TRƯỜNG ĐẠI HỌC ĐÀ LẠT GIÁO TRÌNH TIẾNG ANH (Dành cho sinh viên ngành Toán – Tin) KHOA NGOẠI NGỮ 2001 Tiếng Anh – Toán Tin -2– CONTENT LỜI TỰA UNIT 1: MATHEMATICS UNIT 2: WHAT IS A COMPUTER? 11 EXERCISES 12 UNIT 3: NUMBERS AND MATHEMATICS 16 UNIT 4: CHARACTERISTICS 22 EXERCISES 23 UNIT 5: STATISTICS 31 UNIT 6: MAINFRAMES 37 EXERCISES 38 UNIT 7: CALCULUS 44 UNIT 8: STEPS IN PROBLEM SOLVING 50 EXERCISES 52 UNIT 9: DISCRETE MATHEMATICS 56 EXERCISES 57 UNIT 10: PROGRAMS AND PROGRAMMING LANGUAGES 62 EXERCISES 63 GLOSSARY 70 Tieáng Anh – Toán Tin -3– LỜI TỰA Nhằm đáp ứng kịp thời nhu cầu học Tiếng Anh chuyên ngành sinh viên Toán – Tin, biên soạn, biên tập số học có liên quan in giáo trình Vì khả có hạn, giáo trình tất không tránh khỏi sai sót, kính mong nhận góp ý từ phía bạn đọc để lần tái sau tốt Tháng 12 – 2001 Khoa Ngoại Ngữ Trường Đại học Đà Lạt Tiếng Anh – Toaùn Tin UNIT 1: -4– MATHEMATICS Pre-reading: Would you like to science? Which branch of science you like? You are studying mathematics, why you like it? Mathematics plays an important part of your lives Today mathematics is of the great use to many sciences, so more and more mathematical books are printed in many languages, especially in English Anyone who works with any branch of science or technology needs to be able to talk about numbers and shapes Notice how following numbers and shapes are said in English Numbers: 28% : Twenty-eight per cent 10.3 : Ten point three : Four ninths (four over nine) 42 : Four squared 53 : Five cubed 54 : Five to the power of four 1.623.457 : One million, six hundred and twenty-three thousand, four hundred and fifty seven + : Absolute value of two Derivation of y’= 4x+1 (y’ equals four x plus 1) Function of y = 2x2 + x + (y equals two x squared plus x plus 1) +2 : Positive number two -2 : Negative number two : Three is numerator and four is denominator : Fraction three over ten 10 : Mixed number of integer two three over ten 10 Tiếng Anh – Toán Tin -5– AxB/(A)(B) :Parentheses (A)(B) AxB/A.B : Dots A.B How we can read the following mathematical formulas in English: 2x + 3y – = 3Z 4x (Two x plus three y minus equals three Z devided by four x) Four basic operations of arithmetic are:Addition, subtraction, multiplication, division x = 42 (six times seven is forty two) The symbols and their expressions: a b c d e + (Plus) - (minus) x (multiplied by) : (divided by) = (is equal to) k l m n o f ≈ (is equivalent to) p ≥ (is more than or equal to) ⊂ (is a subset of) < (is less than) ≤ (is less than or equal to) g h i j % (percent) > (is more than) ∈ (is an element of) ∞ (infinity) (cube root) (square root) q r s t x (x squared) x3 (x cubed) x4 (x to the power four) Π (pi) ∞ (infinity) How would the names of the shapes below be read in English? - Two dimensional shapes: B B C C Rectangle square A O A B D B Triangle A Circle C Pentagon C Oval A D E - Three dimensional shapes D’ C’ Cube D C A’ C B A’ A A Pyramid B Tiếng Anh – Toán Tin Teaching points: Active: The simple present Passive: The simple present Suffix: - ion -6– (2) WORKING WITH VOCABULARY A Focus on the reading: Arithmetic Lives Equals Multiplication Formulas Times Dimensional Said Plays Who Choose the best words or phrases above for each sentence, if you need help, look at the reading again (use each word only once) Any one _ works with any branch of science or technology needs to be able to talk about numbers and shapes Notice how the following numbers and shapes are in English Mathematics an important part of our Six _ seven is forty two How we can read the following mathematical _ in English Four basic operations of _ are Addition, subtraction, _ division Two x plus three y minus three z divided by four x Two shapes are… B Focus on new context: Here is more practice with the new words from the reading choose the best word for each sentence (use each word only once) Arithmetic Plays Dimensional Multiplication Tiếng Anh – Toán Tin -7– Equals Times Formulas Said Lives Who If we want to say, for example, that in any circle the diameter is twice the radius we can write: d 2R _ is one branch of mathematics Do you know the girl _ is standing outside the door It is _ that English is an international language It’s difficult to read mathematical in English When she was seven, she learnt by heart the table _ out of number today he is absent from lesson again Because we are students our _ are different from theirs Some students don’t understand the term of _ analysis UNDERSTANDING THE READING A Comprehension questions: * Answer the questions about the reading: Why are more and more mathematical books printed in English? Why scientists and technologists need to be able to talk about numbers and shapes in English? Why does mathematics play an important part of our lives? Can you read: +2; -2 in English? Can you the algebraical maths: If 3a+4 is greater than 16, then a must be a greater than c equal to e greater than b less than d less than B Details: Write T if the sentence is true and F if it is False Mathematics is necessary for us because it helps to research Sciences need mathematics Some branches of science don’t need mathematics Two halves of a circle can be called semi-circle A rectangle has four right angles The symbol: ≥ can be read: more than or equal to C Main idea: Check b the two most important ideas from the reading Some mathematics symbols How to maths Mathematics and its use in our lives Tiếng Anh – Toán Tin -8– The names