#dictionary_3

10) Oscillate — tebranmoq.

11) Infinitely often — cheksiz ko'p marta.

12) Misleading — chalg'ituvchi (jadval bizni chalg'itishi haqida).

13) Between — orasida.

#dictionary_4

14) Left-hand limit — chap tomonlama limit.

15) Right-hand limit — o'ng tomonlama limit.

16) Approaching from the left — chapdan yaqinlashish.

17) If and only if — faqat va faqat shu holdaki (matematik shart).

#dictionary_5

18) Proof,Isbot
19) Assumption / Suppose, —f araz (faraz qilaylik)
20) Contradiction,Ziddiyat — Qarama-qarshilik
21) Statement — Tasdiq / Mulohaza
22) Assume the contrary — Teskarisini faraz qilish
23) Hence / Therefore — Shuning uchun / Demak

#dictionary_6
24) Assume to be false—Noto'g'ri deb faraz qilish
25) Logical deductions—Mantiqiy xulosalar
26) Infinitude — Cheksizlik
27) Prime numbers — Tub sonlar
28) Divisible — Bo'linuvchan
29) Coprime — O'zaro tub

#dictionary_7

30) Statement — Tasdiq (Isbotlanishi kerak bo'lgan gap).

31) Contradict — Zid kelmoq / Qarama-qarshi bo'lmoq.

32) Hypothesis — Gipoteza (Faraz).

33) Conclusion — Xulosa.

34) Integer coefficients — Butun koeffitsiyentlar

35) Curve - egri chiziq
36) point - nuqta
37) which - qaysi
38) slope - qiyalik , og'ish ba'zan burchak koefitsenti ya'ni tan(a)=k

Matematik Olimpiada Lug'ati (Kengaytirilgan jadval)

| Mantiq |

39 )Conjecture -- Taxmin (isbotlanmagan nazariya)
40) Conversely - Aksincha / Teskari holda
41) Assume for the sake of contradiction - Teskarisidan deb faraz qilaylik
42) Imply - Kelib chiqmoq (natija bermoq)

| Analiz |

43) Limit inferior / superior -- Pastki / Yuqori limit
44) Monotonically increasing -- Monoton o'suvchi
45) Bounded above/below -- Yuqoridan/quyidan chegaralangan
46) Convex / Concave - Qavariq / botiq
47) Continuous everywhere -- Hamma joyda uzluksiz
48) Differentiable -- Differensiyalanuvchi (hosilasi mavjud)

| Algebra |

49) Field extension - Maydon kengaytmasi

50) Span (linear span) - Qobiq (vektorlar tizimi)
51) Eigenvalue - Xos qiymat
52) Characteristic polynomial - Xarakteristik ko'phad
53) Invertible matrix - Teskarilanuvchi matritsa

| Sonlar Nazariyasi |

54) Relatively prime - O'zaro tub
55) Modular arithmetic - Modul bo'yicha arifmetika
56) Quadratic residue - Kvadratik qoldiq
57) Divisibility - Bo'linuvchanlik

| Geometriya |

Convex hull | Qavariq qobiq |
| | Incenter / Circumcenter | Ichki/Tashqi chizilgan aylana markazi |
| | Orthocenter | Ortotsentr (balandliklar kesishgan joy) |
| | Isometry | Izometriya (masofani saqlovchi) |
Olimpiada masalalarida tez-tez uchraydigan qolip-iboralari
Bu iboralar masala shartini tushunish uchun eng muhimlaridir:
| Inglizcha ibora | O'zbekcha ma'nosi |
|---|---|
| Let S be a set such that... | S - shunday to'plam bo'lsinki... |
| Find all such that... | ...ni qanoatlantiruvchi barchasini toping |
| Show that the expression is independent of n | Ifodaning n ga bog'liq emasligini ko'rsating |
| Without loss of generality, assume... | Umumiylikni yo'qotmagan holda, faraz qilaylik... |
| Evaluate the following integral/sum | Quyidagi integralni/yig'indini hisoblang |
| Prove or disprove | Isbotlang yoki inkor eting |
| By induction on n | n bo'yicha induksiya usuli bilan |
Muhim eslatma (Strategik maslahat)
* Putnam/IMC darajasidagi olimpiadalarda ko'pincha "Compute" yoki "Evaluate" deganda aniq sonli javob kutiladi, "Show that" yoki "Prove" deganda esa mantiqiy xulosalar zanjiri talab qilinadi.
* "Disprove" deganda siz bitta "kontrmisol" (qarshi misol) keltirishingiz kifoya, lekin uni to'g'ri isbotlab berishingiz kerak.

