Abbildung mapping; (sometimes) illustration

aber but, however, yet

abfassen compose, write up, draw up, word

Abfassung writing, formulation, wording

Abgrenzung definition; delineation, demarcation

abhängen (von) depend (on)

Abkürzung contraction, abbreviation, abridgement

ableiten lead out of; deduce

Ableitung derivative, derivation; deduction

ablesen pick (off), read (off), read out

abmachen settle, arrange; undo, untie

Abmachung arrangement, settlement

abnehmen decrease, take off, remove

Abnehmen reduction

Absatz pause, break, indentation; paragraph

abschätzen estimate, calculate, assess, appraise, etc.

Abschätzung estimate, appraisal, valuation

Abschluß / Abschluss closure (in the topological sense)

Abschnitt intersection; segment; cut, paragraph, part, section

Abschnitt auf der x-achse x-intercept

absehen foresee

absehen von disregard; refrain from

absolut absolute, unconditional, perfectly, utterly

Abstand distance

absteigen descend, come or go down

abzahlbar countable

Abzahlbarkeit countability

abzahlen count, enumerate

achten (auf) pay attention (to)

ähnlich alike, like, similar

all all, every, any

allein only, merely, solely; alone

allerdings certainly (strongest possible affirmative answer)

allgemein general, universal

allmählich gradually, little by little

alsdann then, thereupon, whereupon, after that

analog analogous

Anblick look, view

andere other; next

andererseits on the other hand

ändern alter, change, modify, amend

Änderung change, alteration, modification

andeuten indicate, suggest, hint at, allude to, imply

Anfang origin, beginning, start

anfangen start, begin, commence

angeben indicate, state

angehören be a member (of)

angewandt applied

angrenzen border, adjoin

Anhang appendix, codicil

ankommen arrive (at); depend (on), e.g., "es kommt darauf an" means "it depends on"

Anlaß / Anlass motive, motivation; cause, occasion, incentive, reason

Annäherung approach

Annahme acceptance, adoption

annehmen accept, take, assume, suppose

anordnen arrange, order, command, direct, set in order

Anordnung arrangement

anpassen fit, adapt, adjust, accommodate

Ansage announcement

ansagen announce, declare

anschaffen procure, get

anschließend / anschliessend subsequent (to), adjacent (to); next.

Anschluß / Anschluss connection, union

an(zu)sehen (in order to) look at, have a look at

ansetzen put (on), apply (to); begin

Anspruch claim

Anstoß impact, impluse

anstoßen / anstossen bump against, adjoin

anstreben strive for

anwenden employ, use, make use of

Anwendung application

Anzahl number, quantity

arbeiten work

Art kind, sort, class

auch also, too

auf on, upon, on top of

aufbauen construct

auffassen comprehend, grasp, understand

Aufgabe exercise, problem

aufgehen divide exactly

Auflösung solution, resolution (of)

aufschreiben write down

Aufstellung assertion; list, table

auftragen instruct, order, serve, put on

auftreten appear, occur, behave, act, proceed

Auftritt appearance, entrance

Augenblick moment, instant

aus from, out of

ausarten get out of hand, degenerate into

Ausblick view, outlook, prospect

ausdehnen stretch, expand, extend

Ausdehnung stretching, expansion

ausdrücklich explicit; explictly

Ausdruck expression, phrase, term

ausdrücken express, put into (a form, words)

ausführlich detailed, in detail, full

Ausführung execution, construction; explanation

ausgehen proceed from

ausgewählt selected, chosen, choice

ausgezeichnet excellent

ausmachen consist of, make up, add or amount up to, constitute

Ausnahme exception

ausnahmslos without exception

ausreichen suffice

ausreichend adequate, sufficient, enough

Aussage assertion, statement

aussagen state, express, declare

Außenrand outer boundary

Außenwelt / Aussenwelt environment, world, outside world

außer / ausser out of, outside

außerdem / ausserdem besides, in addition, moreover, as well as

außerhalb / ausserhalb outside, out of

ausstreichen cross out, delete, erase; smooth out

Auswahl choice, selection, assortment

auswählen choose, select, pick out, fix on

auswerten evaluate

auszählen count

auszeichnen designate (notation), mark

Auszeichnung labelling; distinction

Band volume (as of a book)

