OpenLLM-France/wikimedia huggingface dataset:
# Elementary Spanish/Birthday party
## Goals

By the end of this lesson, you should know key vocabulary words for birthday parties.

## Lesson

Let's begin with some vocabulary building excercises.

### Exercise 1: Picture matching

Picture match activity
This is an interactive lesson where your goal is to select the picture that matches the phrase at the top of the screen. If you click on the wrong picture it will gray out and you can click again to choose another picture. If you want to start the lesson over just reload the page.

### Exercise 2: Audio lesson

Audio lesson activity
This is an audio lesson. You can either listen online and read the transcript as you go, or you can download the lesson and listen to it on your phone or music player.

### Exercise 3: Example dialogue
#### Synopsis

In the following scene, a mom lets her daughter know what she will do on her birthday.

#### Dialogue

mamá: ¡Hoy es tu cumpleaños! Feliz cumpleaños.
hija: Gracias, mamá. ¿Vamos a tener una fiesta?
mamá: Si. También vamos a tener un pastel con velas.
hija: ¿Tengo que soplar la lumbre?
mamá: Tienes que soplar la lumbre de las velas, cortar el pastel y quebrar la piñata.
hija: Y comer muchos dulces, también, ¿verdad?
mamá: Si. Es tu cumpleaños.

### Vocabulary words

* cake - pastel
* candles - velas
* piñata - piñata
* fire - lumbre
* birthday - cumpleaños
* candy - dulces
* party - fiesta
* break - quebrar
* cut - cortar
* blow - soplar
# Lessons

* 1. Talking with each other
* 2. Talking with your children
* 3. Talking with acquaintances
# Elementary Spanish/Future Holiday Plans/Talking with each other
## Vocabulary

Word match activity
VOY Chart
| Cooking | Voy a cocinar |
| Presents | Regalos |
| Visiting | Voy a visitar |
| Traveling | Voy a viajar |
| Celebrating | Voy a celebrar |
| Christmas | Navidad |
| Kwanzaa | Kwanzaa |
| Hanukkah | Hanukkah |
| Winter Solstice | Solsticio de Invierno |
| Diwali | Diwali (festival de las luces |
| Day of the Dead | Día de los Muertos |

## Possible questions for language exchange

| What will you be celebrating? | ¿Qué vas a celebrar? |
| How will you be celebrating? | ¿Cómo vas a celebrar? |
| Who will you be celebrating with? | ¿Con quien vas a celebrar? ¿Quién va celebrar con tigo? |
| Where will you go? | ¿Dónde vas a ir? |
| How will you get there? | ¿Cómo vas a viajar allí? |
| How long will you be there? | ¿Cuánto tiempo vas estar allí? |
Practice with these terms in this interactive exercise: Question practice activity

## Dialogue

Audio lesson activity
Tanicia: ¡Feliz días de fiestas!
Lucrecia: ¡Feliz fiestas para ti y tu familia.
Tanicia: ¿Qué vas a celebrar esta época de fiestas?
Lucrecia: Este año vamos a visitar mi familia en Minnesota. Eso indica que vamos a celebrar solamente Navidad este año.
Tanicia: ¿Cómo celebras Navidad con tu familia?
Lucrecia: Mi mama, mis hijos y yo asemos tamales en la cocina juntos.
Tanicia: Mm, que rico. ¿Me guardas unos?
Lucrecia: Por supuesto. ¿Qué vas a celebrar este época de fiestas?
Tanicia: Vamos a celebrar Kwanza este año.
Lucrecia: ¿Vas a un lugar?
Tanicia: Vamos a la casa de unos amigos que viven cercas. Vamos a cocinar juntos y pasar tiempo juntos.
Lucrecia: Vamos a tener un gran tiempo este época de fiestas.

## Links and Resources

* Word match activity
* Question practice activity
* Audio lesson activity
# Elementary Spanish/Autumn clothing
## Goals

By the end of this lesson you will know words for autumn clothing.

## Lesson

Let's begin with some vocabulary building excercises.

### Exercise 1: Picture matching

Picture match activity
This is an interactive lesson where your goal is to select the picture that matches the phrase at the top of the screen. If you click on the wrong picture it will gray out and you can click again to choose another picture. If you want to start the lesson over just reload the page.

### Exercise 2: Audio lesson

[Placeholder for audio lesson activity]
This is an audio lesson. You can either listen online and read the transcript as you go, or you can download the lesson and listen to it on your phone or music player.

