HAY TU HOC LATEX LET SEFTTAUGHT LATEX

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Ch ’u ’ong 1

C´

ˆ

au tr´

uc v˘

an b’an

1. Gi´’

oi thiˆ

e.u v `

ˆ

e TeX v`

a LaTeX

TeX l`a ch ’u ’ong tr`ınh soa.n th ’ao c´ac t`ai liˆe.u khoa ho.c v`a to´an ho.c v´’oi ch ´ˆat l ’u ’o.ng cao.
TeX ¯d ’u ’o.c vi ´ˆet b ’’oi Donald E. Knuth v`ao n˘am 1977. Trong s´ach TeX book, Knuth gı´’oi
thiˆe.u: ”TeX l`a mˆo.t hˆe. th ´ˆong x ´ˆep ch˜’u m´’oi ¯d ’ˆe ta.o ra nh˜’ung cu ´ˆon s´ach ¯de.p v`a ¯d˘a.c biˆe.t l`a
nh˜’ung cu ´ˆon s´ach c´o nhi `ˆeu k´ı hiˆe.u to´an ho.c”.

N˘am 1980, Leslie Lamport ta.o ra hˆe. th ´ˆong soa.n th ’ao v˘an b ’an LaTeX. D ’u.a trˆen ¯di.nh
da.ng c’ua TeX, Lamport vi ´ˆet thˆem c´ac lˆe.nh m´’oi d`ung cho c ´ˆau tr´uc v˘an b ’an gi´up ng ’u`’oi
s ’’u du.ng d ˜ˆe d`ang soa.n th ’ao t`ai liˆe.u.

1.1 C`

ai ¯

d˘

a.t LaTeX v`a c´ac ch ’u ’ong tr`ınh k`em theo

1. C`ai MikTeX 2.7 (download t`’u ma.ng).

2. Ch´ep c´ac th ’u mu.c doc, dvips, fonts, tex trong g´oi vntex v`ao th ’u mu.c C :>
Program Files\MikTeX2.7 (ch´ep ch `ˆong lˆen c´ac th ’u mu.c ¯d˜a c´o).

3. Ch´ep ch `ˆong 2 th ’u mu.c dvips, pdftex trong th ’u mu.c For-Document-Settings lˆen
th ’u mu.c C:\Documents and Settings\All Users\Application Data\MiKTeX\2.7.

4. V`ao: Start → All programs → Miktex 2.7 → Settings → general → Refresh
FNDB.

5. C`ai Ghostview: file gsv46w32.exe
6. C`ai Acrobat Reader.

7. C`ai ch ’u ’ong tr`ınh soa.n th ’ao v˘an b ’an WinEdit 5.5 ho˘a.c Texmarker. Ch ’u ’ong tr`ınh
WinEdit khˆong th ’ˆe nh`ın th ´ˆay ti ´ˆeng Viˆe.t trˆen m`an h`ınh, c`on ch ’u ’ong tr`ınh TeXmarker
c´o th ’ˆe th ´ˆay ti ´ˆeng Viˆe.t trˆen m`an h`ınh (nh ’ung file c´o kh ’a n˘ang nhi ˜ˆem virus).

N ´ˆeu d`ung Texmarker th`ı c `ˆan ch ’inh mˆo.t s ´ˆo ch ˜ˆo sau:
M ’’o Texmaker → Options→ Confirgure Texmaker ch ’inh
i) Commmand (C´ac reader t ’u ’ong ´’ung)

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2 Ch ’u ’ong 1. C ´ˆau tr´uc v˘an b ’an

#Div viewer: ”C:\Program Files\MiKTeX 2.7\miktex\bin\yap.exe” %.dvi
#Ps viewer: ”C:\Program Files\Ghostgum\gsview\gsview32.exe” %.ps

#Pdf viewer: ”C:\Program Files\Adobe\Acrobat 7.0\Reader\AcroRd32.exe” %.pdf
ii) Quick Build Cho.n c´ach di.ch nhanh ho˘a.c theo t`’ung b ’u´’oc.

iii) Editor: Chon Font Unicode: Times New romance, Arial, Courier...
Cho.n c ’’o ch˜’u: Encoding UTF8.

C´ac h`ang ¯d `ˆau trong file tex ¯d ’ua v`ao c´a d`ong lˆe.nh:

\usepackage[utf8]{vietnam}
\usepackage[utf8]{inputenc}

1.2 C´

ac b ’u´’

oc ch´ınh khi d`

ung LaTeX

• B ’u´’oc 1 Soa.n th ’ao: D`ung WinEdit ho˘a.c Texmarker ta.o mˆo.t file tex v´’oi tˆenfilename.tex,
v´ı du. chuong1.tex.

• B ’u´’oc 2 Di.ch: Nh ´ˆan bi ’ˆeu t ’u ’o.ng LaTeX trˆen giao diˆe.n c’ua WinEdit ho˘a.c Texmarker

d ’ˆe di.ch file.

• B ’u´’oc 3 Xem v`a In: Nh ´ˆan bi ’ˆeu t ’u ’o.ng DVI ¯d ’ˆe xem v`a in v˘an b ’an. N ´ˆeu mu ´ˆon xem v`a
in v˘an b ’an b`˘ang GhostView ho˘a.c PDF th`ı ph ’ai di.ch t`’u DVI sang GS ho˘a.c PDF.
D

¯ ’ˆe l`am viˆe.c n`ay ta nh ´ˆan bi ’ˆeu t ’u ’o.ng ”DVI→ PS” ho˘a.c ”DVI → PDF” trˆen giao
diˆe.n c’ua WinEdit.

1.3 C ´

ˆ

au tr´

uc chung c’ua mˆ

o.t file LaTeX

M ˜ˆoi file ngu `ˆon c ’ua LaTeX c´o c ´ˆau tr´uc c ’o b ’an nh ’u sau:

\documentstyle[option]{style} ho˘a.c \documentclass[option]{style}

Ph `ˆan ¯d `ˆau t`ai liˆe.u

\begin{document}

Nˆo.i dung t`ai liˆe.u

\end{document}

trong ¯d´o style l`a mˆo.t trong c´ac ki ’ˆeu t`ai liˆe.u sau article, report, book hay latter

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2. Ki ’ˆeu t`ai li.ˆeu 3

1.4 C´

ac g´

oi thˆ

em v`

ao (Packages)

C´o r ´ˆat nhi `ˆeu g´oi lˆe.nh vi ´ˆet thˆem cho LaTeX. D¯ ’ˆe s ’’u du.ng c´ac g´oi n`ay ta d`ung lˆe.nh

\unpackage. V´ı du. ¯d ’ˆe m ’’o c´ac g´oi vntex ta d`ung lˆe.nh

\usepackage[utf8]{vietnam}

1.5 C´

ac mode x ’’u l´

y

Trong qu´a tr`ınh x ’’u, LaTeX luˆon ’’o mˆo.t trong ba mode:
1. Mode paragraph.

2. Mode to´an.

3. Mode LR (tr´ai−ph ’ai).

2. Ki ’

ˆ

eu t`

ai liˆ

e.u

Lˆe.nh ¯d `ˆau tiˆen trong ph `ˆan ¯d `ˆau c ’ua file LaTeX l`a ki ’ˆeu x ’’u l´y cho to`an v˘an b ’an. C´u ph´ap
cho lˆe.nh n`ay l`a:

\documentstyle[option]{style}
ho˘a.c

\documentclass[option]{style}

* C´ac da.ng c’ua style l`a: book, report, article, letter.

* C´ac da.ng c’uaoptionl`a: 11pt, 12pt, twoside, twocolumn, titlepage, leqno,
fleqn.

11 Font size tiˆeu chu ’ˆan cho v˘an b ’an l`a 11pt thay v`ı 10pt.

12 Font size tiˆeu chu ’ˆan cho v˘an b ’an l`a 12pt thay v`ı 10pt.

twoside Output ¯d ’u ’o.c ¯di.nh da.ng ¯d ’ˆe in hai m˘a.t (m˘a.c nhiˆen cho book style).

twocolumn Output xu ´ˆat hiˆe.n hai cˆo.t trong m ˜ˆoi trang.

... ...

N ´ˆeu cho.n nhi `ˆeu option th`ı c´ac l ’u.c cho.n ¯d ’u ’o.c ng˘an c´ach b’’o d ´ˆau ph ’ˆay. Th´’u tu. c’ua

c´ac t`uy cho.n khˆong quan tro.ng. V´ı du.:

\documentstyle[11pt,twoside]{article}

• Ch´u ´y

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4 Ch ’u ’ong 1. C ´ˆau tr´uc v˘an b ’an

3. ¯ i.nh da.ng trang

D

M ˜ˆoi trang bao g `ˆom ph `ˆan ¯d `ˆau (head), thˆan (body) v`a chˆan (foot). D¯ ’ˆe ¯di.nh da.ng
trang ta d`ung c´ac lˆe.nh sau:

\oddsidemargin: l `ˆe tr´ai cho trang l ’e.
\evensidemargin: l `ˆe tr´ai cho trang ch ˜˘an.
\topmargin: l `ˆe trˆen t´’oi ¯d ’inh c ’ua ph `ˆanhead.
\haedheight: chi `ˆeu cao c ’ua head.

\headsep: kho ’ang c´ach t`’u ¯d´ay c ’uahead t´’oi ¯d ’inh c ’ua body.

\topskip: kho ’ang c´ach t`’u ¯d ’inh c ’ua bodyt´’oi ¯d ’u`’ong c ’o s ’’o c’ua h`ang ¯d `ˆau tiˆen
c ’ua text.

\textheight: chi `ˆeu cao c ’ua body.

\textwidth: chi `ˆeu rˆo.ng c’ua text trong m ˜ˆoi h`ang.
\footheight: chi `ˆeu cao c ’ua foot.

