This document discusses abstraction, generalization, and particularization in mathematics. It defines abstraction as extracting the underlying essence of a concept by removing real-world dependencies and generalizing it. Generalization expresses relationships between concepts that apply broadly. Particularization individualizes mathematical objects. Abstraction reduces complexity by eliminating details while generalization broadens applications. Together, these processes aid in mathematical reasoning and moving between specific and general concepts.

2. Sl no Titel Slide no
1 Introduction 1
2 Abstraction 2
3 Types of abstraction 3
4 Advantages of abstraction 4
5 Generalization 5-6
6 Uses of generalisation 7
7 Particularisation 8-9
8 Conclusion 10

3. In mathematics abstraction is the process of extracting the
underlying essence of mathematical concept removing any
dependency on real world objects with which it might originally
have been connected and generalizing is it so that it has wider
applications are matching among other abstract description of
equivalent phenomena and. Generalization is an inferential
statement which express a relationship of two or more concept
applies to more than one event as predictive and explanatory value .

4. Abstraction is an emphasis on the Idea qualities and properties
rather than the Particulars.
The process of identifying common pattern that have systematic
variations is an abstraction or abstraction represents the common
pattern and provided provides a mean of specifying which
variation to use is abstraction.
Abstraction is usually about reducing complexity by eliminating
unnecessary details for example an abstract class in OOP is a
parent class that contains common future of its children but does
not specify the exact functionality.

5. 1.Category theory Or data structure Abstraction:
Rectangle is an abstraction of a square. It concentrates on
the fact Square has two pairs of opposite sides and it
ignores the fact that adjacent sides of a square are equal.
2.Model theory or a producer Abstraction:
The higher order function map is an abstraction of
procedure which performs some set of operation on a list
of values to produce an entirely new list of values.

6.  It emphasis on the idea qualities and properties rather than the
particulars .
 It helps in reducing complexity by eliminating unnecessary
details .
 It reveals deep connection between different areas of
mathematics.
 Known result in one area can suggest conjectures in related
area .
 Techniques and methods from one area can be applied to
prove results in a related area .

7.  Generalisation is the process of attribution of properly possessed
by what we can see or hear or taste that moves from concrete to
abstract.
 Generalisation is the law or principal or definition derivative
through a series of repeated and similar event .
 Generalisation on the other hand does not try to remove details
but to make function in it applicable to a wider range of item.
 Generic containers are a very good example for that mindset you
wouldn’t want to write an implementation of string least Int -List
and so on which is why you’d rather write a generic list which
applies to all types .

8.  The generalisation structure strategy is used to extend the solution to
broad and more for reaching situations.
 Analyzing the structural future of problem rather than the focusing only on
details often results in insight more significant than the answer to specific
situation posted in the problem. This sort of thinking about generalisation
is very important in developing students mathematical reasoning abilities .

9.  It does not required to avoid details but rather to have some
mechanism to allow for applying the same function to different
argument.
 It is used to extend the solution to border and more farreaching
Situation.
 It helps in developing students mathematical reasoning abilities .
 It broadens of application to encompass A larger domain of object of
the same are different type .

10. Many of the difficulties observed in the teaching and learning
of mathematics are related to the fact that in mathematical
reasoning, to move from the general to the general it is necessary
to pass through the particular. The mechanisms that language
allows us for the particularization or individualization of
mathematical objects are varied, as too are the processes of
generalization (or abstraction). For example, Piaget (2001)
distinguishes between reflective and empirical abstraction.

11.  we have described some aspects of the problem of the particular and its
relation to the general in teaching and learning mathematics.
With respect to the problem of the delimitation of the processes of
particularization and generalization related to the processes of
materialization and idealization.
This is an important distinction as it permits a more detailed analysis,
and consequently a better comprehension of each of these processes as
well as of their combined presence in mathematical activity.

12. Here we have come to the end of the topic "abstraction,
Particularisation and generalisation "Here I would like to share my
experience while doing this Work. I learnt many new things about through
abstraction, Particularisation and generalisation These are the process of
facilitating a specific problem to help designer's solve problems efficiency.
These are reduce complexity and increases creativity. these are interrelated
the quality of dealing with ideas Rather then events and also deprived from
the content connected to particular application I hope that my assignment
or seminar is interesting and even knowledgeable