### Exercise 3: Example dialogue
#### Synopsis

In the following dialogue Diego discusses the needs of autumn clothing with Enrique as he prepares for his first season change. He is used to the warm weather.
See if you could figure out "muchísimas" by finding a familiar root word.

#### Dialogue

Diego: Esta empezando el frío y no tengo ningún suéter.
Enrique: No me gustan los suéteres. Me gustan mas los sudaderos y tengo muchísimas.
Diego: ¿Tienes una gorra que me prestes?
Enrique: Si tengo muchas, pero preparate tambien para la lluvia.
Diego: ¿Lluvia?
Enrique: Si. En otoño, antes del invierno, llueve un poco.
Diego: ¿Necesito botas de la lluvia y impermeables?
Enrique: No es necesario. Si tu quieres.
Diego: ¿Que es necesario?
Enrique: Camisas de manga larga y calcetines.

### Vocabulary words

* sweater - suéter
* sweatshirt- sudadera
* hat - gorra
* long sleeved shirt - camisa de manga larga
* rain boot-botas de lluvia
* raincoat-impermeable
* socks -calcetines
# Elementary Spanish/Beach
## Goals

By the end of this lesson, you should know key vocabulary words for going to the beach.

## Lesson

Let's begin with some vocabulary building excercises.

### Exercise 1: Picture matching

Picture match activity
This is an interactive lesson where your goal is to select the picture that matches the phrase at the top of the screen. If you click on the wrong picture it will gray out and you can click again to choose another picture. If you want to start the lesson over just reload the page.

### Exercise 2: Audio lesson

Audio lesson activity
This is an audio lesson. You can either listen online and read the transcript as you go, or you can download the lesson and listen to it on your phone or music player.

### Exercise 3: Example dialogue
#### Synopsis

In the following scene, three friends, Siena, AJ and Cate, prepare for the beach.

#### Dialogue

Siena: Esta muy caliente.
AJ: Si, esta muy caliente.
Cate: ¿Vamos a la playa?
Siena: Si, pero no tengo toalla.
AJ: Esta bien. Yo tengo muchas toallas.
Cate: Tengo que comprar un traje de baño nuevo.
Siena: Yo tengo que comprar unas sandalias nuevas.
AJ: Bueno, yo tengo todo. Tengo juguetes para jugar en la arena. Podemos hacer un castillo. Tengo sillas para todas.
Cate: Yo tengo gorras!
Siena: Yo tengo paraguas.
AJ: Lo mas importante, yo tengo la caja del almuerzo.

### Vocabulary words

* towel - toalla
* beach - playa
* umbrella - paraguas
* bathing suit - traje de baño
* lunch box - caja de almuerzo
* sandals - sandalias
* sand - arena
* castle - castillo
* toys - juguete
* hat - gorra
* beach chair - silla de playa
# Free Knowledge Culture Calendar/November 11

Today in 2016 the documentary film National Bird had its theatrical release in the US.
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# Free Knowledge Culture Calendar/November 14

Today in 2017 Firefox version 57 was released, the first version with major Rust components from the experimental Servo project enabled. After research into generic solutions for memory and data-race safety in the academic world, some of the solutions were finally transferred to the front line of systems programming by integrating them into a popular, Internet-exposed piece of software.
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# Free Knowledge Culture Calendar/November 13

Today in 1974 Karen Silkwood died when she tried to deliver proof of corporate practices at a Plutonium plant to the press.
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# Free Knowledge Culture Calendar/November 17

Today in 1999 SourceForge.net was launched; the first significant product of its kind: an Internet platform that provides infrastructure for Free Software development, complete with hosting as well as development and collaboration tools.
Under frequently changing ownership and management, SourceForge was working on its own demise with questionable monetization attempts that cost trust and got the site onto on advertising and malware blocklists. For example, it was known for misleading advertisements with fake “download” buttons that were bigger and in more prominent locations than the real one, and incentivized developers to bundle their software with installers for pseudo-free spyware. When one day SourceForge seized several popular accounts and offered the software in question bundled with spyware, masses of users migrated to the now-dominant competitor Github.
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# Free Knowledge Culture Calendar/November 10

Today in 2005 the Open Invention Network, a patent non-aggression community, was founded, mostly by large technology companies.
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# Free Knowledge Culture Calendar/November 12

Today in 2005 TorrentFreak was launched.
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# Free Knowledge Culture Calendar/November 15

Today in 2005 Apple released Darwin, the open-sourced core of its new line of Unix-like operating systems that are otherwise commercial and locked down, a controversial strategy later referred to as the open-core model.
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# Free Knowledge Culture Calendar/November 16

