1. The document discusses simulation as a technique used to study and analyze the behavior of actual or theoretical systems by creating computer-based models. It is used when directly studying real systems is not possible or practical.
2. Simulation models can be static or dynamic, discrete or continuous, and deterministic or stochastic. They are composed of mathematical and logical relationships that are analyzed using numerical rather than analytical methods.
3. Simulation has many applications including manufacturing and materials handling systems. It allows testing designs and systems virtually before implementing them in the real world. It provides insights into how systems work and which variables most impact performance.
This document provides an overview of modeling and simulation. It defines modeling as representing a system to enable predicting the effects of changes. Simulation involves running experiments on a model. The key steps in modeling and simulation projects are: 1) identifying the problem, 2) formulating and developing the model, 3) validating the model, 4) designing simulation experiments, 5) performing simulations, and 6) analyzing and presenting results. Modeling and simulation can be used for a variety of purposes including education, design evaluation, forecasting, and risk assessment.
This document provides an overview of a project report on simulating a single server queuing problem. The report includes an introduction to operations research, simulation, and the queuing problem. It discusses the research methodology, which involves defining the problem, developing a simulation model, validating the model, analyzing the data, and presenting findings and recommendations. The goal is to use simulation to provide optimal solutions to the queuing problem under study.
Modeling, analysis, and control of dynamic systemsJACKSON SIMOES
This document is the preface to the second edition of the textbook "Modeling, Analysis, and Control of Dynamic Systems" by William J. Palm III. It discusses the structure and content of the textbook, which provides an introduction to modeling, analysis, and control of dynamic systems. The textbook covers both classical and modern approaches to systems and control theory and includes examples from various engineering domains. It also introduces digital analysis and control without using the z-transform.
This document provides an introduction to system dynamics. It defines a system as a collection of interacting components with defined boundaries and inputs/outputs. Dynamic systems change over time even if inputs are constant, while static systems only depend on current inputs. Common dynamic systems include mechanical, electrical, thermal, and fluid systems. System dynamics involves defining a system, creating a mathematical model, simulating the model's behavior, and making recommendations. Models allow studying systems without experimenting on real systems. Simulation uses models to compute how systems react to inputs over time.
The document compares techniques for handling incomplete data when using decision trees. It investigates the robustness and accuracy of seven popular techniques when applied to different proportions, patterns and mechanisms of missing data in 21 datasets. The techniques include listwise deletion, decision tree single imputation, expectation maximization single imputation, mean/mode single imputation, and multiple imputation. The results suggest important differences between the techniques, with multiple imputation and decision tree single imputation generally performing better than the others. The choice of technique depends on factors like the amount and nature of the missing data.
-What is Sensitivity Analysis in Project Risk Management?
-Example on Sensitivity Analysis….
-Types of Sensitivity Analysis……
-Advantages & Disadvantages
This document provides an introduction to simulation. It defines simulation as modeling a real system and experimenting with that model to understand the system's behavior or evaluate different operational strategies. The document discusses how simulation allows modeling complex systems in detail and making predictions. It provides examples of simulation applications in computer systems, manufacturing, business, and government for purposes like hardware/software testing, production planning, financial analysis, and military planning. Advantages of simulation are that it can study existing systems without disruption and test proposed systems beforehand. Drawbacks include difficulty interpreting results and high time/costs compared to analytical methods.
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Computer simulation is a technique used in many fields to model real-world systems and processes. It involves developing a mathematical model of a system and representing its dynamic behavior on a computer. The interaction of variables in the simulation can create new situations and rules that evolve over time, similar to the real system. Computer simulations are useful for studying systems that cannot be easily tested in reality and allow observers to measure how changing individual components affects the overall system. They are applied in diverse areas like science, engineering, economics, and education.
This document discusses systems analysis and simulation. It defines a system as a collection of elements that work together to achieve a goal. There are two main types of systems: discrete systems where state variables change at separate points in time, and continuous systems where state variables change continuously over time. A model represents a system in order to study it, as experimenting directly with the real system may not be possible or wise. Simulation models can be static or dynamic, deterministic or stochastic, discrete or continuous. Discrete-event simulation specifically models systems as they progress through time as a series of instantaneous events.
