Importance of Set Theory:
- Set theory gives one unified structure of integers, ordinals and logical models.
- It allows us to formalize everything with similar properties in mathematics in a natural and easy way.
- We use set theory in our daily life also. For example pack of cards, group of companies, list of players who play cricket, flock of birds, bunch of keys etc.
- In mathematics we all are aware of set of natural numbers, whole numbers, prime and composite numbers.
- Set theory helps us to study the various concepts of natural numbers, operations with natural numbers and in solving problems. Therefore, it builds the skills of the students.
- In set theory we study about same collection of objects. Cardinality of sets is an important fundamental notion. One of the important applications of the set theory is proving the existence of transcendental numbers. Set theory is related with logic which we apply in every walk of our life.
- Mathematicians use set theory to compare object.
- Set theory acts as foundation of mathematics.
- Ontological is one way where set theory is used to construct a complete ordered field. It is important because complete ordered fields are very complicated while sets are relatively simple.
- Epistemological is another way where a mathematics question can be reduced to questions in set theory. In logical sense, set theory is the foundation for algebra and calculus in mathematics and we know that modern physics uses algebra and calculus extensively.
- Using set theory we can make clear view about the cosmological arguments for God's existence.
- Set theory helps us to understand the nature of basic configurations.
- Using Venn diagram we can find solutions of complicated questions quite easily.
- We know that, everything in this world is categorized. Set theory helps us to find the solutions of the problems related to sorting of things.
- In today's world set theory is used in almost every sector like business, engineering and medical including health sciences and natural sciences.
- Set theory can be used in smooth running of a business by helping in planning and operations. Each section of business such as accounting, management, operations, production and sales can be grouped in a set.
Difficulties faced by a student while solving Set Theory problems
Representation and understanding the set theory problems
Generally students are not able to represent and understand the set theory problems.
Problem related to computing
Computing the set theory problem is an important area of concern.
Problem related to Venn diagrams
Venn diagram problems require in depth knowledge of the subject. Thus, students get demoralize.
Use of cognitive abilities and Lack of basic mathematics skills
A student must use cognitive abilities in his study for better understanding of the subject. But students generally do not use these cognitive abilities. It is seen that many students are facing problem in correct interpretation and perception, in logical thinking and in quick memorizing and retrieving back the basic facts.
Set theory problems require many mathematical skills in a student. But many students do not have even basic mathematical skills. Therefore, they get frustrated in the starting itself. Therefore, student must get mastery over the subject.
Lack of organized strategy and solving problem
Generally students do not have any strategy on how to start solving the given problem. Therefore, Ultimately either they solve the problem using any long method or they get wrong answer.
Difficulty in transforming the set theory problem into mathematical sentences
Sometimes students face difficulty in transforming a basic set theory problem into mathematical sentences means they are not able to form equations and finding unknown variables.
Set theory problems are related to puzzles
Set theory problems are full of puzzles and students with poor academic background find it difficult to formulate and solve the problem as per requirement.
Few topics Cover under Set Theory
- Fundamental laws of set theory
- Operations on sets
- Venn Diagram
- Word Problems
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