\footskip: kho ’ang c´ach t`’u ¯d´ay c ’ua bodyt´’oi ¯d´ay c ’uafoot.
• V´ı du.:

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4. Section 5

\ topmargin

\ headheight

Head

\ textheight

\ textwidth

Body

Foot

\ footskip

\ footheight

First line of text

\ topskip

\ oddsidemargin

\ evensidemargin

4. Section

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6 Ch ’u ’ong 1. C ´ˆau tr´uc v˘an b ’an

\seccommand*{title} (s ´ˆo c ’ua section khˆong ¯d ’u ’o.c in ra)
Lˆe.nh cho section g `ˆom:

\part \chapter \ section \subsection \subsubsection

\paragraph \subparagraph

5. Lˆ

e.nh v`a mˆoi tr ’u`’ong

5.1 C´

ac l .ˆenh c’ua LaTeX

Mˆo.t lˆe.nh c’ua LaTeX c´o c ´ˆau tr´uc c ’o b ’an nh ’u sau:
\commandname[option]{mandatory argument},

trong ¯d´o commandname l`a tˆen lˆe.nh, option l`a t`uy cho.n v`a mandatory argument l`a bi ´ˆen
b ´˘at buˆo.c.

• T`uy cho.n ph ’ai ¯d˘a.t trong c˘a.p d ´ˆau [ ], bi ´ˆen b ´˘at buˆo.c ph ’ai ¯d˘a.t trong c˘a.p { }.
• Lˆe.nh b´˘at ¯d `ˆau b`˘ang d ´ˆau \ v`a k ´ˆet th´uc b ’’oi k´ı t ’u. tr ´ˆong. V´ı du. lˆe.nh ”\triangle x”
cho ta 4x

5.2 Mˆ

oi tr ’u`’

ong

C´u ph´ap cho mˆoi tr ’u`’ong c´o da.ng
\begin{environment}

Ph `ˆan thˆan c ’ua mˆoi tr ’u`’ong
\end{environment},

environmentl`a mˆoi tr ’u`’ong. LaTeX c´o c´ac mˆoi tr ’u`’ong To´an ho.c nh ’u: theorem, corollary,

lemma, proposition, definition, notation, proof,axiom...
C´ac mˆoi tr ’u`’ong ¯d˜a ¯d ’u ’o.c Viˆe.t ho´a:

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6. C´ac ph `ˆan c ’ua v˘an b ’an 7

5.3 In c´

ac k´ı t ’u. lˆe.nh

C´ac k´ı t ’u. # , $ , ˆ , , % , & , {, }d ’u ’o.c xem nh ’u lˆe.nh. N ´¯ ˆeu mu ´ˆon in c´ac k´ı
t ’u. n`ay ta ¯d˘a.t d ´ˆau \ tr ’u´’oc n´o.

V´ı du.: \# = # , \$= $ , \^ = ˆ , \_ = , \& = &, \{ ={ , \} =}, \S =§.

5.4 C´

ac k´ı hiˆ

e.u ¯d˘a.c biˆe.t

Ta c´o c´ac k´ı hiˆe.u ¯d˘a.c biˆe.t sau:

\S = §, \copyright}= c°, \pounds= £.

5.5 Khai b´

ao

Khai b´ao l`a mˆo.t lˆe.nh l`am thay ¯d ’ˆoi gi´a tri. ho˘a.c ´u ngh˜ia c’ua c’ua mˆo.t lˆe.nh kh´ac. ’Anh
h ’u ’’ong c’ua khai b´ao x ’ay ra t´’uc th`ı v`a k ´ˆet th´uc khi mˆo.t khai b´ao kh´ac c`ung tˆen xu ´ˆat
hiˆe.n sau ¯d´o. Tuy nhiˆen, n ´ˆeu khai b´ao x ’ay ra trong mˆo.t mˆoi tr ’u`’ong ho˘a.c trong c˘a.p m´oc
k´ep {...}th`ı khai b´oo ch ’i c´o t´ac du.ng trong mˆoi tr ’u`’ong ho˘a.c trong ph `ˆan gi˜’ua c˘a.p m´oc
k´ep {...}.

• C´ac v´ı du.

¦ { \bf This text appears in boldface} : khai b´ao\bfchuy ’ˆen ch˜’u sang da.ng
¯

dˆa.m This text appears in boldface.

¦ \setlenght{\parindent}{0.5cm}: canh l `ˆe c ’ua h`ang ¯d `ˆau tiˆen c ’ua mˆo.t ¯doa.n l`a
0.5cm.

5.6 Ch`

en mˆ

o.t nˆo.i dung t`’u mˆo.t file kh´ac

Mu ´ˆon ch`en mˆo.t nˆo.i dung t`’u mˆo.t file kh´ac v`a o file tex ta d`ung lˆe.nh \input.
¦ \input vietnam.sty: go.i style vietnam.

¦ \input khaibao.tex: go.i file khai bao ch´’ua c´ac lˆe.nh ¯d˜a ¯d ’u ’o.c Viˆe.t h´oa.

6. C´

ac ph `

ˆ

an c’ua v˘

an b’an

6.1 ¯ `

D

ˆ

au ¯

d `

ˆ

e c’ua trang

Ph `ˆan n`ay ch ’i d`ung cho v˘an b ’an ki ’ˆeu article.

Mˆo.t ¯d `ˆau ¯d `ˆe c ’ua trang c´o th ’ˆe ¯d ’u ’o.c ta.o ra v´’oi mˆoi tr ’u`’ong

\begin{titlepage} Text cho ¯d `ˆau ¯d `ˆe \end{titlepage}
ho˘a.c v´’oi c´ac lˆe.nh

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8 Ch ’u ’ong 1. C ´ˆau tr´uc v˘an b ’an

\author{Tˆen t´ac gi ’a v`a ¯di.a ch ’i}
\date{Ng`ay}

7. Nh˜

an v`

a tham kh’ao

•Lˆe.nh \label{marker}: ¯d ’u ’o.c d`ung ¯d ’ˆe l`am d ´ˆau ta.i vi. tr´ı n´o xu ´ˆat hiˆe.n trong text,
trong ¯d´o marker l`a tˆen c ’ua nh˜an.

• Lˆe.nh \pageref{marker}: in s ´ˆo trang n ’oi nh˜an marker d ’u ’o.c l`am d ´ˆau.¯

• Lˆe.nh tham kh ’ao: \ref{marker}, trong ¯d´omarker l`a tˆen c ’ua nh˜an ¯d ’u ’o.c tham
kh ’ao.

N ´ˆeu lˆe.nh \label d ’u ’o.c cho sau mˆo.t lˆe.nh section, ho˘a.c lˆe.nh¯ equation, eqnarray,
mˆoi tr ’u`’ong enumerate... th`ı lˆe.nh \ref in s ´ˆo c ’ua section, equation, eqnarray ... n ’oi

marker d ’u ’o.c ¯di.nh ngh˜ia.¯

8. Ch`

en ng`

ay v`

ao v˘

an b’ang

Ng`ay hiˆe.n h`anh ¯d ’u ’o.c ch`en v`ao v˘anb ’ang b`˘ang c´ach d`ung lˆe.nh \today.

9. Mu.c lu.c

Th ’u mıu.c ¯d ’u ’o.c ta.o ra v`a in b’’oi lˆe.nh:

\tableofcontents

L `ˆan ti ´ˆep theo khi LaTeX di.ch v˘an b ’ang n`ay, lˆe.nh \tableofcontents do.c file¯ 
docu-ment name.toc v`a th ’u mu.c ¯d ’u ’o.c in ra.

10. T`

ai liˆ

e.u tham kh’ao

T`ai liˆe.u tham kh ’ao ¯d ’u ’o.c ta.o ra b’’oi mˆoi tr ’u`’ong:
\begin{thebibliography}{sample label}

entries: c´ac mu.c ¯d ’ua v`ao

\end{thebibliography}

M ˜ˆoientries trong bibliography b ´ˆat ¯d `ˆau v´’oi lˆe.nh

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10. T`ai li.ˆeu tham kh ’ao 9

N ´ˆeu khˆong c´o bi ´ˆen t`uy cho.nlabel,\bibitems˜e ta.o ra mˆo.t s ´ˆo (s ´ˆo n`ay cha.y t˘ang d `ˆan)
trong d ´ˆau m´oc vuˆong nh ’u l`a nh˜an cho tham kh ’ao trong text. V´’oilabel, n´o cho th ´ˆay c´ai
ta ¯d˘a.t ra nh ’u tˆen vi ´ˆet t ´˘at c’ua t´ac gi ’a ho˘a.c s ´ˆo tham kh ’ao b ´ˆat k`y. Bi ´ˆen key l`a t`’u kh´oa
tham kh ’ao, n´o khˆong xu ´ˆat hiˆe.n trong bibliography nh ’ung n´o ¯d ’u ’o.c thay th ´ˆe trong text
b ’’oi label.

Text ¯d ’u ’o.c nhˆa.n da.ng sau h`ang ¯d `ˆau tiˆen v´’oi ¯dˆo. d`ai b`˘ang v´’oi ¯dˆo. d`ai c’uasample label.
Trong th ’u.c t ´ˆe, sample labelnˆen l`a mˆo.t s ´ˆo v´’oi nh˜an l´’on nh ´ˆat. V´ı du. 99 n ´ˆeu c´o nhi `ˆeu h´’on
10nh ’ung ´ıt h ’on 100 entries.

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Ch ’u ’ong 2

Tr`ınh b`

ay Text

1. ¯ ’ˆ

D

oi font

Font chu ’ˆan trong LaTeX l`a font Roman v`a size chu ’ˆan l`a 10pt.
• V´ı du. 1

¯ ˆay l`a font Roman size 10pt

1.1 Font ch˜’

u nghiˆ

eng

D`ung lˆe.nh:\em ho˘a.c \it

V´ı du.: ¯ ˆay l`a font ch˜’D u nghiˆeng.