Software engineering ,system modeing >>Abu ul hassan sahadviAbuulHassan2
System modeling involves developing abstract models of a system from different perspectives to help understand its functionality. Common modeling techniques include use case diagrams, which show interactions between a system and external actors, and class diagrams, which define the system's classes and their relationships. Behavioral models depict how a system responds to stimuli over time through states and transitions. System modeling aids communication and ensures requirements and design match customer needs.
CB-SEM assumes normally distributed data which is rarely the case in social sciences research, while PLS-SEM is non-parametric and works well with non-normal distributions. The example showed that CB-SEM resulted in losing many indicator variables to achieve good model fit, whereas PLS-SEM retained more indicators to support both measuring and developing the structural theory. PLS-SEM is preferable when data is non-normal, though CB-SEM can work if the theory and measurement are well established.
This Lecture/Presentation About Means-End Analysis (MEA), and is for the students of BS Computer Science, there may be mistakes and errors, therefore suggestions and corrections are warmly welcome.
Models of Operations Research is addressedSundar B N
Introduction, Meaning and Characteristics of Operations Research is addressed.
MODELS IN OPERATIONS RESEARCH, Classification of Models, degree of abstraction, Purpose Models, Predictive models, Descriptive models, Prescriptive models, Mathematic / Symbolic models, Models by nature of an environment, Models by the extent of generality, Models by Behaviour, Models by Method of Solution, Models by Method of Solution, Static and dynamic models, Iconic models Iconic models, Analogue models.
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Multilevel System Analysis - An Introduction to Systems Thinking David Alman
This document provides an introduction to Multilevel System Analysis (MSA) as a systems thinking approach. MSA uses two keys - perspective levels and cause categories - to analyze problem situations. There are three perspective levels: referential, governance, and transactional. These levels are nested within each other and can be examined separately or together. Cause categories are direct, involving observable causes, or indirect, involving less visible interacting factors. MSA examines problem situations using these two keys to identify root causes and determine the best systems thinking methodology to address the issues.
System modeling and simulation involves creating simplified representations of real-world systems to understand and evaluate their behavior over time. A system is composed of interconnected parts designed to achieve specific objectives. A model abstracts and simplifies a system for analysis. Simulation executes a model over time to observe how a system operates. It allows experimenting with systems that may be too expensive, dangerous or complex to study directly. Simulation has many uses including analyzing systems before implementation, optimizing designs, training, and evaluating "what-if" scenarios. Key areas where simulation is applied include manufacturing, business, healthcare, transportation and the military.
Real World Talent Insights From Computer SimulationsAndrea Kropp
Teaching Talent Analytics executives how to use computer simulations to complement the predictive modeling work in HR. Simulations allow you to examine multiple scenarios and examine their end states and consequences before taking action.
There are three main types of models: physical models, mathematical models, and process models. Physical models are tangible representations of real-world objects or systems used for experimentation, analysis, or communicating ideas. Mathematical models represent systems using mathematical equations to describe, analyze, or predict behavior. Process models illustrate the sequence of activities and tasks involved in a particular process.
This document is a report on computer simulation created by a group consisting of 3 students. It discusses the use of Biosawit simulation and STELLA software to simulate a system involving the relationship between palm, rat, and owl populations. The report includes an introduction to simulation, descriptions of the STELLA programming language and how it was used, aims of the simulation, when simulators are used, applications of simulation, and advantages and disadvantages of computer simulation.
This document discusses the use of computer simulations in education. It provides examples of how simulations can be used to model predator-prey relationships and increase student motivation. Simulations allow students to explore concepts and see the effects of changes. They also guide learning and reflection. While simulations have advantages like interactivity, some disadvantages are a lack of emotional awareness and inability to adapt to different students. Overall, computer simulations are seen as a useful tool to help teach difficult concepts when used alongside teacher guidance.
This document discusses modelling and simulation using the STELLA software. It provides an example of modelling predator-prey dynamics between snowshoe hares and lynx. The document defines modelling and simulation, discusses their uses in education, and outlines the Lotka-Volterra predator-prey model. It then applies this model in STELLA to simulate snowshoe hare and lynx populations over time under different levels of lynx predation.
Modeling and simulation is the use of models as a basis for simulations to develop data utilized for managerial or technical decision making. In the computer application of modeling and simulation a computer is used to build a mathematical model which contains key parameters of the physical model.
