This document provides information about key concepts in mathematics and computer science. It defines important terms like computer, program, data, information, and functions. It also discusses probability and events from both mathematical and non-mathematical perspectives. Finally, it explains integrative and supplementary relative clauses and the importance of clear pronoun reference.

1. English language for mathematics
Week1 1

2. Table of contents
• Part 1 Reading comprehension WHAT IS AN ELECTRONIC COMPUTER: synonyms
disambiguation
• Part 2: Grammar: relative clauses, supplementary and integrative clauses

3. Part1 WHAT IS AN ELECTRONIC COMPUTER
• A most important adjunct to this definition is that a computer is told how to process the
information by instructions, which are stored in coded form inside the computer. A computer thus
differs radically from a calculator, which can do the same thing that a computer does, except that
the instructions are not stored inside the machine. The coded instructions are called a program. Any
computer or calculator contains devices for five main functions: input, storage, arithmetic, control
and output. Input refers to the process by which information is put into a machine. Output is the
process by which the results are moved out of the machine. Storage refers to the mechanism that
can retain information during calculation and furnish it as needed to other parts of the machine.
The arithmetic unit is that part of the machine, which can carry out one or more of the basic
arithmetic operations on the information held in storage. Finally, the control refers to those parts of
the machine that dictate the functions to be performed by all the others parts.
• pavle….pavlovic et.matf.bg.ac.rs
• (Phuong 2003: page 62)

4. Part1: ADJUNCT, ADJUNCTION, CONJUNCTION INTRODUCTIONP
• Conjunction introduction (or and introduction, or adjunction) is the rule of inference that
• P Q P ∧ Q
• T T T
• T F F
• F T F
• F F F
• allows one to infer a conjuction from both of the conjuncts individually. In symbols we have:
• A B
• A ∧ B

5. Part 1: Information – further expressions
• information extraction the act of extracting, by computer, recognizable information from
documents written in a human language; an example would be reading weather reports in English
and constructing a table of dates and temperatures. C

6. Part 1: store – synonyms and useful phrases: TO STORE
• storage area network a computer network that shares disk space using
• DISK SHARING rather than FILE SHARING. Contrast NETWORK ATTACHED
• store to place a data item into a memory device.
• stored program computer a computer that can store its own instructions as well as data. All
modern computers are of this type

7. Part2: Store – nonmathematical context:
• ,
• Gather – search for and get things of the same type from different places
• Assemble – to get and put together something such as proof or information in an organized
manner

8. Part 1: code: disambiguation of the word code (INFORMATCS CONTEXT)
• 1. a way of encrypting information (making it unreadable). See ENCRYPTION.
• 2. a way of representing information on a machine or in some physical form. For example, the bit
patterns in memory can be used as a code to stand for letters and digits.
3. computer programs, whether written in machine language (OBJECT CODE) or a programming
language (SOURCE CODE)

9. Part 1: Code – nonmathematical context
• Code- set of rules that organizations agree to obey but are not forced to obey
• Example: He will be dealt with under our code of discipline.
• Rules and regulations: a set of rules: use this when you think the rules are too detailed or cause
an unnecessary inconvenience
• There were so many rules and regulations that companies stopped exporting some products
• Restriction an official rule that limits what can do
• Example: There are restrictions on what you can bring into the country. Alcohol, for example, is
totally forbidden

10. Part 1: code: mathematical context: other important expressions
coding the process of writing an algorithm or other problem-solving procedure in a computer
programming language
• code base the collection of computer program SOURCE CODE that constitutes a software
product. For example, the code base of Windows Vista is derived from that of Windows NT
• code signing attaching a DIGITAL SIGNATURE to a piece of code so a person who downloads
it will know its origin. If the code comes from a trusted person or organization, the user will be
more likely to grant it permission to take a wider range of actions, such as writing to the local disk
drive.

