Sets are collections of elements denoted with capital letters and curly brackets. The document defines basic set operations like union, intersection, and subset. It then discusses linear relations and how to graph a line using a table of values with x and y coordinates. Finally, it provides a detailed overview of the history and branches of mathematical analysis, including real analysis, complex analysis, functional analysis, differential equations, measure theory, and numerical analysis.
Linear Algebra may be defined as the form of algebra in which there is a study of different kinds of solutions which are related to linear equations. In order to explain the Linear Algebra, it is important to explain that the title consists of two different terms. The very first term which is important to be considered in the same, is Linear. Linear may be defined as something which is straight. Linear equations can be used for the calculation of the equation in a xy plane where the straight lines has been defined. In addition to this, linear equations can be used to define something which is straight in a three dimensional perspective. Another view of linear equations may be defined as flatness which recognizes the set of points which can be used for giving the description related to the equations which are in a very simple forms. These are the equations which involves the addition and multiplication.
The purpose of this communication is to generalize the theorem of Pythagoras using the corresponding area formulas for different geometric figures used in experience; the aim is to look at the possibility of Demosthenes this relationship using different geometric figures squared, showing how calculators can be used to explore the situation and give account of the difficulties that students with geometric concepts.
contains adequate info. about group theory...some contents are not seen coz...thr r images on top of the info.... wud suggest to download and see the ppt on slideshow...content is good and adequate..!!
is used. Mathematics is applied in day to day life, so we can now review the concepts of Algebra and its uses in daily life. Here in our work we have made a small split up of items in a bag while shopping. Basic Algebra is where we finally put the algebra in pre-algebra. The concepts taught here will be used in every math class you take from here on. Well introduce you to some exciting stuff like drawing graphs and solving complicated equations. Since we are learning Algebra, Geometry in the school days. But the is a real life application of Algebra which is used in Geometry. Now a days the social media has improved a lot. We cant able to solve those figured puzzles, hence we can solve them by using algebraic equations. S. Ambika | R. Mythrae | S. Saranya | K. Selvanayaki "Algebra in Real Life" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-2 , February 2019, URL: https://www.ijtsrd.com/papers/ijtsrd21517.pdf
Paper URL: https://www.ijtsrd.com/mathemetics/algebra/21517/algebra-in-real-life/s-ambika
ON THE CATEGORY OF ORDERED TOPOLOGICAL MODULES OPTIMIZATION AND LAGRANGE’S PR...IJESM JOURNAL
A category is an algebraic structure made up of a collection of objects linked together by morphisms. As a foundation of mathematics, categories were created as a way of relating algebraic structures and systems of topological spaces In this paper we define a derivative using cones in the category of topological modules and use the Lagrange’s principle to obtain optimization results in the category.
Cocentroidal and Isogonal Structures and Their Matricinal Forms, Procedures a...inventionjournals
The vector space of all matrices of the same order on a set of real numbers with a non-negative metric defined on it satisfying certain axioms, we call it a JS metric space. This space can be regarded as the infinite union of matrices possessing a special property that there exist infinite structures having the same (virtual) point-centroid. In this paper we introduce the notion of cocentroidal matrices to a given matrix (Root Matrix) in JS metric space wherein the metric is the Euclidean metric measuring the distance between two matrices to be the distance between their centroids. We describe mathematical routines that we envisaged and then theoretically verified for its applicability in a system that is under rotational motion about a point-centroid, and various cases in physics. We have sounded the same concept by considering necessary graphs drawn on the basis of mathematical equations as an additional feature of this article. Isogonality of different cocentroidal structures is the conceptual origin of one of the main concepts, necessitating the notion of convergence in terms of determinant values of a system of cocentroidal matrices.
Linear Algebra may be defined as the form of algebra in which there is a study of different kinds of solutions which are related to linear equations. In order to explain the Linear Algebra, it is important to explain that the title consists of two different terms. The very first term which is important to be considered in the same, is Linear. Linear may be defined as something which is straight. Linear equations can be used for the calculation of the equation in a xy plane where the straight lines has been defined. In addition to this, linear equations can be used to define something which is straight in a three dimensional perspective. Another view of linear equations may be defined as flatness which recognizes the set of points which can be used for giving the description related to the equations which are in a very simple forms. These are the equations which involves the addition and multiplication.