Computer simulations are computer programs that model real-world or theoretical systems by including dynamic variables. They allow experimentation by changing inputs to observe how the outputs are affected. Simulations have various uses including research, design, analysis, training, education, and entertainment. They provide safety, cost savings, and allow experiments that would be impossible in real life due to factors like time and location. Simulations are interactive models that can help enhance learning when used alongside traditional instruction.
Computer simulations are computer programs that model real-world or theoretical systems by including dynamic variables. They allow experimentation by changing inputs to observe how the outputs are affected. Simulations have various uses including research, design, analysis, training, education, and entertainment. They provide interactive learning experiences and have advantages over real experiments such as safety, cost-effectiveness, and the ability to manipulate time and place.
Simulation and Modelling Reading Notes.pptxDanMuendo1
This document discusses simulation and modeling. It defines simulation as imitating real-life situations using computer models. Models represent systems using mathematical relationships. Simulation allows experimenting with models to understand system behavior under different conditions without changing the real system. The document outlines the modeling and simulation process and provides examples of applications in areas like business planning, drug development, and traffic analysis.
The series of presentations contains the information about "Management Information System" subject of SEIT for University of Pune.
Subject Teacher: Tushar B Kute (Sandip Institute of Technology and Research Centre, Nashik)
http://www.tusharkute.com
Machine learning(ML) is the scientific study of algorithms and statistical models that computer systems used to progressively improve their performance on a specific task. Machine learning algorithms build a mathematical model of sample data, known as “Training Data", in order to make predictions or decisions without being explicitly programmed to perform the task. Machine learning algorithms are used in the applications of email filtering, detection of network intruders and computer vision, where it is infeasible to develop an algorithm of specific instructions for performing the task. Machine learning is closely related to computational statistics, which focuses on making predictions using computers. The study of mathematical optimization delivers methods, theory and application domains to the field of machine learning. Data mining is a field of study within machine learning and focuses on exploratory data analysis through unsupervised learning. In its application across business problems, Machine learning is the study of computer systems that learn from data and experience. It is applied in an incredibly wide variety of application areas, from medicine to advertising, from military to pedestrian. Any area in which you need to make sense of data is a potential customer of machine learning.
This document provides an overview of a course on computational modelling for the social sciences. It introduces computational modelling as a methodology that uses models to study and solve complex problems in social phenomena. It discusses different types of models like conceptual, mathematical, physical and computational models. It explains key computational modelling approaches used in social sciences like social simulation, agent-based models, social network analysis and management information systems. The document outlines the course structure and provides contact and software details.
This chapter introduces discrete-event simulation and outlines the key steps in a simulation study. It defines simulation as imitating the operation of a real-world process over time through a conceptual model. Simulation allows experimenting with "what if" scenarios to analyze the potential effects of changes. The chapter describes when simulation is an appropriate tool, its advantages and disadvantages, common application areas, and components of systems and models. It distinguishes between discrete and continuous systems and events, and outlines the development process for discrete-event simulation models.
This chapter introduces discrete-event simulation and outlines the key steps in a simulation study. It defines simulation as imitating the operation of a real-world process over time through a conceptual model. Simulation allows experimenting with "what if" scenarios to analyze the potential effects of changes. The chapter describes when simulation is an appropriate tool, its advantages and disadvantages, common application areas, and components of systems and models. It distinguishes between discrete and continuous systems and events. The final sections outline the development of a discrete-event simulation model and the steps of verifying and validating the model.
This document discusses simulation and modelling software called STELLA. It provides an overview of STELLA's features and how it can be used to simulate systems over time. It also describes the benefits and limitations of using simulations for education. Simulations can increase understanding, provide hands-on learning, and test designs without physical implementation. However, they may oversimplify details and require significant computing resources for complex simulations. Overall, simulations are a useful tool that can enhance the teaching and learning process.
Not sure how to do this case analysis please help me do it!1.Are t.pdfamitbagga0808
Not sure how to do this case analysis please help me do it!
1.Are the regions similar?
2.What would be a good forecasting method to use?
3.Are there more advanced methods that might be considered?
Here is the data
https://docs.google.com/spreadsheets/d/1LYZHLx9f0Av9FJ6NLfULMU61cZPV3voqrVzbJNfV
jKk/edit?usp=sharing
Solution
Most people view the world as consisting of a large number of alternatives. Futures research
evolved as a way of examining the alternative futures and identifying the most probable.
Forecasting is designed to help decision making and planning in the present.