1.2 C´

ac ki ’

ˆ

eu font

\rm Roman \it Italic \sc Small Caps

\bf Bold case \sl Slanted \sf Sans Serif

\tt Typewriter

• Chuy ’ˆen font trong mˆo.t ¯doa.n c’ua text sang font kh´ac ta ¯d˘a.t ¯doa.n ¯d´o trong d ´ˆau
m´oc k´ep v`a d`ung lˆe.nh c’ua font. V´ı du. ta mu ´ˆon chuy ’ˆen c´ac ch˜’u ”Group and Field” t`’u
font Roman sang font Small Caps ta vi ´ˆet nh ’u sau: Ã\scÃGroupÃandÃFieldÃ. Khi ¯d´o
output s˜e c´o da.ng Group and Field.

•¯ ´Dˆoi v´’oi ¯doa.n v˘an b ’an d`ai ta c´o d`ung mˆoi tr ’u`’ong:

\begin{font style } ... text ’’o da.ng font m´’oi ... \end{font style}

1.3 large

\Large

larger

\LARGE

even larger

\huge

still larger

\Huge

largest

V´ı du.: {\Large Roman Font} cho ta

Roman Font

2. Canh gi˜’

ua v`

a thu.t ¯d `

ˆ

au h`

ang

2.1 a) Canh gi˜’

ua

•¯Dˆe canh gi˜’’ ua mˆo.t ¯doa.n ta d`ung mˆoi tr ’u`’ongcenter. V´ı du.:
\begin{center}

line 1 \\
line 2 \\
... \\
line n
\end{center}

trong ¯d´o lˆe.nh \\ cho ta mˆo.t h`ang m´’oi.
V´ı du.:

To´an ho.c
l`a khoa ho.c c’ua

mo.i khoa ho.c
¯

d ’u ’o.c ta.o b’’oi

\begin{center}

To\as n h\oj c\\

l\af\ khoa h\oj c c\ur a\\
m\oj i khoa h\oj c

\end{center}

•¯Dˆe canh gi˜’’ ua mˆo.t h`ang ¯d ’on ta d`ung lˆe.nh \centerline{text}.
V´ı du. lˆe.nh \centerline{Mathematics-Physis} cho ta

Mathematics-Physis

2.2 Canh l `

ˆ

e mˆ

o.t ph´ıa

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3. Li .ˆet kˆe 13

2.3 Canh l `

ˆ

e hai ph´ıa

Mˆo.t ¯doa.n text c´o th ’ˆe tr`ınh b`ay theo c´ach thu.t v`ao hai ph´ıa ¯d `ˆeu nh ’u nhau b ’’oi mˆoi
tr ’u`’ong quote, quotation.

\begin{quote} text \end{quote}

\begin{quotation} text \end{quotation}.

¯ Ch´u ´y S ’u. kh´ac nhau gi˜’ua mˆoi tr ’u`’ong quote v`a quotation l`a trong mˆoi tr ’u`’ong

quotation m ˜ˆoi ¯doa.n text ¯d ’u ’o.c ¯d´anh d ´ˆau b`˘ang c´ach thu.t ¯d `ˆau h`ang c ’ua h`ang ¯d `ˆau tiˆen.
¦ V´ı du. mˆoi tr ’u`’ong quote:

The last twenty years have seen an explosion of interest in the study of
non-linear dynamical system. Scientists in all disciplines have come to realize

the power and the beauty of geometric and qualitative techniques developed
during this period.

Morden dynamical systems theory has a realively short history. It begin with
Poincare, who revolutionized the study of nonlinear differential equations by
introducing the qualitative techniques of geometry and topology.

¦ V´ı du. mˆoi tr ’u`’ong quotation:

To Poincare, a global understanding of the gross behavior of all solutions
of the system was more important than the local behavior of particular,
analytically−pricise solutions.

Birkhoff realized the importance of the study of mapping and emphasized
discrete dynamics as a means of understanding the more difficult dynamics
arising from differential equations .

3. Liˆ

e.t kˆe

C´o 3 mˆoi tr ’u`’ong liˆe.t kˆe l`a: itemize, enumerate, description.

3.1 Mˆ

oi tr ’u`’

ong

itemize

• C´u ph´ap:

\begin{itemize}
\item Nˆo.i dung 1

\item Nˆo.i dung 2

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14 Ch ’u ’ong 2. Tr`ınh b`ay Text

* M ˜ˆoi h`ang b ´˘at ¯d `ˆau b ’’oi mˆo.t ”ch ´ˆam ¯den l´’on” •.

* M ˜ˆoi nˆo.i dung c´ach nhau b ’’oi mˆo.t mˆo.t khˆong gian ¯d´’ung (xu ´ˆong h`ang v`a c´o kho ’ang
c´ach gi˜’ua hai nˆo.i dung).

2 V´ı du.:

\begin{itemize}

\item Ph\aa n c\ow\ s\owr\ h\oj c Tri\ees t h\oj c v\af\ Tin h\oj c.
\item Ph\aaf n chuy\ee n ng\af nh h\oj c c\as c m\ooj n:

Gi\ar i t\is ch h\af m, Gi\ar i t\is ch th\uwj c, ...
\end{itemize}

cho ta

• Phˆan c ’o s ’’o ho.c Tri ´ˆet ho.c v`a Tin ho.c.

• Ph `ˆan chuyˆen ng`anh ho.c c´ac mˆo.n: Gi ’ai t´ıch h`am, Gi ’ai t´ıch th ’u.c, ...

3.2 Mˆ

oi tr ’u`’

ong

enumerate

Mˆoi tr ’u`’ong enumerate c´o c´u ph´ap gi ´ˆong nh ’u mˆoi tr ’u`’ong itemize nh ’ung c´ac mu.c

d ’u ’o.c ¯d´anh s ´ˆo (t˘ang d `ˆan) ch´’u khˆong ph ’ai l`a d ´ˆau ch ´ˆam l´’on• nh ’u trong itemize.
C´ac mu.c d ’u´’oi ¯dˆay

1. Functional Analysis

2. Ordinary Differential Equations
3. Topology

d ’u ’o.c cho b’’oi

\begin{enumerate}

\item Functional Analysis

\item Ordinary Differential Equations
\item Topology

\end{enumerate}

3.3 Mˆ

oi tr ’u`’

ong

description

C´u ph´ap:

</div>
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4. H .ˆop 15

\end{description}

Trong lˆe.nh \item{option}th`ıoption s˜e xu ´ˆat hiˆe.n d ’u´’oi da.ng nh˜an v´’oi ch˜’u ¯dˆa.m.
X´et v´ı du. ¯doa.n sau

B ’u´’oc 1 Soa.n th ’ao file LaTex

B ’u´’oc 2 Di.ch

B ’u´’oc 3 In ra
¯

d ’u ’o.c ta.o ra b’’oi

\begin{description}

\item[B\uw\ows c 1] So\aj n th\ar o file LaTex
\item[B\uw\ows c 2] D\ij ch

\item[B\uw\ows c 3] In ra
\end{description}

4. Hˆ

o.p (Box) trong LaTeX

4.1 Hˆ

o.p LR

Ta ta.o ra hˆo.p ch´’ua text trong mode LR (left to right) b ’’oi c´ac lˆe.nh:

• \mbox{text} : ta.o ra mˆo.t hˆo.p ch´’ua ch˜’utestbˆen trong, ta d`ung lˆe.nh n`ay khi mu ´ˆon
vi ´ˆet text trong mˆoi tr ’u`’ong to´an.

V´ı du.: A∩B ={x∈x:x∈Av`ax∈B} d ’u ’o.c ta.o b’’oi¯

Ã$A\capÃB=\{x\inÃx:Ãx\inÃẪ\;Ã\mbox{v\af}Ã\;Ãx\inÃB\}$Ã.
• \fbox{text}: ta.o mˆo.t hˆo.t ch´’ua text c´o khung bao ngo`ai.

V´ı du.: Rb

a f(x)dx =F(b)−F(a)

• \makebox[width][pos]{text} v`a \framebox[width][pos]{text}

width d ’u ’o.c x´ac ¯di.nh tr ’u´’oc b’’oi bi ´¯ ˆen width.

Bi ´ˆen t`uy cho.npos x´ac ¯di.nh vi. tr´ı c’ua text trong hˆo.p. posc´o th ’ˆe cho.n l`al (canh tr´ai
¯

d ´ˆoi v´’oi text) ho˘a.c l`ar (canh ph ’ai ¯d ´ˆoi v´’oi text). N ´ˆeu khˆong cho.n bi ´ˆen cho th`ı text d u o.c

da.t o giua.
ã V du. 2

Ư \makebox[3.5cm]{centeredtext} ta.o ra centered text .

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16 Ch ’u ’ong 2. Tr`ınh b`ay Text

4.2 D`’

oi hˆ

o.p theo ph ’u ’ong th ’˘ang ¯d´’ung

C´u ph´ap: \raisebox{lift}[height][depth]{text}

ta.o ra mˆo.t \mbox v´’oi nˆo.i dung textd ’ua lˆen d`ong c ’o s ’’o hiˆe.n h`anh mˆo.t s ´¯ ˆo lift. C´ac bi ´ˆen
t`uy cho.n height v`a depth b´ao cho LaTeX m ’’o rˆo.ng hˆo.p v `ˆe ph´ıa trˆen h`ang c ’o s ’’o mˆo.t ¯dˆo.

cao height v`a v `ˆe ph´ıa d ’u´’oi d`ong c ’o s ’’o mˆo.t ¯do. sˆau depth.
V´ı du.:

Baseline \raisebox{0.1in}{high} and \raisebox{-0.in}{low} and back again

cho ta: Baseline high and

lowand back again.

