OpenLLM-France/wikimedia huggingface dataset:
# Real Analysis/Power Series

Please contribute to this section, it has been neglected. I have made a start, but it is not finished.

## Definition

We have already encountered series. A power series is a series of the form
$f(x)=\sum _{n=0}^{\infty }a_{n}x^{n}$ where $a_{n}\in \mathbb {R} \ \forall n\in \mathbb {N}$.
$f$ can also be seen as a real valued function. One of the first questions we will attempt to answer in this section is for which values of $x$ is $f$ is convergent.

## Convergence

We can use the root test here. We can see that
$\limsup _{n\to \infty }{\left\vert a_{n}x^{n}\right\vert }^{1/n}=\vert x\vert \limsup _{n\to \infty }{\left\vert a_{n}\right\vert }^{1/n}=\vert x\vert R$
from before, so we see that there is a radius $r=1/R$ such that $f$ converges for $\vert x\vert <r$ and diverges for $\vert x\vert >r$. This radius has a special significance in Complex analysis, but we will not be concerned with that here.

## Differentiability

We can see by the root test that if $\sum _{n=0}^{\infty }a_{n}x^{n}$ is convergent, then $\sum _{n=0}^{\infty }(n+1)a_{n+1}x^{n}$ is convergent, as $\limsup _{n\to \infty }\vert (n+1)a_{n+1}\vert ^{1/n}=\limsup _{n\to \infty }\vert a_{n}\vert ^{1/n}$, since $\lim _{n\to \infty }(n+1)^{1/n}=1$, so this power series has the same radius of convergence as the original power series. Intuitively, we would guess that this was the derivative of it, but that requires proof. We look at the newton quotient:
$f^{\prime }(x)=\lim _{h\to 0}{\frac {\sum _{n=0}^{\infty }a_{n}(x+h)^{n}-\sum _{n=0}^{\infty }a_{n}x^{n}}{h}}$
$f^{\prime }(x)=\lim _{h\to 0}{\frac {\sum _{n=0}^{\infty }a_{n}(x+h)^{n}-a_{n}x^{n}}{h}}$
$f^{\prime }(x)=\lim _{h\to 0}{\frac {\sum _{n=0}^{\infty }a_{n}(x^{n}+nhx^{n-1}+o(h^{2})-x^{n})}{h}}$
$f^{\prime }(x)=\sum _{n=0}^{\infty }na_{n}x^{n}-1=\sum _{n=0}^{\infty }(n+1)a_{n+1}x^{n}$

## Taylor Series

One use of power series is to approximate functions. We can see that $f(0)=a_{0}$, so if a power series $f$ is a good approximation for $g$, then $a_{0}=g(0)$.
We can also see from [[#Differentiability|]] that we need $1.f^{\prime }(0)=a_{1}$, and that $2.f^{\prime \prime }(0)=a_{2}$, and by induction that $n!.f^{(n)}(0)=a_{n}$, so we define the Taylor series of $f$ as
$\sum _{n=0}^{\infty }{\frac {f^{(n)}(0)}{n!}}x^{n}$
By translation, we can also approximate $f$ by
$\sum _{n=0}^{\infty }{\frac {f^{(n)}(t)}{n!}}(x-t)^{n}$
To do this, we of course require that $f$ is differentiable an infinite number of times at o or t.
# Kumbayah my Lord

Gospel – Text and melody: trad., arranged by Mjchael
* Kum-ba-[D]yah my Lord[(D]-[G)]kumba-[D]yah[D] Kum-ba-[D]yah my Lord[(D]-[G)]kumba-[A]yah[A] Kum-ba-[D]yah my Lord[(D]-[G)]kumba-[D]yah} [(D]- [G)]Oh [D]Lord [(Em]- [A$^{(7)}$)]Kumba [D]yah [D]
* Someone’s[D]laughing, Lord[-[G)]kumba-[D]yah..
* Someone’s[D]crying, Lord[-[G)]kumba-[D]yah...
* Someone’s[D]praying, Lord -[G]kumba-[D]yah...
* Someone’s[D]singing, Lord -[G]kumba-[D]yah...