The purpose of this communication is to generalize the theorem of Pythagoras using the corresponding area formulas for different geometric figures used in experience; the aim is to look at the possibility of Demosthenes this relationship using different geometric figures squared, showing how calculators can be used to explore the situation and give account of the difficulties that students with geometric concepts.
contains adequate info. about group theory...some contents are not seen coz...thr r images on top of the info.... wud suggest to download and see the ppt on slideshow...content is good and adequate..!!
is used. Mathematics is applied in day to day life, so we can now review the concepts of Algebra and its uses in daily life. Here in our work we have made a small split up of items in a bag while shopping. Basic Algebra is where we finally put the algebra in pre-algebra. The concepts taught here will be used in every math class you take from here on. Well introduce you to some exciting stuff like drawing graphs and solving complicated equations. Since we are learning Algebra, Geometry in the school days. But the is a real life application of Algebra which is used in Geometry. Now a days the social media has improved a lot. We cant able to solve those figured puzzles, hence we can solve them by using algebraic equations. S. Ambika | R. Mythrae | S. Saranya | K. Selvanayaki "Algebra in Real Life" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-2 , February 2019, URL: https://www.ijtsrd.com/papers/ijtsrd21517.pdf
Paper URL: https://www.ijtsrd.com/mathemetics/algebra/21517/algebra-in-real-life/s-ambika
ON THE CATEGORY OF ORDERED TOPOLOGICAL MODULES OPTIMIZATION AND LAGRANGE’S PR...IJESM JOURNAL
A category is an algebraic structure made up of a collection of objects linked together by morphisms. As a foundation of mathematics, categories were created as a way of relating algebraic structures and systems of topological spaces In this paper we define a derivative using cones in the category of topological modules and use the Lagrange’s principle to obtain optimization results in the category.
Cocentroidal and Isogonal Structures and Their Matricinal Forms, Procedures a...inventionjournals
The vector space of all matrices of the same order on a set of real numbers with a non-negative metric defined on it satisfying certain axioms, we call it a JS metric space. This space can be regarded as the infinite union of matrices possessing a special property that there exist infinite structures having the same (virtual) point-centroid. In this paper we introduce the notion of cocentroidal matrices to a given matrix (Root Matrix) in JS metric space wherein the metric is the Euclidean metric measuring the distance between two matrices to be the distance between their centroids. We describe mathematical routines that we envisaged and then theoretically verified for its applicability in a system that is under rotational motion about a point-centroid, and various cases in physics. We have sounded the same concept by considering necessary graphs drawn on the basis of mathematical equations as an additional feature of this article. Isogonality of different cocentroidal structures is the conceptual origin of one of the main concepts, necessitating the notion of convergence in terms of determinant values of a system of cocentroidal matrices.
Eucluidian and Non eucluidian space in Tensor analysis.Non Euclidian space AJAY CHETRI
Eucluidian and Non eucluidian space in Tensor analysis.
Introduction to type of system in sphere.Benefit and advantage of using Tensor analysis.EUCLID’S GEOMETRY
VS.
NON-EUCLIDEAN GEOMETRY
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Thesis Statement for students diagnonsed withADHD.ppt
My Report Profile in Math Major 10,11,12
1. Math Major 10
(Set Difference)
Sets are denoted by Capital letters
The number of elements in Set A is 4
Sets use “curly” brackets
3 is an element of A
3A
7 is not an element of A
In ascending order
A 7
This symbol means "is a subset of"
A B this is read "A is a subset of B".
A = {1, 2, 3} B = {1, 2, 3, 4, 5}
A = {1, 2, 3, 4, 5} B = {1, 3, 5, 7, 9}
A B = {1, 2, 3, 4, 5, 7, 9} Remember we do not list elements more than once.
This is the union symbol. It means the set that consists of all elements of set A and all elements
of set B.
A B = {1, 3, 5}
This is the intersect symbol. It means the set containing all elements that are in both A and B.
Math Major 11
(Linear Relations)
Every line is made up of an infinite number of coordinates (x, y). When the
coordinates are close enough together they look like a line!
Before we can graph a line, we must be able to determine the coordinates that make up
that line.
We can do this by using a table of values
2. Let’s look at it a bit further…
• How many points do you need in order to graph a line?
• Why is it a good idea to have more than the minimum number of points?
