1829 Galois had his first mathematics paper published on continued fractions in the Annales de mathématiques. On 25 May and 1 June he submitted articles on the algebraic solution of equations to the Académie des Sciences. Cauchy was appointed as referee of Galois\' paper. Liouville who, in September 1843, announced to the Academy that he had found in Galois\' papers a concise solution ...as correct as it is deep of this lovely problem: Given an irreducible equation of prime degree, decide whether or not it is soluble by radicals. Liouville published these papers of Galois in his Journal in 1846. The theory that Galois outlined in these papers is now called Galois theory. Tangent equation passing through (1,1) is Galois achieved proof by looking at whether or not the “permutation group” of its roots (now known as its Galois group) had a certain structure. He was the first to use the term “group” in its modern mathematical sense of a group of permutations (foreshadowing the modern field of group theory), and his fertile approach, now known as Galois theory, was adapted by later mathematicians to many other fields of mathematics besides the theory of equations. He studied Legendre\'s Géométrie and the treatises of Lagrange. In April 1829 Galois had his first mathematics paper published on continued fractions in the Annales de mathématiques. On 25 May and 1 June he submitted articles on the algebraic solution of equations to the Académie des Sciences. Cauchy was appointed as referee of Galois\' paper. Liouville who, in September 1843, announced to the Academy that he had found in Galois\' papers a concise solution ...as correct as it is deep of this lovely problem: Given an irreducible equation of prime degree, decide whether or not it is soluble by radicals. Liouville published these papers of Galois in his Journal in 1846. The theory that Galois outlined in these papers is now called Galois theory. Galois achieved proof by looking at whether or not the “permutation group” of its roots (now known as its Galois group) had a certain structure. He was the first to use the term “group” in its modern mathematical sense of a group of permutations (foreshadowing the modern field of group theory), and his fertile approach, now known as Galois theory, was adapte.
Report
Share
Report
Share
Download to read offline
Recommended
Please I need help with abstract algebra Will rate quicklySoluti.pdf
Please I need help with abstract algebra Will rate quickly
Solution
In algebra, which is a broad division of mathematics, abstract algebra is a common name for the
sub-area that studies algebraic structures in their own right. Such structures include groups, rings,
fields, modules, vector spaces, and algebras. The specific term abstract algebra was coined at the
beginning of the 20th century to distinguish this area from the other parts of algebra. The term
modern algebra has also been used to denote abstract algebra.
Two mathematical subject areas that study the properties of algebraic structures viewed as a
whole are universal algebra and category theory. Algebraic structures, together with the
associated homomorphisms, form categories. Category theory is a powerful formalism for
studying and comparing different algebraic structures.
History
As in other parts of mathematics, concrete problems and examples have played important roles
in the development of abstract algebra. Through the end of the nineteenth century, many --
perhaps most -- of these problems were in some way related to the theory of algebraic equations.
Major themes include:
Numerous textbooks in abstract algebra start with axiomatic definitions of various algebraic
structures and then proceed to establish their properties. This creates a false impression that in
algebra axioms had come first and then served as a motivation and as a basis of further study.
The true order of historical development was almost exactly the opposite. For example, the
hypercomplex numbers of the nineteenth century had kinematic and physical motivations but
challenged comprehension. Most theories that are now recognized as parts of algebra started as
collections of disparate facts from various branches of mathematics, acquired a common theme
that served as a core around which various results were grouped, and finally became unified on a
basis of a common set of concepts. An archetypical example of this progressive synthesis can be
seen in the history of group theory.
Early group theory
There were several threads in the early development of group theory, in modern language loosely
corresponding to number theory, theory of equations, and geometry.
Leonhard Euler considered algebraic operations on numbers modulo an integer, modular
arithmetic, in his generalization of Fermat\'s little theorem. These investigations were taken
much further by Carl Friedrich Gauss, who considered the structure of multiplicative groups of
residues mod n and established many properties of cyclic and more general abelian groups that
arise in this way. In his investigations of composition of binary quadratic forms, Gauss explicitly
stated the associative law for the composition of forms, but like Euler before him, he seems to
have been more interested in concrete results than in general theory. In 1870, Leopold Kronecker
gave a definition of an abelian group in the context of ideal class groups of a number field,
generalizing .
Maths
Euclid was an influential Greek mathematician known as the "Father of Geometry". His work Elements is one of the most important works in the history of mathematics, where he deduced the principles of Euclidean geometry from a small set of axioms. Euclid also wrote works on other areas of mathematics and may have been a student of Aristotle, founding the school of mathematics in Alexandria.
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.
Famous mathematicians of all time
This document provides brief biographies of famous mathematicians including Euclid, Carl Gauss, Leonhard Euler, Pythagoras, Aryabhata, and Fermat. It discusses their major contributions such as Euclid establishing the principles of geometry, Gauss' work in number theory and algebra, Euler making advances in many fields of mathematics through his notations and methods, Pythagoras discovering relationships in music and numbers, Aryabhata developing India's place value system and early work in trigonometry and algebra, and Fermat's foundational work in number theory and discoveries in analytic geometry and calculus.
Scientists
- Johannes Kepler established that planets orbit the sun in ellipses rather than perfect circles, with the sun located at one focus. Galileo Galilei provided further evidence for the heliocentric model through his astronomical observations with one of the first telescopes.
- Isaac Newton later explained the motions of the planets through his universal law of gravitation and laws of motion. This established a basis for further exploration of celestial mechanics by astronomers like Pierre-Simon Laplace.
- Major 18th century contributors to celestial mechanics included Leonhard Euler, Joseph-Louis Lagrange, and Pierre-Simon Laplace, who further developed and applied Newton's law of gravitation to better understand planetary motions.
Reviewer-in-HOM.docx
This document discusses the history of set theory and problems in the foundations of mathematics. It begins by covering the birth of set theory with George Cantor in the late 1800s. It then discusses paradoxes that arose in set theory, such as Russell's paradox, and early attempts to address these issues through axiomatization by mathematicians like Zermelo. The document also covers the foundational crisis in mathematics around this time and different viewpoints on the issue, such as formalism and intuitionism. It discusses Hilbert's program and Godel's incompleteness theorems. Finally, the document briefly touches on non-Euclidean geometry and number theory.
list of mathematician
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.
Recommended
Please I need help with abstract algebra Will rate quicklySoluti.pdf
Please I need help with abstract algebra Will rate quickly
Solution
In algebra, which is a broad division of mathematics, abstract algebra is a common name for the
sub-area that studies algebraic structures in their own right. Such structures include groups, rings,
fields, modules, vector spaces, and algebras. The specific term abstract algebra was coined at the
beginning of the 20th century to distinguish this area from the other parts of algebra. The term
modern algebra has also been used to denote abstract algebra.
Two mathematical subject areas that study the properties of algebraic structures viewed as a
whole are universal algebra and category theory. Algebraic structures, together with the
associated homomorphisms, form categories. Category theory is a powerful formalism for
studying and comparing different algebraic structures.
History
As in other parts of mathematics, concrete problems and examples have played important roles
in the development of abstract algebra. Through the end of the nineteenth century, many --
perhaps most -- of these problems were in some way related to the theory of algebraic equations.
Major themes include:
Numerous textbooks in abstract algebra start with axiomatic definitions of various algebraic
structures and then proceed to establish their properties. This creates a false impression that in
algebra axioms had come first and then served as a motivation and as a basis of further study.
The true order of historical development was almost exactly the opposite. For example, the
hypercomplex numbers of the nineteenth century had kinematic and physical motivations but
challenged comprehension. Most theories that are now recognized as parts of algebra started as
collections of disparate facts from various branches of mathematics, acquired a common theme
that served as a core around which various results were grouped, and finally became unified on a
basis of a common set of concepts. An archetypical example of this progressive synthesis can be
seen in the history of group theory.
Early group theory
There were several threads in the early development of group theory, in modern language loosely
corresponding to number theory, theory of equations, and geometry.
Leonhard Euler considered algebraic operations on numbers modulo an integer, modular
arithmetic, in his generalization of Fermat\'s little theorem. These investigations were taken
much further by Carl Friedrich Gauss, who considered the structure of multiplicative groups of
residues mod n and established many properties of cyclic and more general abelian groups that
arise in this way. In his investigations of composition of binary quadratic forms, Gauss explicitly
stated the associative law for the composition of forms, but like Euler before him, he seems to
have been more interested in concrete results than in general theory. In 1870, Leopold Kronecker
gave a definition of an abelian group in the context of ideal class groups of a number field,
generalizing .