Today in 1974 humanity made its first attempt at intergalactic communication by sending the Arecibo message. We have not yet received an answer from E.T., which will not be possible for about 60,000 years due to the stagnating progress in physics.
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# Free Knowledge Culture Calendar/November 1

Today in 1984 Hackers: Heroes of the Computer Revolution by Steven Levy was published. It documents the origins of the hacker culture and their philosophy and coined the term “hacker ethic”.
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# Free Knowledge Culture Calendar/November 18

Today in 1997 the first IEEE 802.11 Wifi standard was released. IEEE 802.11b was popularized in 1999 for local area networks in homes, cafés and workplaces (with Apple’s “Airport” routers and Macs and the “Wifi” branding), and later also for wireless community networks.
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# Famous Theorems of Mathematics/√2 is irrational

The square root of 2 is irrational, ${\sqrt {2}}\notin \mathbb {Q}$

## Proof

Assume for the sake of contradiction that ${\sqrt {2}}\in \mathbb {Q}$. Hence ${\sqrt {2}}={\frac {a}{b}}$ holds for some a and b that are coprime.
This implies that $2={\frac {a^{2}}{b^{2}}}$. Rewriting this gives $2b^{2}=a^{2}\!\,$.
Since the left-hand side of the equation is divisible by 2, then so must the right-hand side, i.e., $2|a^{2}$. Since 2 is prime, we must have that $2|a$.
So we may substitute a with $2A$, and we have that $2b^{2}=4A^{2}\!\,$.
Dividing both sides with 2 yields $b^{2}=2A^{2}\!\,$, and using similar arguments as above, we conclude that $2|b$. However, we assumed that ${\sqrt {2}}={\frac {a}{b}}$ such that that a and b were coprime, and have now found that $2|a$ and $2|b$; a contradiction.
Therefore, the assumption was false, and ${\sqrt {2}}$ cannot be written as a rational number. Hence, it is irrational.

## Another Proof

The following reductio ad absurdum argument is less well-known. It uses the additional information √2 > 1.
* Assume that √2 is a rational number. This would mean that there exist integers m and n with n ≠ 0 such that m/n = √2.
* Then √2 can also be written as an irreducible fraction m/n with positive integers, because √2 > 0.
* Then ${\sqrt {2}}={\frac {{\sqrt {2}}\cdot n({\sqrt {2}}-1)}{n({\sqrt {2}}-1)}}={\frac {2n-{\sqrt {2}}n}{{\sqrt {2}}n-n}}={\frac {2n-m}{m-n}}$, because ${\sqrt {2}}n=m$.
* Since √2 > 1, it follows that m > n, which in turn implies that m > 2n – m.
* So the fraction m/n for √2, which according to (2) is already in lowest terms, is represented by (3) in strictly lower terms. This is a contradiction, so the assumption that √2 is rational must be false.
Similarly, assume an isosceles right triangle whose leg and hypotenuse have respective integer lengths n and m. By the Pythagorean theorem, the ratio m/n equals √2. It is possible to construct by a classic compass and straightedge construction a smaller isosceles right triangle whose leg and hypotenuse have respective lengths m − n and 2n − m. That construction proves the irrationality of √2 by the kind of method that was employed by ancient Greek geometers.

## Historical Notes

First mentions of this proof claimed it was authored by Greek mathematicians of Pythagorean school, and indeed the first formal proof was presented later in Euclid's Elements. However, most of contemporaries (as well as many of today's historians of mathematics) were of the opinion that Pythagoreans themselves have borrowed almost all of their mathematics (including this proof) from Egyptian sources. Alas, destruction of the Great Library of Alexandria wiped out almost all the then extant scientific texts of that civilization so it is very likely this will forever remain a mystery.

## Notes

* As a generalization one can show that the square root of every prime number is irrational.
* Another way to prove the same result is to show that $x^{2}-2$ is an irreducible polynomial in the field of rationals using Eisenstein's criterion.
# Faroese/Chapter Ten
## Chapter Six - Corresponding via email

Many of the following examples are taken from the German language guide by Richard Kölbl: Färöisch Wort für Wort. Bielefeld, 2004.

