## BENGKEL WEB 2.0 FOR TEACHING AND LEARNING : SOCIAL MEDIA AND BLOG This workshop is about social media and blog. How to use it in teaching and learning.

What is Web 2.0?

Web 2.0 technologies bring the web to a new phase, which allows users not only to use information but also to be directly involved in generating new information.

Social Media vs Web 2.0?

Social Media as one of the Web 2.0 tools allow social interaction and easy creation of content by users. It can be an effective tool for teaching and learning in higher education. It can help connect students to information and help them generate a dialogue with their teacher and other students about a course.

Blog vs Web 2.0?

Blog is another Web 2.0 facilities which is easy to create and offers variety of interactive facilities. It could give positive impact towards student’s development. This course revealed to academic staff on how to utilize social media and learning and Blog for teaching and learning effectively.

What are the things that I have learn in this workshop?

1. Social Media for Teaching & Learning
2. Concept of Blog and how it can be used in T&L process.
3. Developing Blog for T&L purpose.
4. Blog through Mobile Apps
5. Blog as webometric tools

The trainers/facilitators are very helpful and wonderful. Thanks Dr Noor Dayana Halim and Dr. Norah Md Noor.

Here is the schedule of the workshop. ## Sepetang di CTL

What I am doing here?

As in previous post, I am here as one of the participants for Web 2.0 for T&L : Social Media& Blog. ## Modern Algebra : Factor (Quotient) Groups

Factor (Quotient) Groups

Definitions, examples, and proofs talking about factor (quotient) groups are given.

## Modern Algebra : Cosets and Lagrange Theorem

Cosets and Lagrange’s Theorem

In the following video, definitions, examples, T/F qustions, and proofs talking about cosets and Lagrange’s Theorem are given.

## Modern Algebra : Direct Products/Finitely Generated Abelian

Direct Products/Finitely Generated Abelian

Finitely Generated Abelian Groups are defined and explained in detail. Examples, proofs, and some interesting tidbits

that are hard to come by is given.

## Modern Algebra : Isomorphisms

Group Homomorphisms

Definitions, examples, and proofs talking about group homomorphisms are given.

Homomorphisms

A homomorphism is a function between two groups. Its a way to compare two groups for structural similarities. Homomorphisms are a powerful tool

Isomorphisms

An isomorphism is a homomorphism that is also a bijection. If there is an isomorphism between two groups G and H, then they are equivalent and we

say they are “isomorphic.” The groups may look different from each other, but their group properties will be the same.

The Kernel of a Group Homomorphism

The kernel of a group homomorphism measures how far off it is from being one-to-one (an injection). Suppose you have a group homomorphism f:G ?

H. The kernel is the set of all elements in G which map to the identity element in H. It is a subgroup in G and it depends on f. Different

homomorphisms between G and H can give different kernels.

## Modern Algebra : Permutation/Symmetric Groups

Permutations

In the following video, permutations is introduced, examples and T/F questions are shown.

Symmetric Groups

Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of

permutations on a set of n-elements is denoted S_n.

Orbits & Cycles

Permutations, cycles, and orbits are contrasted, compared, and further defined.

Product of cycles Example 1

Multiplication of Permutations in cycle notation. Example 1

Product and Inverses of Cycles

Product and inverses of permutation in cycle notation

## Modern Algebra : Cyclic Groups

Definition of a Cyclic Group

The definition of a cyclic group is given along with several examples of cyclic groups.

Cyclic Subgroups

A definition of cyclic subgroups is provided along with a proof that they are, in fact, subgroups.

The Structure of Cyclic Groups

The following video looks at infinite cyclic groups and finite cyclic groups and examines the underlying structures of each. By looking at when the orders of elements in these groups are the same, several theorems are introduced and proven.

Cyclic Groups and Generators

What is a Cyclic Group/Subgroup? The following video give examples, theory, and proofs rounding off this topic.

Cyclic Groups and Abelian Groups

The following video explores the relationship between cyclic groups and abelian groups.

## Modern Algebra : Definition and Examples of Subgroups

Learn the definition of a subgroup.

The following video describing the definition of a subgroup along with a few examples.

In this video, the basics of what it means to be a subgroup explain, and some fun problems working with subgroups are shown.

The Subgroup Test

An easier way to show that a subset of a group is a subgroup: just check closure and inverses.

The Center of a Group

The definition of the center of a group is given, along with some examples. Then, a proof that the center of a group is a subgroup of the group is provided.

## Modern Algebra : Some Properties and Proving involving Group

The Order of an Element

The order of an element in a group is the smallest positive power of the element which gives you the identity element. We discuss 3 examples:

elements of finite order in the real numbers, complex numbers, and a 2×2 rotation matrix.

Basic Group Proof 1

Let G be a group and show that if (ab)^2 = a^2b^2 for all a,b in G, then G is abelian.

Basic Group Proof 2

Let G be a group such that every element of G is equal to its own inverse. Show that G is abelian.

Basic Group Proof 3

Let G be a finite group of even order. Show that G has an element a (not equal to the identity) such that a^2=e.