11. Part 1: code: other important expressions
• escape code a code that indicates that the following character is to be handled specially (e.g., as a
printer control code), or a code that stands for a character that cannot otherwise be typed. For
example, in HTML, the characters < > mark the beginning and end of a command, so if you want
them to appear on the screen, you have to type them as the escape code respectively

12. Part 1: code: other important expressions
• error-correcting code any method of encoding data that allows small errors to be corrected.
Contrast CHECKSUM, CYCLICAL REDUNDANCY
• CHECK, and PARITY, which are techniques for detecting errors but not correcting them. A simple
error-correcting code would be to send each message three times, and if some part of the message
does not come out the same in all three copies, let the majority rule. In order to be uncorrectable,
an error would have to corrupt two of the three copies, not just one. Even then, you would know
that an error had been made. Practical error-correcting codes are more concise and are based on

13. Part 1: information – etymology
• information (noun): from inform, whose earliest
• English meaning, in the 14th century, was “to give form to.” During that same century the word
also came to mean “give knowledge of a thing to,” because the form of something provides
knowledge about what the thing is like. Information, then, is knowledge. The word is based on
Latin forma “contour, figure, shape.” The Latin word seems to be a
• metathesis of the sounds in Greek morphe “form, beauty, appearance.”

14. Part 1: Information – etymology: continuation
• Greek morphe is of unknown prior origin. The twentieth century, especially the part in which
computers have proliferated, has been called the InformationAge. If a year has to be chosen as its
beginning, it may be 1948, when the American Claude Shannon published two papers about
sending and receiving messages. The basic unit of information in the computer world is the bit

15. Part 1: data – etymology
• data (plural), singular datum (noun): datum and
• data are past participles of Latin dare “to give.” The data are literally the givens in a situation. The
undo-European root is do- “to give.” Related borrowings from Latin are tradition ( what is given
over from generation to generation) and date, since
• Roman letters often indicated the date by using the phrase “given ( data) on such and such a day.”
Borrowings from French include endow and dowry. Mathematicians often make conjectures after
examining lot of data and noticing patterns. [47]

16. Part 1: Data, information: disambiguation (mathematics, informatics –
context).
• Data- information. The word was originally the plural of datum, which means “a single fact,” but it
is now used as a collective singular.
• Disambiguation: data and information.
• Data is an individual unit that contains raw materials which do not carry any specific meaning.
• Information is a group of data that collectively carries a logical meaning

17. Part1: Data, information – disambiguation (non-mathematical context)
• Information – facts or details about a place, or event
• Data - facts, numbers and other information that have been stored on the computer
• In everyday English, as you can see, the key distinguishing feature is that the information are
deemed to be more general, whereas data are information stored on the computer

18. Part 1: cata – bits
• Bit is the smallest unit of data and its value can be either 0 (zero) or 1 (one). All data are coded in
bits. Hard disks/memories are designed to store data in bit multiples called‚ such as: megabytes,
gygabytes, terabytes
• A retailer such as Wal-Mart is already storing over 200 terabytes of data including information
from its customers and suppliers. The world’s largest print library is the USA’s Library of Congress
in Washington‚ containing about: 26‚000‚000 (19 million books and other print collections)
represent about 10‚000‚000‚000‚000 (10 terabytes of information‚ “Tera” means 1 trillion - 1
followed by 12 zeros.) The above is quite a bit of information but compared to the Internet Archive
(WayBack Machine) it is not that much. The Internet Archive goes back to 1996 and contains:
more than 100 terabytes of data and is growing by 10 to 12 terabytes a month

19. Part 1: Data (elaboration)
• Data are the collection of items of information such as the representations of facts, concepts, or
instructions in a manner suitable for communication, interpretation, or processing by employees or
by automatic means. Data can be in the form of files in a computers volatile or non-volatile
memory, in a data storage (see Bit) device (e.g., tape), or in the form of data in transit across a
transmission medium (see also Data Classification, Reliability, Validity).
• Note: The singular of data is datum. A writer’s sloppiness can result in that the plural noun is
accompanied by a singular verb.