Bauart structure, build, type, model

bauen build, erect, make, manufacture

beachten note, pay attention to

bedecken cover

bedenken consider, weigh, ponder

Bedenken thought, reflection, deliberation

bedeuten mean or signify

bedienen wait on, serve

bedingen cause, determine, or condition

Bedingung condition, stipulation

befassen touch, handle

befassen sich mit concern oneself with, attend to

befriedigen satisfy

begegnen meet, come upon

begnügen mit to be content with

begrenzt bounded, restricted, limited, circumscribed

Begriff idea, notion, concept, term

behandeln deal with, treat, handle

behaupten declare, assert, maintain, retain

Behauptung declaration, assertion

beherrschen rule, master, control

Behrührungspunkt accumulation point, limit point (topology)

bei(m) for; by; at; while; "beim" is short for "bei dem"

Beibehaltung retaining

beiden two, both, either, neither

beiderseits reciprocally, mutually, on both sides

Beiwort adjective

bekannt well known

belasten load, put a load on, make heavy

belegen verify (a proof)

belegt proven; reserved, coated, husky, busy

Beleuchtung elucidation; illumination, lighting

Belieben choice, discretion, convenience, liking, pleasure

belieben wish

beliebig(e) optional, arbitrary

bemerken remark, notice, observe

benötigen need

benutzen use, make use of, employ, utilize

bequem comfortable, easy

Berechnung calculation

Bereich region; (sometimes) open set

bereits already

berücksichtigen bear in mind, consider

Berufung call, vocation, appointment

beruhen auf be based on; be due to

berühren touch, mention, affect, pass through, come in contact

besagen signify, mean

besagt aforesaid

beschaffen procure, provide, supply, get, raise

Beschaffenheit quality, property

Beschaffung acquisition; procurement

beschränken limit, restrict, confine, set limits

beschränkt bounded, limited

beschreiben describe

besitzen possess, own, have

besondere particular, special

besonders especially, particularly, in particular

bestätigen confirm, corroborate, verify

bestehen exist

bestehen aus to comprise of

Bestehen existence

bestehend existing, present

bestimmen determine

bestimmt determined

betonen stress, accent, emphasize

Betracht (in) consideration

betrachten observe

Betrachtung observation, reflection, reason

Betrag value, amount

Betrag, absolut absolute value

betreffen concern, affect, be relevant to, have to do with

betrifft in regards

bewältigen conquer, overcome, master (difficulties)

bewegen move, stir

Beweis proof

beweisen prove, show, demonstrate

bezeichnen designate (by), define

Bezeichnung notation; designation

beziehen (auf) relate or refer (to)

Beziehung relation, connection, respect

Bezug auf, in with respect to, in reference to

bezüglich relative to, relating to

Bezugnahme auf, unter with reference to, in reference to

bieten give, show, offer; present itself

Bild image

bilden form, shape, fashion

binar binary

binden bind, tie unite, join

bisher hitherto, up to now, so far

bisherig(en) as up to the present, former, so far

bisweilen occasionally, sometimes

bleiben remain, stay, continue

Blick view

bloß / bloss merely, only, simply

brauchen require

Brief letter

bringen bring

Bruch fraction

Bruch, echte proper fraction

Buch book

Bündigkeit validity, conclusiveness, conciseness, brevity; compactness

bzw. (beziehungsweise) respectively

da there, because

dabei by or near it or them, in addition, at the same time

dadurch thereby, by this means, in that way

dafür therefore, for it or them, in its place

dagegen on the contrary, conversely, on the other hand, nevertheless

daher therefore

damals then, in those days, at that time

damit consequently; thereby, thereupon, with it or them

danach behind or after it, afterwards, thereupon

dann then, at that time, after that

daraus (folgt) out of this (follows)