Maths
Euclid was an influential Greek mathematician known as the "Father of Geometry". His work Elements is one of the most important works in the history of mathematics, where he deduced the principles of Euclidean geometry from a small set of axioms. Euclid also wrote works on other areas of mathematics and may have been a student of Aristotle, founding the school of mathematics in Alexandria.
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.
Famous mathematicians of all time
This document provides brief biographies of famous mathematicians including Euclid, Carl Gauss, Leonhard Euler, Pythagoras, Aryabhata, and Fermat. It discusses their major contributions such as Euclid establishing the principles of geometry, Gauss' work in number theory and algebra, Euler making advances in many fields of mathematics through his notations and methods, Pythagoras discovering relationships in music and numbers, Aryabhata developing India's place value system and early work in trigonometry and algebra, and Fermat's foundational work in number theory and discoveries in analytic geometry and calculus.
Scientists
- Johannes Kepler established that planets orbit the sun in ellipses rather than perfect circles, with the sun located at one focus. Galileo Galilei provided further evidence for the heliocentric model through his astronomical observations with one of the first telescopes.
- Isaac Newton later explained the motions of the planets through his universal law of gravitation and laws of motion. This established a basis for further exploration of celestial mechanics by astronomers like Pierre-Simon Laplace.
- Major 18th century contributors to celestial mechanics included Leonhard Euler, Joseph-Louis Lagrange, and Pierre-Simon Laplace, who further developed and applied Newton's law of gravitation to better understand planetary motions.
Reviewer-in-HOM.docx
This document discusses the history of set theory and problems in the foundations of mathematics. It begins by covering the birth of set theory with George Cantor in the late 1800s. It then discusses paradoxes that arose in set theory, such as Russell's paradox, and early attempts to address these issues through axiomatization by mathematicians like Zermelo. The document also covers the foundational crisis in mathematics around this time and different viewpoints on the issue, such as formalism and intuitionism. It discusses Hilbert's program and Godel's incompleteness theorems. Finally, the document briefly touches on non-Euclidean geometry and number theory.
list of mathematician
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.
History of Mathematics - Early to Present Period
If you happen to like this powerpoint, you may contact me at flippedchannel@gmail.com
I offer some educational services like:
-powerpoint presentation maker
-grammarian
-content creator
-layout designer
Subscribe to our online platforms:
FlippED Channel (Youtube)
http://bit.ly/FlippEDChannel
LET in the NET (facebook)
http://bit.ly/LETndNET
Leonhard euler
Leonhard Euler was a pioneering Swiss mathematician and physicist born in 1707. He made significant contributions across many areas of mathematics and physics. Some of his key accomplishments included introducing modern mathematical notation and terminology, developing graph theory and topology through his analysis of the Seven Bridges of Königsberg problem, and making important discoveries in calculus, number theory, mechanics, and optics among other fields. He spent most of his career in St. Petersburg and Berlin, and was one of the most prolific and influential mathematicians of all time.
Presentation1
Euclid was a Greek mathematician from Alexandria who is considered the most influential mathematician of ancient times. He wrote Elements, one of the most influential works in mathematics, which was used as a textbook for over 2000 years. He proved many important theorems in number theory and geometry. Archimedes was a Greek mathematician considered the greatest of ancient times. He made important advances in geometry, number theory, algebra, and analysis. He anticipated integral calculus and determined formulas for volumes and areas of spheres. Ramanujan was an Indian mathematician who made extensive contributions to mathematical analysis, number theory, infinite series, and continued fractions despite having no formal training in pure mathematics. He produced over 3000 results, conjectures, and theorems and
Abstract algebra & its applications
Abstract algebra is the study of algebraic structures like groups, rings, and fields. It emerged in the early 20th century to make algebra more rigorous and abstract. Key developments included the study of symmetry in polynomial equations, which led to the concepts of groups, and the algebraic investigation of quadratic and higher-degree equations, which produced the ideas of rings and ideals. Now abstract algebra is used throughout mathematics and in fields like physics, where group theory can simplify differential equations and describe system symmetries.
29364360 the-logic-of-transdisciplinarity-2
This document provides an overview of the development of logic and physics that motivates the need for a new approach called transdisciplinarity. It discusses how non-Euclidean geometries and Gödel's incompleteness theorems challenged classical logic. It also explains how quantum mechanics experiments revealed phenomena like wave-particle duality and nonlocality that are contradictory to classical physics. This introduced issues of incompleteness and plurality into physical theories. The document argues that transdisciplinary logic is needed to provide a formal characterization of theories that accounts for these developments across disciplines.
Earlier a place value notation number system had evolved over a leng.pdf
Earlier a place value notation number system had evolved over a lengthy period with a number
base of 60. It allowed arbitrarily large numbers and fractions to be represented and so proved to
be the foundation of more high powered mathematical development.
Number problems such as that of the Pythagorean triples (a,b,c) with a2+b2 = c2 were studied
from at least 1700 BC. Systems of linear equations were studied in the context of solving number
problems. Quadratic equations were also studied and these examples led to a type of numerical
algebra.
Geometric problems relating to similar figures, area and volume were also studied and values
obtained for π.
The Babylonian basis of mathematics was inherited by the Greeks and independent development
by the Greeks began from around 450 BC. Zeno of Elea\'s paradoxes led to the atomic theory of
Democritus. A more precise formulation of concepts led to the realisation that the rational
numbers did not suffice to measure all lengths. A geometric formulation of irrational numbers
arose. Studies of area led to a form of integration.
The theory of conic sections shows a high point in pure mathematical study by Apollonius.
Further mathematical discoveries were driven by the astronomy, for example the study of
trigonometry.
The major Greek progress in mathematics was from 300 BC to 200 AD. After this time progress
continued in Islamic countries. Mathematics flourished in particular in Iran, Syria and India. This
work did not match the progress made by the Greeks but in addition to the Islamic progress, it
did preserve Greek mathematics. From about the 11th Century Adelard of Bath, then later
Fibonacci, brought this Islamic mathematics and its knowledge of Greek mathematics back into
Europe.
Major progress in mathematics in Europe began again at the beginning of the 16th Century with
Pacioli, then Cardan, Tartaglia and Ferrari with the algebraic solution of cubic and quartic
equations. Copernicus and Galileo revolutionised the applications of mathematics to the study of
the universe.
The progress in algebra had a major psychological effect and enthusiasm for mathematical
research, in particular research in algebra, spread from Italy to Stevin in Belgium and Viète in
France.
The 17th Century saw Napier, Briggs and others greatly extend the power of mathematics as a
calculatory science with his discovery of logarithms. Cavalieri made progress towards the
calculus with his infinitesimal methods and Descartes added the power of algebraic methods to
geometry.
Progress towards the calculus continued with Fermat, who, together with Pascal, began the
mathematical study of probability. However the calculus was to be the topic of most significance
to evolve in the 17th Century.
Newton, building on the work of many earlier mathematicians such as his teacher Barrow,
developed the calculus into a tool to push forward the study of nature. His work contained a
wealth of new discoveries showing the interaction between mathemat.
Numerical presentation
Johann Carl Friedrich Gauss was a German mathematician born in 1777 who made significant contributions to many fields including number theory, algebra, and geometry. He showed early potential in mathematics and attended several universities. Notable achievements include discovering magnetic monopoles do not exist and developing Gaussian elimination to solve systems of linear equations. Gauss also pioneered non-Euclidean geometry and its role in Einstein's theory of general relativity. He received several honors for his scientific work but was a perfectionist who did not publish all his discoveries.
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.
logic and set theory
Logic is the study of valid inference and reasoning. It is used in many intellectual activities but is primarily studied in philosophy, mathematics, semantics, and computer science. In the 19th century, logic became mathematized by British mathematicians such as George Boole, who developed an algebra of logic featuring operators like and, or, not, and exclusive or. Boole saw the potential of applying this algebraic logic to solve problems and argued that logic was a discipline of mathematics rather than philosophy alone.
