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

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5.	Retained in the post-Revolution orthography, but replaced by е in certain words. ^
6.	Replaced by ф in the post-Revolution orthography. ^
7.	Replaced by и in the post-Revolution orthography. ^

The Noun

Russian is an inflected language; its nouns and adjectives are declined into six cases depending upon their function in a sentence. Also, nouns are grouped into three genders, masculine (m.), feminine ( f .), and neuter (n.), and the gender of a given noun may generally be determined by its ending.

A. Functional Description of the Six Cases in Russian

1. Nominative case. A noun in the nominative case denotes the subject or the predicate nominative.

a. Subject.

Мы знаем. > We know.

Студент знает. > The student knows.

b. Predicate nominative.

Они студенты. > They are students.

c. The nominative form is the one listed in the dictionaries.  

2. Genitive case. A noun appears in the genitive case when expressing any of the following:

a. Possession.

работа профессора > the professor's work, the work of the professor

У профессора работа. > The professor has work.

b. 'Of' clauses.

решение уравнения > the solution of the equation

c. Object of negation.

Число X не превосходит этой величины. > The number X does not exceed the magnitude.

d. Complement of certain verbs.

Мы достигнем результата. > We shall achieve the result.

e. Following numbers (except the number one and any compound with the number one):

i. Genitive singular following 2, 3, and 4, as well as any compounds in which the final component is 2, 3, or 4 (e.g., 22, 33, 54): три (3) книги, 'three books'

ii. Genitive plural following 5 through 20, as well as any compounds in which the final component is 5, 6, etc.: пять (5) книг, 'five books'

f. Following words denoting quantity.

Сколько теорем? > How many theorems?

много теорем > a lot of theorems  

3. Dative case. A noun appears in the dative ease in the following environments:

a. Indirect object.

Студент читает доклад профессору. > The student gives (reads) a paper to the professor.

b. Impersonal expressions (sentences in which there is no grammatical subject):

Ивану легко читать по-русски. > It's easy for John to read Russian.

Студенту надо заниматься. > The student must study. It is necessary for the student to study.  

4. Accusative case. A noun in the accusative case denotes the direct object: рассмотрим сумму, 'let us consider the sum.' In the accusative singular of masculine animate nouns, the accusative coincides in form with the genitive singular, while inanimate nouns exhibit the usual accusative endings: он читал доклад (inanimate masculine object доклад), 'he read the paper'; он видел студента (animate masculine object студент), 'he saw the student.' Feminine nouns have only one form of the accusative in the singular. However, in the plural, all animate nouns, regardless of gender, have the form of the accusative which coincides with the genitive plural, while the accusative for inanimate nouns coincides with the nominative plural.  

5. Instrumental case. A noun in the instrumental case denotes the following:

a. Means by which something is done.

выражать формулой > to express by a formula

Он пишет мелом. > He writes with chalk.

b. Agent in a passive construction.

Статья написана Иваном. > The article is written by John.

c. Manner of action.

говорить тихим голосом > to speak in a quiet voice  

6. Locative case. A noun occurs in the locative case after the following prepositions:

в: в городе > in the city

на: на собрании > at the meeting

о: о проблеме > about the problem

In addition to the above uses, each preposition requires its object to be in a particular case. As described above under the Locative case, the three prepositions в, на, and о require the locative case. The preposition между requires the instrumental case, while the preposition около requires the genitive case. The preposition and its object, which may include one or more adjectives as well as the noun or pronoun, are adjacent to each other in a given sentence. See the table of prepositions below.

Also, certain verbs require their objects to be in a particular case. For instance, the verb называться (to be called, to be named) generally requires its object to be in the instrumental case. However, there has been a tendency for this verb to require the nominative case, as well.  

7. Word order. Word order in Russian is flexible because each noun and its modifiers are