4.3 Parbox v`

a minipage

To`an bˆo. ¯doa.n text ¯d ’u ’o.c ¯d˘a.t v`ao c´ac hˆo.p th ’˘ang ¯d´’ung r`’oi nhau v´’oi lˆe.nh:
\parbox[pos]{width}{text}

ho˘a.c v´’oi mˆoi tr ’u`’ong

\begin{minipage}[pos]{width} text \end{minipage}
C ’a hai ta.o ra mˆo.t hˆo.p th ’˘ang ¯d´’ung v´’oi b `ˆe ngang width.

Bi ´ˆen t`uy cho.n vi. tr´ıpos c´o th ’ˆe l ´ˆay c´ac gi´a tri.:

b s ´˘ap th`anh h`ang ¯d ´ˆoi v´’oi m´ep ¯d´ay c ’ua hˆo.p so v´’oi h`ang c ’o s’’o hiˆe.n h`anh.

t s ´˘ap th`anh h`ang ¯d ´ˆoi v´’oi m´ep ¯d ’inh c ’ua hˆo.p so v´’oi h`ang c o so hie.n h`anh.
ãCac v du.:

Ư V du. cho lˆe.nh parbox:

\parbox{3.5cm} {This is a 3.5cm wide parbox. It is vertically centered on}
\hfill THE CURRENT LINE \hfill

\parbox{5.5cm}{Narrow pages hard to format.

They usually produce many warning messages on the therminal. }

cho ta

This is a 3.5cm
wide parbox. It is
vertically centered
on

THE CURRENT LINE

Narrow pages hard to format.
They usually produce many
warning messages on the
ther-minal.

¦ V´ı du. cho mˆoi tr ’u`’ong minipage:

\begin{minipage}[b]{4.5cm}

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5. B ’ang 17

\end{minipage}
\hfill

\parbox{3.0cm}{middle of this narrow parbox, which in turn is
aligned with}

\hfill

\begin{minipage}[t]{4cm}

the top line of the right hand minipage. It is recommended that
the user experiment with the positioning arguments to get used
to their effects.

\end{minipage}

cho ta

The minipage
environ-ment produces a
verti-cal box like the parbox
command. The bottom
line of this minipage is
aligned with the

middle of this
narrow parbox,
which in turn is
aligned with

the top line of the right
hand minipage. It is
recommended that the
user experiment with the
positioning arguments to
get used to their effects.

4.4 Hˆ

o.p va.ch (Rule box)

Hˆo.p va.ch l`a mˆo.t h`ınh ch˜’u nhˆa.t ¯d ’u ’o.c bˆoi ¯den. C´u ph´ap:
\rele[lift]{width}{height}

ta.o ra mˆo.t h`ınh ch˜’u nhˆa.t ¯d ’u ’o.c bˆoi ¯den v´’oi b `ˆe ngang width, chi `ˆeu cao height v`a ’’o trˆen
d`ong c ’o s ’’o hiˆe.n h`anh mˆo.t s ´ˆo lift.

V´ı du.: \rule{8mm}{3mm} cho ta .

5. B’ang

5.1 C ´

ˆ

au tr´

uc b ’ang

C´ac mˆoi tr ’u`’ongtabular, tabular* v`aarray l`a c´ac cˆong cu. cho b ’ang v`a ma trˆa.n.

C´u ph´ap:

\begin{array}[pos]{cols} rows \end{array}
\begin{tabular}[pos]{cols} rows \end{tabular}

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18 Ch ’u ’ong 2. Tr`ınh b`ay Text

Mˆoi tr ’u`’ong arraych ’i s ’’u du.ng trong mode to´an ho.c. C´ac mˆoi tr ’u`’ong n`ay ta.o ra mˆo.t

minipage. ´Y ngh˜ia c ’ua c´ac bi ´ˆen nh ’u sau:

pos bi ´ˆen vi. tr´ı th ’˘ang ¯d´’ung, n´o c´o th ’ˆe l ´ˆay c´ac gi´a tri.:

t h`ang ¯d `ˆau c ’ua b ’ang ¯d ’u ’o.c s´˘ap c`ung h`ang v´’oi h`ang c ’o s’’o c’ua h`ang
ngo`ai hiˆe.n h`anh c’ua text.

b h`ang cu ´ˆoi c`ung c ’ua b ’ang ¯d ’u ’o.c s´˘ap c`ung h`ang v´’oi h`ang c ’o s’’o ’’o ngo`ai.
N ´ˆeu khˆong c´o bi ´ˆen vi. tr´ı th`ı b ’ang ¯d ’u ’o.c ¯d˘a.t gi˜’ua h`ang c ’o s’’o ngo`ai.

width Bi ´ˆen n`ay ch ’i ´ap du.ng cho mˆoi tr ’u`’ongtabular*v`a x´ac ¯di.nh ¯dˆo. d`ai to`an
bˆo. c’ua n´o.

cols Bi ´ˆen ¯di.nh da.ng cˆo.t. C´ac k´ı hiˆe.u ¯di.nh da.ng cˆo.t:

l nˆo.i dung trong cˆo.t ¯d ’u ’o.c canh l `ˆe tr´ai

r nˆo.i dung trong cˆo.t ¯d ’u ’o.c canh l `ˆe ph ’ai

r nˆo.i dung trong cˆo.t ¯d ’u ’o.c ¯d˘a.t ’’o gi˜’ua

rows Ch´’ua c´ac mu.c trong b ’ang, m ˜ˆoi h`ang ngang ¯d ’u ’o.c k ´ˆet th´uc b ’’oi \\. C´ac
h`ang ch´’ua c´ac cˆo.t ¯d ’u ’o.c ng˘an c´ach b’’oi d ´ˆau &. Nh ’u vˆa.y m ˜ˆoi h`ang trong
b ’ang ch´’ua c`ung s ´ˆo cˆo.t nh ’u trong ¯di.nh ngh˜ia cols.

C´ac k´ı hiˆe.u ¯di.nh da.ng cho bˆen tr´ai v`a ph ’ai c’ua cˆo.t l`a:
| v˜e mˆo.t ¯d ’u`’ong th ’˘ang ¯d´’ung

k v˜e mˆo.t ¯d ’u`’ong th ’˘ang ¯d´’ung.

\hline Lˆe.nh n`ay xu ´ˆat hiˆe.n tr ’u´’oc h`ang ¯d `ˆau tiˆen ho˘a.c xu ´ˆat hiˆe.n t´’uc th`ı sau lˆe.nh

k ´ˆet th´uc h`ang\\. N´o v˜e mˆo.t l`˘an ngang theo b `ˆe ngang c ’ua b ’ang ’’o d ’u´’oi
h`ang v`’ua k ´ˆet th´uc ho˘a.c ta.i ¯d `ˆau b ’ang n ´ˆeu n´o xu ´ˆat hiˆe.n tr ’u´’oc ¯d `ˆau tiˆen.
Hai lˆe.nh \hline liˆen ti ´ˆep ta.o ra hai l`˘an ngang v´’oi mˆo.t khˆong gian nh ’o
gi˜’ua ch´ung.

\multicolumn{num}{col}{text}

Lˆe.nh n`ay k ´ˆet h ’o.n num cˆo.t th`anh mˆo.t cˆo.t ¯d ’on v´’oi t ’ˆong ¯dˆo. d`ai c’ua ch´ung bao

g `ˆom c´ac khˆong gian cˆo.t bˆen trong.

Bi ´ˆen col l`a mˆo.t trong c´ac k´ı hiˆe.u vi. tr´ı: l, r, c v´’oi bi ’ˆeu th´’uc @ v`a ¯d ’u`’ong
th ’˘ang ¯d´’ung |.

\vline Lˆe.nh n`ay v˜e mˆo.t ¯d ’u`’ong th ’˘ang ¯d´’ung v´’oi chi `ˆeu cao c ’ua cˆo.t ta.i vi. tr´ı n´o

xu ´ˆat hiˆe.n.

B ’ang th ’u`’ong ¯d ’u ’o.c ¯d˘a.t trong mˆoi tr ’u`’ongcenter:
\begincenter table \endcenter

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5. B ’ang 19

Position Clubs Games W T L Goals

1 Amesville Rockets 33 19 13 1 66:31

2 Clarkson Chargers 33 17 7 9 70:44

3 Daysdon Bombers 33 14 10 9 66:50

4 Edgartown Devils 33 16 6 11 63:53

5 Freeburg Fighters 33 15 7 11 64:47

B ’ang trˆen ¯d ’u ’o.c cho b’’oi

\begin{center}

\begin{tabular}{rlcrrrc}

Position & Clubs & Games & W & T & L & Goals \\ \hline
1 & Amesville Rockets & 33 & 19 & 13 & 1 & 66:31 \\
2 & Clarkson Chargers & 33 & 17 & 7 & 9 & 70:44 \\
3 & Daysdon Bombers & 33 & 14 & 10 & 9 & 66:50 \\
4 & Edgartown Devils & 33 & 16 & 6 & 11 & 63:53 \\

5 & Freeburg Fighters & 33 & 15 & 7 & 11 & 64:47 \\ \hline
\end{tabular}

\end{center}

¦ V´ı du.:

Regional Soccer League — Final Results 1992/93

Club W T L Goals Points Remarks

1 Amesville Rockets 19 13 1 66:31 51:15 League Chammps
2 Clarkson Chargers 17 7 9 70:44 41:25

3 Daysdon Bombers 14 10 9 66:50 38:28
4 Edgartown Devils 16 6 11 63:53 38:28
5 Freeburg Fighters 15 7 11 64:47 37:29

Candidates

B ’ang trˆen ¯d ’u ’o.c cho cho b’’oi

\begin{center}

\begin{tabular}{|r|l||rrr|r@{:}l|r@{:}l||c|}\hline

\multicolumn{10}{|c|}{\bf Regional Soccer League
---Final Results 1992/93}\\ \hline

