Do not be fooled into thinking either that the student’s manner of thinking is overbearing (i.e. imperialist) or that it is detached because of certain stereotypes about mathematics. Instead, the sentence expresses that the student gives her thoughts of reality a certain “coloring” because of her mathematical work. Such a “coloring” could be called a “cast” in the sense of being the general character of something. Think of the word as a metaphorical usage of “cast” in the strong sense of “physical mold” but becoming somewhat loosened in meaning to mean much more generally the “character” (i.e. the physical, emotional, intellectual, etc. shape) of something.

The key point to note is that academic positions were seen to be limited to the members of the clergy, who were the specific group to whom this work fell. A “preserve” is used at times to describe a place set aside for private hunting. More generally, we can think of it as a given activity (or group of activities) that are reserved for a specific group. In our example, it is as though the academic world was a preserved location for the clergy to do their supposed jobs.

The key phrase that helps to discern the closest term from the less proper ones is “with great east.” If someone can do something with facility, they are able to do so well and with ease. The word is related to others like “facile” and “facilitate” that are derived from the Latin for to do or make, but the sense of “facile” includes the notion of being easily accomplished.

Based on the data provided in this sentence, the most that can be said about the annual event is indicated by the key expression “gathered together.”  A “convocation” is a “calling together” or a meeting of this sort where a group comes together, often as a formal ceremony.  The word comes from the prefix “con-,” meaning “with” or (by extension) “together” and “vocation,” meaning “to call.”  The former is found in words like “contiguous” and “congruent,” as well as “colloquy” and “cooperate.”  The later is related to words like “vocal,” “vocative,” and “advocate.”

The sentence wishes to indicate that Catherine thought that her story was short, but not so short as to merit such seeming scorn.  A “novella” is a short novel (or a long short story), the word being derived from the obvious base “novel” with an added diminutive ending.  Diminutive endings make the word to mean something “smaller” than the base word.  The forms of such endings often differ from language to language.  “Novella” comes from Italian roots, and such diminution can be found in a name like “Monticello,” Thomas Jefferson’s House, whose name literally means “little mountain” after the hill upon which it sits.

The implication in this sentence is that the summer heat had modified Mary’s body temperature extremely (clearly by increasing it).  Since she needed to cool herself, it is arguable that her condition was one of “hyperthermia.”  The “hyper-” prefix means “beyond or above,” as when one is “hyperactive,” he or she is “beyond” being merely active.  The “-thermia” portion is related to other English “temperature” words like “thermal,” “geothermal,” and “hypothermia.”

The contrast and surprise found here is in the fact that the wealthy man so often could be a miser, that is, one who is very sparing in the outlaying of money.  Such a disposition can be called “meanness,” not in the sense of being nasty or rude but being sparing or ungenerous.

The sense that this sentence conveys is that the author does not live in accord with the tone and content of his own writing.  Therefore, his writing and life are “out of harmony” with each other.  The word “dissonance” literally means “bad sounding,” from the prefix “dis+” meaning “apart from” or even (in some contexts) “bad / negative” and the base “-sonance,” which is related to other “sound words” like “sonar,” “resonance,” and “consonant.”  The term can be applied more broadly to any situation in which two incompatible things are compared to each other.

Since the sentence explicitly mentions the burning of such persons, the best option is “pyres,” which are large structures of material used in burning, particularly in funerals.  The word “pyre” comes from the Greek word for “fire,” which itself is the root for words in English related to “purity” (as though such pure items were cleansed by fire).

Here, specific vocabulary knowledge helps, as all of the options are acceptable on some level.  An “inquest” is an investigation that is related to a judicial process; hence, it is a better option than the other more general terms.  The word is related to similar terms like “inquisition,” “question,” “inquire,” and “inquisitive”—all words pertaining to the asking of questions.