dargestellt described

darin in it or in them, there

darstellen represent, portray, present, describe

Darstellung representation, description

darunter beneath or under (it or them), in it, among(st) them

dass that

dasselbe, denselbe, derselbe, dieselbe, usw. the same

davon from it, of it, away from it

definieren define

denen (to) them or those, (to) those

denken think, imagine, mean, intend

denn than, for, because, unless, except

derart in such a way or manner, to such an extent

derartig such, of that kind

deren of them, (of) that, (of) those

derjenige (adjective) that; (pronoun) the one; he

derselbe the same

desgleichen such a thing; the likes of which; likewise

deshalb therefore, for this reason

desselbe the same

deuten interpret, explain or indicate

dicht dense (in topology); tight, thick

dichten tighten; write

dichtesten densest

Dichtigkeit density; conciseness

diejenige (adj) that; (pron) the one; he

diesmal this time

Ding object, thing, matter

dingen hire, engage, bargain, haggle

diskutieren discuss

doch but, though, yet, however, nevertheless

dort there, over there, yonder

dortig in or of that place, there

Dreieck triangle

drucken to print; to press

drücken put (into); press; squeeze

durch through

durchblicken be apparent or obvious

durchblicken lassen make apparent or obvious

durchdringen force one's way, penetrate

durchführen take or lead through, accomplish

Durchführung accomplishment, execution, development

durchlaufen run or pass through, traverse

Durchschnitt intersection; average

dürfen may, might

Ebene plane

ebenfalls likewise, also, too

ebenso likewise, in the same manner

echte genuine, real, true

Eck corner

Eichkörper standard ball, unit ball

Eigenschaft property, quality

eigentlich actual; actually, really

einander one another, each other

eindeutig unique; unambiguous, clear, plain

Eindeutigkeit uniqueness

eineindeutig one to one

einerseits on the one hand

einfach simply; simple, easy

Einfluß / Einfluss influx, influence

einführen introduce

Einführung introduction, presentation

Eingang entrance

eingehen enter into

eingreifen catch, hold; intervene or interfere in

Einheit unit

einheiten unimodular

einig united, at one

einige some, several

einigen unite, unify; agree

einklammern bracket, put into parentheses

Einlagerung deposit, intercalation, storage

einleiten lead into; introduce

Einleitung introduction, prelude

einmal once, at once

einschalten insert; intervene

einschließen / einschliessen include

Einschränkung restriction

einsehen inspect, consult, realize

einsetzen insert, put or place in, substitute

Einsetzung putting in; substitution

einstellen put or place (in the proper place); appear, show up

einteilen divide, distribute, classify

Einteilung classification

einzelnen individual

einzig only, e.g., "darstellen einzig" means "to show unique"

endlich finite; final, ultimate

entdecken discover, detect, find out

entfernen move away

entfernt distant

Entfernung distance, range

enthalten hold, contain, comprise, include

Entscheidung decision

entsprechen correspond (to)

entsprechend correspondingly, accordingly

entstehen originate, arise from

entweder either

Entwicklung development (e.g., of power series)

erfahren experienced

erfahren find out, experience

erfordern require, need, necessitate, render necessary

erfüllen fill, fulfill, perform, carry out

ergänzen complete, complement, restore

ergänzend complementary

ergänzt completed

ergeben produce, yield, show, establish, prove

ergeben sich (aus) result (from)

Ergebnis result, solution, answer

ergiebig productive, rich, abundant

erhalten obtain, get, receive

erhalten preserved

erinnern remind

erkennen make out, recognize, detect, realize

erklären explain

erlangen reach, get

erlauben allow

erlautern explain, elucidate, comment on

Erlauterung explanation, illustration

erleichtern facilitate

ermitteln ascertain, find out, discover

Ermittelung determination

ernennen name, select

erneuern renew, renovate

eröffnen open, unseal, disclose, reveal

erörtern discuss, argue, debate

erreichbar attainable, accessible, available, within reach or distance

erreichen reach, attain, obtain, achieve

Ersatz replacement, substitution

erscheinen appear, show itself

Erscheinung appearance; phenomenon

erschöpft spent, exhausted, at an end

ersehen gather (from)

ersetzen replace, compensate for

Ersetzung replacement, substitution

ersichtlich obvious, evident, apparent

ersinnen think out, devise, think up

erst first, at first, just, only

erstrecken extend, stretch, run, reach

erwähnen mention, make mention of, refer to

erwähnt mentioned

Erweis proof

erweisen prove, establish, demonstrate

erweitern widen, extend, broaden (one's knowledge)

erweiterte extended

erzeugen produce, make, generate

erzeugend productive, generative

erzielen obtain, attain, achieve, reach

etwa around, about, approximately; perhaps, by (any) chance

etwas something, some, a little, anything, somewhat

eventuell possibly, maybe, perhaps

fähig capable, liable, apt

Fähigkeit ability, capability

Fall (in this) case, instance

falls in (the) case

Faltung fold, convolution

Faser fiber

Faserraum fiber bundle

fassen grasp, seize, take hold of

fast almost, about

Fehlen absence

fehlen do wrong, fail, be short of; be missing, be absent

fern far, distant, remote, far off

ferner further, farther, furthermore, moreover

fest firm, stable, fixed, stationary

festhalten hold on to

festsetzen arrange, settle, establish, fix, stipulate, prescribe

Festsetzung requirement, stipulation

feststehen stand firm or steady, be certain, settled, established as a fact

feststellen ascertain

Fläche surface

Folge consequence

Forderung claim

Förderung promotion, encouragement

Form form, figure, shape

formal formal

Formulierung formulation, wording, definition

fortsetzen continue (e.g., analytic continuation); e.g., "setzen das Verfahren fort" means "to continue the procedure"