## Rhythm problems

The first chord change occurs in the middle of the bar without a chord change at the beginning of the bar. This is a particular difficulty for beginners. Normally you do not notate a chord again if there has been no change of fingering beforehand. It is also unusual for normal songbooks to indicate a quick chord change with brackets. You need some playing experience in order not to be surprised by such a quick chord change. So you need to remember everything you have learned about the quick chord change in order to play a chord for 1½ bars and then only change to the next chord in the second half of the bar.
* You start with an upbeat.
* Then you play the D major chord for a whole bar.
* Then you play the D for another half bar,...
* ...before switching to G in the second half of the bar.
In the course of the individual verses, less and less help is given. With some playing experience, you will later be able to hear when a fingering change is necessary.
Kumbayah my Lord Kumbayah my Lord Kumbayah my Lord Kumbayah my Lord Kumbayah my Lord Kumbayah my Lord Kumbayah my Lord
# Songbook/Introduction

This textbook grows by volunteer cooperation of all, who like to contribute to it. All chapters of this book can be created and expanded by anybody.
The goal is to get a songbook with freely licensed songs for various occasions. These songs can be arranged for all instruments. Thus the song book addresses itself to a quite large target group. Above all, however, lyrics with chord accompaniments will be collected.
In this book collected songs (folk songs) or just pieces of melody and exercise .
This collection is used to supply examples for the book projects like a guitar course.
The preparation of this book have been done from the German Wikibooks. The already prepared songs shall be the basis for this book.
These Songbook can be supplemented and be expanded by anybody.
Please help to take the songs of the German Wikibooks. It is much easier for a native speaker to insert the necessary headers and right categories.

## Cross Reference
### results in

Guitar/Quick Chord Change

## Songheader
### results in

myFolksong – Alternative title: my2ndTitle, Text: myPoet, Melody : myComposer, Text and melody: myAuthor, Key: myModes, arranged by it'sMe and helpsMe and noWikibooksUser

### copy
## Song
### 1st

Text [G]text text [Em]text text Text [C]text text [D]text text

### Chorus

Text [G]text text [D7]text text
Copy chord's or templates for notes and tablatures from similar songs and adapt them to your needs.
# Mama Don't Allow

“Mama Don't Allow” is a traditional song from the United States. The first recording is by YT Riley Puckett (1928). The song was the focus of the cartoon YT "The Kids in the Shoe" (1935).
The film and the song are about a mother who doesn't allow music in her own four walls, but her children don't care about that.
The song has been covered numerous times by various artists with different lyrics, melodies and musical styles (blues, jazz, country, swing, bluegrass, rock'n'roll...} and is equally suitable for the opening, as an encore or as a musical introduction to the artists involved. The melody is varied more or less in almost every verse.
* Johnny Cash performed the song on February 17, 1971 on The Johnny Cash Show with his wife June Carter and many other guest artists.
* Dudley Moore performed it on The Muppet Show in 1979.
* In 1975 it appeared with Steve Goodman on the album Jessie's Jig and Other Favorites and Doc Watson on the album Memories.

## Mama Don't Allow
### 1

[G]Mama don't allow no music playin' round here Mama don't allow no music playin' round [D]here Well, [G]we don't care what Mama don't allow Gonna [C]play that music anyhow [G]Mama don't allow no [D]music playin' round [G]here

### 2

[G]Mama don't allow no guitar playin' round here Mama don't allow no guitar playin' round [D]here Well, [G]we don't care what [G7]Mama don't allow Gonna [C]play that guitar anyhow [G]Mama don't allow no [D7]guitar playin' round [G]here

### 3

[G]Mama don't allow no singin' round here Mama don't allow no singin' round [D7]here Well, [G]we don't care what [G7]Mama don't allow
Gonna [C]sing that song [A7]anyhow [G]Mama don't allow no singin' round [G]here