Kiosk presentation
This document provides biographies of five famous French mathematicians and their contributions: René Descartes developed analytical geometry and standard algebraic notation; Pierre de Fermat discovered factorization methods and made contributions to calculus, probability, and geometry; Blaise Pascal invented the mechanical calculator and contributed to probability theory and projective geometry; Andre Weil made connections between number theory and algebraic geometry and developed theories on algebraic curves and quadratic forms; Joseph Fourier developed Fourier series to analyze heat transfer and vibrations through mathematical expressions.
1.-FUNDAMENTO-MATEMATICAS-DISCRETAS__32605__0.pdf
The document discusses the topics of discrete mathematics and notable historical figures in the field. It begins with definitions of discrete mathematics and its relationship to computer science. It then profiles 12 important mathematicians and logicians such as Aristotle, Leibniz, Gauss, Euler, Boole, Cantor, and Church, highlighting their major contributions in areas like logic, calculus, number theory, set theory, and computability. It provides brief biographical information on each figure.
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.
Gauss
Carl Friedrich Gauss was one of the greatest mathematicians in history. At a young age, he invented the method of least squares and proved that a 17-sided polygon can be constructed using a straightedge and compass. His doctoral thesis proved the Fundamental Theorem of Algebra. Gauss made significant contributions to fields like differential geometry, algebra, complex functions, and potential theory. In addition to mathematics, Gauss had keen interests in astronomy and physics, and held a position at the Göttingen observatory for nearly 50 years.
International Journal of Computational Engineering Research(IJCER)
This document provides a historical overview of the development of the Fundamental Theorem of Algebra. It discusses early contributions from mathematicians like Diophantus, Cardan, Euler, and Gauss. It describes how earlier proofs were flawed because they assumed the existence of roots before proving them. The first rigorous proof is credited to Gauss in 1799, who showed that assuming the existence of roots first is circular reasoning. Later proofs include one by Argand in 1814 using the concept of minimization of continuous functions.
Lilian bariga@yahoo.hehehehttp://www.slideshare.net/jacobsonsea/edgar-dales-c...
This document provides brief biographies of 13 mathematicians from history: Felix Hausdorff, Omar Khayyám, Adrien-Marie Legendre, Hippocrates of Chios, Gerolamo Cardano, Johann Heinrich Lambert, Paul Erdős, Alexis Claude de Clairaut, Marius Sophus Lie, Archytas, and lists some of their key contributions to mathematics.
n
This document profiles 12 mathematicians from history and provides 1-4 contributions associated with each one. It includes mathematicians such as Felix Hausdorff, who founded modern topology, and Omar Khayyám, a Persian polymath who wrote on multiple fields including mathematics, astronomy and poetry. Paul Erdős published more papers than any other mathematician and worked on problems in fields like number theory and graph theory.
Maths
The document is a maths presentation submitted by Mayank Yadav containing information about famous mathematicians including Sir Isaac Newton, Srinivasa Ramanujan, Pierre de Fermat, and Euclid. It provides brief biographies of each mathematician summarizing their major contributions and accomplishments in the field of mathematics.
Arithmetization of Analysis
The document discusses the arithmetization of analysis in the 19th century by German mathematicians. It describes how early mathematicians like d'Alembert, Lagrange, Gauss, and Cauchy began establishing rigorous foundations for calculus by developing theories of limits and defining calculus concepts like continuity, derivatives, and integrals in terms of limits. Later, Weierstrass and Riemann further arithmetized analysis by basing it on rigorous definitions of real numbers and developing analysis from set and number theory. Their work established analysis on logical foundations and rid it of intuition.
Bonaventura ,Cavalieri and Sir George Gabriel Stokes, First Baronet,
- Bonaventura Francesco Cavalieri was an Italian mathematician born in 1598 who developed the method of indivisibles, a precursor to integral calculus.
- His method treated areas as composed of lines and volumes as composed of planar areas, allowing him to solve problems involving areas, volumes, and centers of mass.
- Though crude, his method provided practical techniques for computing areas and volumes and influenced later mathematicians like Kepler and Galileo.
b.) GeometryThe old problem of proving Euclid’s Fifth Postulate.pdf
b.) Geometry:
The old problem of proving Euclid’s Fifth Postulate, the \"Parallel Postulate\", from his first
four postulates had never been forgotten. Beginning not long after Euclid, many attempted
demonstrations were given, but all were later found to be faulty, through allowing into the
reasoning some principle which itself had not been proved from the first four postulates. Though
Omar Khayyám was also unsuccessful in proving the parallel postulate, his criticisms of
Euclid\'s theories of parallels and his proof of properties of figures in non-Euclidean geometries
contributed to the eventual development of non-Euclidean geometry. By 1700 a great deal had
been discovered about what can be proved from the first four, and what the pitfalls were in
attempting to prove the fifth. Saccheri, Lambert, and Legendre each did excellent work on the
problem in the 18th century, but still fell short of success. In the early 19th century, Gauss,
Johann Bolyai, and Lobatchewsky, each independently, took a different approach. Beginning to
suspect that it was impossible to prove the Parallel Postulate, they set out to develop a self-
consistent geometry in which that postulate was false. In this they were successful, thus creating
the first non-Euclidean geometry. By 1854, Bernhard Riemann, a student of Gauss, had applied
methods of calculus in a ground-breaking study of the intrinsic (self-contained) geometry of all
smooth surfaces, and thereby found a different non-Euclidean geometry. This work of Riemann
later became fundamental for Einstein\'s theory of relativity.
William Blake\'s \"Newton\" is a demonstration of his opposition to the \'single-vision\' of
scientific materialism; here, Isaac Newton is shown as \'divine geometer\' (1795)
It remained to be proved mathematically that the non-Euclidean geometry was just as self-
consistent as Euclidean geometry, and this was first accomplished by Beltrami in 1868. With
this, non-Euclidean geometry was established on an equal mathematical footing with Euclidean
geometry.
While it was now known that different geometric theories were mathematically possible, the
question remained, \"Which one of these theories is correct for our physical space?\" The
mathematical work revealed that this question must be answered by physical experimentation,
not mathematical reasoning, and uncovered the reason why the experimentation must involve
immense (interstellar, not earth-bound) distances. With the development of relativity theory in
physics, this question became vastly more complicated.
c.) Algebra:
1. Babylonian algebra
The origins of algebra can be traced to the ancient Babylonians, who developed a positional
number system that greatly aided them in solving their rhetorical algebraic equations. The
Babylonians were not interested in exact solutions but approximations, and so they would
commonly use linear interpolation to approximate intermediate values. One of the most famous
tablets is the Plimpton 322 tablet, .
On April 18, 1906, an earthquake killed over 3,000 people when it hi.pdf
On April 18, 1906, an earthquake killed over 3,000 people when it hit San Francisco, with a
magnitude of 8.3 on the Richter Scale. On March 11, 2011 the “Tohoku” earthquake hit central
Japan with a magnitude of 9.0 on the Richter Scale, and killed 15, 894 people. How much greater
was the 2011 earthquake than the 1906 earthquake?
Solution
The formula of magnitude of earthquake is
M=log(I/S)
I is the intensity of the earthquake And S is the intensity of the standard earthquake
8.3 = log(I1/S) and 9= log(I2/S)
9-8.3= log(I2/S) -log(I1/S)
.7= log(I2/I1)
I2/I1=10.7
I2=5 I1
Therefore the earhquake occurs in 2011 is 5 times more intense as compared to earthquake
occurs in 1906.
On the planet of Caracas, in the Stellar Solorais Ka Chunk Galaxy, th.pdf
On the planet of Caracas, in the Stellar Solorais Ka Chunk Galaxy, there is a population of
Nugget Arians. Two phenotypes of interest are: Peanuts; and Carmelaoid. Each is a single gene
trait, and for each gene there are two alleles. A cross between a female with Peanuts and a male
with Carmelaoid (each of which is homozygous for the wild-type (non-trait) allele at the other
gene) produces the following F1 counts: The mode of inheritance for each phenotype is: Peanuts
= Autosomal Recessive. Carmelaoid = Autosomal Dominant. Peanuts = Autosomal Recessive.
Carmelaoid = Autosomal Recessive. Peanuts = Autosomal Recessive. Carmelaoid = X-linked
Recessive. Peanuts = Autosomal Dominant. Carmelaoid = Autosomal Recessive. Peanuts =
Autosomal Dominant. Carmelaoid = Autosomal Dominant.