Forecasts empower people because their use implies that we can modify variables now to alter
(or be prepared for) the future. A prediction is an invitation to introduce change into a system.
There are several assumptions about forecasting:
1. There is no way to state what the future will be with complete certainty. Regardless of the
methods that we use there will always be an element of uncertainty until the forecast horizon has
come to pass.
2. There will always be blind spots in forecasts. We cannot, for example, forecast completely
new technologies for which there are no existing paradigms.
3. Providing forecasts to policy-makers will help them formulate social policy. The new social
policy, in turn, will affect the future, thus changing the accuracy of the forecast.
Many scholars have proposed a variety of ways to categorize forecasting methodologies. The
following classification is a modification of the schema developed by Gordon over two decades
ago:
Genius forecasting - This method is based on a combination of intuition, insight, and luck.
Psychics and crystal ball readers are the most extreme case of genius forecasting. Their forecasts
are based exclusively on intuition. Science fiction writers have sometimes described new
technologies with uncanny accuracy.
There are many examples where men and women have been remarkable successful at predicting
the future. There are also many examples of wrong forecasts. The weakness in genius forecasting
is that its impossible to recognize a good forecast until the forecast has come to pass.
Some psychic individuals are capable of producing consistently accurate forecasts. Mainstream
science generally ignores this fact because the implications are simply to difficult to accept. Our
current understanding of reality is not adequate to explain this phenomena.
Trend extrapolation - These methods examine trends and cycles in historical data, and then use
mathematical techniques to extrapolate to the future. The assumption of all these techniques is
that the forces responsible for creating the past, will continue to operate in the future. This is
often a valid assumption when forecasting short term horizons, but it falls short when creating
medium and long term forecasts. The further out we attempt to forecast, the less certain we
become of the forecast.
The stability of the environment is the key factor in determining whether tren.
A Comparison of Traditional Simulation and MSAL (6-3-2015)Bob Garrett
This document compares traditional simulation approaches to the Model-Simulation-Analysis-Looping (MSAL) approach. It provides background information on system modeling and simulation basics, including conceptual models, simulation programs, sensitivity analysis, Monte Carlo methods, and simulation optimization. It then discusses risk and uncertainty, modeling systems of systems, and the current state of modeling and simulation in systems engineering. Finally, it introduces the MSAL approach, which uses graphs, analytics, and repeated simulation loops to address the increased complexity and uncertainty in systems of systems compared to traditional approaches. The MSAL approach aims to provide benefits like improved handling of uncertainty and complexity.
This document discusses simulation and the STELLA software package. It provides an introduction to simulation and explains that simulation allows investigation of a system's behavior over time by developing a model. STELLA is introduced as a modeling software that uses diagrams and charts to help users visualize relationships between variables in a system. The document then discusses advantages of simulation such as testing changes without disrupting systems and disadvantages such as potential oversimplification.
The ancient Egyptians used a decimal numerical system represented by hieroglyphs to denote quantities, with single strokes, drawings of tools and plants, and human figures representing the values of 1, 10, 100, 1,000, 10,000, 100,000, and 1,000,000, respectively.
1. The document discusses simulation as a technique used to study and analyze the behavior of systems over time. Simulation involves creating a computer-based model of a real-world system to draw conclusions about how it operates.
2. Simulation can be used for task training, decision-making, scientific research, and predicting the behavior of natural systems. It allows testing alternatives without committing resources.
3. The document provides examples of how simulation can be used to model the operations of cooperative societies and banks to help students better understand commercial mathematics topics.
Lesson Transcript - Surface Area Of a Cubesupriyamahesh
The document describes a lesson on teaching 8th grade students how to calculate the surface area of a cube. It includes:
1) An introduction where the teacher reviews rectangular prisms and squares to build on previous knowledge.
2) A presentation where students examine cube models and determine all sides are equal, defining it as a cube.
3) An activity where students use the surface area formula for a rectangular prism to derive the formula for a cube: Surface Area = 6a2, where a is the length of one side.
4) Practice problems are assigned to reinforce calculating the surface area of cubes using the formula.
There are three main measures of central tendency used to represent data with a single value: mean, median, and mode. The mean is calculated by adding all values and dividing by the total number of values. The median is the middle value when data is arranged from lowest to highest. The mode is the value that occurs most frequently in the data. These measures provide a single number to represent the central or average value for a data set.