Fortsetzung continuation (sp. analytic)

fortwährend lasting, continual; always

Frage question

fragen ask

freilich indeed, certainly

früher earlier, previous, prior, former

fügen join; be fitted or proper

führen lead

gab gave (simple past of geben)

ganz integer; whole; entire (complex functions)

ganzzahlig integer-valued (e.g., linear combination)

gar entirely, absolutely, fully, very, quite

Garbe sheaf

geben give

Gebiet area, region, domain; (sometimes) open connected set

gebildet educated, cultured, refined, shaped, fashioned

Gebrauch use

gebrauchen use, employ

gebrochen broken, bent, deflected

gebunden bound, latent, tied up (with), controlled

geeignete suitable, appropriate, desired, wanted

Gefallen favor

gefallen please, appease

gefunden found (past participle of finden)

gegeben given, state, accepted (past participle of geben)

gegen against; to, e.g., "konvergieren gegen" means "converge to"

Gegenbeispiel counterexample

Gegensatz converse theorem; however, "im Gegensatz zu" means "in opposition to, in contrast to"

Gegenstand object, thing, subject matter

gegenüber opposite to; with respect to; compared with

gehen go

gehören belong (to, with); be proper, be right

gehörig belonging to

gehört belonging (to, with); proper

gelangen attain, reach

gelegen located; convenient, opportune

gelernt practiced, experienced (at)

gelocht(e) punctured

gelten hold true

geltend effective, applicable, valid

gemach slowly, by degrees

gemächlich leisurely, comfortably

gemäß / gemäss according to

gemein common

gemeinsam common, mutual, combined

gemeinschaftlich common, joint, mutual

gemischt mixed, combined, diffused

Genauigkeit precision, accuracy

genannt above mentioned, called, surnamed

genau exact, accurate, precise, detailed

genau dann precisely then (i.e., iff)

genügen be sufficient or enough, suffice; satisfy (a condition)

genügt suffices

geordnet orderly, disciplined, systematic

gerade even (numbers); just, right, now

Gerade line

geradlinig straight-lined, rectilinear

gerichtlich legal, judicial, court

gern(e) willingly

gesamt whole, entire, complete, common, general

geschehen take place, happen, occur

geschichtlich historical

Geschlecht genus (of a surface)

geschlossen closed, enclosed

geschult schooled, trained

gesetzmäßig / gesetzmässig legal, legitimate

gesetzt fixed

Gestalt form, figure, shape

gestatten permit, allow, grant

gestern yesterday

gesucht desired, sought after, choice

getan no sooner said than done

getrennt separated

gewählt chosen; selected, choice, select

Gewicht weight

gewinnen win, obtain, acquire

gewiß / gewiss sure, certain, assured, true, positive

Gewißen / Gewissen conscience

gewöhnlich usual, customary, normal

gezeichnet drawn, marked

gezeigt shown

gibt gives; however "es gibt" means "there is"

gilt is true (inf. gelten); "es gilt" means "it is true

Gitter lattice

Gittermasche fundamental paralleltope of a lattice

glatt smooth, even, glossy, flat

gleich equal

gleichbedeutend equivalent (to)

gleichen equal

gleichfalls likewise, as well, too, in the same way

Gleichheit equality

Gleichheitzeichen equality sign (=)

gleichmäßig / gleichmässig uniform (continuity); proportional, constant, symmetric

Gleichung equality

Glied term; link

Grad degree, order

greifen grab, seize; choose

Grenze limit; boundary

grenzen border, adjoin

Grenzwert limit, limiting value

groß / gross large

Größe / Grösse quantity, size

grunden establish, found; be based on

Grundgedanke basic idea, motivation, fundamental idea

Grundlage foundation, basis, groundwork

grundlegend basic, fundamental

Gruppe group

Gültigkeit validity, legality, availability

Güte goodness

haben have

haften cling, adhere, stick

handeln act, take action, proceed

handelt acts (inf. handeln); "es handelt sich um" means "it is a matter of"

hängen hang, suspend, attach, fasten, fix

häufig frequent

Häufung accumnnulation, multiplication, piling up

Häufungspunkt accumulation point

Haupt head, chief, principal, main

heben lift, raise; increase; enhance

heißen / heissen to be called; however, "d. h. = das heißt / heisst" means "that is, in other words, i.e."

