A. J. Lohwater's Russian-English Dictionary of the Mathematical Sciences

1.	Literally, "such а δ that"; this is the usual Russian construction. ↑
2.	Adverbial participle; note that фиксировать is both perfective and imperfective. ↑
3.	Same comment as in note 1. ↑

7. Может показаться, что такое явление трудно объяснить. → This phenomenon may seem difficult to explain.

8. Если бы мы имели в своём распоряжении большее число точных наблюдений, ... → If we could have at our disposal a large number of precise observations, ...

9. Если мы проинтегрируем функцию 1/(1 + x²) от 0 до ∞, мы сможем определить значение π. → If we integrate the function 1/(1 + x²) from 0 to ∞, we shall be able to determine the value of π.

10. Ответ на этот вопрос может дать ключ ко всей проблеме. → The answer to this question may give the key to the whole problem.

The Adverb

Unlike the noun and the adjective in Russian, the form of the adverb is invariable.

A. Formation of the Adverb

1. Most adverbs are formed from corresponding adjectives by replacing the adjectival ending (-ый, -ий, -ой) with the adverbial suffix (-о, -е):

хороший – хороши → good – well

плохой – плохо → bad – badly

интересный – интересно → interesting – interestingly

могучий – могуче → powerful – powerfully

Note that these forms may resemble the neuter short-form adjective and should not be confused.

2. Adjectives ending in -ский form corresponding adverbs in -и, with or without the prefix по-:

английский – по-английски → English – in English

практический – практически → practical – practically

теоретический – теоретически → theoretical – theoretically

3. Adverbs may also be formed by use of case endings, resulting in an invariable form:

a. по- plus the dative singular of the corresponding adjective:

настоящий – по-настоящему → real – really

b. The instrumental singular of a noun:

полностью → fully

4. Some adverbs are not formed from corresponding adjectives by adverbial suffixation. These include the following:

здесь → here

там → there

сюда → to here

туда → to there

отсюда → from here

оттуда → from there

очень → very

5. The adverb may express degree:

a. The adverbial comparative degree is equivalent in form to that of the adjective. The suffix -ее is used:

интересно → interestingly (adv.)

интереснее → more interesting (adj.), more interestingly (adv.)

Он говорит интересно. → He speaks interestingly.

Она говорит интереснее, чем он. → She speaks more interestingly than he does.

b. The superlative degree is the comparative degree plus всех (of all):

Он решил задачу раньше всех. → He solved the problem earlier than all the rest.

c. As in adjectival comparative constructions, the comparative conjunction than is expressed by using the word чем:

Они решили задачу раньше, чем мы. → They solved the problem earlier than we (did).

B. Uses of the Adverb

1. Adverbs may modify verbs, adjectives, and other adverbs:

Он правильно решил задачу. → He solved the problem correctly.

Профессор читал очень интересный доклад. → The professor read a very interesting paper.

Студент очень быстро ответил на вопрос профессора. → The student answered the professor's question very quickly.

2. Adverbs may be used in the predicate in impersonal constructions (sentences which lack a grammatical subject):

a. These constructions may express a state or condition:

i. State of environment

Здесь холодно. → It is cold here.

В кабинете тепло и светло. → It is warm and light in the study.

Эту задачу трудно решить. → It is difficult to solve this problem.

ii. State of necessity or possibility

Нужно правильно решить задачу. → It is necessary to solve the problem correctly.

Здесь нельзя курить. → Smoking is not allowed here.

b. When a logical subject is required, a noun or pronoun in the dative case may be used:

Ему холодно. → He is cold.

Эту задачу студенту трудно решить. → It is difficult for the student to solve this problem.

Note that the verb in such constructions is in the infinitive.

c. In the past tense, these constructions use the neuter past form of to be (было), while in the future tense the singular form of to be is used (будет). This occurs because there is no grammatical subject in the sentences; thus the verb has nothing with which to agree.

Трудно было решить задачу. → It was difficult to solve the problem.

Профессору будет легко выполнить это задание. → It will be easy for the professor to carry out this task.

The Preposition