There are three main measures of central tendency used to represent data with a single value: mean, median, and mode. The mean is calculated by adding all values and dividing by the total number of values. The median is the middle value when data is arranged from lowest to highest. The mode is the value that occurs most frequently in the data. These measures provide a single number to represent the central or average value for a data set.
There are three main measures of central tendency used to represent data with a single value: mean, median, and mode. The mean is calculated by adding all values and dividing by the total number of values. The median is the middle value when data is arranged from lowest to highest. The mode is the value that occurs most frequently in the data. These measures provide a single number to represent the central or average tendencies of a data set.
Talk at the 1st FPGA Developers' Forum (FDF) meetingMirko Mariotti
Since 2017 we started R&D on framework development for co-designing (HW/SW) computational systems, targeting mainly FPGAs. The main innovation of the project, named BondMachine (BM), is the creation of a new type of architecture, dynamically adapted to the specific problem. The framework contains a set of tools to manipulate the architectures, spanning from the creation to the simulation and the implementation in terms of HDL code. We also developed the support to enable the creation of BMs staring from high-level languages. To this end a compiler allow to build the BM while compiling the code; an assembler transforms fragments of assembly code into BMs and uses them as building blocks for more complex systems.
This talk will provide an overview of the described framework detailing also how it can be used to put Neural Networks and Quantum Computing simulators on FPGAs.
Astro microbiology, exo microbiology,
Space microbiology,
Life in solar system
Extreme conditions in space,
Microbes in space
Tardigrades,
Plant in space,
Future applications
This pdf is about the Eight Millennium Development Goals (MDGs).
For more details visit on YouTube; @SELF-EXPLANATORY; https://www.youtube.com/channel/UCAiarMZDNhe1A3Rnpr_WkzA/videos
Thanks...!
The Black Soldier Fly (Hermetia illucens) is an environmentally beneficial insect known for its impressive ability to decompose organic waste efficiently. Native to the Americas, this fly has gained global attention due to its larvae's ability to convert waste into valuable products. The larvae consume a wide range of organic materials, including food scraps, manure, and agricultural waste, significantly reducing the volume of waste and producing nutrient-rich frass, which can be used as a high-quality organic fertilizer. Additionally, the larvae themselves are rich in proteins and fats, making them an excellent source of animal feed, particularly for poultry, fish, and pigs. The use of Black Soldier Fly larvae in waste management and sustainable farming practices presents an innovative solution to some of the pressing environmental challenges related to waste disposal and food production. This insect not only helps in managing waste but also contributes to the circular economy by transforming waste into valuable resources.
Another Story of Pattern Recognition.
Is Deep Learning the only way?International Computer Vision Summer School (ICVSS) 2016 presentation held in Sicily on 22nd July 2016.
The emergence of heat and humidity too severe for human toleranceSérgio Sacani
Humans’ ability to efficiently shed heat has enabled us to range over every continent, but a wet-bulb temperature
(TW) of 35°C marks our upper physiological limit, and much lower values have serious health and productivity impacts.
Climate models project the first 35°C TW occurrences by the mid-21st century. However, a comprehensive
evaluation of weather station data shows that some coastal subtropical locations have already reported a TW of
35°C and that extreme humid heat overall has more than doubled in frequency since 1979. Recent exceedances of
35°C in global maximum sea surface temperature provide further support for the validity of these dangerously
high TW values. We find the most extreme humid heat is highly localized in both space and time and is correspondingly
substantially underestimated in reanalysis products. Our findings thus underscore the serious challenge posed
by humid heat that is more intense than previously reported and increasingly severe.
1. 1
ON-LINE ASSIGNMENT
SIMULATION
Submitted by,
Supriya.M
Reg No: 13971020
Mathematics optional
K U C T E, Kumarapuram
2. 2
INTRODUCTION
A broad collection of methods used to study and analyze
the behavior and performance of actual or theoretical systems. Simulation
studies are performed, not on the real-world system, but on a (usually
computer-based) model of the system created for the purpose of studying
certain system dynamics and characteristics. The purpose of any model is
to enable its users to draw conclusions about the real system by studying
and analyzing the model. The major reasons for developing a model, as
opposed to analyzing the real system, include economics, unavailability
of a “real” system, and the goal of achieving a deeper understanding of
the relationships between the elements of the system.