herausgreifen choose, select, pick, single out

hergeleiteth derived, deduced

herleiten derive, deduce

Herleitung derivation

herrühren originate, derive, spring, proceed

herstellbar producible

herstellen produce, prepare, make

herum around, about

hervor forth, out, out of, from under

hervorgehen come (from); emerge (from)

heute today

hierin herein, in this

hiermit herewith, (along) with this, saying or doing this

Hilfe help, aid, support

Hilfesatz lemma

Hilfsmittel device, tool, aid

hindurch through, throughout, during

hinfort in the future

hinlänglich sufficient, adequate

hinreichend sufficient

hinweisen point to or towards, indicate

hinzu to, towards, near; in addition, moreover

hinzufugen append, attach

hoch high, tall, lofty

höchstens at the most, not exceeding

hohe high, tall, lofty

Höhe height, altitude

Hülle, abgeschlossene closure (in the topological sense)

identisch identical

ihnen (to) them

im voraus in advance

immer always

in Anbetracht in consideration of

in der Tat in truth, in fact, in reality

indem while, as; by

Inhalt area, volume; contents, subject matter

Inhaltsverzeichnis table of contents

innere interior, internal, inner

irgend any

irgendein someone (or other), anyone

je ever, at any time; always, at all times

je nachdem depending on how, as the case may be

jede every

jedoch however

jetzt now, at present

jeweils at times, from time to time, at any given time; respectively

kaufen buy

kein none, not any

kennen know, become acquainted with

Kenntnis knowledge

Kennzeichen distinguishing mark, criterion, sign, characteristic

Kern kernel, core, heart

Kette chain, range

Kettenkomplex chain complex

Klammer clamp, clip

Klammer, eckige (bzw. runde) brackets, square (resp. round, i.e., parentheses)

klammern clamp, clasp

klar clear, transparent

Klasseneinteilung classification

Klassenkörper (Hilbert) class field

klein little, small, tiny, minute

knüpfen tie, join, attach, fasten

kommen come, happen

komponieren compose

kontrahierbar contractible

konvergieren converge

Körper field

kräftig with force, heavily

Kreisring annulus

Kreisscheibe closed disk

Kriterium criterion

Kugel ball, globe, sphere

lange long

Länge length

langsam slow

lassen leave, part with; let, e.g., "es lässt sich zeigen" means "it can be shown"

lauten sound; read, say (a word)

läuten to toll, to chime

lauter louder; clear, pure, unmixed

Leben life, existence

leben live

lediglich merely, only

leer empty, vacant, void

legen put, place, set

Lehre theory, teaching, instruction, lesson

Lehrsatz thesis, proposition, theorem, precept

leicht light, easy, lightly, easily

leiden suffer, bear, tolerate

leiten lead

lenken guide, direct

letzen gratify, refresh, comfort

letzt last, final

licht light

liefern supply, provide, yield

liegen lie, be located or situated

links left (side)

Lochrand hole boundary

lösbar soluble, solvable, resolvable

lösen settle, resolve, answer

Lösung solution

Lot perpendicular (line)

Mädchen girl

mag wants (inf. mögen)

Mangel want, need, deficiency, scarcity

Mannigfaltigkeit manifold

Mass measure

mehrere several

mehrfach repeated, multiple, over and over again

meiden avoid, shun, flee

meist most

Menge set

mindestens at least, at the very least, not less than

mithin consequently

mitsamt together with

Mittel means, measures, medium, instrument, device, method

mittels by means of

mittlerer interior

modifizieren modify, qualify

modifiziert modified

mögen want, wish, desire; however, "es möge(n)" means "let", and "es möge hinreichen zu sagen" means "let it suffice to say"