Solution
The answer is C. Peanuts=Autosomal Recessive
Carmeloid=X-linked recessive.
As
Autosomal characters of male are not carried to progeny so autosomal inheritance is othrwise
called maternal inheritance. As carmelaoid phenotype from male is expressed in F1 so it has to
be in cromosome and from the probability of expression it is evident that it is present in X
cromosome. The male counterpart like sperm carry very little of cytoplasmic material but half of
chromosomal meterial. In human type sex determination i.e.XY male and XX female X linked
recessive genes only express in homozygous i.e. XX condition..
More Related Content
Similar to What was Galois’ contribution to the theory of algebraic equations a.pdf
History of Mathematics - Early to Present Period
If you happen to like this powerpoint, you may contact me at flippedchannel@gmail.com
I offer some educational services like:
-powerpoint presentation maker
-grammarian
-content creator
-layout designer
Subscribe to our online platforms:
FlippED Channel (Youtube)
http://bit.ly/FlippEDChannel
LET in the NET (facebook)
http://bit.ly/LETndNET
Leonhard euler
Leonhard Euler was a pioneering Swiss mathematician and physicist born in 1707. He made significant contributions across many areas of mathematics and physics. Some of his key accomplishments included introducing modern mathematical notation and terminology, developing graph theory and topology through his analysis of the Seven Bridges of Königsberg problem, and making important discoveries in calculus, number theory, mechanics, and optics among other fields. He spent most of his career in St. Petersburg and Berlin, and was one of the most prolific and influential mathematicians of all time.
Presentation1
Euclid was a Greek mathematician from Alexandria who is considered the most influential mathematician of ancient times. He wrote Elements, one of the most influential works in mathematics, which was used as a textbook for over 2000 years. He proved many important theorems in number theory and geometry. Archimedes was a Greek mathematician considered the greatest of ancient times. He made important advances in geometry, number theory, algebra, and analysis. He anticipated integral calculus and determined formulas for volumes and areas of spheres. Ramanujan was an Indian mathematician who made extensive contributions to mathematical analysis, number theory, infinite series, and continued fractions despite having no formal training in pure mathematics. He produced over 3000 results, conjectures, and theorems and
Abstract algebra & its applications
Abstract algebra is the study of algebraic structures like groups, rings, and fields. It emerged in the early 20th century to make algebra more rigorous and abstract. Key developments included the study of symmetry in polynomial equations, which led to the concepts of groups, and the algebraic investigation of quadratic and higher-degree equations, which produced the ideas of rings and ideals. Now abstract algebra is used throughout mathematics and in fields like physics, where group theory can simplify differential equations and describe system symmetries.
29364360 the-logic-of-transdisciplinarity-2
This document provides an overview of the development of logic and physics that motivates the need for a new approach called transdisciplinarity. It discusses how non-Euclidean geometries and Gödel's incompleteness theorems challenged classical logic. It also explains how quantum mechanics experiments revealed phenomena like wave-particle duality and nonlocality that are contradictory to classical physics. This introduced issues of incompleteness and plurality into physical theories. The document argues that transdisciplinary logic is needed to provide a formal characterization of theories that accounts for these developments across disciplines.
Earlier a place value notation number system had evolved over a leng.pdf
Earlier a place value notation number system had evolved over a lengthy period with a number
base of 60. It allowed arbitrarily large numbers and fractions to be represented and so proved to
be the foundation of more high powered mathematical development.
Number problems such as that of the Pythagorean triples (a,b,c) with a2+b2 = c2 were studied
from at least 1700 BC. Systems of linear equations were studied in the context of solving number
problems. Quadratic equations were also studied and these examples led to a type of numerical
algebra.
Geometric problems relating to similar figures, area and volume were also studied and values
obtained for π.
The Babylonian basis of mathematics was inherited by the Greeks and independent development
by the Greeks began from around 450 BC. Zeno of Elea\'s paradoxes led to the atomic theory of
Democritus. A more precise formulation of concepts led to the realisation that the rational
numbers did not suffice to measure all lengths. A geometric formulation of irrational numbers
arose. Studies of area led to a form of integration.
The theory of conic sections shows a high point in pure mathematical study by Apollonius.
Further mathematical discoveries were driven by the astronomy, for example the study of
trigonometry.
The major Greek progress in mathematics was from 300 BC to 200 AD. After this time progress
continued in Islamic countries. Mathematics flourished in particular in Iran, Syria and India. This
work did not match the progress made by the Greeks but in addition to the Islamic progress, it
did preserve Greek mathematics. From about the 11th Century Adelard of Bath, then later
Fibonacci, brought this Islamic mathematics and its knowledge of Greek mathematics back into
Europe.
Major progress in mathematics in Europe began again at the beginning of the 16th Century with
Pacioli, then Cardan, Tartaglia and Ferrari with the algebraic solution of cubic and quartic
equations. Copernicus and Galileo revolutionised the applications of mathematics to the study of
the universe.
The progress in algebra had a major psychological effect and enthusiasm for mathematical
research, in particular research in algebra, spread from Italy to Stevin in Belgium and Viète in
France.
The 17th Century saw Napier, Briggs and others greatly extend the power of mathematics as a
calculatory science with his discovery of logarithms. Cavalieri made progress towards the
calculus with his infinitesimal methods and Descartes added the power of algebraic methods to
geometry.
Progress towards the calculus continued with Fermat, who, together with Pascal, began the
mathematical study of probability. However the calculus was to be the topic of most significance
to evolve in the 17th Century.
Newton, building on the work of many earlier mathematicians such as his teacher Barrow,
developed the calculus into a tool to push forward the study of nature. His work contained a
wealth of new discoveries showing the interaction between mathemat.
Numerical presentation
Johann Carl Friedrich Gauss was a German mathematician born in 1777 who made significant contributions to many fields including number theory, algebra, and geometry. He showed early potential in mathematics and attended several universities. Notable achievements include discovering magnetic monopoles do not exist and developing Gaussian elimination to solve systems of linear equations. Gauss also pioneered non-Euclidean geometry and its role in Einstein's theory of general relativity. He received several honors for his scientific work but was a perfectionist who did not publish all his discoveries.
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.
logic and set theory
Logic is the study of valid inference and reasoning. It is used in many intellectual activities but is primarily studied in philosophy, mathematics, semantics, and computer science. In the 19th century, logic became mathematized by British mathematicians such as George Boole, who developed an algebra of logic featuring operators like and, or, not, and exclusive or. Boole saw the potential of applying this algebraic logic to solve problems and argued that logic was a discipline of mathematics rather than philosophy alone.
Kiosk presentation
This document provides biographies of five famous French mathematicians and their contributions: René Descartes developed analytical geometry and standard algebraic notation; Pierre de Fermat discovered factorization methods and made contributions to calculus, probability, and geometry; Blaise Pascal invented the mechanical calculator and contributed to probability theory and projective geometry; Andre Weil made connections between number theory and algebraic geometry and developed theories on algebraic curves and quadratic forms; Joseph Fourier developed Fourier series to analyze heat transfer and vibrations through mathematical expressions.
1.-FUNDAMENTO-MATEMATICAS-DISCRETAS__32605__0.pdf
The document discusses the topics of discrete mathematics and notable historical figures in the field. It begins with definitions of discrete mathematics and its relationship to computer science. It then profiles 12 important mathematicians and logicians such as Aristotle, Leibniz, Gauss, Euler, Boole, Cantor, and Church, highlighting their major contributions in areas like logic, calculus, number theory, set theory, and computability. It provides brief biographical information on each figure.
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.
Gauss
Carl Friedrich Gauss was one of the greatest mathematicians in history. At a young age, he invented the method of least squares and proved that a 17-sided polygon can be constructed using a straightedge and compass. His doctoral thesis proved the Fundamental Theorem of Algebra. Gauss made significant contributions to fields like differential geometry, algebra, complex functions, and potential theory. In addition to mathematics, Gauss had keen interests in astronomy and physics, and held a position at the Göttingen observatory for nearly 50 years.