### 4

[G]Mama don't allow no hand clapping here [(/C /B /A)] Mama don't allow no hand clapping [D]here [(/D /E /F#)] Well, [G]we don't care what [G7]mama don't allow We're gonna [A7]clap our hands [D7]anyhow [G]Mama don't a-[Em]llow no [A7]hand [D7]clapping [G]here [(/G /E /F#)]

### 5

[G]Mama don't allow no foot stompin' round here Mama don't allow no foot stompin' round here Well, [G]we don't care what [G7]Mama don't allow Gonna [C]stomp my feet [A7]anyhow [G]Mama don't a-[Em]llow no [A7]foot stomp[D7]in' round [G]here[C]-[G]
* No banjo playing
* No Lindy dancing
* No trombone blowing
* No jazz playing
* etc.

## Weblinks

* no:Mama Don’t Allow (source for the infos)
* en:The Kids in the Shoe
* YT Mama Don't Allow
* YT Mama Don't Allow (Pokey LaFarge)
* YT Mama Don't Allow (Johnny Cash)
* YT Mama Don't Allow (Dudley Moore + Muppets)
* YT Mama Don't Allow (Steve Goodman)
* ↑ [(/C /B /A)] = Individual bass notes that together form a bass line
# My Bonny Is Over The Ocean

Shanty – Alternative title: "Bring Back My Bonnie To Me","My Bonnie Lies Over The Ocean", Text and melody: trad., arranged by Mjchael
These Scottish folk song was first published in 1882 by Charles E. Pratt. It probably goes back to even earlier versions. The song became an evergreen and was even sung by the Beatles.
A woman dreams of the death of her husband, whom she misses dearly. She wishes that the sea winds would bring him back, which they do.

## My Bonnie is over the ocean
### 1st (simple major cadence)

My [D]Bonnie is [G]over the [D]ocean,
my Bonnie is [G]over the [A]sea, my [D]Bonnie is [G]over the [D]ocean,
O [G]bring back my [A]Bonnie to [D]me.

### Chorus

[D]Bring back, [G]bring back,
O [A]bring back, my [A7]Bonnie to [D]me, to me, Bring back, [G]bring back,

### 2nd (with relative minor)

[D]O blow ye [G]winds over the [D]ocean,
O blow ye [Em]winds over the [A]sea, [A7] [D]O blow ye[G] winds over the[D] ocean,
and [Em]bring back my [A]Bonnie to [D]me.

### chorus

[D]Bring back, [Em]bring back,
O [A]bring back, my [A7]Bonnie to [D]me, to me, Bring back, [Em]bring back, O [A7]bring back my Bonnie to [D]me.

### 3th (with secondary dominant)

Last [D]night as I [G]lay on my [D]pillow,
last night as I [E7]lay on my [A]bed, [A7]
last [D]night as I [G]lay on my [D]pillow,
I[E7] dreamed that [A7]my Bonnie was [D]dead.

### Chorus

[D]Bring back, [E7]bring back,
O [A]bring back, my [A7]Bonnie to [D]me, to me, Bring back, [E7]bring back,
O [A7]bring back my Bonnie to [D]me.

### 4th (with alternating bass and bass line)

The [D]winds have blown [G] over the [D]ocean, [/A] the winds have [E7] blown over the[A] sea, [/A /B /C#]
the [D]winds have [G]blown over the [D]ocean, [/A] and [Em] brought back my [/A /B /C#] Bonnie to [D]me.

### Chorus

[D/A]brought [D]back, [Em/B]brought [Em]back O [A]brought back, my [/A /B /C#]Bonnie to [D]me, to[D/F#] me, [D/A]brought [D]back, [Em/B] brought [Em]back, O [A]brought back, my [/A /B /C#]Bonnie to [D]me.
Do you know the lyrics a little differently? Don't wonder! With old folk songs the lyrics and the melody vary just as much as the rhythm.

