| Top 5 student :: | ||
| NAME | MATH'S | PERCENT |
| Rekha Namdev | 93 | 87% |
| Devansh | 92 | 83% |
| Nikita | 89 | 81% |
| Sonali | 82 | 71% |
| Ravina yadav | 86 | 69% |
12th class result
Topology
The word topology is derived from two Greek words, 'topos' meaning 'surface' and 'logos' meaning 'study'. Topology thus literally means the study of surface but this is unadequate for a understanding of the spirit of the subject as its stands today, the best way to appreciate what topology is about is by comparing it with geometry. The two being akin to each other in so many respects.
Geometry as its stand today can be defined as the study of geometrical properties of objects the objects we are dealing is geometry are lines, planes,circles,cube cylinder various types of surface and curves.
Geometry as its stand today can be defined as the study of geometrical properties of objects the objects we are dealing is geometry are lines, planes,circles,cube cylinder various types of surface and curves.
Sets
Countable and Uncountable Sets
A set which is either finite or denumerable is said to be countable
otherwise it is uncountable denumerable is also known as countably
infinite.
Example :The set Z of all integers is countably infinite the function
F : Z -- Z + defined by
f (x) =2n if n > 0
=2n +1 if n <=0
is a bijection.
THEOREM ::
1. Every infinite subset of a countable set A is countable,
2. A countable union of countable sets is countable,
3. A finite product of countable sets is countable.
A set which is either finite or denumerable is said to be countable
otherwise it is uncountable denumerable is also known as countably
infinite.
Example :The set Z of all integers is countably infinite the function
F : Z -- Z + defined by
f (x) =2n if n > 0
=2n +1 if n <=0
is a bijection.
THEOREM ::
1. Every infinite subset of a countable set A is countable,
2. A countable union of countable sets is countable,
3. A finite product of countable sets is countable.
Classification depending the data transferred PORT
" SERIAL PORT "
This ports transmits data bit by bit. Therefore only wire is
provided at this port to transmit one bit at a time . This type of
port is used to connect slow IO devices or communication devices such
as modem . Terminals are also connected to serial ports.
"Parallel Ports"
In a parallel port all the bits of a data is transmitted at the
same time . For example to transmit 8-bit word, Eight wires are
provided on this port. Faster data transfer takes place when we use
these ports .
This ports transmits data bit by bit. Therefore only wire is
provided at this port to transmit one bit at a time . This type of
port is used to connect slow IO devices or communication devices such
as modem . Terminals are also connected to serial ports.
"Parallel Ports"
In a parallel port all the bits of a data is transmitted at the
same time . For example to transmit 8-bit word, Eight wires are
provided on this port. Faster data transfer takes place when we use
these ports .
Classification of Ports
"Programmable Port"
This port is also an integrated circuit in which function of a
port can be changed with the help of a program. One port can be used
as an input port at one time. The same port can be used as an output
port at other time by giving some command to this port. Also each port
can be utilized in different modes with the help of software. Each
programmable port must have a CONTROL REGISTER. The function of
control register is to hold the necessary command word for the
operation of the port .
The programmable ports also have STATUS
REGISTER to read the status of different ports in the chip. For
example IC8255 is having three 8-bit programmable ports.
"Non - Programmable Port "
This port operates as input port or as output port for the whole
life. The function of this port cannot be changed with the help of a
program. For example a tristate Buffer always works as an input port
and a latch always works as an output port. Intel IC 8212 is a non -
programmable input - output port. That IC can be connected to work as
an input port or as an output port. But ones it is connected it the
circuit us function cannot be changed by user.
This port is also an integrated circuit in which function of a
port can be changed with the help of a program. One port can be used
as an input port at one time. The same port can be used as an output
port at other time by giving some command to this port. Also each port
can be utilized in different modes with the help of software. Each
programmable port must have a CONTROL REGISTER. The function of
control register is to hold the necessary command word for the
operation of the port .
The programmable ports also have STATUS
REGISTER to read the status of different ports in the chip. For
example IC8255 is having three 8-bit programmable ports.
"Non - Programmable Port "
This port operates as input port or as output port for the whole
life. The function of this port cannot be changed with the help of a
program. For example a tristate Buffer always works as an input port
and a latch always works as an output port. Intel IC 8212 is a non -
programmable input - output port. That IC can be connected to work as
an input port or as an output port. But ones it is connected it the
circuit us function cannot be changed by user.