Möglichkeit possibility

muss must

müssen to need to, to have to

nach after, following, behind, to, toward, according to

nach dem relative to, according to

nachdem afterwards

nachprüfen verify

nächst next, following

nachträglich supplementary, subsequent

Nachweis proof, evidence

nachweisen prove, establish, authenticate

nahe near, close, forthcoming

Nähe proximity

naheliegend obvious, nearby, near lying

näher nearer, closer, shorter, more precise, specific, detailed

nähern approach, close in (on), bring or place near

Näherung approximation

nämlich the same; namely, that is to say; of course

neben beside, in addition to, near

nehmen take, receive, accept

nehmen, in Anspruch make use of

nennen name, call, designate, term

neu new

nichtleere nonempty

nie never

niedrig low, humble, base, mean

niemals never

nirgends nowhere (at all), not anywhere

noch still, in addition to, even, nor

nochmal once more

normieren standardize, normalize

Normierung normalizing; normalization

nötigen urge, force

notwendig necessary

Nullpunkt origin

nullte zeroeth

nun now

nunmehr now, at present, by this time, henceforth, then, since then

nur only, but

nützlich useful

ob over, above, on, upon; if, whether

oben (erwähnt) (mentioned) above, at the top

obig above, above mentioned

obliegen apply, be devoted to, prevail over, be incumbent upon

obwohl though, although

offen open

offenbar apparent, obvious

offenbaren show, disclose

offensichlich obviously

oft often

ohne without

ohne weiteres without further ado

ordnen arrange or order

ort local

Paar pair

passend appropriate, fitting, suited

Pflanze plant

pflegen tend, care for; be used to, be in the habit of

Pfund pound

Potenzmenge power set

Potenzreihe power series

Primzahl prime number

Prinzip principle

Punkt point, dot, spot

punktfremde disjoint

Quadrat square

quadratisch square

Quadratwurzel square root

Quadratzahl(en) integer square(s)

quadrierbar quadrable, squarable

quadrieren square

Rand boundary

Randpunkte boundary point

rasch rapid

Raum space (e.g., metric, vector, etc.)

rechnen count, calculate, reckon

Rechnung calculation

rechtfertigen justify, vindicate

rechtwink(e)lige orthogonal (e.g., coordinates)

Regel rule, standard, regulation, e.g., "in der Regel" means "as a general rule, generally"

rein clean, neat, tidy, pure

reisen travel

Rest remainder (rest, residue, remains, difference)

retten save, rescue, escape, deliver

richtig right, correct, true, accurate

Richtung direction, course, trend

rotieren revolve, rotate

Rücksicht respect, regard, consideration, notice

rund round

sagen say, tell

sämtlich(e/en) complete, total, entire (e.g., collected works)

Satz proposition, theorem

Schar group, bunch, crowd

scheinen seem, appear, look

schließen / schliessen shut, close, finish, conclude, terminate

schließlich / schliesslich (doch) last, final, ultimate, eventual; finally, at last (after all)

Schluß / Schluss closing, end, termination, conclusion, inference, deduction, result

schneiden intersect; cut

schnell fast

Schnelligkeit speediness

Schnittpunkte point of intersection, vertex

schon already

Schranke boundary, bound

Schritt step, measure

schwer heavy, difficult

schwierig difficult, hard, arduous

sehr very

sein to be

seinerseits at one time, formerly, in due course, in its proper time

Seite side

Seitensimplexe faces of a simplex

selten rare

senkrecht perpendicular

setzen set (esp. a value); put or place

sich oneself, itself

sind are

Singularität singularity

Sinn sense (in the sense of); faculty, mind

sinnen think, brood, meditate, reflect, ponder, speculate

Sinnen thinking, planning, thoughts, aspirations

sinnend musing, pensive, contemplative

sinnvoll meaningful, sensible

skizzieren sketch

so so, in such a way or manner

so ... wie as ... as

sobald as soon as

sofern provided, if, inasmuch as, (in) so far as

sofort immediately, right away

sogar even

sogleich immediately, right away

solcher such

Solidität solidity

sollen should

somit consequently

sondern but; separate, sever, part, sort out, classify

sonst otherwise, besides, formerly, moreover

soweit as far as, so far

sowie just as, as soon as, the moment when, as well as

sowohl ... als auch both ... and

Spalten columns

spalten split (e.g., exact sequences)

sparen save

spät late

später later

späterhin later on

speziell specifically

spielen play

stammen originate

ständig permanent, steady, constant; continually

Standpunkt(e) standpoint(s), perspective(s)

statt instead of, in the place of

stattfinden take place, happen, occur

stehen be, occur, exist

Stelle place, spot, position, job, agency

stellen put, place

stetig continuous (function); continual, steady

Stetigkeit continuity

stets always, regularly, continually, constantly

stillschweigen be silent, acquiesce in

stillschweigend still, silent, tacit

stimmen be true or correct

Stoff subject, material

Störung disturbance, trouble, breakdown, interruption

streng strict, rigorous, severe

suchen seek, desire, want

süß / süss sweet

Tat deed, action, feat, accomplishment

Tatsache fact

tatsächlich real, actual, factual, matter of fact

Teil part

teilbar divisible, separable

Teilerfolge partial success

Teilmenge subset

Teilraum subspace

ternar ternary

Tier animal

tragen carry

Träger support (of a function)

