By Yukitaka Miyagawa

Units and Mappings, Monoid, staff, Sub monoid, Subgroup, staff homomorphism, Kernel of a bunch homomorphism, picture of a gaggle homomorphism, staff isomorphism, staff automorphism, Operations of subsets of team, Coset, Lagrange's theorem, basic subgroup, Equivalence relation, average staff homomorphism, Homomorphism theorem of crew, First isomorphism theorem of team, moment isomorphism theorem of workforce, Subgroup generated by way of a subset of the crowd, Cyclic team, crew tables of finite crew, Order of a finite cyclic workforce, Subgroup of limitless cyclic staff, Subgroup of finite cyclic workforce,

In this booklet, I describe units and mappings, monoid, staff as in short as possible.

Feature of this ebook is that good judgment symbols( for instance, ∃, ∀,⇒,⇔, ∃1 and so forth. )were used,

without hesitations. I defined the meanings of those symbols of course.

Feature of this e-book is that brackets(For instance, ( ), [ ] etc.)were used, with no hesitations.

By utilizing those symbols, i believe proud that i used to be in a position to exhibit the fragile contents of

mathematics as devoted as possible.

Contents of arithmetic in senior highschool, were assumed as heritage knowledges.

Because i guess reader of this publication is an formidable pupil of senior high

school.

Because i suppose reader of this ebook is someone of science-oriented first yr class

of university.

Because i suppose reader of this ebook is a scholar of the dept of Mathematics.

Because i suppose reader of this publication is somebody who've a very good understanding

until highschool arithmetic, yet don’t have a very good realizing math on the University.

I use many formulation as attainable. simply because i feel that the formulation are nucleus of mathematics.

When be learn this booklet, please learn whereas being proven by means of a pencil and pc always.

If learn whereas being proven via a pencil and workstation, it is possible for you to to get pleasure from relatively

easily.

I am unhappy that during contemporary years, and within the schooling, the sensible part is simply too emphasised. I

am unhappy that during fresh years, and within the schooling, the richness of the spirit is neglected.

I am unhappy the disappearance of the salon in Japan lately, within the similar as these.

Atmosphere and house like salon won't healthy a conventional factor in Japan originally?

However, that there's to spare, is that there are numerous the ambience and house as a

salon. Or Japan has develop into so bad society? As there's not monetary energy which has the

atmosphere and area as a salon.

I wish a minimum of during this e-book, are looking to be within the surroundings and house, equivalent to a salon of

people who love arithmetic tradition. and that i intend to write down that way.

Humble contribution of my paintings will be. Even will be modest.

It will be a nonsense that to debate the practicality of mathematics.

The physique of arithmetic is an entity that exists on this planet of Gods.

Mathematics are found in the lofty tremendous, to the excessive locations of the dimension.

Only perspective we mediocre Human can take for arithmetic is that to like earnestly and

longing her.

I want to devote this publication to each person of realizing the maths during this way.

Though we humans are inferior within the presence, let’s contact to arithmetic as described

above besides Jacobi.

For the glory of the human spirit.