### Weblinks

My Bonnie
Template:Navigation hoch Liederbuch/ Vorlage:Kategorien
# Oh, Mary, don't you weep

Spiritual – arranged by Mjchael
The song tells the Biblical story of Mary of Bethany and her distraught pleas to Jesus to raise her brother Lazarus from the dead.

## CHORUS

[G] Oh, Mary, don't you [D] weep, don't mourn; [D7] Oh, Mary, don't you [G] weep, don't mourn; [C] Pharaoh's army got [G] drowned, Oh, [D] Mary, don't you [G] weep.

## 1

[G] Well if I could I surely [D] would, [D7]Stand on the rock where [G] Moses stood. [C] Pharaoh's army got [G] drowned, Oh, [D] Mary, don't you [G] weep.

## 2

[G] One of these morns about [D] twelve o' clock [D7] This old world is going to [G] reel and rock [C] Pharaoh's army got [G] drowned, Oh, [D] Mary, don't you [G] weep.

## Weblinks

* YT Mary Don't You Weep
# Ox-Driving Song

Folk Song (USA) – Text and melody: Jimmie Driftwood (*1907–†1998), arranged by Mjchael

## Ukulele (gcea)

| Am | G |

## With tabs

The 0 in parentheses only means that the note from the previous bar (the syllable "mud") is held out.

## The Ox-Driving Song
### 1

[Am]Pop my whip and I bring the blood I [G]make the leaders take the mud; We grab the [Am]wheels and we turn them around One [G]long, long pull and we're [Am]on hard ground.

### Chorus

To me [Am]rol, to me rol, to my rideo To me [G]rol, to me rol, to my rideo To my ride- [Am]o, to my rudeo To me [G]rol, to me rol, to my [Am]rideo

### 2

On the [Am]fourteenth day of October-o I [G]hitched my team in order-o To drive the [Am]hills of Saludio To me [G]rol, to me rol, to my [Am]rideo

### 3

When [Am]I got there the hills were steep, 'Twould [G]make any tender-hearted person weep To hear me [Am]cuss and pop my whip And [G]see my oxen [Am]pull and slip.

### 4

When I [Am]get home I'll have revenge, I'll [G]land my family among my friends. I'll bid ad- [Am]ieu to the whip and line And [G]drive no more in the [Am]wintertime.

## Weblinks

YT Ox-Driving Song auf Youtube
* Adapted from the German Wikibooks: b:de:Liederbuch/ Ox-Drawing-Song
# Songbook/La Bamba

Mexican folk song – Text and melody: trad. from Mexico (Veracruz) at the end of the 16th century., arranged by Mjchael

# La Bamba
## Ukulele (gcea)

| D | G | A |

## (D G) A (2x)

    Para bailar la[(D]Bamba[G)] - [A]
    Para bailar la[(D]Bamba. - Se[G)]neces-[A]ita
    una poca de [(D]gracia[G)] - [A]
    Una poca de [(D]gracia pa[G)] mi y pa[A]ti
    Y arriba y ar-[(D]riba,[G)] - [A]
    Y arriba y ar-[(D]riba. Por [G)]ti se-[A]ré,
    por ti se-[(D]ré, por[G)]ti se-[A]ré,
    Yo no soy mari-[(D]nero.[G)] - [A]
    Yo no soy mari-[(D]nero.[G)]Soy capi-[A]tán.
    Soy capi-[(D]tán. Soy[G)]capi-[A]tán.[A]
    [(D]Bam-[G)]ba,[A]bamba
    [(D]Bam-[G)]ba,[A]bamba
    [(D]Bam-[G)]ba,[A]bamba.