of shapes The methods of studying mathematics D Writing Write two following basic properties of numbers in English x = or (-2)(-3) = +6 (+5)(-10) = -50 or (-6)(+8) = -48 WORD STUDY A The passive and active in the simple present tense In passive, we are more interested in the objects of the active sentence This is because the subjects are not important at the moment or because we don’t know who or what is responsible for the event Form: The passive is formed by putting the verb to be into the same tense as the active verb The subject of the active verb becomes the “agent” of the passive verb Example: Active: My grandfather plants this tree Passive: This tree is planted by my grandfather (The example above indicates that the passive of the simple present requires the simple present form) The simple present is used: - To express a habit - To express a fact which is always true Ex: Vegetarians don’t eat meat - To express a fact which is always true for a long time Ex: We study at Dalat University Practice: Put the verbs in the correct forms, all the verbs are in simple present, either in the active or in the passive Complex algebraical fraction by the same method used in arithmetic (simplify) The oldest villagers to attend a meeting (invite) They science books in English (print) English in many parts of the world (speak) The doctor on the patient (operate) She from bad headaches (suffer) She in touch with her family by phoning home every Sunday (keep) Wood in water (not sink) Three persons in a car cash (injure) 10 Water from the rivers by women and children (bring) 11 That film on TV tonight (not show) Tiếng Anh – Toán Tin -9– B Word forms: Nouns Sometimes verbs and nouns are the same forms; sometimes we can change verbs to nouns by adding suffix ION SAME FORM Verbs Nouns Verbs Nouns Subtract - Subtraction Play - Play Communicate - Communication Change - Change Act - Action Work -Work Retract - Retraction Use - Use PRACTICE: Choose the correct forms of the words above to complete each sentence (use each word only once) We can the form of y-x by factoring out -1 The government plans to make important to the tax system In the serf system people could a sheep for a hammer Casino is a place where people gambling games for money Youth is the time for , Age is the time for repose I didn’t get into with him for long If we _7 from 10, we have Many of Shakespear’s are tragedies under the feudalism He is a person who kindly toward everyone 10 I saw her last on the flight to Hanoi since then we haven’t _for years 11 The boss the workers too hard 12 The of building the bridge spaning Danh River took two years 13 Ten from seven is a very simple BUILDING VOCABULARY SKILLS Vocabulary review Match each word in column A with the word in column B that has opposite meaning: A B Negative number Less than or equal to Subtracting Is the same as Greater than Positive number Absolute value Less than Negative infinity Multiplication Not equal to Minimum value Greater than or equal to Positive infinity Adding Tiếng Anh – Toán Tin - 10 – CONTEXT CLUES Choose the answer that is closest in the meaning to each word or phrase underlined use context clue: He knew it was a waste of time to carry on studying archaeology and the moment he started gaderning again a conitnue b begin c finish d start It is very dry today will you help me water the plants? a moisten b wet c irrigate d sprinkle Can you please tell me a little about yourself? a speak b talk c say to d explain Do you mind my turning the TV on now? a show b disapprove c want d like The enjoyable thing about travelling by train rather than by car is that you can sleep or read during the journey a cheerful b pleasurable c interested d pleased She had taken over the cooking at home for her father’s dinner parties and she had started to make up her own recipes a discover b c invent d work She has always enjoyed taking care of her sister a training b looking after c bringing d training Tiếng Anh – Toán Tin - 58 – We can find out many optimization techniques if we have necessary mathematical background of _ 10 We can’t in our studies without mathematical background III Understanding words Refer back to the text and find the words that mean: Unconnected Connection Suitable Separate Basis Information needed to understand a problem Ability to understand something Discussion based on reasoning Means of gaining something desired 10 Arranging things in group IV Understanding the text Decide whether the following sentences are true (T) or false (F) or no information (NI) by referring back to the text Students will find many computer science courses difficult Discrete optimization techniques are worked in operation research courses Discrete math can only be used under some conditions You can use discrete math to many kinds of sorting Elementary math is much simpler than discrete math Discrete math is used when there is a limit of objects It’s difficult to study other branches of math without discrete mathematical background Discrete math has no application in other natural sciences Discrete math helps study math, in general, better 10 Students of English don’t need discrete mathematics V Understanding the details Discrete math helps solve problems such as: Tieáng Anh – Toaùn Tin - 59 – Studying discrete math, students will work on the following math courses: Applications of discrete math Giving background for solving: - In general, three elements that