OpenLLM-France/wikimedia huggingface dataset:
# Complex semi-simple Lie algebras and their representations

under construction
In this course we learn the basics of w:complex semi-simple Lie algebras.

## Why?

* the classification of compact Lie groups reduces to the classification of semi-simple Lie algebras
* the key notion of a root system reappears in many branches of mathematics and theoretical physics
* Lie algebras and their representations are intimately related to quantum mechanics

## some references
### on paper

In increasing order of details:
* J.-P. Serre, Complex semi-simple Lie algebras (translated from French: Algebres de Lie complex semi-simple
* J. E. Humphreys, Introduction to Lie algebras and representation theory , ISBN 978-0-387-90053-7
* W. Fulton, J. Harris, Representation theory, A first course

### on line

There is plenty of lecture notes and other good references on line to suit every taste.
* google:semisimple+Lie+algebras

## lessons

* Lie algebra
* Linear Lie algebras
* /derivations and automorphisms
* soluable and nilpotent Lie algebras
* representations of Lie algebras
* examples: classical Lie algebras
* example: representations of sl2
* Lie's theorem and Engel's theorem
* Schur's lemma
* Casimir element
* Weyl's theorem on complex reducibility
* Killing form
* Cartan subalgebra
* Borel subalgebra
* roots and weights of a Lie algebra
* root system
* Cartan matrix
* Dynkin diagram
* Verma module
* Harish-Chandra's theorem
* Weyl character formula
* Kostant's multiplicity formula
* Poincare-Birkhoff-Witt theorem

## beyond

* Lie group
* algebraic group
* Kac-Moody algebra
* quantum algebra
* vertex algebra
# Complex socio-ecological systems/Applying resilience and systems analysis

Discussants: Adam and Danielle
Carpenter, Steve, Brian Walker, J. Mary Anderies and Nick Abel. 2001. From metaphor to measurement: resilience of what to what? Ecosystems 4: 765-781.
Levin, Simon A. and Jane Lubchenco. Resilience, robustness and marine ecosystem-based management. BioScience 58(1): 27(6).
Ostrom, Elinor. 2009. A General Framework for Analyzing Sustainability of Social-Ecological Systems. Science 319: 422-425.
Wilson, J., L. Yan, and C. Wilson. 2007. The precursors of governance in the Maine lobster fishery. PNAS: September 25, 2007 vol. 104 no. 39. http://www.pnas.org/cgi/doi/10.1073/pnas.0702241104
# Lunar Boom Town/Boarding Habitat

This habitat rents short term and long term living volume to lunar workers and lunar settlers during their work shifts or initial arrival. Many workers and settlers may not wish to establish a private residence, preferring to depend upon our lunar housing specialists to assist them with their personal living arrangements.
Products and Services: Various size and privelege rooms. Hourly air rates, pay for what is used. Meals, pay for those consumed. Brown bag meals to carry to work. Laundry
This habitat has many of the same requirements, needs, capabilities and services of the Lunar tourist hotel but is more utilitarian in space and services available and thus more cost efficient.

## Possibly Applicable Information Resources

"Lunar Base Development Issues and Models
Prototyping and analysis using available earth assets.

## Useful tasks necessary to project startup cashflow requirements

Simulate a lunar landing from scratch to setup the first cabin space for rent to wealthy adventurous tourists. Possible approach below or devise your own or fork this one and tailor it to your satisfaction. Remember, first cuts do not need to be perfect. This is a wiki and we will collaboratively merge the best and rest is archived for us automatically in the history log.
Caution In an engineering simulation or role playing game it is necessary to avoid risks. Particularly potentially fatal risks. Never place any airtight material including plastic around the head or face. This can impair breathing and will be fatal. Keep plastic and airtight bags out of the hands of small children and supervise others adequately to avoid problems.