Many topics in mathematics that have immediate utility value
can be best introduced using the technique of simulation that is enacting a
real situation in the class. Topics that have commercial concern is an
example.
Simulation can be used in task or situational training areas
in order to allow humans to anticipate certain situations and be able to
react properly; decision-making environments to test and select
alternatives based on some criteria; scientific research contexts to analyze
and interpret data; and understanding and behavior prediction of natural
systems, such as in studies of stellar evolution or atmospheric conditions.
The word “system” refers to a set of elements (objects)
interconnected so as to aid in driving toward a desired goal. This
definition has two connotations: First, a system is made of parts
(elements) that have relationships between them (or processes that link
them together). These relationships or processes can range from relatively
simple to extremely complex. One of the necessary requirements for
creating a “valid” model of a system is to capture, in as much detail as
possible, the nature of these interrelationships. Second, a system
constantly seeks to be improved. Feedback (output) from the system must
be used to measure the performance of the system against its desired goal.
Both of these elements are important in simulation.
With simulation a decision maker can try out
new designs, layouts, software programs, and systems before committing
resources to their acquisition or implementation; test why certain
3. 3
phenomena occur in the operations of the system under consideration;
compress and expand time; gain insight about which variables are most
important to performance and how these variables interact; identify
bottlenecks in material, information, and product flow; better understand
how the system really operates (as opposed to how everyone thinks it
operates); and compare alternatives and reduce the risks of decisions.
Systems can be classified in three major ways.
They may be deterministic or stochastic (depending on the types of
elements that exist in the system), discrete-event or continuous
(depending on the nature of time and how the system state changes in
relation to time), and static or dynamic (depending on whether or not the
system changes over time at all). This categorization affects the type of
modeling that is done and the types of simulation tools that are used.
Models, like the systems they represent, can be static or
dynamic, discrete or continuous, and deterministic or stochastic.
Simulation models are composed of mathematical and logical relations
that are analyzed by numerical methods rather than analytical methods.
Numerical methods employ computational procedures to run the model
and generate an artificial history of the system. Observations from the
model runs are collected, analyzed, and used to estimate the true system
performance measures. See Model theory.
There is no single prescribed methodology in which
simulation studies are conducted. Most simulation studies proceed around
four major areas: formulating the problem, developing the model, running
the model, and analyzing the output. Statistical inference methods allow
the comparison of various competing system designs or alternatives. For
example, estimation and hypothesis testing make it possible to discuss the
outputs of the simulation and compare the system metrics.
Many of the applications of simulation are in the area of
manufacturing and material handling systems. Simulation is taught in
many engineering and business curricula with the focus of the
applications also being on manufacturing systems. The characteristics of
these systems, such as physical layout, labor and resource utilization,
equipment usage, products, and supplies, are extremely amenable to
simulation modeling methods. See Computer-integrated manufacturing,
Flexible manufacturing system.
4. 4
Simulation is the imitation of the operation of a real-world process
or system over time. The act of simulating something first requires that a
model be developed; this model represents the key characteristics or
behaviors/functions of the selected physical or abstract system or process.
The model represents the system itself, whereas the simulation represents
the operation of the system over time.
Simulation is used in many contexts, such as simulation of
technology for performance optimization, safety engineering, testing,
training, education, and video games. Often, computer experiments are
used to study simulation models. Simulation is also used with scientific
modelling of natural systems or human systems to gain insight into their
functioning. Simulation can be used to show the eventual real effects of
alternative conditions and courses of action. Simulation is also used when
the real system cannot be engaged, because it may not be accessible, or it
may be dangerous or unacceptable to engage, or it is being designed but
not yet built, or it may simply not exist.
Key issues in simulation include acquisition of valid
source information about the relevant selection of key characteristics and
behaviours, the use of simplifying approximations and assumptions
within the simulation, and fidelity and validity of the simulation
outcomes.
The process of imitating a real phenomenon with a set of
mathematical formulas. Advanced computer programs can simulate
weather conditions, chemical reactions, atomic reactions, even biological
processes. In theory, any phenomena that can be reduced to mathematical
data and equations can be simulated on a computer. In practice, however,
simulation is extremely difficult because most natural phenomena are
subject to an almost infinite number of influences. One of the tricks to
developing useful simulations, therefore, is to determine which the most
important factors.
