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VOCABULARY
accumulation (n)s tch lu
assign to (v.p)gn cho
assumption (n)gi thit
express (v)din t, th hin
extensive (adj)rng, !ao "ut
#ield (n)l$nh vc
#ormula (n)c%ng th&c
#orge (y)d'n d'n (a n
#unction (n)h)m
generali*ed (ad)(+c hi "ut h-a
get the s"uare root o# (v.p)l./ cn !0c hai c1a
indicate 2v3ch4 ra5ngenious (a)t)i t6nh, h7o l7o
in terms o# (pp)!8ng cch
o##shoot (n)nhnhpoint out (v.p)ch4 ra
propert/ (n)9c tnh, tnh ch.t
"uantit/ (n)i l(+ng
represent (v)i din cho
scope (n )phm vi
stand #or (v.p)tha/ th cho
su!division (n )ph'n, ! ph0n, nhnh
ta!ulation (n)s l0p th)nh !ng
toss (v + n) tung l:n
varia!le (n )!in s;
axiom < postulate 2n3 ti:n 7appreciate (v )nh gi =ng, nh gi cao, hiu r> gi tr?
approximation 2n3 x.p xi, g'n =ng!ehavior (n)dng iu
alge!ra o# order (n.p)i s%@ c- c.p
alge!ra o# Aorder (n.p)i s; c- c.p
complement (n )ph'n !B 2c1a mt t0p h+p3
con#usion (n )s lCn ln, nh'm lCn
distinct (adj)hc !it
totalit/ 2n3 tDng s;
un!ounded 2adj3 h%ng !? ch9nvaria!le 2E3 !in s;a!scissa 2n3 ho)nh advance (n )tin !conversel/ (adv)ng(+c licoordinate 2n3 to correspond 2vF t(cmg &ng
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curvature 2n3 congdeduce 2v3 su/ ra, lu0n rade#inite (adj)xc dinh
ar!itraril/ (Jv)mt cch tuG H
arroI 2#l3 mJi t:n
attraction 2#l3 s&c h=t
!od/ 2K3 v0t th
characteri*ation (n )s m% t
charge 2#l3 in tch
direction 2#l3 ph(Lng h(Mng
electron 2#l3 in tNO electron
#orce 2nPv3 lc
initial (adf)hQi 'u, g;c
instantaneous velocit/ 2#lOp3 v0n t;c t&c thRi
magnitude 2#l3 lMn, d)i
mass 2#l3 h%i l(+ngnorm 2#l3 chuSn
resistance 2#l3 in trR
scalar 2n3 i l(+ng v% h(Mng
scale 2n3 thang, tT l
segment (n)on thUng
terminal (adj)cu;i
vector 2n3 i l(+ng c- h(Mng, v7cAtL
alge!raic invariants (n.p)!.t !in i s;
arra/ 2n3 mng, dV/ !ngcoe##icient 2E3 h s;
commutative {ad])giao hon
contri!ute (v )-ng g-p A c%ng tc
contri!ution 2n3 s -ng g-p
credit 2n3 s c%ng nh0n
curve Witting 2X63 vY (Rng cong thc nghimXtheo cc imO
determinant 2E3 ?nh th&c
dilatation 2n3 s giVn, ph7p giVn
elegant {adj)tao nhV 5 thanh l?ch
explicit (adf)d(+c din t r> r)ng v) '/ 1
collect4on 2n) t0p h+p
conversel/ 2adv)ng(+c li
de#ne (v )?nh ngh$a, xc ?nh
derive 2v3 nh0n (+c tZ
empt/ set {n.p)t0p r[ng
enclose (v )v\/ "uanh, !ao "uanh
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endpo4nt 2n3 im 'u m=t
enumeration notation 2nOp3 H hiu s; m
even num!er (n.p)s; ch]n
handle (V)gii "u/t
herd < #loc < school 2n3 )n, !'/
illustrate (v)minh ho
indicate (v )ch4 ra, cho !it, ra d.u
intersect (v )giao, c^t
irrational num!er 2n.p3 s; v% t4
lieIise (conj3 t(ong t
line segment 2n.p3 on thUng
list (v )lit :
mem!er < element (n)phSn tN
natural num!er (n.p)s; t nhi:n
notation 2XK3 H hiu
odd num!er _nAp3 s; l`
proper su!set (,np)t0p con thc s
rational num!er (rip) shbu ti
set 2#i3 t0p
setA!uilder notation 2nOp3 H hiu th)nh phSn t0p