&\it Club & \it W &\it T & \it L & \multicolumn{2}{c|}{\it Goals}
& \multicolumn{2}{c||}{\it Points} & \it Remarks \\ \hline \hline
1 & Amesville Rockets & 19 & 13 & 1 & 66 & 31 & 51 & 15 & League Chammps

\\ \hline

2 & Clarkson Chargers & 17 & 7 & 9 & 70 & 44 & 41 & 25 & \\ \cline{1-9}
3 & Daysdon Bombers & 14 & 10 & 9 & 66 & 50 & 38 & 28 & \\ \cline{1-9}
4 & Edgartown Devils & 16 & 6 & 11 & 63 & 53 & 38 & 28 & \\ \cline{1-9}
5 & Freeburg Fighters & 15 & 7 & 11 & 64 & 47 & 37 & 29 &

\raisebox{0.3in}[0pt]{Candidates}\\ \hline
\end{tabular}

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20 Ch ’u ’ong 2. Tr`ınh b`ay Text

6. Footnotes v`

a marginal notes

6.1 Footnotes (ch´

u th´ıch ’’o cu ´

ˆ

oi trang)

Footnote ¯d ’u ’o.c ta.o ra v´’oi lˆe.nh
\footnote{footnote text}.

N´o ¯d´’ung sau ch˜’u ¯d`oi h ’oi mˆo.t s ’u. gi ’ai th´ıch trong footnote. footnote text xu ´ˆat hiˆe.n ’’o
footnote da.ng ch˜’u nh ’o ta.i ¯d´ay c’ua trang.

6.2 Marginal notes (ch´

u th´ıch ’’o l `

ˆ

e)

Ch´u th´ıch ’’o l `ˆe trang ¯d ’u ’o.c ta.o ra v´’oi lˆe.nh:
bshmarginpar{note text}

note textd ’u ’o.c ¯d˘a.t l `¯ ˆe ph ’ai ta.i h`ang m`a lˆe.nh ¯d ’u ’o.c cho.

7. ¯ i `

D

ˆ

eu ch’inh text

7.1 Ch`

en khˆ

ong gian

¦ Mˆo.t khˆong gian v´’oi ¯dˆo. d`ai ¯di.nh tr ’u´’oc ¯d ’u ’o.c ch`en v`ao text v´’oi c´ac lˆe.nh:
\hspace{space}

\hspace*{space}

trong ¯d´o space l`a ¯dˆo. d`ai c’ua khˆong gian ¯d ’u ’o.c ch`en (v´ı du.0.2in, 2cm).

¦ Lˆe.nh \hfill ch`en khˆong gian l`am cho text hai bˆen bi. ¯d ’ˆay v `ˆe ph´ıa tr´ai v`a phar i.
V´ı du. lˆe.nh ÃLeft\hfillÃRightÃ cho ta

Left Right

¦ C´ac lˆe.nh\quad v`a\qquad ch`en khˆong gian ngang b`˘ang v´’oi loa.i size hiˆen h`anh, v´ı

du. 10pt cho size 10pt v`a \qquad c´o khˆong gian g ´ˆap ¯dˆoi.

7.2 Ch`

en c´

ac ch ´

ˆ

am v`

a va.ch

D`ung c´ac lˆe.nh:

\dotfill} \tab {\verb* Thay v`ı ch`en khˆong gian tr ´ˆong, c´ac lˆe.nh n`ay l`am ¯d `ˆay
khˆong gian v ’oi c´ac ch ´ˆam v`a va.ch.

¦ V´ı du. lˆe.nh ÃStart\dotfillÃFinishÃcho ta

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7. D¯ i `ˆeu ch ’inh text 21

Left Right

7.3 B ’e g˜

ay h`

ang

¯ ’ˆe b ’e g˜ay h`ang ta d`ung c´ac lˆe.nh:
\\

\\[space]
\\*[space]

Bi ´ˆen t`uy cho.n spacel`a ¯dˆo. d`ai ¯d˘a.c biˆe.t h´oa khˆong gian h`ang thˆem v`ao ¯d ’u ’o.c ¯d˘a.t gi˜’ua
c´ac h`ang. N ´ˆeu c `ˆan ph ’ai b ´˘at ¯d `ˆau mˆo.t trang m´’oi th`ı khˆong gian h`ang thˆem v`ao khˆong c`on
t´ac du.ng v`a mˆo.t trang m´’oi b´˘at ¯d `ˆau v´’oi h`ang k ´ˆe ti ´ˆep c ’ua text. Lˆe.nh \\*[space] ph`ong
ch ´ˆong mˆo.t trang m´’oi x ’ay ra gi˜’ua hai h`ang.

V´ı du. ¯d ´ˆoi v´’oi lˆe.nh Ã\\*[10cm]Ã th`ı h`ang hiˆe.n h`anh ¯d ’u ’o.c k ´ˆet th´uc v`a mˆo.t khˆong

gian ¯d´’ung 10cm ¯d ’u ’o.c ch`en v`ao tr ’u´’oc h`ang k ´ˆe ti ´ˆep.

Lˆe.nh \newline d `¯ˆong nh ´ˆat v´’oi lˆe.nh \\. Mˆo.t h`ang m´’oi ¯d ’u ’o.c b´˘at ¯d `ˆau m`a khˆong c´o
khˆong gian thˆem v`ao v`a b ’e g˜ay trang c´o th ’ˆe x ’ay ra ta.i ¯di ’ˆem ¯d´o.

7.4 Khˆ

ong gian gi˜’

ua c´

ac ¯

doa.n

Khˆong gian chu ’ˆan gi˜’ua c´ac ¯doa.n ¯di.nh b ’’oi ¯dˆo. d`ai c’ua \parskip}.N´o c´o th ’ˆe ¯d ’u ’o.c
thay ¯d ’ˆoi t`’u gi´a tri. m˘a.c ¯di.nh v´’oi lˆe.nh \setlenght

\setlenght{parskip}{space}

Ta c´o th ’ˆe ch`en khˆong gian ¯d´’ung v´’oi chi `ˆeu cao space gi˜’ua hai ¯doa.n b`˘ang c´ach d`ung
c´ac lˆe.nh:

\vspace{space}
\vspace*{space}

Lˆe.nh \vspace*{space} thˆem v`ao mˆo.t khˆong gian ¯d´’ung thˆa.m ch´ı khi mˆo.t trang m´’oi
xu ´ˆat hiˆe.n ho˘a.c khi lˆe.nh xu ´ˆat hiˆe.n ’’o ¯d `ˆau trang m´’oi. Da.ng chu ’ˆan \vspace{space} ng˘an
ch˘a.n khˆong gian ¯d´’ung thˆem v`ao trong t`ınh hu ´ˆong n`ay.

Ngo`ai ra, ta c`on c´o c´ac lˆe.nh l`am t˘ang khˆong gi˜’ua c´ac ¯doa.n l`a:

\vskip, \smallskip, \medskip, \bigskip

7.5 Qua trang m´’

oi

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22 Ch ’u ’ong 2. Tr`ınh b`ay Text

8. Ch´

u th´ıch trong text

</div>
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Ch ’u ’ong 3

Cˆ

ong th´’

uc to´

an

1. Mˆ

oi tr ’u`’

ong Math

C´ac cˆong th´’uc to´an ¯d ’u ’o.c vi ´ˆet trong mode to´an. C´ac cˆong th´’uc ph ’ai ¯d ’u ’o.c ¯d˘a.t gi˜’ua
d ´ˆau $ v`a $ khi ’’o trong h`ang ho˘a.c gi˜’ua $$ v`a $$ n ´ˆeu ’’o mˆoi tr ’u`’ong to´an (xu ´ˆong h`ang v`a

d˘a.t ’’o gi˜’ua). V´ı du.:

• $\lim_{n\to\infty}\frac{1}{n}=0$ cho ta limn→∞ n1 = 0
ã $$\lim_{n\to\infty}\frac{1}{n}=0$$ cho ta

lim
n

1
n = 0
.

Ư Trong mode toan, ta c´o th ’ˆe d`ung $ v`a $ thay cho $ v`a $; ho˘a.c d`ung \[ v`a \]

thay cho $$ v`a $$.

¦ Trong cˆong th´’uc to´an, c´ac s ´ˆo v`a tˆen h`am ¯d ’u ’o.c d`ung font Roman ¯d´’ung, c`on c´ac
bi ´ˆen th`ı in nghiˆeng.

¦Cˆong th´’uc to´an trong h`ang mu ´ˆon ¯d ’u ’o.c in da.ng size l´’on ta d`ung lˆe.nh\displaystyle.

2. C´

ac k´ı hiˆ

e.u To´an ho.c

2.1 M ˜

ˆ

au t ’u. Hy La.p

a) Ch˜’u th ’u`’ong

α \alpha θ \theta o \o τ \tau

β \beta ϑ \vartheta π \pi υ \upsilon

γ \gamma ι \iota $ \varpi φ \phi

δ \delta κ \kappa ρ \rho ϕ \varphi

² \epsilon λ \lambda % \varrho χ \chi

ε \varepsilon µ \mu σ \sigma ψ \psi

ζ \zeta ν \nu ς \varsigma ω \omega

η \eta ξ \xi

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24 Ch ’u ’ong 3. Cˆong th ´’uc to´an

b) Ch˜’u in

Γ \Gamma Λ \Lambda Σ \Sigma Ψ \Psi

∆ \Delta Ξ \Xi Υ \Upsilon Ω \Omega

Θ \Theta Π \Pi Φ \Phi

2.2 C´

ac k´ı hiˆ

e.u to´an ho.c kh´ac

LaTeX c`on c´o mˆo.t s ´ˆo k´ı hiˆe.u c´o mˆo.t ´y ngh˜ia n`ao ¯d´o trong v˘an b ’an to´an ho.c.