## Draft Procedure

Use two hiking tents, set one up in backyard. Load it up with the second tent and a simulated space suit (layers of fabric meeting simulated requirements, plastic for airtight, tight cotton/wool etc. for comfortable internal pressure liners, gloves, etc.) load small lightweight bag kits for everything you need to complete the mission -- medical kits, MREs(or bagged meals), coke bottles(oxygen), radio communicator (wireless to overhead satellite?), lights, heaters, radiators, etc.
* Go through the mission plan step by step estimating time required to deploy the second tent and equip it as an initial rental/science base.
* Estimate the total mass of payload too be delivered to the moon.
Remember, we are only setting up the office cabin and the rental cabin. We are contracting with Lunar Boom Town/Cargo Imports for cargo delivery to specified locations.
# Lunar Boom Town/Building and construction facility

Building & Construction facility
Any town is constantly growing. So it needs qualified builders & domestic engineers, which will be capable of bringing any business up. The engineers will inevitably have a need to have a place, where orders are considered and planned, architects prepare projects, where builders and workers are hired, where the building machinery, cranes, tools, spacesuits etc. are stored. In fact this business should be established first to support rapid construction of other facilities.
Building on moon has certain advantages, as 6 times lighter gravity provides much less power requirements for lifting machinery, less requirements for construction stiffness etc. Any supporting construction can be finely built from aluminum, or some other cheap and unsuitable for earth construction materials.
From the other side - the lack of atmosphere gives much stricter requirements for building places, where human presence is necessary. Very hardy constructions and reliable systems must be implemented in any new building, which should contain regenerated and heated air. Buildings, suited for human beings also require all sorts of domestic communications, like water, heating, maybe common canalization, food delivery, transportation of some kind(possibly underground) and more. From this point of view - the other businesses on moon are best suited(financially) for robotic beings.

## Successful facility work depends on

-materials
   * Lunar_Boom_Town/Steel_Production
   * Lunar_Boom_Town/Begillion_resource_harvesting
-machinery maintenance -electricity production -Oxygen Lunar_Boom_Town/LOX_Domestic_and_Exports -Fabrication methods s:Advanced_Automation_for_Space_Missions

## Support Systems

* Robotic cranes

## Popular Construction Approaches

* /Land prefab and bury
* /Dig in and remodel
* /Assemble and relocate
* /Onsite fabrication
# Lunar Boom Town/Brainstorming

w:Self-replicating spacecraft
# Lunar Boom Town/Carbon commodity imports and futures

Carbon Commodities Dealer
Background: Carbon is extremely scarce on the moon yet it is required for everything including: breathing, eating, carbon spacecraft components, feul (biodiesal, methane), farming, etc.
Possible sources: Earth imports, Mars (atmosphere CO2), Venus (atmosphere CO2), Titan (ambient methane), Carbonaceous Asteroids, Spacecraft waste,
Pricing: Volatile. Varies with supply and demand.
# Lunar Boom Town/Begillion resource harvesting

Bagillion is a large multinational corporation which harvests readily materials from the regolith. It's primary product is He3 which requires it to move millions upon millions of cubic meters of regolith per year. Naturally, it is more profitable to turn some of the moved material into other products after the He3 is extracted than not.
Slag remaining after materials processing is sintered (heated until it clumps together in a mold) into paving blocks and used to create roads.
Construction is currently under on the equatorial belt highway and the nearside Pole to Pole freeway. These highways are intended to support widespread lunar settlement on generous land grants recently issued by the U.N. Extraterrestial Settltement Agency. The Equatorial Belt Highway is intended to allow solar road trains to follow the sun around the moon as they transport critical cargo.
Technical Papers
# Lunar Boom Town/Boomtown Ice Skating Rink
## Revenue Sources

* Skaters Fees
* Water Storage
* Emergency Cooling Reserve
* Bar & Grill
* Vending machines
* Arcade
* Skating Games

## Construction Costs

    Estimate per cubic meter cost excavation cavern then price and estimate schedule for tiny, medium, large, maximum (roof limited)
* Construction Design, Specification, and Details