signi#icant (adj)"uan trng
su!set (rt.p) t0p con
s/ m!oli*e (v )!iu t(+ng ho, 9c tr(ng cho
to !e in use (v )ang trong sN dng
abbreviate (v) vit ttaim 2v3 mc ch
associate ()li:n t, li:n !p
characteri*e (v )m% t tnh cch, 9c im
constant 2adj3 h%ng [i
constant mapping 2E3 nh x h%ng DiXnh x h8ng
converse (adj)o, o 2n3
domain (ri)min xc ?nh
gumdrop (ri)fo g%m
identit/ mapping (ri)nh x Dng nh.t
image (ri)nh
index (ri)ch4 s;
index mapping 2X43 nh x ch4 s;
into mapping (ri)nh x v)o
map 2v3 nh x
mapping (ri)nh x
onto mapping (ri)nh x 4:n
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compress (v)n/n
corporate (a)thuc v c%ng t/corporation (n)t0n" c1n" tyalternate (adj)tha/ thapproach 2vPXi3 tip c0nargument (r');i s;
associate to (v.p)li:n h vMi, li:n "uan n!ehavior (23)dng iu
!ounded (adj)!? ch9n
!/ means o# 2pOp3 !8ng cch
constant 2n3 h8ng s;
adding *ero tric (n.p)th1 thu0t cng th:m adopt (v)sN dngapplica!le (adj)p dng (+c
ar!itrar/ (adj)!.t G
criterion (n )ti7u chuSn
drop (v )! di
exhi!it v)d(a ra, t ra, tr(ng !)/, cho th./
extract (V)trch, tch, gii n7n (tin)
implicit (adj) 4n
chain rule (n.p)"u/ t^c o h)m c1a h)m hp
constant rule (n.p)"u/ t^c h)m h8ng
deceptive (adj)d nh'm lCn
densit/ (n )m0t
derivative (n)o h)m
di##erential (n)vi ph\n
directional derivatives (n.p)o h)m theo h(Mngdi##erentiation (25)ph7p tnh o h)m
di##erentia!ilit/ (n )tnh h vi
di##erentia!le (adj)h vi
adopt (v )ch.p nh0n
antiAdi##erential (n.p)ngu/:n h)m
assert (v )hUng ?nh
assume 2vF gi ?nh
cloud ?5 che ph1, l)m mR i
conFecture (v )phng on, (Mc on
dumm/ varia!le (n.p)!in gielongate 2v3 7o d)i
em!race (v )!ao gm, !ao trBm
evaluate (v )nh gi
illustration (n)s minh ha
inde#inite integral (n.p)tch ph\n !.t ?nh
additivit/ 2n3 cng tnh
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assign 2v3 gn
dense 2n3 d)/ 9c
extended real num!er (n.p)s; thc mR rng
n dimensional space (n .p ) h%ng gian n chiu set
#unction (n.p)h)m t0p 2h+p3
set theoretical operations (n.p)cc ph7p ton tr:n t0p h+p
the intuitive point o# vieI (n.p)mt cch trc "uanaccumulation 2X43 tch tapparent (adj)r> r)ngappraise 2v3 nh giassociation 2n3 hi, t h+passume 2v3 gi ?nhcategor/ 2n3 loi, phm trBconstitute 2v3 to th)nh, c.u th)nh, l0p n:ncontinuum 2n3 vD hncontradiction 2n3 m\u thuCnextent 2n3 phm vigenerali*e 2v3 tDng "ut ho
germane (ac2j)thch h+p, phB h+pinner measure 2E3 do trongintimate (adj)gn gJilegitimate 2adj3 c- lH, logicmeasura!le 2ad#3 o (+cnonAdimensional (adj)h%ng th& ngu/:nouter measure m d o ngo)i
persist 2v3 du/ tr6principle 2n3 ngu/:n t.ctopolog/ 2n3 tAp%vital {ad6)"uan trng, mang tnh s;ng cn*ero set _nOp3 t0p c- o
!ounded 2adF3 !? ch0nclosed sets 2nOp3 t0p -ngclosure o# a set (n.p)!ao -ng c1a mt t0p h+p