International Journal of Computational Engineering Research(IJCER)
This document provides a historical overview of the development of the Fundamental Theorem of Algebra. It discusses early contributions from mathematicians like Diophantus, Cardan, Euler, and Gauss. It describes how earlier proofs were flawed because they assumed the existence of roots before proving them. The first rigorous proof is credited to Gauss in 1799, who showed that assuming the existence of roots first is circular reasoning. Later proofs include one by Argand in 1814 using the concept of minimization of continuous functions.
Lilian bariga@yahoo.hehehehttp://www.slideshare.net/jacobsonsea/edgar-dales-c...
This document provides brief biographies of 13 mathematicians from history: Felix Hausdorff, Omar Khayyám, Adrien-Marie Legendre, Hippocrates of Chios, Gerolamo Cardano, Johann Heinrich Lambert, Paul Erdős, Alexis Claude de Clairaut, Marius Sophus Lie, Archytas, and lists some of their key contributions to mathematics.
n
This document profiles 12 mathematicians from history and provides 1-4 contributions associated with each one. It includes mathematicians such as Felix Hausdorff, who founded modern topology, and Omar Khayyám, a Persian polymath who wrote on multiple fields including mathematics, astronomy and poetry. Paul Erdős published more papers than any other mathematician and worked on problems in fields like number theory and graph theory.
Maths
The document is a maths presentation submitted by Mayank Yadav containing information about famous mathematicians including Sir Isaac Newton, Srinivasa Ramanujan, Pierre de Fermat, and Euclid. It provides brief biographies of each mathematician summarizing their major contributions and accomplishments in the field of mathematics.
Arithmetization of Analysis
The document discusses the arithmetization of analysis in the 19th century by German mathematicians. It describes how early mathematicians like d'Alembert, Lagrange, Gauss, and Cauchy began establishing rigorous foundations for calculus by developing theories of limits and defining calculus concepts like continuity, derivatives, and integrals in terms of limits. Later, Weierstrass and Riemann further arithmetized analysis by basing it on rigorous definitions of real numbers and developing analysis from set and number theory. Their work established analysis on logical foundations and rid it of intuition.
Bonaventura ,Cavalieri and Sir George Gabriel Stokes, First Baronet,
- Bonaventura Francesco Cavalieri was an Italian mathematician born in 1598 who developed the method of indivisibles, a precursor to integral calculus.
- His method treated areas as composed of lines and volumes as composed of planar areas, allowing him to solve problems involving areas, volumes, and centers of mass.
- Though crude, his method provided practical techniques for computing areas and volumes and influenced later mathematicians like Kepler and Galileo.
b.) GeometryThe old problem of proving Euclid’s Fifth Postulate.pdf
b.) Geometry:
The old problem of proving Euclid’s Fifth Postulate, the \"Parallel Postulate\", from his first
four postulates had never been forgotten. Beginning not long after Euclid, many attempted
demonstrations were given, but all were later found to be faulty, through allowing into the
reasoning some principle which itself had not been proved from the first four postulates. Though
Omar Khayyám was also unsuccessful in proving the parallel postulate, his criticisms of
Euclid\'s theories of parallels and his proof of properties of figures in non-Euclidean geometries
contributed to the eventual development of non-Euclidean geometry. By 1700 a great deal had
been discovered about what can be proved from the first four, and what the pitfalls were in
attempting to prove the fifth. Saccheri, Lambert, and Legendre each did excellent work on the
problem in the 18th century, but still fell short of success. In the early 19th century, Gauss,
Johann Bolyai, and Lobatchewsky, each independently, took a different approach. Beginning to
suspect that it was impossible to prove the Parallel Postulate, they set out to develop a self-
consistent geometry in which that postulate was false. In this they were successful, thus creating
the first non-Euclidean geometry. By 1854, Bernhard Riemann, a student of Gauss, had applied
methods of calculus in a ground-breaking study of the intrinsic (self-contained) geometry of all
smooth surfaces, and thereby found a different non-Euclidean geometry. This work of Riemann
later became fundamental for Einstein\'s theory of relativity.
William Blake\'s \"Newton\" is a demonstration of his opposition to the \'single-vision\' of
scientific materialism; here, Isaac Newton is shown as \'divine geometer\' (1795)
It remained to be proved mathematically that the non-Euclidean geometry was just as self-
consistent as Euclidean geometry, and this was first accomplished by Beltrami in 1868. With
this, non-Euclidean geometry was established on an equal mathematical footing with Euclidean
geometry.
While it was now known that different geometric theories were mathematically possible, the
question remained, \"Which one of these theories is correct for our physical space?\" The
mathematical work revealed that this question must be answered by physical experimentation,
not mathematical reasoning, and uncovered the reason why the experimentation must involve
immense (interstellar, not earth-bound) distances. With the development of relativity theory in
physics, this question became vastly more complicated.
c.) Algebra:
1. Babylonian algebra
The origins of algebra can be traced to the ancient Babylonians, who developed a positional
number system that greatly aided them in solving their rhetorical algebraic equations. The
Babylonians were not interested in exact solutions but approximations, and so they would
commonly use linear interpolation to approximate intermediate values. One of the most famous
tablets is the Plimpton 322 tablet, .
Similar to What was Galois’ contribution to the theory of algebraic equations a.pdf (20)
Earlier a place value notation number system had evolved over a leng.pdf
Earlier a place value notation number system had evolved over a leng.pdf
Science and contribution of mathematics in its development
Science and contribution of mathematics in its development
International Journal of Computational Engineering Research(IJCER)
International Journal of Computational Engineering Research(IJCER)
Lilian bariga@yahoo.hehehehttp://www.slideshare.net/jacobsonsea/edgar-dales-c...
Lilian bariga@yahoo.hehehehttp://www.slideshare.net/jacobsonsea/edgar-dales-c...
Bonaventura ,Cavalieri and Sir George Gabriel Stokes, First Baronet,
Bonaventura ,Cavalieri and Sir George Gabriel Stokes, First Baronet,
b.) GeometryThe old problem of proving Euclid’s Fifth Postulate.pdf
b.) GeometryThe old problem of proving Euclid’s Fifth Postulate.pdf
More from arracollection
On April 18, 1906, an earthquake killed over 3,000 people when it hi.pdf
On April 18, 1906, an earthquake killed over 3,000 people when it hit San Francisco, with a
magnitude of 8.3 on the Richter Scale. On March 11, 2011 the “Tohoku” earthquake hit central
Japan with a magnitude of 9.0 on the Richter Scale, and killed 15, 894 people. How much greater
was the 2011 earthquake than the 1906 earthquake?
Solution
The formula of magnitude of earthquake is
M=log(I/S)
I is the intensity of the earthquake And S is the intensity of the standard earthquake
8.3 = log(I1/S) and 9= log(I2/S)
9-8.3= log(I2/S) -log(I1/S)
.7= log(I2/I1)
I2/I1=10.7
I2=5 I1
Therefore the earhquake occurs in 2011 is 5 times more intense as compared to earthquake
occurs in 1906.
On the planet of Caracas, in the Stellar Solorais Ka Chunk Galaxy, th.pdf
On the planet of Caracas, in the Stellar Solorais Ka Chunk Galaxy, there is a population of
Nugget Arians. Two phenotypes of interest are: Peanuts; and Carmelaoid. Each is a single gene
trait, and for each gene there are two alleles. A cross between a female with Peanuts and a male
with Carmelaoid (each of which is homozygous for the wild-type (non-trait) allele at the other
gene) produces the following F1 counts: The mode of inheritance for each phenotype is: Peanuts
= Autosomal Recessive. Carmelaoid = Autosomal Dominant. Peanuts = Autosomal Recessive.
Carmelaoid = Autosomal Recessive. Peanuts = Autosomal Recessive. Carmelaoid = X-linked
Recessive. Peanuts = Autosomal Dominant. Carmelaoid = Autosomal Recessive. Peanuts =
Autosomal Dominant. Carmelaoid = Autosomal Dominant.
Solution
The answer is C. Peanuts=Autosomal Recessive
Carmeloid=X-linked recessive.
As
Autosomal characters of male are not carried to progeny so autosomal inheritance is othrwise
called maternal inheritance. As carmelaoid phenotype from male is expressed in F1 so it has to
be in cromosome and from the probability of expression it is evident that it is present in X
cromosome. The male counterpart like sperm carry very little of cytoplasmic material but half of
chromosomal meterial. In human type sex determination i.e.XY male and XX female X linked
recessive genes only express in homozygous i.e. XX condition..