Treffen encounter, meeting

treffen meet; touch; affect

trennen separate, divide, part, sever, detach

Trennungseigenschaft separation property

treten step, walk, tread, stride

Tritt step

trotzdem in spite of, nevertheless, although

tun do, perform, execute, make, act

Übelstand disadvantage, drawback, grievance

überall everywhere, all over

Überaufgabe(n) practice exercise(s)

überblicken survey, view, prospect

überdecken cover (as in open covering)

überdies besides, moreover, what is more

übereinstimmen be in agreement, concur

übereinstimmend agreeing, harmonious, corresponding

überführen conduct or lead across, transport, transform, bring over

übergang transformation

übergehen go over, carry over; omit, overlook; run across, go over

überlegung reflection, thought, consideration, deliberation, investigation

überschneiden intersect, cross, overlap

übertragbar transferable

übertragen carry over

übertragung carrying over, assignment, transfer, translation

überzählig surplus, spare, left over

üblich customary, usual, common

übrig remaining, residual, superfluous

übriglassen leave over, leave a remainder

Umfang circumference; range

umfassend far reaching, sweeping, drastic, complete, full

umformen reshape, convert

umgeben surround

Umgebung neighborhood

umgekehrt conversely

Umgrenzung boundary, enclosure, limitation

umkehrbar invertible

umkehren invert

Umkehrung converse

Umstand circumstance, factor, fact; details

umwandeln change

unabhängig independent

Unabhängigkeit independence (e.g., linear)

unausführbar impracticable, not feasible, impossible

unbekannt unknown

unendlich infinite, endless

ungeändert unchanged

ungefähr approximately

ungelöst unsolved

ungerade odd (number)

Ungleichheit inequality

Ungleichung inequality

unmittelbar immediate, direct; directly

untergeschieden subdivided

unterhalb below

unterliegen be dominated (as a series); be beaten (by), lose (to)

unterscheiden distinguish

Unterschied difference, distinction

untersuchen examine, investigate

Untersuchung investigation, examination, scrutiny

Unterteilung subdivision

unterwerfen subdue, subjugate, submit, yield

unveränderlich constant, unchangeable, invariant

Urbild preimage

Ursprung origin, source, beginning, cause

ursprünglich original, primitive, primary, initial; originally, initially

usw. (und so weiter) and so forth, etc.

verallgemeinen generalize

Verallgemeinerung generalization

veränderlich changing, changeable, variable

Veränderlich variable

verändern to change

veranschaulichen make clear, illustrate

verbessern improve

verbinden unite, join, combine

Verbindung binding, joining, connecting, relationship

verbunden united, joined, combined

Vereinfachung simplification, reduction

vereinzeln isolate

vereinzelt sporadic

verfahren bungle, err; act, behave, proceed

Verfahren procedure, method, process

Vergleich comparison

vergleichen to compare

vergröbern coarsen, make (an estimate) less sharp

verhalten hold back, hold, suppress

Verhältnis proportion, ratio

Verhältnisse circumstances, conditions

verhandeln discuss, negotiate, argue

verkaufen sell

verknüpfen tie together, connect, combine, relate

verknüpft related, associated, linked

verkörpern embody, personify

verlangen demand, require

Verlauf course (in the course of things)

verletzen violate

Verminderung lessening, diminution, reduction

vermitteln meditate, intervene, adjust, arrange, settle

vermittels by means of, through

vermöge by virtue of

verneinen deny, answer in the negative

versagen deny, refuse; fail, fail to work

verschaffen get, obtain

verscharfen sharpen (an inequality); intensify

verscharfte sharpened (an inequality); intensified

verschieben translate (as an isometry or affine transformation)

verschieden distinct, different

verschoben translated (as an isometry or affine transformation)

verschwinden vanish, disappear

versehen hold (a position), perform (a job)

versehentlich by mistake, erroneously, inadvertently

Verschärfung sharpening (of an estimate)

verständlich understandable

verstehen understand, see, make out, realize

Versuch attempt, test, try, trial

versuchen try, tempt, taste

vertauschbar interchangeable; (algebra) commutable

vertauschen (gegen) exchange (for)

Vertauschung exchange, substitution

vertrauten familiar

verwandeln change or transform (into)

verweisen refer (to); banish, expel

verwenden use, employ, apply (to)

Verwendung application, use, employment

Verwirklichung realization

Verzeichnis index (of a book); list, catalogue

vgl. (vergleichen) compare, c.f.