cluster point 2nOp3 im tcluster point #rom the le#t 2right3 2nOp3 im t !:n tri 2phi3compact 2n3 comAp^ccompactness 2nOp3 tnh comAp^cconstitute 2v3 lp th)nh, to th)nhcover 2v3 phBcovering (n)c-i p7deleted neigh!ourhood 2nOp3 l\n c0n hDng t\m 2hu/t3dense 2adF3 trB m0tderived set (n.p)t0p diem t 2tp dCn xu.t3discrete (adj)rRi rcexterior point (n.p)im ngo)i#amil/ (n)h 2cc tp h+p3in#imum (ti)ch9n d(Mi lMn nh.tin#erior point (n.p)im trongcomplementar/ #unction (n.p) h)m !D sungcomplete primitive _nOp3 n"8y9n :% '/ 1degree o# the e"uation 2nOp3 b;c c1ap
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normed space (n.p)h%ng gian chununi#orml/ continuous (adj)li:n tc u
implicit #orm (n.p) d&n" 4n
linear com!ination 2nOp3 t0 h+p t8yn t'n
order o# the e"uation 2nOp3 c>p c7a p
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claim 2v? "u "u/t, hUng ?nh
sample (n)mCu
statistic (n)m%n th;ng :
statistics (n)m%n th;ng :, ng)nh th;ng :
descriptive statistics (n.p)th;ng : m% t
in#erential statistics (n.p)th;ng : su/ lu0ntag (v)!uc, g^n, dn
Ihooping crane (rt.p)lo)i su to Q !^c m
derive 23 su/ ra
die A 2pl3 dice (n )consGc sc
event (n )!in c, sH Ii*n
de#inite event (n.p) bin c ccch^n
null event (n.p)!in ch%ng th
experiment (n) p/pthN ngCu nhi:n
#lip (v)!=ng, l0t nhanh
outcome (n)t "u, h\u "u
#avora!le outcome (n.p)t "u thu0n l+i
possi!le outcome (n.p)t "u c- th
reasona!le (adj)h+p l, c- l
roll (v)"ua/, cu;nsample space (n.p)h%ng gian mCu
5 assert (adj)hUng ?nh
challenge (v )thch th&c
classic (adj) cdin
concede 2v3 thZa nh0n l) d=ng
den/ 2v3 tZ ch;i, h%ng thZa nh0n
emerge 2v3 nDi l:n, hin ra
extend 2v3 mQ rng, 7o d)i
in#inite (adj)v% s;, v% hn
intersect 2v3 c^t, giao nhau
Fusti#/ 2v3 ch&ng minh l) =ng
mechanics 2n) c=hc
prove 2v3 ch&ng minh
revelation 2E3 s pht hin, pht gic
sane 2adj3 tinh to, c- lH tr
sel#evident (adj)hin nhi:n l) =ng
su!stitute 2v3 tha/ th term 2n3 thu0t ngbtheorem (n)?nh lH
the outset 2nOp3 s hi 'u
unexpected i#ldO#i !.t ngR, h%ng (+c tt%ng +i
discourse (n )!)i ging, !)i thu/t tr6nh
e"ualit/ (n )Ung th&c
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#undamental (ad) c= sK, c=!n
location (r3)v? trH
locus (n )t0p h+p im, "u tch
notion (n)hi nim, H nim
notIithstanding (prep)!.t ch.p, h%ng n
o!tain < gain 2v3 t (+c, thu (+c
ordered pair (n.p)c9p th& t
ordinate (n)tung
origin (n)im g;c
original (adj)g;c
philosopher (n)nh) trit gia
"uadrant (n)g-c, cung ph'n t(
respectivel/ (adv)mt cch l'n l(+t
slope (ri) d;c
speci#/ 2v3 xc ?nh, ch4 r>
totalit/ (n )tDng s;
trace 2v3 m% t, ra, vch ra
Ior out 2vOp3 t6m ra, pht hi:n ra
elimination 2E3 ph7p hN
explicitl/ (n )r> r)ng, chnh xc, hin, t(Rng minh
exploit 2v3 sN dng, hai thc
#amiliarit/ (t3)s hiu !it r>, s "uen !it
impressive 2adj3 hBng v$, ngu/ nga, s\u s^c, g\/ .n t(+ng
insights (r3)s hiu !it !n ch.t
linear e"uation 2n.p3 ph(Lng tr6nh tu/n tnh
linearit/ (n)tnh ch.t tu/n tnh
linear s/stem 2n.p3 h tu/n tnh
managea!ilit/ (n )c- th "un lH (+c
parameter (ti)tham s;
poIer (r3)s; mJ
prosaic 2adF3 n%m na
roughl/ (adv)mt cch g'n =ng, mt cch sL !
