LOG#086. Group theory(VI).

We are going to be more explicit and to work out some simple examples/exercises about elementary finite and infinite groups in this post. Example 1. Let us define the finite group of three elements as where , and such as … Continue reading

LOG#085. Group theory(V).

Other important concepts and definitions in group theory! Definition (22). Normal or invariant group. Let be a subgroup of other group G. We say that is a normal or invariant subgroup of G if the following condition holds: Proposition. Let … Continue reading

LOG#084. Group theory (IV).

Today we are going to speak about two broad and main topics: cyclic groups and some general features of finite groups (a few additional properties and  theorems). A cyclic group is, informally speaking, a group that can be generated by … Continue reading

LOG#083. Group Theory (III).

Today we are going to study some interesting aspects of group theory. Definition (14). Subgroup. Given a group and a nonempty subset of G, then H is said to be a subgroup of if and only if Check: If is … Continue reading

LOG#082. Group Theory (II).

Basic definitions of group theory: that is the topic today! We need some background previous to the “group axioms”. Definition (1). Set is a collection of objects with some properties. Objects in the set are called “elements” or “members” of … Continue reading

LOG#081. Group Theory (I).

I am going to build a “minicourse” thread on Group Theory in this and the next blog posts. I am trying to keep the notes self-contained, since group theory is a powerful tool and common weapon in the hands of … Continue reading

LOG#078. Averages.

I am going to speak a little bit about Statistics. The topic today are “averages”. Suppose you have a set of “measurements” where . Then you can define the following quantities: Arithemtic mean. Geometric mean. Harmonic mean. Remark: In the … Continue reading

LOG#053. Derivatives of position.

Position or displacement and its various derivatives define an ordered hierarchy of meaningful concepts. There are special names for the derivatives of position (first derivative is called velocity, second derivative is called acceleration, and some other derivatives with proper name), … Continue reading