Muv is homozygous You have a C. elegans worm with the following geno.pdf
Muv is homozygous You have a C. elegans worm with the following genotype: + dpy/lov +;
muv Where, dpy, lov and muv are alleles for these recessive phenotypes: Dpy = dumpy (short
and fat) Lov= mating behavior defective Muv = multivulva After taking a minute to feel sorry
for this poor worm, answer the following questions: What gene(s) is this animal heterozygous
for? What gene(s) is this animal homozygous for? What genes(s) are located on the same
chromosome? What is the phenotype of this animal? Assuming lov and dpy loci are 20cM
apart, what are the phenotypes, genotypes and expected frequencies of this hermaphrodite\'s self-
progeny? Percentage Phenotype
Solution
5.1: The animal is heterozygous for dpy and lov genes.
5.2: The animal is homozygous for muv gene.
5.3: The dpy and muv genes are located on the same chromosome.
5.4: Phenotype of animal= long and thin; mating behaviour, multivulva..
Material Science (Solidification)What is the solute atoms concent.pdf
Material Science: (Solidification)
What is the solute atoms concentration with position for a directional solidification of alloy?
Please don\'t answer if you don\'t know the right answer. Thanks.
Solution
During directional solidification, the solute atom concentration increases with increase in
distance from the outside surface. For example during solidification of a spherical casting, the
solute concentration will be maximum at the core and minimum on the surface..
Let P[x] denote the vector space of all polynomials. Let E be the set.pdf
Let P[x] denote the vector space of all polynomials. Let E be the set of polynomials which only
contain terms of even degree of even degree. Is E a subspace of P[x]? Explain.
Solution
Let E be the set as given in the problem
E = { f(x)| f(x) contains only terms of even degree}
= { g(x2)| g any polynomial in F[x]}
If g and h are any polynomials in F[x], clearly g+h and cg are polynomials in F[x] and
(g+h)(x2) and cg(x2) belong to E (for any scalar c in F).
So E is closed under vector addition and scalar multiplication. So E is a subspace of F.
Investment in Note ReceivableSuppliesPrepaid RentBuildingsAc.pdf
Investment in Note Receivable
Supplies
Prepaid Rent
Buildings
Accumulated Depreciation—Buildings
Unearned Service RevenueDebitCredit
Investment in Note Receivable$24,000
Supplies23,500
Prepaid Rent3,200
Buildings280,000
Accumulated Depreciation—Buildings$140,000
Unearned Service Revenue11,900
Solution
1) Interest receivble (24000*12%/12) 240 Interest income 240 2) Supplies expense
(23500-15200) 8300 Supplies 8300 3) Rent expense (3200/4) 800 Prepaid rent 800
4) Salaries and wages expense 2700 Salaries and wages payable 2700 5) Depreciation
expense-Buildings (6720/12) 560 Accumualated depreciation-Buildings 560 6)
Unearned service revenue 4800 Service revenue 4800 7) Repairs and maintenane
expense 2300 Accounts payable 2300.
In a tube containing 1 ml of a 15 dilution of A, and 4 ml of a 110.pdf
In a tube containing 1 ml of a 1:5 dilution of A, and 4 ml of a 1:100 dilution of B:
What is the final dilution of substance A?
What is the final dilution of substance B?
Solution
What is the final dilution of substance A?
When 1mL substance A is mixed with 4 mL of Substance B, four dilution of substance A
happens.
original=1/5
Further =1/4
Final = 1/5 x1/4 = 1/20 fold dilution
What is the final dilution of substance B?
When 4mL substance B is mixed with 1 mL of Substance A, = times
original=1/100
Further =4/5
Final = 1/100 x 4/5 = 4/500 fold dilution.
Implement a function called getElements() that takes in two lists. T.pdf
Implement a function called getElements() that takes in two lists. The first list L consists of any
type of items and the second list P consists of a list of integers. The implemented function will
return a list consisting of the element in L that are in positions indicated by P. For example, if
P=1, 7, 3, then the element in position 1, 7 and 3 in the list L must be returned. The function
must be implemented using the C++ list SLT API. Hint: The implementation for this function
will require some thought. Here are some hints for one approach to solve the problem. Use a for-
loop to walk through list P in a similar way as done in the printList() function. Consider creating
an index variable to track the item number in list L. Also, set the value of the iterator equal to a
variable in this loop. For example: int index = 0; // Track the position int position = (*itr) ; // Get
the item in P Create a second loop embedded within the first loop to walk through the elements
in list L. If the index equals position-1 then you know you have found the element. Thus, call the
push_back() function on the resultList to add the element. At the end of this loop increment the
index variable by 1. Note that your iterator variable for the second loop must be named
differently than the first loop. For example you can all it itr2. Output: The output from the
program once the function is implement will be:
/**
* List.cpp - This program implements and tests the getIntersection
* and getUnion functions.
*
* TODO: Include your name and course number here.
*/
#include
#include
#include
using namespace std;
template
void printList(list list1);
template
list getElements(list L, list P);
int main(int argc, char **argv)
{
// Declare list variables
list list1;
list list2;
// Add data to list 1
list1.push_back(\"the\");
list1.push_back(\"quick\");
list1.push_back(\"brown\");
list1.push_back(\"fox\");
list1.push_back(\"jumped\");
list1.push_back(\"over\");
list1.push_back(\"the\");
list1.push_back(\"lazy\");
list1.push_back(\"dog\");
// Add data to list 2
list2.push_back(4);
list2.push_back(3);
list2.push_back(9);
list2.push_back(6);
list2.push_back(7);
// Print out the lists
cout << \"List 1: \" << endl;
printList(list1);
cout << \"List 2: \" << endl;
printList(list2);
cout << endl;
cout << \"Results of getElements():\" << endl;
printList(getElements(list1, list2));
cout << \"\ ** Press any key to continue **\ \";
getchar();
return 0;
}
template
void printList(list list1)
{
cout << \" \";
// Use an iterator to walk the list. Print the value of
// for each node.
typename list::iterator itr;
for (itr = list1.begin(); itr != list1.end(); itr++)
{
// Get the contents of each node
Object value = (*itr);
// Print the value of the node
cout << \" \" << value;
}
cout << endl;
return;
}
template
list getElements(list L, list P)
{
//A result list to return to the caller
list resultList;
// TODO: Implement the details for the function.
return resultList;
}
Solution
/**
* List.cpp - Thi.
gnmenttakeAssignmentMaindoinvoker assignmentstakeAssignmernt Dr. L. .pdf
gnment/takeAssignmentMaindoinvoker assignmentstakeAssignmernt Dr. L. M. Paton is an
ophthalmologist As of December 31, Dr. Patton owned the following property that elated tos
prfessional practice, Pattion Eye Clinic Cash, 2,720 Professional Equipment, $62,400 Office
Equipment, $11,220 On the same date, he owed the following business creditors Munez Supply
Compay $5,320 Martin Equlpment Sales, $6,180 Compute the following amounts in the
accounting equation Assets Equity
Solution
Assets 76330 =2720+62400+11210 Liabilities 11500 =5320+6180 Owner\'s Equity 64830
=76330-11500.
Every cell in our bodies expresses the same genes. True or False.pdf
Every cell in our bodies expresses the same genes. True or False?
Solution
Answer : The given statement is FALSE. Although all the cells in our body contains same
amount of DNA/number of genes, different cells expresses different genes which gives their
identity. This phenamenan is called differential gene expression..
Describe the partition of Z resulting from the equivalence relati.pdf
Describe the partition of Z resulting from the equivalence relation = (mod 4).
Solution
a=b mod 4
implies and b give the same remainder modulo 4
There are only 4 least residues modulo 4: 0,1,2,3
So total 4 equivalence classes
The partitions are
[0]= Multiples of 4
[1]=INtegers of the form 4k+1
[2]=Integers of the form 4k+2
[3]=Integers of the form 4k+3.
describe what is meant by Rh factor when typing blood.Solution.pdf
describe what is meant by Rh factor when typing blood.
Solution
Ans). Rh derives from rhesus and the terms rhesus blood group system. Rh factor is an inherited
protein on the surface of red blood cells. It consists of many blood-group antigens, among which
the five antigens D, C, c, E, and e are the most important..