## Operating Costs

Interest on the capital invested in water storage in ice.
Salary for 24/7 attendent trained in first aid and Zamboni operation.
Salary for Manager/Promotions/Event operations staff.
# Lunar Boom Town/Boomtown Plaza Bakery

Even if we face the twin paradox, everyone will want to eat delicious cakes on birthdays, and more so on occasions like weddings and anniversaries. What are we to do? Probably go to the Boomtown Plaza Bakery.
# Lunar Boom Town/Bubbler air particle reducer

waste streams
* contaminated household air with suspended particulates such as dust, allergens, smoke,noxious gases
process air out is hopefully lower in particulate but probably definately higher in humdity. start with semi manual switch because I am interested in
proposed component process - use fan to blow waste stream into water tank under diffusion layer such as sand or weave fabric etc. recycle air if testing shows it helps at some cost threshold of particle removed per expense of pumping air around feedback loop rather that staight one pass through
possible advantages over existing units
* disect existing units --> first glop opportunity if can acquire broken or waste unit cheaper than just purchasing for testing
* identify precise target benefit in some process
How to measure in reasonable range ?? time for some googling One possible use is
commercially available airprocessers
* given requirements on air out to atmosphere
* goolge(industrial,waste,gas,emissions)
# Korean/Words/친

* ㄱ ㄲ ㄴ ㄷ ㄸ ㄹ ㅁ ㅂ ㅃ ㅅ ㅆ ㅇ ㅈ ㅉ ㅊ ㅋ ㅌ ㅍ ㅎ -ㄱ-ㄲ-ㄴ-ㄷ-ㄸ-ㄹ-ㅁ-ㅂ-ㅃ-ㅅ-ㅆ-ㅇ-ㅈ-ㅉ-ㅊ-ㅋ-ㅌ-ㅍ-ㅎ- 말+/말씀+/물+/불+ a2z/Basics/News/Notes/Table/Legend/Sandbox

## 친
### Prefix

* ‘혈연관계로 맺어진’의 뜻을 더하는 접두사.
    (adjective) kin

### Uses

* 친아버지 (-abeoji, "real father")
* 친어머니 (-eomeoni, "real mother")
* 친아들 (-adeul, "real son")
* 친딸 (-ttal, "real daughter")
* 친족 (親族, chin-jog, "relatives")
* 친척 (親戚, chin-cheog, "relatives")
* ↑ Chinese Romanization: qin
* ↑ https://ko.dict.naver.com/#/search?query=친
* ↑ https://en.wiktionary.org/wiki/친
* ↑ This adjective is kin or akin to English king and its kins or cognates.
# Korean/Words/키질

* ㄱ ㄲ ㄴ ㄷ ㄸ ㄹ ㅁ ㅂ ㅃ ㅅ ㅆ ㅇ ㅈ ㅉ ㅊ ㅋ ㅌ ㅍ ㅎ -ㄱ-ㄲ-ㄴ-ㄷ-ㄸ-ㄹ-ㅁ-ㅂ-ㅃ-ㅅ-ㅆ-ㅇ-ㅈ-ㅉ-ㅊ-ㅋ-ㅌ-ㅍ-ㅎ- 말+/말씀+/물+/불+ a2z/Basics/News/Notes/Table/Legend/Sandbox

## 키질
### Noun

* 키로 곡식 따위를 까부르는 일.
    winnowing by a fan or "winnowing basket"

### Elements

* 키 (ki, "fan" as a basket for tossing and receiving grains in winnowing)
* 질 (jil, "deal")

### Relatives

* 까부르다 (kkabureuda, roughly "to winnow")
* 까불다 (kkabulda, "To act rashly or impetuously; to be tossed up and down")