simpli#/ 2v3 r=t gn, Ln gin
setch 2v3 phc ho
slope (adj)d;cspherical (adj)c- h6nh c'u
s"uee*e 2v3 v^t
visuali*e 2v3 h6nh dung, m(Rng t(+ng
expression 2n3 !i:u thbc
geneticist 2n3 nh) di tru/n hc
implicit 2adj3 A in sth (n )ng.m ng'm, Sn
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implicit/ (n )tnh Sn
invariant (adj)!.t !in
investigate 2v3 nghi:n c&u, iu tra
linear trans#ormation 2n.p3 ph7p !in Di tu/n tnh
matrix calculus {n.p)ph7p tnh ma tr0n
mode 2n3 ph(Lng th&c, ph(Lng php, h6nh th&c
matrix,p2 .matrices (n )ma tr0n
originate 2n3 sng to ra, l) t.c gi c1a
phenomena 2n3 hin t(+ng
"uantum mechanics 2n3 cL hc l(+ng tN
re#lection 2n3 ph7p phn chiu, s phn x, s ;i x&ng
remain 2v3 cn li, v]n
rotation 2n3 ph7p "ua/
simpli#ication 2E3 s Ln gin, s r=t gnsimultaneous linear e"uations (n.p)h ph(Lng tr6nh tu/n tnh t(Lng thch
shorthand 2n3 t;c H so#orth 2adv)v\n v\n
s/stemati*e 2v3 h th;ng ho
undou!tedl/ 2adv)r> r)ng ch^c ch^n
fa%i2y ot set q h cc t;p
#ield o# set q tr(Rng cc t0p
#ormulate qp-t biL8
generali*ed !oolean alge!ra 2nOp3 i s; un hi "ut h-a
hold F v3 =ng vMi
impose 2v3 p 9t
induction 2tt3 ph(Lng php "u/ np
insert 2v3 ch`n v)o
intersection 2n3 giao 2c1a hai t0p h+p3
ordered pair (n.p)c0p s^p th& t
product 2n3 tch
proFection (n)h6nh chiu
proposition (n)mnh
respectivel/ (adv)mt cch l'n l(+t, theo th& t, t(Lng &ng
retain 2v3 gib liso #ar as smt concerned (a.p)trong chZng mc ai, ci g6 c- li:n "uan
statement < proposition 2n3 mnh d
striing (adj)nDi !t
trivial (adj)nh nht, v0t vVnh, t'm th(Rng
union 2n3 h+p 2cBa hai tp hp3
universal class 2nO p3 lMp ph% dng
universal set 2nOp3 t0p vn nng
valid 2adF3 c- hiu lc
rate (n)t;c , t6 l
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reenter (v)v)o lirevenue (n )doanh thuroughl/ (adv) s=l(+csigni#icance (n )t'm "uan trngspring (n )l xostretch (v )7o cngtangent line (n.p)(Rng tip tu/n
to !e applica!le to (v.p)c- th &ng dng (+c v)oto !e credited Iith (v.p)#
determine 2v3 "u/t ?nh, xc ?nh
domain 2X43 min xc ?nh
encounter 2v3 g9p, chm trn
explicit 2adF3 hin, t(Rng minh
#inite _adF3 xc inh, hbu hn
#ormulae 2n3 c%ng th&c
#unction 2XX3 h)m s;
give rise to 2vOp3 pht sinh, n/ sinh
graph 2E3 th?