Inglizcha atama O'zbekcha tarjimasi
Determine Aniqlang, toping
All Barcha, hamma
Positive integers Musbat butun sonlar
Exist Mavjud bo'lmoq, mavjud
Satisfying ...ni qanoatlantiruvchi
Equation Tenglama

Sequence Ketma-ketlik
Nonzero Nolga teng bo‘lmagan
Real numbers Haqiqiy sonlar
Such that Shunday bo‘lsaki (shartni bildiradi)
Prove (that) Isbotlang (shuni)
There exists Mavjud (bo‘lishi kerak)
For all Barcha ... uchun
Term Had (ketma-ketlik hadi)
Recurrence relation Rekurrent munosabat
Independent of n n ga bog‘liq bo‘lmagan
Constant O‘zgarmas (son)

1. Qo‘shish — Addition
2. Ayirish — Subtraction
3. Ko‘paytirish — Multiplication
4. Bo‘lish — Division
5. Tenglama — Equation
6. Ildiz — Root
7. Daraja — Power (Exponent)
8. Kasr — Fraction
9. Tub son — Prime number
10. Juft son — Even number

11.Increasing — O'suvchi

12.Decreasing — Kamayuvchi

13.Convergent — Yaqinlashuvchi (masalan, yaqinlashuvchi ketma-ketlik)

14.Periodic — Davriy

15.Exists — Mavjud (matematik simvoli: $\exists$)

16.Consider — Ko'raylik, faraz qilaylik yoki qaraylik (masalan, "biror funksiyani qaraylik")

17.Such that — Shunday ...-ki (shartni belgilash uchun ishlatiladi)

18.Evaluate — Hisoblamoq yoki qiymatini topmoq

19.Hence — Shunday qilib, demak (oldingi fikrdan kelib chiqqanda)

20.Therefore — Shuning uchun, xulosa qilib aytganda

To'plamlar va Mantiq (Sets and Logic)
Set — To'plam

Subset — Qism-to'plam

Element / Member — Element

Union — Birlashma

Intersection — Kesishma

Distinct — Turli xil, o'zaro farql

iAssume — Faraz qilaylik

Contradiction — Ziddiyat (isbotlashda "teskarisidan faraz qilaylik" usuli uchun)

If and only if (iff) — Faqat va faqat shu holdaki (zaruriy va yetarli shart)

Prove / Proof — Isbotlamoq / Isbot

Funksiyalar va Matematik Analiz (Functions and Calculus)

Domain — Aniqlanish sohasi

Range — Qiymatlar sohasi

Continuous — Uzluksiz

Differentiable — Differensiallanuvchi

Derivative — Hosila

Limit — Limit

Infinite / Infinity — Cheksiz / Cheksizlik

Bounded — Chegaralangan

Arbitrary — Ixtiyoriy

Algebra va Sonlar Nazariyasi (Algebra and Number Theory)

Coefficient — Koeffitsient

Variable — O'zgaruvchi

Prime number — Tub son

Divisible — Bo'linuvchi (qoldiqsiz bo'linish)

Remainder — Qoldiq

Identity — Ayniyat

Inequality — Tengsizlik

Solutions set — Yechimlar to'plami

Geometriya (Geometry)

Perpendicular — Perpendikulyar

Parallel — Parallel

Tangent — Urinma

Vertex (Vertices) — Uch (Uchlari)

Edge / Side — Qirra / Tomon

Angle — Burchak

Circle — Aylana

Teorema va Masalalarda uchraydigan iboralar
Given that... — Berilganiga ko'ra...

Show that... — Ko'rsatingki... (isbotlang)

Let $x$ be... — $x$ ... bo'lsin.

Without loss of generality (WLOG) — Umumiylikka zarar yetkazmagan holda

Respectively — Mos ravishda