## Weblinks

* YT La Bamba
* La Bamba (song)
Kategorie:Liederbuch/ Lagerfeuerdiplom Kategorie:Liederbuch/ Lieder auf Spanisch
* ↑ For the dance La Bamba (The "Sway" from Spanish: "bambolear" = "to rock, to swing up and down“. Another interesting wordplay is "Bambolero", which means a fickle man and is usually used in the sense of "boaster, braggart, show-off", and could therefore refer to the text. (see article in Wikipedia)
* ↑ you need (literally: it is necessary)
* ↑ ein wenig (von der) Grazie
* ↑ for me and for you
* ↑ and on (in the sense of "and off we go - let's go")
* ↑ I will be (one) for you.
* ↑ I am not a sailor
* ↑ (but) a captain
# Songbook/Oh, Susanna

Liederbuch/ Vorlage:Querverweis

# Oh, Susanna

Liederbuch/ Vorlage:Liedheader
Stephen Collins Foster (*1826 - †1864) was the most famous songwriter in the USA at the time. Many of his songs are still well-known 150 years after they were written. The song "Oh Susanna" is Stephen Foster's biggest hit.

## Oh, Susanna

| Gitarre | Ukulele (gcea) | Ukulele (adf#h) |
| | G C D | G C D |

## With tabs
### 1

    I[G]came from Alabama, with my banjo on my[D]knee,
    I'm[G]going to Louisiana, my[D]true love[']for to[G]see;
    It[G]rain'd all night the day I left, the weather it was[D]dry,
    The[G]sun so hot, I froze to death, Su-[D]sanna[']don't you[G]cry.

### Ref.

    O-[C]-oh! Susanna, oh[G]don't you cry for[D]me,
    I've[G]come from Alabama with my[D]banjo[']on my[G]knee.

### 2

    I[G]had a dream the other night when every thing was[D]still,
    I[G]thought I saw Susanna a[D]coming[']down the[G]hill;
    The[G]buck-wheat cake was in her mouth, the tear was in her[D]eye;
    Says[G]I, "I'm coming from the South. Oh, Su-[D]sanna[']don't you[G]cry."

### 3

    I[G]soon will be in New Orleans, and then I'll look[D]around,
    And[G]when I find Susanna, I will[D]fall up-[']on the[G]ground.
    And[G]if I do not find her,
    this darkey'll surely[D]die,
    And[G]when I'm dead and buried.
    Oh, Su-[[G]sanna,[D]]don't you[G]cry.
After you have completed the fifth lesson, you can also use the D a little later by means of a "quick chord change".

### Accompanying proposal

These chords and rhythm have been simplified for beginners. The D major chord is played a little earlier than necessary in the simplified version, which makes the accompaniment easier.
The song sounds better (in my opinion) if you play D major half a bar later. For this you need a quick chord change which is described in lesson 5 of the campfire diploma. The "later" version of the D major chord is marked with an apostrophe.

## Solo

There is a solo version of the song for b:de:Gitarre: Melodiepicking - Oh Susanna

## Weblinks

* (en) Oh! Susanna
* (en) Stephen Foster
* Template:Youtube-Suche
# Oh My Darling Clementine

American folksong – Alternative title: "Oh my Darling" / "Clementine", Text: Percy Montrose (publ. 1884) ascribed; sometimes Barker Bradford, Melody : is probably acquired by the song "Down by the River Liv'd a Maiden" by HS Thompson (publ. 1863), arranged by Mjchael
| Gitarre | Ukulele (gcea) |
| | C G G7 |

## Oh My Darling Clementine
### 1.)

    In a[C]cavern, in a canyon, - Excavating for a[G]mine
    Dwelt a[G7]miner forty[C]niner, - And his[G]daughter Clemen-[C]tine

### Chorus

       Oh my[C]darling, oh my darling, - Oh my darling, Clemen-[G]tine!
       Thou art[G7]lost and gone for-[C]ever - Dreadful[G]sorry, Clemen-[C]tine.

### 2.)

    Light she[C]was and like a fairy, - And her shoes were number[G]nine,
    Herring[G7]boxes, without[C]topses, - Sandals[G]were for Clemen-[C]tine.