should be gained when we want to use discrete mathematics are: a b c _ The importance of discrete math is that _ VI Understanding structures A The use of Whenever, Wherever, However, Whoever, Whatever The words above mean “no mater when, no mater where…” Example: - My roof leaks whenever it rains - Whoever cleans the windows, doesn’t make the floor clean - I would rather have a room of my own, however small it is, than share a room Practice: Rewrite the following sentences, using Whenever, Wherever, However, Whoever, Whatever You can eat anything you like You’ll see this product advertised every where you go It doesn’t mater who you are, come and sit down It doesn’t mater how hard I worked, she was not satisfied He says he’ll come to us any time he has spare-time Tieáng Anh – Toaùn Tin - 60 – B The use of “Between” and “Among” - Between is used with two nouns - Among is used with three or more nouns or a phrase noun Practice: Fill in the gaps, using “Between” and “Among” Rich and his wife can usually solve their problem them Profits are decided the stockholders of corporation The votes were evenly decided the Democratic candidates and the Republican candidates The property was decided equally his son and daughter There is a link two computer in a network The work is distributed the secretary and receptionist BUILDING VOCABULARY SKILLS A Vocabulary review: Choose the best word for each sentence Dimension Function Even Elements Odd Equation Triangle Paid Reduces x – y = 2x = 2y + How many solutions does the system of above have? The high cost of advertising is invariably by the consumers If a, b, c are the lengths of sides of the right with C greater than a, b then … If the argument of a f runs through a set M, in which the function also takes its value, then f is called an algebraic operation on M If the orders of all of a periodic group are bounded, then the lowest common multiple of their orders is called exponent of the group The figure shows the of a rectangular box that is … Every mathematical theory ultimately to study two kinds of objects: sets and function on sets B Context clues: Choose the answer that is closest in meaning to each word underlined They set out a dramatic journey a) Spectacular b) cheerful c) exciting d) interesting They spent her first day in Hanoi and took a sightseeing tour around this fascinating city a) Boring b) exciting c) absorbing d) busy Tiếng Anh – Toán Tin - 61 – The fact lies in that every one assumes heavy tasks assigned and fulfil with a high sense of responsibility a) work b) duty c) profession d) job The whole relationship changed and they became tremendous friends a) close b) friendly c) wonderful d) awful 5.The British parliament’s Big Ben clock tower is starting to tilt slightly and could become London’s own leaning tower a) Tighten b) fasten c) slant d) lift Thousands of protesters marched on Saturday in front of White House demanding the United States’ lifting embargo against Cuba a) Paraded b) operated c) walked d) moved Tiếng Anh – Toán Tin - 62 – UNIT 10: PROGRAMS AND PROGRAMMING LANGUAGES Computers can deal with different kinds of problems if they are given the right instructions for what to Instructions are first written in one of the high-level languages, e.g FORTRAN, COBOL, ALGOL, PL/1, PASCAL or BASIC, depending on the type of problem to be solved A program written in one of these languages is often called a source program, and it cannot be directly processed by the computer until it has been compiled, which means interpreted into machine code Usually a single instruction written in a high-level language, when transformed into machine code, results in several instructions Here is a brief description of some of the many high-level languages: FORTRAN acronym for FORmula TRANslation This language is used for solving scientific and mathematical problems It consists of algebraic formulae and English phrases It was first introduced in the United States in 1954 COBOL acronym for Comon Business-Oriented Language This language is used for commercial purposes COBOL, which is written using English statements, deals with problems that not involve a lot of mathematical calculations It was first introduced in 1959 ALGOL acronym for ALGOrithmic Language Originally called IAL, which means International Algebraic Language It is used for mathematical and scientific purposes ALGOL was first introduced in Europe in 1960 PL/1 Programming Language Developed in 1964 to combine features of COBOL and ALGOL Consequently, it is used for data processing as well as scientific applications BASIC acronym for Beginner’s All-purpose Symbolic Instruction Code Developed in 1965 at Dartmouth College in the United States for use by students who require a simple language to begin programming Other such languages are APL (developed in 1962) and PASCAL (named after Blaise Pascal and developed in 1971) Tiếng Anh – Toán Tin - 63 – When a program written in one of these high-level languages is designed to a specific type of work such as calculate a company’s payroll or calculate the stress factor on a roof, it is called an applications program Institutions either purchase these programs as packages or commission their own programmers to write them to meet the specifications of the users The program produced after the source program has been converted into machine code is referred to as an object program or object module This is done by a computer