ℵ \aleph 0 \prime ∀ \forall \ \backslash

h \hbar ∅ \emptyset ∃ \exixts ∞ \infty

ı \imath ∇ \nabla ¬ \neg 4 \triangle

 \jmath √ \surd [ \flat ♣ \clubsuit

` \ell ∂ \partial \ \natural ♦ \diamondsuit

℘ \wp > \top ] \sharp ♥ \heartsuit

< \Re ⊥ \bot k \| ♠ \spadesuit

= \Im 6 \angle 0 \mho

V´ı du. n→ ∞ ta.o nˆen b ’’oi n\to\infty.

2.3 Font ch˜’

u Calligraphic

A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,X,Y,Z
D

¯ ’ˆe vi ´ˆet c´ac ch˜’u font Calligraphic ta d`ung lˆe.nh Ã$\calÃ{word}$Ã , trong ¯d´o word
l`a ch˜u c `ˆan vi ´ˆet.

V´ı du. A: Ã{\calÃA}

2.4 K´ı hiˆ

e.u cho c´ac tˆa.p s ´

ˆ

o th ’u.c

Ta c´o th ’ˆe thi ´ˆet k ´ˆe k´ı hiˆe.u cho tˆa.p s ´ˆo t ’u. nhiˆen, s ´ˆo nguyˆen, s ´ˆo h˜’uu t ’y, vˆo t ’y, s ´ˆo th ’u.c
v´a tˆa.p s ´ˆo ph´’uc nh ’u sau:

\newfont{\bb}{msbm10 scaled\magstep1}
\newcommand{\bN}{\mbox{\bb N}}

\newcommand{\bZ}{\mbox{\bb Z}}
\newcommand{\bQ}{\mbox{\bb Q}}
\newcommand{\bI}{\mbox{\bb I}}
\newcommand{\bR}{\mbox{\bb R}}

•V´ı du.:

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2. C´ac k´ı hi.ˆeu To´an ho.c 25

2.5 C´

ac ph´

ep to´

an nhi. phˆan (binary operations)

Hai ¯da.i l ’u ’o.ng to´an ho.c ¯d ’u ’o.c k ´ˆet h ’o.p v´’oi mˆo.t ph´ep to´an ¯d ’u ’o.c go.i l`a ¯d ’u ’o.c n ´ˆoi b ’’oi mˆo.t
ph´ep to´an nhi. phˆan. C´ac k´ı hiˆe.u c´o th ’ˆe cho c´ac ph´ep to´an nhi. phˆan l`a:

± \pm ∩ \cap ◦ \circ ° \bigcirc

∓ \mp ∪ \cup • \bullet 2 \Box

ì \times ] \uplus Ư \diamond 3 \Diamond

ữ \div u \sqcap Â \lhd 4 \bigtriangleup

Ã \cdot t \sqcup Ô \rhd 5 \bigtriangledown

∗ \ast ∨ \vee £ \unlhd / \triangleleft

? \star \wedge Ơ \unrhd . \triangleright

\dagger \ \setminus đ \oslash ⊕ \oplus

‡ \ddagger o \wr ¯ \odot ª \ominus

q \amalg

2.6 C´

ac quan hˆ

e.

Khi hai ¯da.i l ’u ’o.ng to´an ho.c ¯d ’u ’o.c so s´anh, ch´ung ¯d ’u ’o.c n ´ˆoi v´’oi nhau b ’’oi mˆo.t quan hˆe..
C´ac loa.i kh´ac nhau c’ua c´ac k´ı hiˆe.u quan hˆe. cho b ’’oi

≤ \le \leq ≥ \ge \geq 6= \neq ∼ \sim

¿ \ll À \gg =. \doteq ' \simeq

⊂ \subset ⊃ \supset ≈ \approx ³ \asymp

⊆ \subseteq ⊇ \supseteq ∼= \cong ^ \smile

< \sqsubset = \sqsupset ≡ \equiv _ \frown

v \sqsubseteq w \sqsupseteq ∝ \propto ./ \bowtie

∈ \in 3 \ni ≺ \prec Â \succ

` \vdash a \dashv ¹ \preceq º \succeq

|= \models ⊥ \perp k \parallel \| | \mid |

2.7 M˜

ui tˆ

en

← \leftarrow \gets ←− \longleftarrow ↑ \uparrow

⇐ \Leftarrow ⇐= \Longleftarrow ⇑ \Uparrow

→ \rightarrow −→ \longrightarrow ↓ \downarrow

⇒ \Rightarrow =⇒ \Longrightarrow ⇓ \Downarrow

↔ \leftrightarrow ←→ \longleftrightarrow l \updownarrow

⇔ \Leftrightarrow ⇐⇒ \Longleftrightarrow m \Updownarrow

7→ \mapsto 7−→ \longmapsto % \nearrow

←- \hookleftarrow ,→ \hookrightarrow & \searrow

( \leftharpoonup * \rightharpoonup . \swarrow

) \leftharpoondown + \rightharpoondown - \nwarrow

*

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26 Ch ’u ’ong 3. Cˆong th ´’uc to´an

2.8 C´

ac ch ´

ˆ

am trong mˆ

oi tr ’u`’

ong to´

an

C´ac lˆe.nh liˆen quan ¯d´ˆen d ´ˆau ch ´ˆam trong mˆoi tr ’u`’ong to´an.
\ldots . . . c´ac d ´ˆau ch ´ˆam th ´ˆap.

\cdots · · · c´ac d ´ˆau ch ´ˆam gi˜’ua h`ang.
\vdots ... c´ac d ´ˆau ch ´ˆam th ’˘ang ¯d´’ung.
\ddots . .. c´ac d ´ˆau ch ´ˆam ¯d u`ong cheo.
ãV du.

Ư x1+x2+. . .+xn sinh b oi le.nh $x_1+x_2+\dots+x_n$.

2.9 C´

ac d ´

ˆ

au tro.ng ˆam to´an ho.c

a \hat{a} ˘a \breve{a} a` \grave{a} ¯a \bar{a}

a \dot{a} ˇa \check{a} a´ \acute{a} a \tilde{a}

~a \vec{a} ăa \ddot{a}

3. T

en c

ac h`

am

Cac h`am trong LaTeX cho b ’’oi c´ac lˆe.nh:

\arccos \cos \csc \exp \ker \limsup \min \sinh

\arcsin \cosh \deg \gcd \lg \ln \Pr \sup

\arctan \cot \det \hom \lim \log \sec \tan

\arg \coth \dim \inf \liminf \max \sin \tanh

4. C´

ac ph `

ˆ

an t’’u ch´ınh c’ua mode to´

an

4.1 L˜

uy th`’

ua v`

a ch’i s ´

ˆ

o

x2 : x^2 x2n: x^{2n} axy

: a^{x^y}

ai : a_i xmn : x_{mn} xij : x_{i_j}

Cm

n: C^m_n

4.2 M˜

u

Ta c´o c´ac lˆe.nh cho m˜u: \hat, \widehat, \tilde, \widetilde.
¦V´ı du.:

\hat{A} cho ta ˆA.

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4. C´ac ph `ˆan t ’’u ch´ınh c ’ua mode to´an 27

\widetilde{xyz} cho ta xyz.g

4.3 Vect ’o

C´u ph´ap: \vec{obj} , trong ¯d´oobj l`a ¯dˆo.i t ’u ’o.ng c’ua vector.
¦ V´ı du.:

\veci cho ta ~i.
\vec{AB} cho ta AB~ .

4.4 Th ’u ’ong

D`ung lˆe.nh \frac{tu}{mau}, trong ¯d´otu l`a t ’’u s ´ˆo v`a mau l`a m ˜ˆau s ´ˆo.
a+b

c+d: \frac{a+b}{c+d}

1+x2 + 1+1y2

1 + x−y
x+y

: \frac{\frac{1}{1+x^2}+\frac{1}{1+y^2}}{1+\frac{x-y}{x+y}}

a0+

1
a1+ a2+1 1

a3+a14

\displaystyle a_0+\frac{1}{a_1+\frac{1}{a_2+
\frac{1}{a_3+\frac{1}{a_4}}}}

4.5 C˘

an th´’

uc

D`ung lˆe.nh \sqrt[n]{arg}, trong ¯d´o n l`a ch ’i s ´ˆo c˘an v`a argl`a bi ’ˆeu th´’uc d ’u´’oi d ´ˆau
c˘an. Ch´u ´y khi vi ´ˆet c˘an bˆa.c hai ta d`ung lˆe.nh \sqrt{arg}.

2 +

2 +. . .+√2: Ã\sqrt{2+\sqrt{2+\dots+\sqrt{2}}}Ã

3
q

xn

1+y2n: Ã\sqrt[3]{\frac{x^n}{1+y^{2n}}}Ã

4.6 Gi´’

oi ha.n

limx→0sinx : Ã\lim_{x\toÃ0}Ã\sinÃxÃ
lim

x→0

y→0

xy

1 +x2+y2 : Ã\lim_{x\toÃ0\atopÃy\toÃ0}\frac{xy}{1+x^2+y^2}Ã

4.7 Hˆ

o.i, giao v`a t´ıch

∩n

i=1Ai : Ã\cap_{i=1}^nÃA_i$Ã

n

i=1

Ai : Ã\bigcap_{i=1}^nÃA_iÃ

∪n

i=1Xi : Ã\cup_{i=1}^nÃX_i$Ã

n

[

i=1

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28 Ch ’u ’ong 3. Cˆong th ´’uc to´an

Qn

i=1Yi: Ã\prod_{i=1}^nÃY_iÃ

n

i=1

Yi: Ã\displaystyleÃ\prod_{i=1}^nÃY_iÃ

4.8 T ’

ˆ

ong

D`ung lˆe.nh \sum_{i=1}^n bieuthuc.

