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

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 in a particular case which expresses a specific meaning. In English, the word order subject-verb-object is the standard, while in Russian this order is not mandatory. Because the subject of a sentence is in the nominative case, the subject may appear at the end of the sentence; the reader can always identify the subject by its case. Similarly, the direct object is in the accusative case, while the indirect object appears in the dative case; these objects may appear anywhere in the sentence because the reader can always identify them by their cases. However, the word order subject-verb-object appears frequently. There are constraints, of course, in the ordering of components within a sentence. For instance, a preposition is not separated from its object, nor is a noun separated from its adjective in a noun phrase. Thus, noun phrases and prepositional phrases are generally placed as units within a sentence.

Mathematical symbols are of course not inflected, so that, strictly speaking, Russian cannot say "the number of edges of Q" but has to say число граней конуса Q ("the number of edges of the cone Q"). The extra word is not needed in English, and consequently a translation will read better if the extra конуса is omitted. However, some Russian authors now disregard the rule, apparently when "the syntax is clear from the context," and write число граней Q to mean "the number of edges of Q," where the translator has to insert the "of" to prevent the reader from thinking that the edges are what is denoted by Q.

A further very common ambiguity arises when an author wants to describe an object and give it a name. For example, if we have a sequence of increasing continuous functions and want to name it S, we would be likely to write "a sequence S of increasing continuous functions." Russian prefers to put the descriptive phrase first: последовательность возрастающих непрерывных функций S. A reader who is not aware of this construction is quite likely to translate the phrase as "a sequence of increasing continuous functions S," and give the impression that the functions are called S, whereas the author's intention was to call the sequence itself S.  

B. Nominative Endings of Nouns