### Semantic paradigm shifts and descendants

* Latin: vannus "winnowing basket"
** Dutch: wan "winnowing basket"
** English: fan "winnowing basket"
** French: van "winnowing basket"
** German: Wanne "winnowing basket; tub"
*** Estonian: vann "bath, bathtub"
*** Polish: wanna "bath, bathtub"
*** Russian: ва́нна (vánna) "bath, bathtub"
**** Uzbek: vanna "bathtub"
**** Latvian: vanna "bathtub; tub; bathing"
**** Ukrainian: ва́нна (vánna) "bath, bathtub, bathroom; bathing"
**** Armenian: վաննա (vanna) "bath, bathtub, bathroom; bathing"
* Handheld fans
* An electric fan
* Vanna #Latvian "bathtub"
* Saules vanna #Latvian "sunbath"
* ↑ The fan here means a "winnowing basket," "by moving which the grain is tossed and agitated, and the chaff is separated and blown away."
* ↑ https://ko.dict.naver.com/#/search?query=키질
* ↑ https://en.wiktionary.org/wiki/키질
* ↑ A device for tossing and receiving grains in winnowing.
* ↑ "키를 위아래로 흔들어 곡식의 티나 검불 따위를 날려 버리다." To flap the fan up and down so that the grains are tossed up and the chaffs are blown away.
* ↑ This sense is overridden by that of "blower".
* ↑ The original sense "winnowing basket" has shifted to "tub," "bathtub," and even "bathing," at last!
* ↑ Old High German wanna "tub" (Why no "winnowing basket"?)
# Korean/Words/타다

* ㄱ ㄲ ㄴ ㄷ ㄸ ㄹ ㅁ ㅂ ㅃ ㅅ ㅆ ㅇ ㅈ ㅉ ㅊ ㅋ ㅌ ㅍ ㅎ -ㄱ-ㄲ-ㄴ-ㄷ-ㄸ-ㄹ-ㅁ-ㅂ-ㅃ-ㅅ-ㅆ-ㅇ-ㅈ-ㅉ-ㅊ-ㅋ-ㅌ-ㅍ-ㅎ- 말+/말씀+/물+/불+ a2z/Basics/News/Notes/Table/Legend/Sandbox

## 타다
### Verb

* 불씨나 높은 열로 불이 붙어 번지거나 불꽃이 일어나다.
    to burn
* 피부가 햇볕을 오래 쬐어 검은색으로 변하다.
    to tan

### Attributive form

* 탄 (tan)

### Comparatives

* tan #Translations
* Germanic
* Danish: blive brun
* Dutch: bruinen
* English: tan
* German: bräunen
* Norwegian: sole, brune
* Swedish: sola
* Romance
* French: bronzer
* Portuguese: bronzear
* Spanish: broncearse
* Asiatic
* Japanese: 日焼けする (hiyake-suru)
* Korean: 타다 (tada)
* ↑ https://ko.dict.naver.com/#/search?query=타다
* ↑ https://en.wiktionary.org/wiki/타다
* ↑ From Old English tannian (“to tan a hide”), from Latin tannare. To change to a tan colour due to exposure to the sun. To change an animal hide into leather by soaking it in tannic acid.
# Korean/Words/짐승
## 짐승

RR: jimseung
* 몸에 털이 나고 네 발을 가진 동물.
* 사람이 아닌 동물을 이르는 말.
* 매우 잔인하거나 야만적인 사람을 비유적으로 이르는 말.

### Etymology

    From Buddhist 衆生(중생, jungsaeng)
* ↑ Excluded 날짐승 또는 물짐승 (bird or fish) wikt: deer #English 4. (obsolete...) an animal, especially a quadrupedal mammal, as opposed to a bird, fish, etc. 1606, William Shakespeare, King Lear, Act III. IV But mice and rats and such small deer, have been Tom's food for seven long year.
# Korean/Words/찬송
## 찬송

    RR: chan-song (讚頌)
* to praise, extol, pay tribute to
* hyms, psalm
* to praise god

### Hypernyms

* 찬 (chan) 讚 #Chinese
* 송 (song) 頌 #Chinese

### Relatives

* 기리다 (girida, "to praise")
* 기림 (girim, "praise")
* 기림2 (girim, dialectal "oil")

### Comparatives

* chanson #English
** Any song with French words, but more specifically a classic, lyric-driven French song.
** (obsolete) A religious song.