identi#/ 2v3 nh0n dng
immaterial 2adF3 h%ng "uan trng
implicit 2adF3 Sn, ng'm
in#inite 2adF3 v% hn
irrational 2nPadF3 v% t4
5n this manner 2pOp3 theo cch n)/
ordinate set 2nOp3 t0p tung
range o# #unction 2nOp3 min gi tr? cBa h)m s;
rational iPadF3 hbu t4
restrict 2v3 hn ch
signi#/ 2v3 !iu th?, !iu hi:n
speci#/ 2v3 xc ?nh, ch4 r>
terminate 2v3 t th=c
monotone decreasing (n. p)Ln iu gim
monotone increasing (n.p) #=niu tng
monotonicit/ (n )tnh Ln iu
oscillate (v)dao ng
pattern (n)mCu, h6nh th&c
poIer series (n.p)chu[i lu thZa
recursive (adj)l9p, tru/ hDi
series (n )chu[i
strictl/ decreasing (a.p)gim nghi:m ng9t
strictl/ increasing (a.p)tng nghi:m ngt
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su!se"uence (n )dV/ con
theorem (n)?nh lH
triangle ine"ualit/ (n.p)!.t Ung th&c tam gic
tric (2i)th1 php, thB thu0t
uni"ue (adj)du/ nh.t
di##erential calculus (n.p)ph7p tnh vi ph\n
di##erentiate (y )tnh o h)m
dissolution (n)ph\n rV
higherorder derivatives (n.p)o h)m c.p cao
increment (n)s; gia
in#inite derivatives (n.p)o h)m v% hn
instantaneous velocit/ (rt.p) v0n t;c t&c thRi
mani#estation (n)s !iu th?
marginal pro#it (n.p)l+i ch c0n !i:n
onesided derivatives (rt.p)o h)m mt phapartial derivatives (n.p)o h)m ri:ng 2theo !in3
poIer rule (n.p)"u/ t^c h)m lu thZa
productX"uotient rule (n.p)"u/ t^c o h)m tchXth(Lng
preserve 2v3 !o to)n
tangent line (n.p)tip tu/n
theme (n)ch1
integra!le (ac2j)h tch
integrand n)h)m l./ tch ph\n
int7gration 2n3 ph7p tnh tch ph\n
inter val 2n3 on thUng, hongintuition 2n3 trc gic
intuitive 2adF3 mang tnh trc gic
landmar 2n3 m;c
loIer integral 2l$Op3 tch ph\n d(Mi
loIer sum 2nOp3 tDng d(Mi
partition 2n3 ph\n hoch
proposition 2n3 mnh
strip 2n3 di
su!division (n )ph\n hoch
throughout (prep)xu/:n su;t
to !e concerned Iith (v.p)li:n "uan n, "uan tm n
additivit/ 2#i3 cng tnh
assign 2v3 gn
dense in3 tr) m0t
extended real num!er 2nOp3 s; thc mQ rng
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n dimensional space 2XAp3 h%ng gian n chiu
set #unction 2nOp3 h)m t0p 2h+p3
set theoretical operations 2nOp3 cc ph7p ton tr:n t0p h+p the intuitive
point o# vieI 2nOp3 mt cch trc "uan
isolated point 2nOp3 im c% l0p
midpoint 2t63 im giba
neigh!ourhoods 2n3 l\n c0n
nested 2adF3 lng nhau
per#ect 2adF3 ho)n ch4nh
point o# accumulation 2nOp3 im tch t
real varia!le theor/ 2nOp3 lH thu/t !in thc
se"uences o# closed sets 2nOp3 dV/ cc t0p -ng
su!#amil/ 2n3 h con
supremum 2n3 chn tr:n nh nh.t
the !oundar/ o# a set 2nOp3 !i:n c1a t0p h+p
the interior, the exterior o# a set 2nOp3 ph'n trong, ngo)i
come into !eing 2vOp3 !^t Su tn ti
condense 2v3 l)m c% ng
contaminate 2v3 l)m % nhi:m
discrete 2adF3 rRi rc
endangered species 2nOp3 lo)i v0t c- ngu/ cL tit ch1ng
gather 2v3 thu th0p, t0p h+p
giant panda 2nOp3 g.u tr=c
in more general sense 2prepOp3 Q ngh$a hi "ut hLn
involve 2v3 !ao h)m managea!le 2adF3 c- th "un l (+cmeasurements 2n3 ph7p o, h th;ng o
misuse 2v3 lm dng
monogam/ 2n3 ch mt v+ mt chng
name !ut a #eI 2vOp3 ch4 mt s;
o!servation 2n3 s "uan st
o!tain 2v3 gi)nh (+c, c- (+c
parameter 2n3 tham s;, th%ng s;
population 2n3 "u\n th
procedure 2n3 !in php
"ualitative data 2nOp3 db liu ?nh tnh"uantitative data 2nOp3 dZ liu dinh l(+ng
radon 2n3 h4 ph-ng x do s phn gii c1a ra di
roughl/ speaing 2nOp3 nDi nm na