Pn

i=1x2i: Ã\sum_{i=1}^nx_i^2$Ã
n

i=1

x2i: Ã\displaystyleÃ\sum_{i=1}^nx_i^2$Ã

4.9 T´ıch phˆ

an

D`ung lˆe.nh \int cho t´ıch phˆan b ´ˆat ¯di.nh, \int_a^b cho t´ıch phˆan x´ac ¯di.nh trˆen
[a, b] v`a \oint}cho t´ıch phˆan ¯d ’u`’ong.

R sinx

1+cosxdx: Ã\frac{\sinÃx}{1+\cosÃx}dxÃ

Z π

sinx

1 + cos2xdx: Ã\int_0^{\pi}\frac{\sinÃx}{1+\cos^2x}dxÃ

I ∞

0 (t

2+ 1)dt: \oint_0^{\infty}(t^2+1)dt.

LaTeX khˆong c´o lˆe.nh cho t´ıch phˆan bˆo.i. Ta c´o th ’ˆe thi ´ˆet k ´ˆe lˆe.nh cho t´ıch phˆan hai
l´’op v`a ba l´’op nh ’u sau:

T´ıch phˆan hai l´’op:

\newcommand{\dint}[1]{{\int\!\!\! \int\limits_{\hspace{-8pt}\cal #1}\,}}

V´ı du. RR
D

(x2 +y2)dxdy: \dint{D}(x^2+y^2)dxdy

* T´ıch phˆan ba l´’op:

Ã\newcommand{\tint}[1]{{\intÃ\!\!\!Ã\intÃ\limits_{\calÃ#1}Ã\!\!\!Ã\intÃ\,}}Ã

V´ı du. RR
V

R 1

1−x−y−zdxdydz: \tint{V}{\frac{1}{1-x-y-z}dxdydz}

5. D´

ˆ

au ngo˘

a.c

5.1 M´

oc ¯

d ’on

1
x2 + 1

´n

: Ã\left(Ã\frac{1}{x^2}+1Ã\right)^nÃ

5.2 M´

oc vuˆ

ong

h
x4
2 +
1
2
i1

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6. ÃL.ˆenh atop v`a choose 29

5.3 M´

oc k´

ep

a) Da.ng m ’ang

signx=






−1 khi x <0
0 khi x= 0
1 khi x >0

sign x=\left\{
\begin{array}{ccc}
-1 & \mbox{khi} & x<0\\
0 & \mbox{khi} & x = 0\\
1 & \mbox{khi} & x>0
\end{array}

\right.

6. ÃLˆ

e.nh

atop

v`

a

choose

Lˆe.nh \atop v`a \choose ta.o ra mˆo.t c ´ˆau tr´uc gi ´ˆong nh ’u mˆo.t th ’u ’ong nh ’ung khˆong
c´o l`˘an ga.ch ngang. D¯ ´ˆoi v´’oi lˆe.nh \choose th`ı c ´ˆau tr´uc ¯d ’u ’o.c ¯d˘a.t trong d ´ˆau ngo˘a.c ¯d ’on l´’on
(trong to´an ho.c c ´ˆau tr´uc n`ay ¯d ’u ’o.c go.i l`a hˆe. s ´ˆo nhi. th´’uc).

C´u ph´ap:

{ top \atop bottom }

{ top \choose bottom }
¦ V´ı du. lˆe.nh

$\displaystyle \lim_{x\to 0 \atop y\to 0}\frac{xy}{\sqrt{x^2+y^2}}\$

cho ta lim

x→0

y→0

xy
√

x2+y2.
¦ V´ı du. lˆe.nh

${n+1\choose k}= {n \choose k} + {n \choose k-1}$

cho ta ³n+1k ´=³kn´+³k−n1´

7. Cˆ

ong th´’

uc ¯

d ’u .’oc ¯

d´

ong khung

Ta d`ung lˆe.nh \fbox{congthuc}.

Z b

a f(x)dx= limn→∞
n

i=1

f(ξi)4xi

\fbox{$\displaystyle\int_a^b f(x)dx

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30 Ch ’u ’ong 3. Cˆong th ´’uc to´an

8. Text bˆ

en trong cˆ

ong th´’

uc

Ta d`ung lˆe.nh \mbox{text}.

V´ı du. A={x∈X :xÃl`a ph `ˆan t ’’u b ´ˆat kh ’a quy}

Ã$A=\{x\inÃX:Ãx\;Ã\mbox{\l\af\Ãph\aafÃnÃt\uwr\Ãb\aasÃtÃkh\ar\Ãquy}\}$Ã

9. K´ı hiˆ

e.u x´

ˆ

ep ch `

ˆ

ong lˆ

en

stackrel

D`ung lˆe.nh: Ã\stackrel{upper_sym}{lower_sym}Ã

• ~xdef= (x1, x2, . . . , xn): Ã\vec{x}\stackrel{def}{=}(x_1,x_2,\dots,x_n)Ã

• X −→f Y: ÃX\stackrel{f}{\longrightarrow}YÃ

10. ¯ ’u`’

D

ong, m´

oc ’’o trˆen ho˘

a.c d ’u´’oi

D`ung lˆe.nh: \overline{}, underline{}, \overbrace{}, underbrace{}

• x2+xy: $\overline{\overline{x}^2+xy}$

• limxn: $\underline{\lim}x_n$

α

z }| {

x1 +x2+. . .+xn

| {z }

n

$\underbrace{\overbrace{x_1+x_2}^{\alpha}+\dots+x_n}_n$

11. M’ang

11.1 Ma trˆ

a.n







a11 a12 . . . a1n
a21 a22 . . . a2n
. . . . . . . . . .
am1 am2 . . . amn







$\left(

\begin{array}{cccc}

a_{11} & a_{12} & \dots & a_{1n}\\
a_{21} & a_{22} & \dots & a_{2n}\\
\dots & \dots & \dots & \dots \\
a_{m1} & a_{m2} & \dots & a_{mn}
\end{array}

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12. Ph ’u ’ong tr`ınh 31

11.2 ¯ i.nh th´’

D

uc

¯
¯
¯
¯
¯
¯
¯

1 0 0

0 1 0
0 0 1

¯
¯
¯
¯
¯
¯
¯
$\left|
\begin{array}{ccc}
1 & 0 & 0\\

0 & 1 & 0\\
0 & 0 & 1
\end{array}
\right|$

11.3 Hˆ

e. ph ’u ’ong tr`ınh

a11x1+a12x2+. . .+a1nxn = b1
a21x1+a22x2+. . .+a2nxn = b2
. . . .
am1x1+am2x2+. . .+amnxn = bm

$\begin{array}{ccc}

a_{11}x_1+a_{12}x_2+\dots+a_{1n}x_n & = & b_1\\
a_{21}x_1+a_{22}x_2+\dots+a_{2n}x_n & = & b_2\\

\multicolumn{3}{c}{\dotfill}\\

a_{m1}x_1+a_{m2}x_2+\dots+a_{mn}x_n & = & b_m
\end{array}$

12. Ph ’u ’ong tr`ınh

12.1 Ph ’u ’ong tr`ınh mˆ

o.t cˆo.t

D`ung mˆoi tr ’u`’ong equation:

\begin{equation}
...
\end{equation}

V´ı du.:

(1 +x)n=Xn
k=1

Ck

nxk (3.1)

\begin{equation}

(1+x)^n=\sum_{k=1}^nC^k_nx^k
\end{equation}

12.2 Ph ’u ’ong tr`ınh nhi `

ˆ

eu cˆ

o.t

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32 Ch ’u ’ong 3. Cˆong th ´’uc to´an

\begin{eqnarray}
line1 \\
line2 \\
.... \\
line n
\end{eqnarray}

M ˜ˆoiline c´o da.ng: Bi ’ˆeu th´’uc 1 & = &Bi ’ˆeu th´’uc 2.

M ˜ˆoi h`ang s˜e ¯d ’u ’o.c ¯d´anh s ´ˆo. N ´ˆeu mu ´ˆon mˆo.t h`ang n`ao ¯d´o khˆong ¯d ’u ’o.c ¯d´anh s ´ˆo ta d`ung
lˆe.nh \nonumberd˘a.t tr ’u´’oc lˆe.nh xu ´¯ ˆong h`ang \\.

V´ı du.

(x+y)(x−y) = x2−xy+xy−y2 (3.2)

= x2+ (xy−xy)−y2

= x2−y2 (3.3)

d ’u ’o.c cho b’’oi c´ac lˆe.nh

\begin{eqnarray}

(x+y)(x-y) & = & x^2-xy+xy-y^2 \\

& = & x^2+(xy-xy)-y^2 \nonumber \\
& = & x^2 - y^2

\end{eqnarray}

•Mˆoi tr ’u`’ongeqnarray*: gi ´ˆong nh ’u mˆoi tr ’u`’ong eqnarray nh ’ung m ˜ˆoi ph ’u ’ong tr`ınh khˆong
¯

d ’u ’o.c ¯d´anh s ´ˆo.

13. ¯ i `

D

ˆ

eu ch’inh trong mode to´

an

13.1 Ch`

en khˆ

ong gian tr ´

ˆ

ong

Khˆong gian tr ´ˆong c´o th ’ˆe ¯d ’u ’o.c ch`en v`ao mode to´an v´’oi c´ac lˆe.nh sau:

\, khˆong gian nh ’o | |

\: khˆong gian trung b`ınh | |

\; khˆong gian l´’on | |

\quad khˆong gian l´’on h ’on | |

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13. D¯ i `ˆeu ch ’inh trong mode to´an 33

13.2 ¯ ’

D

ˆ

oi size trong cˆ

ong th´’

uc

Mu ´ˆon ¯d ’ˆoi size trong cˆong th´’uc trong h`ang l´’on h ’on ta d`ung lˆe.nh \displaystyle.