USE OF PORTS
"Ports"
The input-output devices are not directly connected to the CPU. Because he the IO devices are directly connected, it will reduce the number of IO devices that can be connected to CPU.
The interface between IO devices and CPU is called Port. Ports are the electronic circuits used to transfer the data to an output device and used to accept data from an input device. Each port in the computer system is identified with the help of an address called PORT ADDRESS.
Now a days the whole circuit of the port can be packed in a single integrated circuit (IC). There are so many ways to classify a port.
1. Input Port - This ports accepts data from an input device and then
supply this data to the CPU. The CPU enables this port by providing
appropriate port address and necessary control signals to the
supporting logic circuit of the port.
2. Output Port - This port accepts data from CPU and supplies this
data to output device. CPU enables this port by providing appropriate
port address and necessary control signals.
The input-output devices are not directly connected to the CPU. Because he the IO devices are directly connected, it will reduce the number of IO devices that can be connected to CPU.
The interface between IO devices and CPU is called Port. Ports are the electronic circuits used to transfer the data to an output device and used to accept data from an input device. Each port in the computer system is identified with the help of an address called PORT ADDRESS.
Now a days the whole circuit of the port can be packed in a single integrated circuit (IC). There are so many ways to classify a port.
1. Input Port - This ports accepts data from an input device and then
supply this data to the CPU. The CPU enables this port by providing
appropriate port address and necessary control signals to the
supporting logic circuit of the port.
2. Output Port - This port accepts data from CPU and supplies this
data to output device. CPU enables this port by providing appropriate
port address and necessary control signals.
VECTOR SPACE
VECTOR SPACE
Vector spaces play a role in many branches of mathematics and its
applications .In fact,in various practical problems we have a set X
whose elements may be vectors in three-dimensional space, or spectrum
of numbers,or function,and these elements can be added and multiplied
by constants in a natural way,the result being again an element of X.
Such concrete situations suggest the concept of a vector space as defined below.
The definition will involve a general field K.but in functional analysis,K will be R or C. The elements of K are called scalars;hence in our case they will be real or complex numbers.
Vector spaces play a role in many branches of mathematics and its
applications .In fact,in various practical problems we have a set X
whose elements may be vectors in three-dimensional space, or spectrum
of numbers,or function,and these elements can be added and multiplied
by constants in a natural way,the result being again an element of X.
Such concrete situations suggest the concept of a vector space as defined below.
The definition will involve a general field K.but in functional analysis,K will be R or C. The elements of K are called scalars;hence in our case they will be real or complex numbers.
METRIC SPACE
reflection shows that in limit processes and many other considerations
we use the fact that on R we have available a distance function,call
it d.which associates a distance d(x,y)=|x-y|with every pair of points
x,y€R.In the plane and in "ordinary" three-dimensional space the
situation is similar.
In functional analysis we shall study more general "spaces" and
"functions" defined on them.We arrive at a sufficiently general and
flexible concept of a "space" as follows.We replace the set of real
numbers underlying R by an abstract set X and introduce on X a "distance function"which has only a few of the most fundamental properties of the distance function on R.
But what do we mean by "most fundamental"?
This question is far from being trivial. In fact,the choice and formulation of axioms in a definition always needs experience,familiarity with practical problems and a clear idea of the goal to be reached.
DIGITAL COMPUTER
1.High processing speed.
2.Can perform iterative operations.
3.Has a large storage capacity.
4.Can take decision if proper program is written.
5.It is capable of accepting information in various forms from outside
world and can provide results in various forms.
Any information stored or processed by computer is in the form of data.But before storing or processing, the data needs to be converted into suitable form.
The way of transforming the data into suitable form so that it can be stored or processed by computer is called representation of information.
There are two ways of representing the information :--
1.External Data Representation.
2.Internal Data Representation.
Numeric and Non-numeric Data :-
The information in a proper form is a data.There are two basic types of data;binary number or octal number over these numbers,Each number has a value.
On the other hand non-numeric data includes letters and special symbols.e.g.A,B,+,$,*etc.are non-numeric data.Even space is also a non-numeric data.These are popularly known as characters.
Name of a particular person or a place such as MUKESH, INDORE form String of characters.
Each character in the computer,ASCII and EBCDIC are two popular character codes.
Subscribe to:
Posts (Atom)