• From your graph, determine 2 more points on the line. By using the equation, PROVE
they are on the line.
Using a Table of Values
Rectangle
Number, n
Perimeter, p (cm)
x y
-1 -1
0 0
1 1
2 2
3 3
y 2x 2
3. 1
2
3
4
24Pn
Math Major 12
(Mathematical Analysis History)
• Mathematical analysis is a branch of mathematics that includes the theories of
differentiation, integration, measure, limits, infinite series, and analytic functions. These
theories are usually studied in the context of real and complex numbers and functions.
Analysis evolved from calculus, which involves the elementary concepts and techniques
of analysis. Analysis may be distinguished from geometry; however, it can be applied to
any space of mathematical objects that has a definition of nearness (a topological space)
or specific distances between objects (a metric space).
History of Mathematical analysis
• Mathematical analysis formally developed in the 17th century during the Scientific
Revolution, but many of its ideas can be traced back to earlier mathematicians. Early
results in analysis were implicitly present in the early days of ancient Greek
mathematics. For instance, an infinite geometric sum is implicit in Zeno's paradox of the
dichotomy. Later, Greek mathematicians such as Eudoxus and Archimedes made more
explicit, but informal, use of the concepts of limits and convergence when they used the
method of exhaustion to compute the area and volume of regions and solids. The explicit
use of infinitesimals appears in Archimedes' The Method of Mechanical Theorems, a
work rediscovered in the 20th century. In Asia, the Chinese mathematician Liu Hui used
the method of exhaustion in the 3rd century AD to find the area of a circle.Zu Chongzhi
established a method that would later be called Cavalieri's principle to find the volume of
a sphere in the 5th century. The Indian mathematician Bhāskara II gave examples of the
derivative and used what is now known as Rolle's theorem in the 12th century.
In mathematics, a metric space is a set where a notion of distance (called a metric)
between elements of the set is defined.
4. • Much of analysis happens in some metric space; the most commonly used are the real
line, the complex plane, Euclidean space, other vector spaces, and the integers. Examples
of analysis without a metric include measure theory (which describes size rather than
distance) and functional analysis (which studies topological vector spaces that need not
have any sense of distance).
• Formally, A metric space is an ordered pair (M,d) where M is a set and d is a metric on
M, i.e., a function
• d colon M times M right arrow mathbb{R}
• such that for any x, y, z in M, the following holds:
• d(x,y) ge 0 (non-negative),
• d(x,y) = 0, iff x = y, (identity of indiscernible),
• d(x,y) = d(y,x), (symmetry) and
• d(x,z) le d(x,y) + d(y,z) (triangle inequality) .metric spaces
Real analysis
• Real analysis (traditionally, the theory of functions of a real variable) is a branch of
mathematical analysis dealing with the real numbers and real-valued functions of a real
variable. In particular, it deals with the analytic properties of real functions and
sequences, including convergence and limits of sequences of real numbers, the calculus
of the real numbers, and continuity, smoothness and related properties of real-valued
functions.
Complex analysis
• Complex analysis is particularly concerned with the analytic functions of complex
variables (or, more generally, meromorphic functions). Because the separate real and
imaginary parts of any analytic function must satisfy Laplace's equation, complex
analysis is widely applicable to two-dimensional problems in physics.
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by
the study of vector spaces endowed with some kind of limit-related structure (e.g. inner
product, norm, topology, etc.) and the linear operators acting upon these spaces and
respecting these structures in a suitable sense.
Differential equations
• A differential equation is a mathematical equation for an unknown function of one or
several variables that relates the values of the function itself and its derivatives of various
orders prominent role in engineering, physics, economics, biology, and other disciplines.
5. Measure theory
A measure on a set is a systematic way to assign a number to each suitable subset of that set,
intuitively interpreted as its size.[20] In this sense, a measure is a generalization of the concepts
of length, area, and volume. A particularly important example is the Lebesgue measure on a
Euclidean space, which assigns the conventional length, area, and volume of Euclidean
geometry to suitable subsets of the n-dimensional Euclidean space mathbb{R}^n. For instance,
the Lebesgue measure of the interval left[0, 1right] in the real numbers is its length in the
everyday sense of the word – specifically,
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to
general symbolic manipulations) for the problems of mathematical analysis (as distinguished
from discrete mathematics).