### References

* ↑ Naver: 찬송2 미덕을 기리고 칭찬함. [같은 말] 찬송가(1. 신성한 대상을 찬미하는 노래). [기독교] 하나님의 은혜를 기리고 찬양함. 또는 그런 일. Wikt: 讚頌 to extol, praise
* ↑ to praise; to commend; to eulogize
* ↑ to laud, acclaim hymn i.e., song! ode
* ↑ Quotations 1602 : Hamlet by William Shakespeare, act 2 scene 2 line 357 The first row of the pious chanson will show you more
# Korean/Words/참나무

* ㄱ ㄲ ㄴ ㄷ ㄸ ㄹ ㅁ ㅂ ㅃ ㅅ ㅆ ㅇ ㅈ ㅉ ㅊ ㅋ ㅌ ㅍ ㅎ -ㄱ-ㄲ-ㄴ-ㄷ-ㄸ-ㄹ-ㅁ-ㅂ-ㅃ-ㅅ-ㅆ-ㅇ-ㅈ-ㅉ-ㅊ-ㅋ-ㅌ-ㅍ-ㅎ- 말+/말씀+/물+/불+ a2z/Basics/News/Notes/Table/Legend/Sandbox

## 참나무
### Noun

* 참나뭇과의 낙엽 교목. 높이는 20~25미터이며, 잎은 어긋나고 긴 타원형으로 가장자리에 톱니가 있다. 5월 무렵에 누런 갈색 꽃이 피고 열매는 다음 해 10월에 견과(堅果)를 맺는다. 열매는 묵을 만드는 데 쓰고 목재는 가구의 재료로 쓴다. 한국, 중국, 대만, 일본, 미얀마, 네팔 등지에 분포한다.
    oak

### Synonyms

* 악나무* (ak-namu)
* 떡갈나무 (tteoggal-namu, "Japanese emperor oak")
* 상수리나무 (sangsuri-namu, "sawtooth oak")

### Relatives

* 도토리 (dotori, "acorn")
* 상수리 (sangsuri, "acorn")

### Compounds

* 참나무숯 (-sut, "oak charcoal")
* 참숯 (cham-sut, "oak charcoal")

### Comparatives

* oak #Translations
* Danish: eg, egetræ
* Dutch: eik
* English: oak
* Faroese: eik, eikitræ
* Icelandic: eik
* Norwegian: eik, eiketre
* Swedish: ek
* German: Eiche

### See also

* 너도밤나무 (neodo-bamnamu, a kind of "beech")
* 박달나무
* ↑ https://ko.dict.naver.com/#/search?query=참나무
* ↑ https://en.wiktionary.org/wiki/참나무
# Korean/Words/책벌레

* ㄱ ㄲ ㄴ ㄷ ㄸ ㄹ ㅁ ㅂ ㅃ ㅅ ㅆ ㅇ ㅈ ㅉ ㅊ ㅋ ㅌ ㅍ ㅎ -ㄱ-ㄲ-ㄴ-ㄷ-ㄸ-ㄹ-ㅁ-ㅂ-ㅃ-ㅅ-ㅆ-ㅇ-ㅈ-ㅉ-ㅊ-ㅋ-ㅌ-ㅍ-ㅎ- 말+/말씀+/물+/불+ a2z/Basics/News/Notes/Table/Legend/Sandbox

## 책벌레
### Noun

* 지나치게 책을 읽거나 공부하는 데만 열중하는 사람을 놀림조로 이르는 말.
    bookworm
    cf. Bookworm (insect)
    The term is also used idiomatically to describe an avid or voracious reader, or a bibliophile. In its earliest iterations, it had a negative connotation, referring to someone who would rather read than participate in the world around them. Over the years its meaning has drifted in a more positive direction.

