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

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

The meanings of many of the common English prepositions are already embodied in the case endings of the Russian nouns and pronouns; the most obvious instance is, of course, the implicit rendering of the preposition 'of' by the genitive case, the preposition 'by' with the instrumental, for example, применённый автором (applied by the author), etc. The table below gives some of the more commonly used Russian prepositions, including adverbial participles, and the corresponding cases together with some typical phrases.

Preposition	Case	Illustration
без (безо) without	gen.	без потери общности > without loss of generality
		без кратных точек > without multiple points
благодаря due to, because of	dat.	благодаря применению новых методов > because of the application of new methods