### 3.)

    Drove she[C]ducklings to the water - Ev'ry morning just at[G]nine,
    Hit her[G7]foot against a[C]splinter, - Fell in-[G]to the foaming[C]brine.

### 4.)

    Ruby[C]lips above the water, - Blowing bubbles, soft and[G]fine,
    But, alas, I[G7]was no[C]swimmer, - So I[G]lost my Clemen-[C]tine.

### 5.)

    How I[C]missed her! How I missed her, - How I missed my Clemen-[G]tine,
    But I kissed her[G7]little[C]sister, - I for-[G]got my Clemen-[C]tine.
    Guitar - Oh My Darling Clementine - Folkpicking.mid (help·info)
    Media:Guitar - Oh My Darling Clementine - Folkpicking.pdf
# Rock my Soul

Songbook/Template:Liedheader Abraham's bosom alludes to "The parable of the rich man and Lazarus"; a biblical story from the New Testament. (see Template:Bible) Only children are actually allowed to sit on the lap of a grandfather (symbolic of Abraham's forefather). And then it is usually the grandchildren and close relatives who enjoy a close relationship of trust. The song thus expresses the deep desire to experience such trust in God for oneself.
There is hardly a gospel choir that does not have this song in its repertoire. The text is so easy that the audience can sing along immediately. This gospel has been covered very often. To name just a few: Golden Gate Quartet (1938), Les Humphries Singers, Peter, Paul & Mary, Louis Armstrong, Nana Mouskouri, Elvis Presley and many more.
| Gitarre | Westernschlag | Ukulele (gcea) |
| | | D A |
(The accompaniment was generated automatically and is only similar to the guitar accompaniment.)

## Verse 1

    [D]Rock my soul in the bosom of Abraham, [A]Rock my soul in the bosom of Abraham,
    [D]Rock my soul in the bosom of Abraham, [A]oh rock my[D]soul.

## Verse 2

    So[D]high, you can't get over it, so[A]low, you can't get under it,
    so[D]wide, you can't get round of it, [A]oh rock my[D]soul.

## Verse 3

[D]Rock - my - soul - [A] Rock - my - soul [D]Rock - my - soul - [A] oh rock my[D]soul.

## Rock my Soul (in E major)

| guitar | 4/4-strumming | Ukulele (adf#h) |
| File:Crd B7.svg | | E B7 |

## Rock my Soul
### Verse 1

    [E]Rock my soul in the bosom of Abraham, [B7]Rock my soul in the bosom of Abraham,
    [E]Rock my soul in the bosom of Abraham, [B7]oh rock my[E]soul.

### Verse 2

    So[E]high, you can't get over it, so[B7]low, you can't get under it,
    so[E]wide, you can't get round of it, [B7]oh rock my[E]soul.

### Verse 3

[E]Rock - my - soul - [B7] Rock - my - soul [E]Rock - my - soul - [B7] oh rock my[E]soul.

## Weblinks

* YT Rock my Soul
Template:Navigation hoch Songbook/Template:categories
# Partial Differential Equations/Introduction

The theory of partial differential equations is a tour de force through undergraduate analysis and serves well to connect several topics as methods for the solution of a common problem.
There are several lines of attack towards PDEs, and we aim to present some of the most useful ones. Some very important classical partial differential equations have their own chapter, for sometimes the solution techniques geared towards them do not generalize to any other equation, at least not verbatim.
# Partial Differential Equations/Elliptic equations

Proposition (existence and uniqueness of weak solutions of a simple elliptic equation):
Let $I=[a,b]$ be a real interval and $A\in L^{\infty }(I)$ s.t. there exists $\alpha >0$ s.t. for almost every $x\in I$ we have $A(x)\geq \alpha$. The equation
    ${\begin{cases}-\partial _{x}(A(x)u(x))=f(x)&x\in I\\u(x)=0&x=a,b\end{cases}}$
admits a unique weak solution $u\in H_{0}^{1}(I)$.
# Plural