The functioning of a co-operative be society or bank cited as
examples. First the students may be taken to such institutions to observe
the nature and techniques of the various activities going on there. Notes
may be taken. In order to reinforce and to make the activity more familiar
the working of such institutions may be enacted in the class. The
simulation should be carefully arranged so as to make the insight as
5. 5
meaningful as possible. For example, there is a school co-operative
society. The working of the society may be observes and the salient
features of how it was organized and what the activities taken up are
noted.
Then imagine that the learners are planning to start a class co-operative
society. The steps such as selling of shares to pool the capital required,
election of various office bearers, nature of transaction involved the style
of keeping records concerning the various aspects including the Account
book, the technique of preparing a balance sheet, calculation and
dispersal of dividends to the share holders, etc. may be simulated.
This will not only help in realizing the utility value of
mathematics, but also will give realistic insights into the related
commercial mathematics. Further the roles played in simulation will
create interest among the learners.
6. 6
APPLICATION
Natural numbers
The natural numbers are 1, 2, 3, 4, 5,……… in the set of
natural numbers, which in math- Numbers ematics is referred to as N.
Additions can be executed without limit as well as multiplications, which
are to be understood as multiple additions: 3. 4 = 4 + 4 + 4.
In using number notation, one differentiates between ordinal
numbers (the third – in an imagined sequence) and cardinal numbers
(three pieces). Toddlers of 3–4 years often know the ordinal numbers up
to 10 and they can also execute simple additions via counting. The more
abstract notion of the cardinal number children mostly understand only
when they start school; in addition, even for the adult, the number of units
that can
Simulation. Spontaneous grasping of the number of elements in a set
(cardinal numbers) A random number generator produces red points,
whose number lies between 1 and the maximum number in the number
field (in the figure the maximum number is 5, 5 are shown). The sets
change with a frequency that can be adjusted with the slider from 1 to 10
per second be grasped at a glance is quite limited (to around 5–7, which is
also what intelligent animals are capable of); for fast calculations with
cardinal numbers, the relationship is memorized or simplified in our
thoughts (5+7 = 5+5+2 = 10+2 = 12). If one realizes this fact, one gains a
deeper understanding of the difficulty that children have with learning the
elementary rules of arithmetic. Simply assuming the memorized routines,
which are present in an educated adult, leads to severely underestimating
7. 7
the natural hurdles of understanding that the children have to overcome
when they learn arithmetic.
The simulation in Figure visualizes the sharp threshold that nature
imposes for spontaneously grasping the number of elements of a set. In
this simulation, points are shown in a random arrangement that can be
spontaneously grasped as a group.
The number changes with a frequency that can be specified between 1
and a maximum number.
Even numbers are a multiple of the number 2; a prime number cannot
be decomposed into a product of natural numbers, excluding 1.
The lower limit of the natural numbers is the unity 1. This number had a
close to mystical meaning for number theoreticians of antiquity, as the
symbol for the unity of the computable and the cosmos. It also has a
special meaning in modern arithmetic as that number which, when
multiplied with another number, produces the same number again.
There is, however, no upper limit of the natural numbers: for each
number there exists an even larger number. As a token for this
boundlessness, the notion of infinity developed, with the symbol∞, which
does not represent a number in the usual sense.
Already, the preplatonic natural philosophers (Plato himself lived from
427–347 BC) worked on the question of the infinite divisibility of matter
(If one divides a sand grain infinitely often, is it then still sand?) and time
(if one adds to a given time interval infinitely often half of itself, will that
take infinitely long?)
Zenon of Elea (490–430 BC) showed in his astute paradoxes, Achilles
and the tortoise and the arrows,11 that the ideas of movement and number
theory at the time were in contradiction to each other.
Subtraction is the logical inversion of addition: for natural numbers it is
only permissible if the number to subtract is smaller than the original
number by at least 1.
Division is the natural inversion of multiplication. For natural numbers it
is permissible if the dividend is an integer multiple of the divisor –
6 : 2=3.
8. 8
CONCLUSION
Simulation - Attempting to predict aspects of the
behaviour of some system by creating an approximate (mathematical)
model of it. This can be done by physical modelling, by writing a special-purpose
computer program or using a more general simulation package,
probably still aimed at a particular kind of simulation (e.g. structural
engineering, fluid flow).
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REFERENCES
Mathematics in Education- Dr .K Sivarajan
Net Reference-Wikipedia
Teaching of Mathematics –Anice James
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