20. Part 1: Data (elaboration): derived words
• Data Aggregation is the case when combining seemingly innocuous data to get confidential
information.
• Database is a large collection of data organized for rapid search and retrieval for indexing,
updating, and retrieval purposes (see also Copyright— Databases).
• Data Capture is the process of entering data into a computer manually (e.g., keyboard or by
scanner) or automatically (e.g., system is receiving transmission from another program or server)

21. Part 1: Input: disambiguation
• input information that is given to a computer; the act of giving information to a computer. (Note
that the terms input and output are always used from the computer’s point of view.) The input
data may be either numbers or character strings (e.g., a list of names). The computer receives
input through an input device, such as a keyboard, or from a storage device, such as disk drive

22. Part 1: Input – everyday English
• Input to put an information into a computer The example: The user inputs the data, and the
computer stores it in its memory)
• Enter to put information into a computer by pressing a key The example Enter the amount of
money you wish to take out of account
• Load – to put a program into a computer so that it s ready to be used The example LOAD is the
program which loads a new program from the file
• The example: The program can be encoded onn the disk’s surface and then loaded into the
microprocessor

23. Part 1: output
• output the information that a computer generates as a result of its calculations. Computer output
may be either printed on paper, displayed on a monitor screen, or stored on disk or tape. output
device a device that shows, prints, or presents the results of a computer’s work. Examples of
output devices include MONITORs, PRINTERs, and IMAGESETTERs.

24. Part 1: process
• a series of instructions that a computer is executing in a multitasking operating system. Many
processes execute concurrently. From the user’s viewpoint, processes may be programs or parts of
programs (such as the editing routine and the printing routine in a word processor that can print
while editing). See MULTITASKING; UNIX.

25. Part 1: program
• Program is a specific set of ordered operations for a computer to perform. Programs can be
characterized as interactive or batch in terms of what drives them and how continuously they run.
An interactive program receives data from an interactive user (or possibly from another program
that simulates an interactive user). A batch program runs and does its work, and then stops. Batch
programs can be started by interactive users who request their interactive program to run the batch
program. A command interpreter or a Web browser is an example of an interactive program. A
program that computes and prints out a company payroll is an example of a batch program. Print
jobs are also batch programs

26. Part 1: control Panel (in Windows)
• a group of utility programs for making settings that affect the computer’s operation. These range
from desktop color, mouse tracking, and the like, to network communication parameters and
printer drivers.

27. Part 1: function (strictly mathematical and informatics contexts)
• function
• 1. (in mathematics) a value that depends on one or more arguments in such a way that, for any
particular set of arguments, the function has only one value. For example, the positive real square
root of a number is a function of that number. The sum of two numbers is a function of the two
numbers. A function need not exist for all possible arguments; for example, negative numbers have
no (real) square roots.
• 2. (in computer programming) a subprogram that acts like a mathematical function: given a
particular set of argument values, the function returns a unique result.

28. Part 1: reading comprehension: text 2
• In mathematical language the choice, the probability of success is the ratio of the number of ways
in which the trial can succeed to the total number of ways in which the trial can result. Here
nothing favors the choice of any particular circle; they are all on the same page, and you are just as
likely to cover one as another. The trial can result in five ways; there are five black circles. The
trial can result in nine ways; there are nine circles in all (Phuong 2003).

29. Part 1: probability – mathematical and nonmathematical contexts
• Mathematical context: Probability, likelihood : A measure associated with an event A and
denoted by Pr (A) which takes a value such that 0 less than Pr(A) less than 1. Essentially the
quantitative expression of the chance that an event will occur. In general the higher the value of
Pr(A) the more likely it is that the event will occur. If an event cannot happen Pr(a) is zero ; if an
event is certain to happen Pr(A) is ¼ 1.

