Recommended
Recommended
More Related Content
Similar to Unit 18-Group Theory- Snow.pptx
Similar to Unit 18-Group Theory- Snow.pptx (20)
Recently uploaded
Recently uploaded (20)
Unit 18-Group Theory- Snow.pptx
- 1. Presented by Snow@Thet Mon Ei Date: 30 Jan 2020
- 2. What is a Group Theory? Group Theory and Axioms Why is group theory important? Conclusion
- 3. Groups are sets equipped with an operation such as Multiplication addition Composition Used in nearly every branch of mathematics and the science fields. When dealing with an object that appears symmetric, group theory can help with the analysis.
- 4. In modern algebra, the study of groups, which are systems consisting of a set of elements and a binary operation that can be applied to two elements of the set, which together satisfy certain Axiom. Group Axiom includes: Associativity- For any x,y,z , we have (x∗y)∗z=x∗(y∗z). Identity- There exists an e ∈ G, such as e*x = x*e = x for any x ∈ G and e is said to be an identity element of G. Inverse- For any x ∈ G , there exists a y ∈ G such that x*y = e =y *x and y is said to be the inverse of x. Closure- For any x,y ∈G , x∗y is also in G.
- 5. Group theory shows up in many other areas of geometry. Examples include different kinds of groups, such as the fundamental group of a space. Classical problems in algebra have been resolved with group theory. The mathematics of public-key cryptography uses a lot of group theory. Related to Identification numbers are all around us, such as the ISBN number for a book and the VIN (Vehicle Identification Number) for your car. What makes them useful is their check digit, which helps catch errors when communicating the identification number over the phone or the internet or with a scanner.
- 6. It is essential for the students to be taught about group theory in schools or colleges. The world is becoming more advance in technology each day and group theory is essential in almost all the science field. It can become handy in the near future. Becoming an important part of education.
Editor's Notes
- Generally speaking, group theory is the study of symmetry. We apply the label symmetric to anything which stays invariant under some transformations. This could apply to geometric figures (a circle is highly symmetric, being invariant under any rotation), but also to more abstract objects like functions: x2 + y2 + z2 is invariant under any rearrangement of x, y, and z
- Group is also very-much associated with modern algebra. Axiom is a type of logic principle or a rule that is found to be accepted generally by mathematicians.
- Group theory is essential to modern algebra their basic structure can be found in many mathematical phenomena. Groups can be found in geometry, representing phenomena such as symmetry and certain types of transformations. Group theory has applications in physics, chemistry, and computer science, and even puzzles like Rubik’s Cube can be represented using group theory. mathematicians often rely on algebraic invariants like the fundamental group to help us verify that two spaces are not the same. mathematicians found analogues of the quadratic formula for roots of general polynomials of degree 3 and 4 Public-key cryptography, or asymmetric cryptography, is an encryption scheme that uses two mathematically related, but not identical, keys - a public key and a private key. Unlike symmetric key algorithms that rely on one key to both encrypt and decrypt, each key performs a unique function. The public key is used to encrypt and the private key is used to decrypt. Different cryptosystems use different groups, such as the group of units in modular arithmetic recipes for constructing a check digit from another string of numbers are based on group theory.