### Synonyms

* 공붓벌레 (gonbu-s-beolle, lit. "study worm")

### Relatives

* 책 (chaeg, "book")
* 벌레 (beolle, "worm")
** 딱정벌레 (ttagjeong-, "beetle")
** 좀벌레 (jom-, "moth")

### Comparatives

* From bookworm #Translations
* Danish: bogorm
* Dutch: boekenwurm
* English: bookworm
* German: Bücherwurm
* Korean: 책벌레 (chaekbeolle)
* Norwegian: bokorm
* Swedish: bokmal
* ↑ https://ko.dict.naver.com/#/search?query=책벌레
* ↑ Any of various insects that infest books. (figuratively) An avid book reader.
* ↑ Literally meaning "book moth," its sound is close to bokmål "Norwegian language".
# Korean/Words/치우
## 치우
### Hanja: 蚩尤

* 고대 동북 아시아의 전설적 전쟁신
    Chiyou, the ancient Far-East god of war.

### Comparatives

* Tiu or Tiw
* Tyr or Týr

### See also

* Tuesday, meaning "Tiw's day"
* Thing, the ancient Germanic assembly
* Mars Thingsus in Latin, meaning "Mars or the war god characteristic of the Thing"
* Tinghus in Norwegian, meaning "Courthouse", literally, "Thing-house" cf. Korean/Words/텽집
* ↑ Mandarin (Pinyin): Chīyóu
* ↑ "The ancient Germanic god of war, identified with Tyr of Norse mythology. Possibly the god after whom Tuesday was named."
* ↑ Týr is the relevant Wikipedia page.
* ↑ "(Norse mythology) The Norse god of war, identifiable with Tiu or Tiw."
* ↑ "Týr is the namesake of the Tiwaz rune (ᛏ), a letter of the runic alphabet corresponding to the Latin letter T. By way of the process of interpretatio germanica, the deity is the namesake of Tuesday ('Týr's day') in Germanic languages, including English. Interpretatio romana, in which Romans interpreted other gods as forms of their own, generally renders the god as Mars, the ancient Roman war god, and it is through that lens that most Latin references to the god occur. For example, the god may be referenced as Mars Thingsus (Latin 'Mars of the Thing') on 3rd century Latin inscription, reflecting a strong association with the Germanic thing, a legislative body among the ancient Germanic peoples."
# Korean/Words/참개구리

* ㄱ ㄲ ㄴ ㄷ ㄸ ㄹ ㅁ ㅂ ㅃ ㅅ ㅆ ㅇ ㅈ ㅉ ㅊ ㅋ ㅌ ㅍ ㅎ -ㄱ-ㄲ-ㄴ-ㄷ-ㄸ-ㄹ-ㅁ-ㅂ-ㅃ-ㅅ-ㅆ-ㅇ-ㅈ-ㅉ-ㅊ-ㅋ-ㅌ-ㅍ-ㅎ- 말+/말씀+/물+/불+ a2z/Basics/News/Notes/Table/Legend/Sandbox

## 참개구리
### Noun

* 개구릿과의 하나. 몸의 길이는 5~9cm이며 대개 녹색을 띤 갈색에 어두운 갈색이나 검은 무늬가 있다. 머리는 세모지고 등 쪽에는 주름과 혹 같은 돌기가 많으며 배는 희거나 누런색이다. 한국, 몽골, 중국, 일본 등지에 분포한다.
    true frog

### Hypernyms;

* 개구리 (gaeguri, "frog")
* 머구리 (meoguri, "frog")

### Comparatives

* w: True frog
* Danish: Egentlige frøer
* Dutch: Echte kikkers
* English: True frog
* German: Echte Frösche (Familie)
* Korean: 악머구리 (ak-meoguri)
* Norwegian: Ekte frosker
* Swedish: Äkta grodor

### See also

* 악머구리 (ak-meoguri, "true frog")
* ↑ https://ko.dict.naver.com/#/search?query=
* ↑ https://en.wiktionary.org/wiki/
* ↑ https://ko.dict.naver.com/kokodict/#/entry/koko/악머구리 잘 우는 개구리라는 뜻으로, ‘참개구리’를 이르는 말.
# Mathematical Properties/Distributive Property

The Distributive Property means to multiply the number on the outside of the parenthesis, by each term on the inside.