V´ı du. P∞

n=1un c´o th ’ˆe ¯d ’ˆoi th`anh
∞

n=1

un ta d`ung lˆe.nh

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Ch ’u ’ong 4

H`ınh ’anh

1. Style psfig

¯ ’ˆe s ’’u du.ng style psfig ta ph ’ai go.i style n`ay b ’’oi lˆe.nh \input psfig.sty. File

psfig.sty d ’u ’o.c ch´ep v`ao th ’u mu.c c’ua file tex ¯dang soa.n. Ta save h`ınh c `¯ ˆan ch`en
v`ao c´o tˆen da.ng *.psho˘a.c *.eps.

C´u ph´ap

\psfig{figure=filename.eps,height=chieu cao, width=chieu rong, angle=gocquay}
V´ı du. lˆe.nh \psfig{figure=matmuc02.eps,height=2in,width=3in,angle=-90}
cho ta h`ınh

0
0.2
0.4
0.6
0.8
1
z
-1

-0.5
0.5

1
y

-1
-0.5
0.5

2. Lˆ

e.nh epsfbox

¯ˆe d`ung lˆe.nh’ \epsfbox ta ph ’ai khai b´ao style epsf v`ao cho t`uy cho.n trong h`ang
\documentstyle ho˘a.c \documentclass. V´ı du.

\documentstyle[12pt,epsf]{book}.
¦ C´u ph´ap:

\epsfbox{hinh.eps}

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36 Ch ’u ’ong 4. H`ınh ’anh

\epsfysize=y lenght: chi `ˆeu cao c ’ua h`ınh.

• V´ı du. h`ınh c´o tˆen matmuc02.eps ¯d ’u ’o.c ¯d ’ua v`ao v˘an b ’an b’’oi c´ac lˆe.nh sau:

\begin{center}

\epsfbox{matmuc02.eps}
\epsfxsize=3in

\epsfysize=3in
\end{center}

–1
–0.5

0
0.5
1

–1 –0.5 0 0.5 1

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Ch ’u ’ong 5

T´

ˆ

oi ’uu cho ng ’u`’

oi s’’u du.ng

1. ¯ i.ng da.ng la.i trang

D

Ta c´o th ’ˆe canh l `ˆe, ¯d ’ˆoi chi `ˆeu d`ai v`a chi `ˆeu rˆo.ng c’ua trang la.i theo ´y mu ´ˆon c ’ua m`ınh theo
c´ac lˆe.nh ¯di.nh da.ng trang. V´ı du.

\parindent 20pt
\textwidth 6.1in
\textheight 9.4in
\oddsidemargin 0.3in
\evensidemargin -0.3in
\topmargin -0.4in

2. Thay ¯

d ’ˆ

oi s ´

ˆ

o trang v`

a s ´

ˆ

o ch ’u ’ong

¯ˆe thay ¯’ d ’ˆoi s ´ˆo ch ’u ’ong ho˘a.c s ´ˆo trang ta d`ung c´ac lˆe.nh:
\setcounter{chapter}{chapter before}

\setcounter{page}{new page}

trong ¯d´o chapter before l`a s ´ˆo c ’ua ch ’u ’ong tr ’u´’oc, c`on new page l`a s ´ˆo c ’ua trang c `ˆan ¯d´anh
s ´ˆo la.i.

• V´ı du.

\setcounter{chapter}{1}: ch ’u ’ong hiˆe.n h`anh c `ˆan ¯d´anh s ´ˆo s˜e l`a ch ’u ’ong 2.

\setcounter{page}{10}: trang hiˆe.n h`anh s˜e ¯d ’u ’o.c ¯d´anh s ´ˆo 10.

3. ¯ i.nh ngh˜

D

ia lˆ

e.nh m´’oi

Lˆe.nh m´’oi ¯d ’u ’o.c ¯di.nh ngh˜ia hoa.c ¯di.nh ngh˜ia la.i b’’oi c´ac lˆe.nh sau:
\newcommand{com name}[narg]{definition}

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38 Ch ’u ’ong 5. T ´ˆoi ’uu cho ng ’u`’oi s ’’u du.ng

\renewcommand{com name}[narg]{definition}
trong ¯d´o

¦ com name l`a tˆen lˆe.nh m´’oi ch ’ua ¯d ’u ’o.c ¯d˘a.t tˆen.

¦ narg l`a s ´ˆo gi˜’ua 1 ¯d ´ˆen 9 ¯d˘a.c biˆe.t h´oa s ´ˆo bi ´ˆen c ’ua lˆe.nh m´’oi.
¦ definition l`a ¯di.nh ngh˜ia cho lˆe.nh m´’oi.

•V´ı du. lˆe.nh t´ınh t´ıch phˆan x´ac ¯di.nh.

\newcommand{\sint}[2]{\int \limits_{\hspace{-4pt}#1}^{#2}}

V´’oi lˆe.nh n`ay, khi vi ´ˆet \int a^ b f(x)dx intta ¯d ’u ’o.c Rabf(x)dx

• V´’oi lˆe.nh \newcommand ta c´o th ’ˆe ¯d ’ˆoi la.i tˆen lˆe.nh cho ng´˘an h ’on ¯d ’ˆe ¯d´anh cho nhanh
(gi ´ˆong nh ’u ph´ım t´˘at trong Microsoft Word). V´ı du. ta s ’’ua lˆe.nh\backslash th`anh lˆe.nh

\bhstheo lˆe.nh sau: \newcommand{\bsh}{\backslash}.
• V´ı du. ta mu ´ˆon ta.o ra lˆe.nh l`am viˆe.c cho ¯da.o h`am riˆeng:

Ã\newcommand{\dhr}[2]{\frac{\partialÃ{\#1}}{\partial{\#2}}}

Lˆe.nh \$\dhr{f}{x}\$ cho ta ∂f
∂x.

• V´ı du. ta mu ´ˆon Viˆe.t h´oa mˆoi tr ’u`’ong ¯di.nh l´y ta l`am theo c´ac b ’u´’oc sau:

B ’u´’oc 1: ¯ ’Dˆoi tˆen lˆe.nh \theorem th`anh\dl b ’’oi lˆe.nh
\newcommand{\dl}{\theorem}

B ’u´’oc 2: S ’’ua ch˜’u Theoremd ’u ’o.c in ra th`anh¯ •¯ i.nh l´D y

\newtheorem{theorem}{$ \Delta$ D¯i.nh l´y}

4. ¯ i.nh ngh˜

D

ia mˆ

oi tr ’u`’

ong m´’

oi

Mˆoi tr ’u`’ong c´o th ’ˆe ¯d ’u ’o.c ta.o ra ho˘a.c thay ¯d ’ˆoi v´’oi c´ac lˆe.nh:
\newenvironment{env name}[narg]{beg def}{end def}
ho˘a.c

\renewenvironment{env name}[narg]{beg def}{end def}
trong ¯d´o

¦ env name l`a tˆen c ’ua mˆoi tr ’u`’ong

</div>
(39)<div class='page_container' data-page=39>

5. S ’’ua la.i file book.cls 39

• V´ı du.: ¯ ’Dˆe ta.o ra mˆoi tr ’u`’ong¯ i.nh ngh˜D ia b`˘ang ti ´ˆeng Viˆe.t ta l`am nh ’u sau:

B ’u´’oc 1: Ta.o ra lˆe.nh\dn v´’oi tiˆeu ¯d `ˆe¯ i.nh ngh˜D ia.
\newtheoremdn{¯ i.nh ngh˜D ia}[chapter]
B ’u´’oc 2: Mˆo t ’a mˆoi tr ’u`’ong D¯ i.nh ngh˜ia

\newenvironment{dinhnghia}{\begin{dn}}{ $\Box$\nolinebreak\end{dn}

5. S’’ua la.i file book.cls

</div>

HAY TU HOC LATEX LET SEFTTAUGHT LATEX

Ch ’u ’ong 1

C´

ˆ

au tr´

uc v˘

an b’an

1.

Gi´’

oi thiˆ

<sub>e.u v `</sub>

ˆ

e TeX v`

a LaTeX

1.1

C`

ai ¯

d˘

<sub>a.t LaTeX v`a c´ac ch ’u ’ong tr`ınh k`em theo</sub>

1.2

C´

ac b ’u´’

oc ch´ınh khi d`

ung LaTeX

1.3

C ´

ˆ

au tr´

uc chung c’ua mˆ

<sub>o.t file LaTeX</sub>

1.4

C´

ac g´

oi thˆ

em v`

ao (Packages)

1.5

C´

ac mode x ’’u l´

y

2.

Ki ’

ˆ

eu t`

ai liˆ

<sub>e.u</sub>

3.

<sub>¯ i.nh da.ng trang</sub>

D

\ topmargin

\ headheight

<i><b>Head</b></i>

\ textheight

\ textwidth

<i><b>Body</b></i>

<i><b>Foot</b></i>

\ footskip

\ footheight

<b>First line of text</b>

\ topskip

\ oddsidemargin

\ evensidemargin

4.

Section

5.

Lˆ

<sub>e.nh v`a mˆoi tr ’u`’ong</sub>

5.1

C´

<sub>ac l .ˆenh c’ua LaTeX</sub>

5.2

Mˆ

oi tr ’u`’

ong

5.3

In c´

<sub>ac k´ı t ’u. lˆe.nh</sub>

5.4

C´

ac k´ı hiˆ