< Order of words in a sentence < ^ Polish ^ > Noun cases >
Like most other Indo-European languages, and unlike Chinese or Japanese, in Polish, the grammatical number of nouns, pronouns, adjectives, and verbs can be either singular or plural (pojedyncza and mnoga).
Let's first examine how verbs change in the singular and plural forms.
| Meaning | Singular | Singular | Singular | Plural | Plural | Plural |
| Meaning | First person | Second person | Third person | First person | Second person | Third person |
| To eat | jem | jesz | je | jemy | jecie | jedzą |
| To drink | piję | pijesz | pije | pijemy | pijecie | piją |
| To see | widzę | widzisz | widzi | widzimy | widzicie | widzą |
| To read | czytam | czytasz | czyta | czytamy | czytacie | czytają |
| To write | piszę | piszesz | pisze | piszemy | piszecie | piszą |
| To be | jestem | jesteś | jest | jesteśmy | jesteście | są |
| To have | mam | masz | ma | mamy | macie | mają |
| To think | myślę | myślisz | myśli | myślimy | myślicie | myślą |
| To drive | jadę | jedziesz | jedzie | jedziemy | jedziecie | jadą |
| To give | daję | dajesz | daje | dajemy | dajecie | dają |
Now, let's look at how some nouns change in the singular and plural forms:
| Gender | Meaning | Singular | Singular | Plural | Plural |
| Gender | Meaning | Nominative | Accusative | Nominative | Accusative |
| Feminine | Girl | Dziewczyna | Dziewczynę | Dziewczyny | Dziewczyny |
| Neuter | Child | Dziecko | Dziecko | Dzieci | Dzieci |
| Neuter | Beer | Piwo | Piwo | Piwa | Piwa |
| Person-masculine | Boy | Chłopak | Chłopaka | Chłopcy | Chłopców |
| Animate-masculine | Cat | Kot | Kota | Koty | Koty |
| Inanimate-masculine | Computer | Komputer | Komputer | Komputery | Komputery |
As you can see, with the exception of person-masculine, the nominative and accusative are the same in the plural (in the person masculine accusatives are the same as genitives).
Like in other Indo-European languages, the verb agrees with the subject.
* Basia ma chomiki. - Basia has (owns) hamsters.
* Dziewczyny mają komputer. - The girls have a computer.
* Koty piją mleko. - The cats are drinking milk.
< Order of words in a sentence < ^ Polish ^ > Noun cases >
# Polish/Order of words in a sentence

< More on nouns - genders < ^ Polish ^ > Plural >
In Polish, word order within a sentence is flexible, and the subject or object can be omitted if they are clear from the context.
Consider the following sentences, all of which translate to "Henia has a cat", but are used in different contexts:
* Henia ma kota (simple statement)
* Henia kota ma (emphasizing that it's a cat that Henia has)
* Kota ma Henia (emphasizing that it's Henia who has a cat)
* Ma Henia kota
* Kota Henia ma (emphasizing the action "has")
* Ma kota Henia
The first word order is the most common. Other orders are used for emphasis.
If the subject, object, or verb is clear from the context, it can be dropped:
* Ma kota - can be used if it's clear who is being talked about
* Ma - can be an answer to "Czy Henia ma kota?" (Does Henia have a cat?)
* Henia - can be an answer to "Kto ma kota?" (Who has a cat?)
* Kota - can be an answer to "Co ma Henia?" (What does Henia have?)
* Henia ma - this is less natural. In Polish, there is a tendency to drop the subject rather than the object, especially when the object is known but the subject is not. If the question was "Kto ma kota?" (Who has a cat?), the answer should be "Henia" alone, without a verb.
In particular, the pronouns "ja" and "ty", and their plural equivalents "my" and "wy", are almost always dropped.
< More on nouns - genders < ^ Polish ^ > Plural >