viel much, many

vielfach(es) multiple

vielmehr rather, on the contrary

viertens fourthly, in the fourth place

vollenden bring to a close; finish, terminate, achieve

völlig full, total, entire, complete

vollkommen perfect, consummate, complete

vollstandig complete (sp. metric spaces), total, integral

vollziehen effect, carry out; take place

Vollziehung execution, discharge, accomplishment, fulfilment

von from, off of, of, by, at

vorangehend preceding, foregoing

voraus in front, ahead (of)

vorausgesetzt assumed

voraussetzen suppose, assume

Voraussetzung assumption, supposition, (induction) hypothesis

Vorbehalt reservation, proviso

Vorbemerkung preliminary remark, preamble

vorbereitend preparatory

Vorbereitung preparation, introductory material

Vorgabe points, handicap

vorhanden present, at hand, available, existing

vorigen former, preceding, previous

vorkommen happen, take place, be found

vorläufig for the present, for the time being, preliminary, tentative

Vorlesung lecture, reading, recital

vorliegen be under consideration, be present or there, exist

vorliegend present, existing, at issue, in hand or in question

vornehmen take up, undertake

vornherein from the first

vorstehend above

vorweg before, beforehand, to begin with

Vorzeichen sign (of a number)

Vorzug preference, advantage, superiority, priority, excellence

waagrecht horizontal

Wachsen growth, development, increase, expansion

wachsen increase

wachsend growing, increasing

wachst grown, increased

Wahl choice, option, seletion

wählen choose

während during, while, whereas

Wahrheit truth, reality, fact

wär(en) would be (subjunctive of sein)

Wechsel change, shift

weder ... noch neither ... nor

wegen because of, on account of

wegfallen be omitted or suppressed, become void, come to nothing

weggeben give away, dispose of

weghaben have received, got the knack of

weglassen leave out, omit, let go

weil because

Weise manner, way, method, mode

weiß / weiss white; knows

weit far, distant, extensive, wide, broad

weiten widen, broaden

weiter further, farther, additional

weiterhin furthermore, again

welcher which

wenden turn, turn over, turn up, change

Wendung turn; change

wenig little, few

weniger less, minus

wenigstens at least, at all events

werden become

Wert value, price, worth

Wesen essence, substance, entity

wesentlich(e) essential

wichtiges weighty, important, essential

Widerspruch contradiction, e.g., "führen zu Widerspruch" means "to lead to a contradiction"

wie as, like, such as

wieder again, afresh, once more

wiederentdecken rediscover

wiederholen repeat

wiederum again; on the other hand

wiegen weigh

willkürlich arbitrary, random

Winkel angle

wird becomes (pres. of werden)

wirklich actual, real, substantial

Wirklichkeit (actual) fact, reality

wissen know

Wissenschaft knowledge

wobei whereby, whereat, in the course of which

wodurch by or through which, whereby, by which means

wofern provided that, so far as, in case

wohin where (to)

wohl probably

wohlbekannt well known, familiar

wollen wish, desire

worauf on which, upon or after which, whereupon

woraus from which

Wort word

wortwörtlich word-for-word, verbatim

worüber upon, over, or about which

wünschen wish, desire, want, request

würde could, (could) become (subjunctive of werden)

Würfel cube

z. B. (zum Beispiel) for example, e.g.

Zahl number

Zeichen symbol

zeigen show, display, exhibit

Zeile row, line

zerfallen separate; disconnect; fall apart, decompose

zerlegen resolve, cut up, decompose

Zerlegung partition, decomposition; dismantling, dissection

Zerlegung der Einheit partition of unity

zerspalten split

zerstörbar destroyable

zerstören destroy, demolish, ruin

zerstreuten scatter

zgl. (zugleich) respectively

ziehen extract; pull, pull out

Ziel aim, mark, goal

ziemlich (oft) fairly, quite (often)

Ziffer digit, numeral

zitieren quote

zudem moreover, besides

zuerst first

zufolge in consequence of, as a result of

zugänglich accessible

zugehörig belonging to

zugelassen allowed, admitted

zugleich at the same time

zugleich mit together with

zulassen allow, admit

zulässig permissible

zunächst for the time being, in the first place

zuordnen adjoin, coordinate, associate

zurechnen add, number, reckon

Zurechnung addition, inclusion, attribution

zurück back, backwards, behind, points down

zurückkehren return (to)

zusammenfallen mit to coincide with

zusammenfassen condense, summarize, combine, unite

Zusammenhang connectedness (topolgical); connection

Zustand state, condition

zustreben strive for

zuweilen sometimes

zwar indeed, certainly

Zweck aim, purpose, objective

zwischen between, betwixt, among