### Write an Email

* skriva eitt teldubræv [skriːva aiʰt ˈtɛlduˌbɹɛav] - write an Email
* við telduposti [viː ˈtɛlduˌpɔstɪ] - via Email
* Kæra Sára! [ˈkɛaɹa] - Dear Sára!
* Kæri Jón! [ˈkɛaɹɪ] - Dear Jón!
* Góða Marjun! [ˈgɔʊwa ˈmaɹjʊn] - Dear Marion!
* Góði Petur! [ˈgɔji peːtʊɹ] - Dear Peter!
* takk fyri teldubrævið [ˈtɛldubɹɛavɪ] - thanks for the Email
* orsaka at eg skrivi á enskum - excuse me, for writing in English
* men tú kanst svara á føroyskum - but you can answer in Faroese
* vinaliga - sincerely yours
* vit hoyrast - we hear from each other
# Faroese/Chapter Eight
## Chapter Eight - Lodging

Do you have any rooms available? - Eru nøkur leys kømur? ( Eh-roo nuhk-ur luhys kuhm-ur )
How much is a room for one person/two people? - Hvat kostar ein einkultkamar/dupultkamar? ( Kvat kost-ar ayn-kult-kam-ar/dup-ult-kam-ar? )
Does the room come with... Kemur tað við... ( Kem-ur tya vuhy... ) ...bedsheets? ...songløkum? ( song-luhk-um ) ...a bathroom? ...bað? ( bya ) ...a telephone? ...einari telefon? ( ayn-ar-ee tel-eh-fon ) ...a TV? ...einum sjónvarpi?
May I see the room first? - Kann e.g. sleppa at síggja tað? ( Kan eh slep-a at suhy-ja tya? )
Do you have anything quieter? - Eru nøkur við stillari kami? ( Eh-roo nuhk-ur vuhy stihl-ar-ee kam-ee? )
...bigger? ...stórari? ( stur-ar-ee? )
...cleaner? ...reinari? ( rayn-ar-ee? )
...cheaper? ...bíligari? ( buhy-lee-ar-ee? )
OK, I'll take it. - Tað er fínt, e.g. taki tað. ( Tya ehr fuhynt, eh tak-ee tya )
I will stay for _____ night(s). - E.g. steðgi í _____ nátt/nætur. ( Eh steh-ee uhy _____ nott/nyat-ur )
Can you suggest another hotel? - Kunna tit bjóða annað hotell? ( Kun-a teet bju-a yana hotehl? )
Do you have a safe? Hava tit trygg? ( Hav-a teet treeg? ) ...lockers? ...skáp? ( skop? )
Is breakfast/supper included? - Er morgunmatur/døgurði uppi í? ( Ehr morg-un-mat-ur/duh-ur-ee upp-ee uhy? )
What time is breakfast/supper? - Nær er morgunmatur/døgurði? ( Nyar ehr morg-un-mat-ur/duh-ur-ee upp-ee? )
Please clean my room. - Kunna tit reinsa kamar mín? ( Kun-a teet rayn-sa kam-ar muhyn? )
Can you wake me at _____? - Kunna tit vakna meg klokkan _____? ( Kun-a teet vak-na meh klok-an _____? )
I want to check out. - Kann e.g. fáa rokningina? ( Kan eh fo-a rok-neeng-een-a? )
# Faroese/Chapter Six
## Chapter Six - Time

Many of the following examples are taken from the German language guide by Richard Kölbl: Färöisch Wort für Wort. Bielefeld, 2004.
now - nú ( noo )
early - árla ( aur-la )
later - eftir ( eft-ir )
before - fyrr ( feer )
morning - morgun ( morg-un )
afternoon - seinnapartur ( sayn-a-part-ur )
evening - kvøld ( kvuhld )
night - nátt ( nott )

### Clock Time

The Faroe Islands use the 24hr clock format like most of Europe.
one o'clock AM - klukkan er eitt (kluk-an er aytt)
two o'clock AM - klukkan er tvey (kluk-an er tvuee)
noon - á miðdegi (o mi-de-ee)
one o'clock PM - klukkan er trettan (kluk-an er tret-an)
two o'clock PM - klukkan er fjúrtan (kluk-an er fyoor-tan)
midnight - midnátt (mid-nott)
# Faroese/Chapter Four
## Chapter Four - Getting to know someone

Many of the following examples are taken from the German language guide by Richard Kölbl: Färöisch Wort für Wort. Bielefeld, 2004.
On this level, the familiar form tú is used. Be careful not to address elderly persons with it, before they don't say tú to you.