## How to rewrite an equation with the Distributive Property
### Part I

Directions: Rewriting the Equation using the Distributive Property.

#### Example

    5 x 73 = (5 x 70) + (5 x 3)
So, for this problem, add a parenthesis, then add "5 x". Then add "7" after the "x", then add "0" and then parenthesis. Now add "+", another parenthesis, "5" and "x", then "3.
It's like breaking down the "73" here. For the first parenthesis problem, add "7", but since there's "3" in "5 x 73", add a placeholder, 0. Then in the second parenthesis, it's "5 x 3", but since there's no number behind the "3", add nothing. Leave 3.
Still don't understand? Take a look at these problems to help you:

#### Example

    6 x 92 = (6 x 90) + (6 x 2)

#### Example

    9 x 25 = (9 x 20) + (9 x 5)

#### Example

    7 x 71 = (7 x 70) + (7 x 1)

#### Example

    4 x 66 = (4 x 60) + (4 x 6)
Go to Mathematics Properties/Distributive Property/Part I Pretest to take the short Pretest.

### Part II

Directions: Solve for the unknown number.

#### Example

5 x 13 = (5 x _) + (5 x _)
This shouldn't be difficult. "13" - for the first equation, remember there's "1", and another number after it: 3. But you need to replace the "3" with "0". So like: (5 x 10) + (5 x 3).
Add "3", since that's the number behind "1", in "13".
This should be easy for you:

#### Example

5 x d = (5 x 30) + (5 x 9) = d is 39

#### Example

1 x z = (1 x 60) + (1 x 5) = z is 65

#### Example

4 x a = (4 x 20) + (4 x 3) = a is 23

#### Example

9 x u = (9 x 90) + (9 x 4) = u is 94
Go to Mathematics Properties/Distributive Property/Part II Pretest to take the short Pretest
# Mathematical Statistics

INTRODUCTION OF STATISTICS
The modern Development in the field of not only Management, Commerce, Economics, Social Science, Mathematics and so on but also in our life like public service, defence banking, insurance sector, tourism and hospitality police and military etc. are dependent on a particular subject known as statistics. Statistics does play a vital role in enriching a specific domain by collecting data in that field, analysing the data by applying various statistical techniques and finally making statistical inferences about the domain. In the present world, statistics has almost a universal application. Our Government applies statistics to make the economic planning in an effective and a pragmatic way. The businessman plan and expand their horizons of business on the basis of the analysis of the feedback data. The political parties try to impress the general public by presenting the statistics of their performances and accomplishments. Most of the research scholars of today also apply statistics to present their research papers in an authoritative manner. Thus the list of people using statistics goes on and on and on. Due to these factors, it is necessary to study the subject of statistics in an objective manner.
# Mathematical jigsaw puzzle

Mathematical jigsaw puzzles are, at their simplest, the rectangular cards, dominoes, triangles or other shapes that fit together like jigsaws. The pieces of this jigsaw, when correctly put together, form equalities on their faces.
To use such a learning activity the teacher can compose a number of pairs of like equations and then print out all the shapes for the pupils to find the like equations and put the jigsaw together. There is a free software (Formulator Tarsia, ) helping teachers to prepare jigsaw learning activities.
Formulator Tarsia (known earlier as Jigsaw 2005) was initially published as part of the package of resources ‘’Improving learning in mathematics: challenges and strategies’’ received in 2006 by all English secondary schools from the DFES Standards Unit. Currently, Formulator Tarsia is reworked and released in the second version by its creators at Hermitech Laboratory in Ukraine.