Describe the causes, symptoms, and treatment of conjunctivitisSo.pdf
Describe the causes, symptoms, and treatment of conjunctivitis
Solution
Conjuctivits is a condition that is associated with the redness and inflammation of the conjuctiva.
Conjuctiva is a thin transparent layer of tissue lining the inner surface of the eyelid covering the
white part of the eye. It is a common disease and is usually referred toas the \"pink eye\".
CAUSES OF CONJUCTIVITIS
Three types of conjuctivitis include:
Allergic Conjunctivitis
Infectious Conjuctivitis
Chemical Conjunctivitis
SYMPTOMS OF CONJUCTIVITIS
TREATMENT OF CONJUCTIVITIS
The appropriate treatment for conjunctivitis depends on its cause:.
Discuss the relationship between gap rule gene mutations, pair-rule .pdf
Discuss the relationship between gap rule gene mutations, pair-rule gene mutations, and segment
polarity gene mutations in Drosophila melanogaster.
Solution
Segmentation in Drosophila is controlled by gene expression cascade that occur in a sequential
order. The maternal effect genes form the anterior and posterior poles in the embryo. The spatial
pattern of segments is controlled by transcription regulation of gap genes. The gap genes express
the overlapping segments of anterior and posterior poles. The gap genes regulate next set of
genes called pair rule genes. These genes are expressed in 7 stripes corresponding to each
segment. Pair rule genes express the transcription factors regulating the segment polarity genes.
These genes are expressed as 14 segmentally repeated stripes. The segment polarity genes
express regulatory proteins and transcription factors that maintain interaction between cells and
finally, homeotic genes control the character of each segment.
The missing segments producing gaps are known by Krüppel mutants resulting in missing of T1-
A5 segments. Hunchback mutants are missing head segments and knirps mutants lack posterior
segments. Mutations in pair-rule genes- result in half the number of parasegments.The fushi-
tarazu mutants lack odd-numbered parasegments and even-skipped mutants lack even-numbered
parasegments. Mutations in segment polarity genes- result in duplication of the anterior or
posterior half within each segment. The gooseberry and engrailed mutants have the posterior part
of each segment replaced by the anterior part of the adjacent segment..
Create a directory your virtual machine. Within that directory creat.pdf
Create a directory your virtual machine. Within that directory create the html file index.html.
This should be an HTML5 formatted file, with the following elements and text defined
Links to an external JavaScript file q2.js in the same directory as index.html.
Contains a button with the text \"ClickMe\" (no quotes) that will invoke the callback function
\"go()\" when the button is clicked.
Contains a paragraph with id \"output\" (no quotes) which contains the text \"Change Me\". (no
quotes)
When the ClickMe button is pushed, the text in the HTML element with id \"output\" should be
updated as follows using JavaScript code in q2.js. (Note: the number given below should reset
when the page is reloaded and all effects below are cumulative.)
The first time the button is pushed, the colour of the text in output to be set to red.
The second time the button is pushed, the font of the text in output should be set to \"sans-serif\"
The third time the button is pressed, the text should be changed to five copies of whatever text is
currently found as the innerHTML of the output element. Do not add extra spaces or line breaks
to this value.
If the button is pushed four or more times, the text in output should be set to \"QUESTION
DONE\" (no quotes).
Solution
index.html
Title
Change MeClick Me
q2.js
var num_clicks = 0;
function clickme(){
num_clicks = num_clicks + 1;
if (num_clicks==1){
document.getElementById(\"output\").style.color=\"red\"; //change color to red on 1 click
}
else if (num_clicks==2){
document.getElementById(\"output\").style.fontFamily=\"sans-serif\"; //change font family
on 2 clicks
}
else if (num_clicks==3){
text = document.getElementById(\"output\").innerHTML;
document.getElementById(\"output\").innerHTML = text + text + text + text + text;
//change text on 3 clicks
}
else if (num_clicks>=4){
document.getElementById(\"output\").innerHTML = \"QUESTION DONE\"; //question
done text on 4 clicks
}
}.
Compare between the two light microscope SolutionFeature1. .pdf
Compare between the two light microscope:
Solution
Feature
1. Similar functional parts : source of light is same - visible light is used by focusing the light
either through lenses or prism on the specimen.
2. Dissimilar functional parts : Compound microscope- has multiple objective lenses with one
eyepiece;
Dissecting Microscope- has single objective lens with two eyepiece lenses
3. Purpose of use : Dissecting microscope: used to perform small dissections under the
microscope and to view live specimen , compound microscope- used to visualise things that are
too small to be seen via the naked eye.
7. Maximum magnification: Compound microscope- up to 1000x ; Dissecting microscope- up to
70x
4. Image dimension : -
5. Image orientation : -
6. Image development: no image development or orientation or dimensions- these are all
properties of electron microscopes
3. Purpose of use : Dissecting microscope: used to perform small dissections under the
microscope and to view live specimen , compound microscope- used to visualise things that are
too small to be seen via the naked eye.
7. Maximum magnification: Compound microscope- up to 1000x ; Dissecting microscope- up to
70x
4. Image dimension : -.
Chordin, Tolloid and Sizzled all play important roles in BMP signal r.pdf
Chordin, Tolloid and Sizzled all play important roles in BMP signal regulation. Discuss Name
the three embryonic germ layers and briefly discuss how the BMP-Chordin axis determines the
fate of one of these germ layers
Solution
Ques-1: In Xenopus embryos, the cell differentiation of ectodermal and mesodermal layers are
mainly through the dorso- ventral axis and this differentiation is determined by the bone
morphogenetic proteins (BMPs) where cells are mainly exposed in the excellylar region.
Therefore, chordin activity (chondrin and Noggin are released by Spearmann organizer) has
mainly increased and tolloid family members can control these chondrin activity to promote
BMPs in generating organ systems such as blood or neural tubes. Sizzeled and chonrin activities
are mainly according to BMP gradient during gastrulation of embryonic development in xenopus
Answer: Ques-2:
Three embryonic layers: ectoderm, mesoderm and endoderm
The BMP-chondrin axis is going to determine the fate of formation of ectoderm or mesoderm
organ formation for example, inhibition of BMP is leading to formation of neural tube from
mesoderm instead of blood. Therefore, the factors such as Noggin, chondrin are going to be
regulated by these BMP factors during embryonic development.
Chills are used in casting where the part is likely to form a cavity.pdf
Chills are used in casting where the part is likely to form a cavity.They are used in thicker
regions to increase the solidification rate.
A. False
B. True
Solution
TRUE
To maximize the heat tranfer rate a metalic object is provided called CHILL. Chill is inserted
into the cavity created due to removal of pattern and inserted in moulding sand.
By changing the direction of the chill the direction of solidification also changes.
Chill is a metalic object which is conductive so heat transfer rate is high compare to moulding
sand..
A drug that disrupts tubulin polymerzation is applied to some cell.pdf
A drug that disrupts tubulin polymerzation is applied to some cells. What specific part of the cell
cycle will be disrupted?
A drug that disrupts tubulin polymerzation is applied to some cells. What specific part of the cell
cycle will be disrupted?
Solution
Microtubule assembly .... anaphase ... as chromosomes pass along microtubules towards poles of
new dividing cells ....and if micotubule disassembly occurs they cannot move also cargo cannot
move in the cells from one location to other location hence affecting the cells overall.
At the second metaphase of meiosis Chromosomes have single chromatid.pdf
At the second metaphase of meiosis Chromosomes have single chromatids and align in
homologous pairs. Chromosomes have single chromatids and do not align in homologous pairs.
Chromosomes have two chromatids and align in homologous pairs. Chromosomes have two
chromatids and do not align in homologous pairs. Chromosomes have two chromatids and are
separating to opposite poles of the cell. Incomplete dominance at a single locus always results
from the mutant protein having partial function results in a self-crossed population with identical
phenotypic and genotypic ratios cannot be distinguished from epistasis can generate a true
breeding intermediate phenotype gives the same genetic ratios as 2 unlinked genes each showing
complete dominance
Solution
1. The correct option is e. In the second metaphase of meiosis, the chromosomes have two
chromatids and are separating to opposite poles of the cell which is very similar to mitosis.
2. The correct option is d. This is because in incomplete dominance both the alleles are unable to
express themselves completely. Thus resulting in an F1 hybrid with an intermediate phenotype of
the two parental phenotype..