### What's your name?

* hvussu eitur tú? [kʊsːʊ aitʊɹ tʉu] - whatˈs your name?
* eg eiti Sára [eː aitɪ 'sɔaɹa] - my name is Sarah
* og tú? [oˈtʉu] - and you?
* eg eri Jón [ˈeː eːɹɪ jɔun] - I am John
* vælkomin, Sára! [ˈvɛalkoːmin] - welcome Sarah! (f.)
* vælkomin, Jón! [ˈvɛalkoːmin] - welcome John! (m.)
* mær ein gleði [mɛaɹ ain gleːjɪ] - pleased to meet you ("a pleasure for me")

### Where are you from?

* ert tú onglendingur? [ɛʂtʉu ɔŋglɛndɪŋʒʊɹ] - are you Englishman/woman?
* nei eg eri úr Amerika [nai eː eːɹɪ ʉʊr aˈmeːɹɪka] - no, I am from America
* hvar býrt tú? [ˈkvɛaɹ bʊʂt tʉu] - where do you live?
* eg búgvi í/hjá ... [ˈeː bɪgvɪ ʊi]/[ˈʧɔa] - I live in/at ...

### How old are you?

* Hvussu gamal/gomul ert tú? - How old are you? (masc./fem.)
* eg eri x ára gamal/gomul - I am x years old (masc./fem)

### Tell me about your family

* ert tú giftur/gift? [ɛʂtʉu gɪftʊr]/[gɪft] - are you married? (m./f.)
* eg eri stakur/støk [eː eːɹɪ stɛakʊɹ]/[støːk] - I am single (m./f.)
* hetta er maður/kona/drongur/genta mín [ˈhɛʰtːa eːr mɛavʊɹ]/[ˈkoːna]/[ˈdɹɔŋgʊɹ]/[ʤɛnta mʊin] - this is (may i introduce?) my husband/wife/boyfriend/girlfriend
* hevur tú børn? [ˈheːvʊr tʉu bœdn] - do you have children?

### How long will you stay?

* hevur tú verið leingi her? [ˈheːvʊɹ tʉu veɹɪ ˈlɔɲʤɪ heːr] - have you been here long?
* eg kom í gjár [eː koːm ʊiˈʤɔaɹ] - I came yesterday
* eg verði eina tvær vikur [eː veːɹɪ aina tvɛaɹ viːkʊɹ] - I will stay about two weeks
* Føroyar dámar mær væl [ˈfœrjaɹ ˈdɔamaɹ mɛaɹ vɛal] - I like the Faroes much

### Visiting someone's home

* ... vitjanina [ˈviːʧanɪna] - ... the visit
* takk fyri seinast [ˈsainast] - thanks for last time
* ... okkum/meg [ˈɔkːʊn]/[meː] - ... us/me (thanks for inviting us/me)
* set teg! [seːt teː] - sit down
* vilt tú hava ein kaffimunn? [ˈviɪlt tʉu hɛava ain kafːɪmʊn] - do you like a cup of coffee?
* e.g. vil fegin havt te [eː vɪl feːjin haft teː] - I would like some tea
* meira? [maiɹa] - more?
* tað smakkar væl [tɛa smakːaɹ vɛal] - it tastes good
* manga takk [maŋga taʰkː] - thank you very much (after a meal)
* vælgagnist [vɛalgagnɪst] - enjoy your meal (reply to the above phrase)
* e.g. má fara [eː mɔa fɛara] - I have to go
* takk fyri meg [taʰk fiːɹɪ meː] - thank you for the invitation
# Faroese/Chapter Seven
## Chapter Seven - Transportation

Many of the following examples are taken from the German language guide by Richard Kölbl: Färöisch Wort für Wort. Bielefeld, 2004.

### Going on a trip

* Where are you going to?: Hvagar fert tú? (Vahar fair-dooh)
* Have a nice trip: Góða ferð (goodah fair)
Note: There are no trains in the Faroe Islands.

### Bus

A single ticket to _____. Kundi e.g. fingið einvegis ferðasil til _____? (Kun-dee eh finj-ee ayn-vay-ees fer-a-seel teel _____?)
A return ticket to _____. Kundi e.g. fingið ferðasil aftur og fram til _____? (Kun-dee eh finj-ee fer-a-seel aft-ur o fram teel _____?)
How much does that cost? Hvat kostadddr tað? (Kvat kost-ar ta?)
Where does this bus go? Hvar fer bussurin? (Kvar fer buss-ur-in?)
Where is the bus to _____? Hvar er bussurin til _____? (Kvar fer buss-ur-een teel _____?)
Does this bus stop at _____? Steðgar bussurin hjá _____? (Ste-ar buss-ur-een hjo _____?)
When does the bus leave? Nær fer bussurin? (Nyar fer buss-ur-een?)
When does the bus leave for _____? Nær fer bussurin til _____? (Nyar fer buss-ur-een teel _____?)
When does the bus arrive? Nær kemur bussurin? (Nyar kem-ur buss-ur-een?)
When will the bus arrive in _____? Nær kemur bussurin í _____? (Nyar kem-ur buss-ur-een uee _____?)