30. Part 1: mathematical context: likelihood
• Likelihood: The probability of a set of observations given the value of some parameter or set of
parameters. For example, the likelihood of a random sample of n observations, x1; x2; ... ; xn
with probability distribution

31. Part 1: Probability: nonmathematical contexts
• Likelihood
• Probability – use this especially in where you can calculate fairly exactly how something is likely
to happen
• Example:The probability of catching the disease is extremely low
• Prospect - the something you hope will happen very soon Example: The prospects for peace are
growing
• Chances
• How likely it is something you hope will actually happen
• Examples: The new treatment will increase their chances for survival

32. Part 1: event – mathematical context: etymology
• event(noun): the prefix is Latin ex, shortened to e before a consonant “out of”; the main part of the
word is from ventus, the past participle of Latin venire “to come.” The Indo-European is gwa- or
gwem-, with the same meaning as the English cognate come. Related borrowings from Latin
include invent ( to come upon) and convene ( come together). In the study of probability, an event
is literally the way something “comes out” or happens. If an event is random, it comes “out of the
blue,” so to speak. Notice that the English word outcome is an exact translation of event. [49, 77

33. Part 1: event – mathematical context
• In probability theory, an event is a set of outcomes of an experiment (a subset of the sample
space) to which a probability is assigned

34. Part 1: Non- mathematical context: event
• Event: something that happens, especially something important that happens
• Occurrence
• Incident
• Happening

35. Part 1: mathematical context: disambiguation
• Occurrence- something that happens,. Use this especially whether something often or not often:
Vicious fights argument were a daily occurrence.
• Incident – something unusual and unpleasant: One violent incident turned into a political and
family tragedy
• Happening – a strange event: The happening of the last days and made me dazed.
• Compare: In probability theory, occurrence and events can be used interchangeably

36. THE PART II: PRONOUN REFERENCE and RELATIVE CLAUSES
• An antecedent is the word, phrase, or clause to which a pronoun refers.
• A sentence may be confusing if the pronoun and its antecedent are not clearly identifiable. A
missing antecedent cannot be assumed to be “obvious from context,” and an ambiguous reference
should always be corrected. In the statement
• The monkey was operated on by the surgeon when he was six weeks old
• the reader cannot tell whether it was the surgeon or the monkey who was six weeks old at the time
of the surgery.

37. THE PART (II): difference between the integrative and supplementary clause
• :
• The articles, which stem from the 1970s and the early 1980s, show Lefort intent on persuading
the reading public about the totalitarian nature of the Soviet Union and the countries of the Eastern
bloc (supplementary clause)
• The articles that stem from the 1970s and the early 1980s show Lefort intent on persuading the
reading public about the totalitarian nature of the Soviet Union and the countries of the Eastern
bloc (integrative clause)
• Examples taken from https://explorationsofstyle.com/2012/02/28/commas-and-relative-clauses/

38. THE PART (II): Further examples of supplementary clause
• The example 1 Given the educational conditions in Malawi, which is located in eastern Africa,
creative teacher training programs are essential.
• The example 2: Using transactional memory, which requires special hardware or software support,
will address the problems associated with using locks
• . https://explorationsofstyle.com/2012/02/28/commas-and-relative-clauses/

39. THE PART (II)The example of supplementary and integrative relative clauses:
explanation
• In each of these cases, the antecedent of the relative clauses is completely sufficient without the
relative clause. A country is a useful example since it is easy to see that you don’t need any
additional information to know what is meant by Malawi. Its location within its continent is
obviously supplementary information. Likewise, ‘transactional memory’ is a fully defined term: the
fact that it requires special hardware or software support is extra information. Take that information
away and the term itself is just as informative. In the third example, even though the supplementary
relative clause claims to be defining ‘gender equity’, it is doing so in a supplementary way. The
sentence is telling us that gender equity is crucial and it is also clarifying what gender equity means
in this context.
• The text taken from https://explorationsofstyle.com/2012/02/28/commas-and-relative-clauses/