More from arracollection (20)
On April 18, 1906, an earthquake killed over 3,000 people when it hi.pdf
On April 18, 1906, an earthquake killed over 3,000 people when it hi.pdf
On the planet of Caracas, in the Stellar Solorais Ka Chunk Galaxy, th.pdf
On the planet of Caracas, in the Stellar Solorais Ka Chunk Galaxy, th.pdf
Muv is homozygous You have a C. elegans worm with the following geno.pdf
Muv is homozygous You have a C. elegans worm with the following geno.pdf
Material Science (Solidification)What is the solute atoms concent.pdf
Material Science (Solidification)What is the solute atoms concent.pdf
Let P[x] denote the vector space of all polynomials. Let E be the set.pdf
Let P[x] denote the vector space of all polynomials. Let E be the set.pdf
Investment in Note ReceivableSuppliesPrepaid RentBuildingsAc.pdf
Investment in Note ReceivableSuppliesPrepaid RentBuildingsAc.pdf
In a tube containing 1 ml of a 15 dilution of A, and 4 ml of a 110.pdf
In a tube containing 1 ml of a 15 dilution of A, and 4 ml of a 110.pdf
Implement a function called getElements() that takes in two lists. T.pdf
Implement a function called getElements() that takes in two lists. T.pdf
gnmenttakeAssignmentMaindoinvoker assignmentstakeAssignmernt Dr. L. .pdf
gnmenttakeAssignmentMaindoinvoker assignmentstakeAssignmernt Dr. L. .pdf
Every cell in our bodies expresses the same genes. True or False.pdf
Every cell in our bodies expresses the same genes. True or False.pdf
Describe the partition of Z resulting from the equivalence relati.pdf
Describe the partition of Z resulting from the equivalence relati.pdf
describe what is meant by Rh factor when typing blood.Solution.pdf
describe what is meant by Rh factor when typing blood.Solution.pdf
Describe the causes, symptoms, and treatment of conjunctivitisSo.pdf
Describe the causes, symptoms, and treatment of conjunctivitisSo.pdf
Discuss the relationship between gap rule gene mutations, pair-rule .pdf
Discuss the relationship between gap rule gene mutations, pair-rule .pdf
Create a directory your virtual machine. Within that directory creat.pdf
Create a directory your virtual machine. Within that directory creat.pdf
Compare between the two light microscope SolutionFeature1. .pdf
Compare between the two light microscope SolutionFeature1. .pdf
Chordin, Tolloid and Sizzled all play important roles in BMP signal r.pdf
Chordin, Tolloid and Sizzled all play important roles in BMP signal r.pdf
Chills are used in casting where the part is likely to form a cavity.pdf
Chills are used in casting where the part is likely to form a cavity.pdf
A drug that disrupts tubulin polymerzation is applied to some cell.pdf
A drug that disrupts tubulin polymerzation is applied to some cell.pdf
At the second metaphase of meiosis Chromosomes have single chromatid.pdf
At the second metaphase of meiosis Chromosomes have single chromatid.pdf
Recently uploaded
Wound healing PPT
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
Walmart Business+ and Spark Good for Nonprofits.pdf
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
Solutons Maths Escape Room Spatial .pptx
Solutions of Puzzles of Mathematics Escape Room Game in Spatial.io
Temple of Asclepius in Thrace. Excavation results
The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
clinical examination of hip joint (1).pdf
described clinical examination all orthopeadic conditions .
Main Java[All of the Base Concepts}.docx
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
Physical pharmaceutics notes for B.pharm students
How to deliver Powerpoint Presentations.pptx
"How to make and deliver dynamic presentations by making it more interactive to captivate your audience attention"
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
-------------------------------------------------------------------------------
Find out more about ISO training and certification services
Training: ISO/IEC 27001 Information Security Management System - EN | PECB
ISO/IEC 42001 Artificial Intelligence Management System - EN | PECB
General Data Protection Regulation (GDPR) - Training Courses - EN | PECB
Webinars: https://pecb.com/webinars
Article: https://pecb.com/article
-------------------------------------------------------------------------------
For more information about PECB:
Website: https://pecb.com/
LinkedIn: https://www.linkedin.com/company/pecb/
Facebook: https://www.facebook.com/PECBInternational/
Slideshare: http://www.slideshare.net/PECBCERTIFICATION
Constructing Your Course Container for Effective Communication
Communicating effectively and consistently with students can help them feel at ease during their learning experience and provide the instructor with a communication trail to track the course's progress. This workshop will take you through constructing an engaging course container to facilitate effective communication.
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...Nguyen Thanh Tu Collection
https://app.box.com/s/qhtvq32h4ybf9t49ku85x0n3xl4jhr15Recently uploaded (20)
Walmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdf
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
IGCSE Biology Chapter 14- Reproduction in Plants.pdf
IGCSE Biology Chapter 14- Reproduction in Plants.pdf
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
B. Ed Syllabus for babasaheb ambedkar education university.pdf
B. Ed Syllabus for babasaheb ambedkar education university.pdf
Constructing Your Course Container for Effective Communication
Constructing Your Course Container for Effective Communication
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
What was Galois’ contribution to the theory of algebraic equations a.pdf
- 1. What was Galois’ contribution to the theory of algebraic equations and what were some of the reasons why it was so remarkable? Solution Tangent equation passing through (1,1) is Galois achieved proof by looking at whether or not the “permutation group” of its roots (now known as its Galois group) had a certain structure. He was the first to use the term “group” in its modern mathematical sense of a group of permutations (foreshadowing the modern field of group theory), and his fertile approach, now known as Galois theory, was adapted by later mathematicians to many other fields of mathematics besides the theory of equations. He studied Legendre's Géométrie and the treatises of Lagrange. In April 1829 Galois had his first mathematics paper published on continued fractions in the Annales de mathématiques. On 25 May and 1 June he submitted articles on the algebraic solution of equations to the Académie des Sciences. Cauchy was appointed as referee of Galois' paper. Liouville who, in September 1843, announced to the Academy that he had found in Galois' papers a concise solution ...as correct as it is deep of this lovely problem: Given an irreducible equation of prime degree, decide whether or not it is soluble by radicals. Liouville published these papers of Galois in his Journal in 1846. The theory that Galois outlined in these papers is now called Galois theory. Tangent equation passing through (1,1) is Galois achieved proof by looking at whether or not the “permutation group” of its roots (now known as its Galois group) had a certain structure. He was the first to use the term “group” in its modern mathematical sense of a group of permutations (foreshadowing the modern field of group theory), and his fertile approach, now known as Galois theory, was adapted by later mathematicians to many other fields of mathematics besides the theory of equations. He studied Legendre's Géométrie and the treatises of Lagrange. In April 1829 Galois had his first mathematics paper published on continued fractions in the Annales de mathématiques. On 25 May and 1 June he submitted articles on the algebraic solution of equations to the Académie des Sciences. Cauchy was appointed as referee of Galois' paper. Liouville who, in September 1843, announced to the Academy that he had found in Galois' papers a concise solution ...as correct as it is deep of this lovely problem: Given an irreducible equation of prime degree, decide whether or not it is soluble by radicals.
- 2. Liouville published these papers of Galois in his Journal in 1846. The theory that Galois outlined in these papers is now called Galois theory. Galois achieved proof by looking at whether or not the “permutation group” of its roots (now known as its Galois group) had a certain structure. He was the first to use the term “group” in its modern mathematical sense of a group of permutations (foreshadowing the modern field of group theory), and his fertile approach, now known as Galois theory, was adapted by later mathematicians to many other fields of mathematics besides the theory of equations. He studied Legendre's Géométrie and the treatises of Lagrange. In April 1829 Galois had his first mathematics paper published on continued fractions in the Annales de mathématiques. On 25 May and 1 June he submitted articles on the algebraic solution of equations to the Académie des Sciences. Cauchy was appointed as referee of Galois' paper. Liouville who, in September 1843, announced to the Academy that he had found in Galois' papers a concise solution ...as correct as it is deep of this lovely problem: Given an irreducible equation of prime degree, decide whether or not it is soluble by radicals. Liouville published these papers of Galois in his Journal in 1846. The theory that Galois outlined in these papers is now called Galois theory.