### Boat

Which harbour is next? Hvor er næsta havn? ( Kvor ehr nya-sta havn? ) Is this the ferry for _____? Er hetta ferjan til _____? ( Ehr het-a fer-yan teel _____? )
# Faroese/Chapter Three
## Chapter Three
### Numbers

* 0 Null [ˈnʊlː]
* 1 Eitt [ˈaɪʰtː]
* 2 Tvey [ˈtvɛi]
* 3 Trý [ˈtɹʊi]
* 4 Fýra [ˈfʊiɹa]
* 5 Fimm [ˈfɪmː]
* 6 Seks [ˈsɛks]
* 7 Sjey [ˈʃɛi]
* 8 Átta [ˈɔʰtːa]
* 9 Níggju [ˈnʊʤ̊ːʊ]
* 10 Tíggju [ˈtʊʤ̊ːʊ]
* 11 Ellivu [ˈɛd̥lɪvʊ]
* 12 Tólv [ˈtœlv]
* 13 Trettan [ˈtɹɛʰtːan]
* 14 Fjúrtan [ˈfjʏɻ̊ʈan]
* 15 Fimtan [ˈfɪm̥tan]
* 16 Sekstan [ˈsɛkstan]
* 17 Seytjan [ˈʃɛiʧan]
* 18 Átjan [ˈɔaʧan]
* 19 Nítjan [ˈnʊiʧan]
* 20 Tjúgu [ˈʧʉuwʊ]
* 21 Ein og tjúgu [ ˈain ɔ ˈʧʉuwʊ]
* 22 Tvey og tjúgu [ ˈtvɛi ɔ ˈʧʉuwʊ]
* 30 Tretivu/Tríati [ˈtɹeːd̥(ɪ)vʊ/ˈtɹʊijatiː]
* 40 Fjøruti/Fýrati [ˈfjøːɹʊtɪ/ˈfʊiɹatiː]
* 50 Hálvtrýss(instjúgu)/Fimmti [hɔl̥ˈtɹʊʃː(ɪn̥sˌʧʉuwʊ)/ˈfɪm̥ːtiː]
* 60 Trýss(instjúgu)/Seksti [ˈtɹʊʃː(ɪn̥sˌʧʉuwʊ)/ˈsɛkstiː]
* 70 Hálvfjerðs(instjúgu)/Sjeyti [hɔl̥ˈfjɛʂː(ɪn̥sˌʧʉuwʊ)/ˈʃɛitiː]
* 80 Fýrs(instjúgu)/Áttati [ˈfʊʂː(ɪn̥sˌʧʉuwʊ)/ˈɔʰtːatiː]
* 90 Hálvfems(instjúgu)/Níti [hɔl̥ˈfɛm̥s(ɪn̥sˌʧʉuwʊ)/ˈnʊitiː]
* 100 Hundrað [ˈhʊnd̥ɹa]
* 1.000 (Eitt) túsund [(ˈaɪʰtː) ˈtʉusʊnd̥ > ˈtʉusɪn]
# Functional Analysis/Harmonic Analysis/Topological Groups
## Introduction

The main algebraic structure studied in harmonic analysis is the topological group. In summary, a topological group is a group whose underlying set possesses a topology compatible with the group structure.

## Exercises

* Exercises
** Hints
** Solutions

## Appendices

Here, you will find a list of unsorted chapters. Some of them listed here are highly advanced topics, while others are tools to aid you on your mathematical journey. Since this is the last heading for the wikibook, the necessary book endings are also located here.
* List of Mathematical Symbols
* List of Theorems
* References
* Index
# Functional Analysis/Harmonic Analysis/Topological Groups/Exercises

1) Give as many examples as you can of topological groups which do not fall within any of the examples we gave in section Functional Analysis 9.1.
2) Prove that the inverse of an isomorphism.
3) show that for each $x\in G$ the maps $L_{x}(y)=xy$ and $R_{x}(y)=yx$ are topological group homomorphisms.
4)
# Issues in Interdisciplinarity 2018-19/Sample chapter

This is a sample chapter for Issues in Interdisciplinarity 2018-19. The purpose is to explain how chapters will link to the main page of the Wikibook.
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