program called the compiler, which is unique for each computer Consequently, a computer needs its own compiler for the various high-level languages if it is expected to accept programs written in those languages For example, in order that an IBM system 370 may process a program in FORTRAN, it needs to have a compiler that would understand that particular model and the FORTRAN language as well The compiler is a systems program, which may be written in any language, but the computer’s operating system is a true systems program which controls the central processing unit (CPU), the input, the output, and the secondary memory devices Another systems program is the linkage editor which fetches required systems routines and links them to the object module (the source program in machine code) The resulting program is then called the load module, which is the program directly executable by the computer Although systems programs are part of the software, they are usually provided by the manufacturer of the machine Unlike systems programs, software packages are sold by various vendors and not necessarily by the computer manufacturer They are a set of programs designed to perform certain applications which conform to internationally accepted rules, irrespective of the particular specifications of the user Payroll is an example of such a package which allows the user to input data – hours worked, pay rates, special deductions, names of employees − and get salary calculations as output These packages are coded in machine language (0s and 1s) on magnetic tapes or disks which can be purchased, leased or rented by users who choose the package that most closely corresponds to their needs EXERCISES Main idea Tieáng Anh – Toaùn Tin - 64 – Which statement best expresses the main idea of the text? Why did you eliminate the other choices? Without software packages, it would be difficult to use the computer in solving problems such as payroll Compilers are indispensable to a computer Source programs written in high-level languages have to be changed to machine code before the computer can operate on them Understanding the passage Decide whether the following statements are true or false (T/F) by referring to the information in the text Then make the necessary changes so that the false statements become true BASIC was developed to help students FORTRAN is very wordy and therefore not as efficient a computer language as COBOL in solving scientific problems All high-level programs must be translated to machine code before the computer can execute them The best place to buy software packages is from the manufacturer An example of an application program is calculating the stress on a roof An operating system program controls input and output operations Software packages are not written in high-level languages Different high-level languages suit different problems IBM machine code is the same as that of CDC 10 It is a must for a programmer to be able to understand machine code Locating information Find the passages in the text where the following ideas are expressed Give the line references _1 Systems programs control the work of the computer system _2 Software packages are not always sold by the manufacturer _3 Usually, every high-level instruction translates into many more in machine code _4 Systems programs are usually provided by the manufacturer _5 Programmers may be required to write software for their employers Contextual reference Tieáng Anh – Toaùn Tin - 65 – Look back at the text and find out what the words in bold typeface refer to If they are given the right (paragraph.1) _ it cannot be directly processed (paragraph.1) _ it is called an applications program (paragraph.2) _ commission their own programmers (paragraph.2) _ to write them to meet (paragraph.2) _ that would understand (paragraph.3) _ which controls the central (paragraph.4) _ links them to the object (paragraph.4) They are a set of programs (paragraph.5) 10 which can be purchased (paragraph.5) Understanding words Refer back to the text and find a synonym for the following words converted buy brings agree with, comply with rented Now refer back to the text and find an antonym for the following words lengthy _ unchanged separate reject 10 depending on Word forms First choose the appropriate form of the words to complete the sentences Then check the differences of meaning on your dictionary instruction, instruct, instructed, instructor a Our maths explained to us the principles of binary arithmetic Tieáng Anh – Toaùn Tin - 66 – b We were to document our programs very carefully c Both _ and data have to be changed to machine code before the computer can operate on them compilation, compiler, compile, compiled a Our university computer does not have a PASCAL b Usually, a programmer _ his program before he puts in the data c A source program cannot be directly processed by the computer until it has been description, describe, described a Our introductory programming text included a brief of the many high-level languages b It is difficult to the memory of a microcomputer without referring to ‘chips’ result, results, resulting a The linkage editor links systems routines to the object module The program, referred to as the load module, is directly executable by the computer b The _ of these mathematical operations were obtained from the university mainframe and not from my micro specification, specify, specific, specified, specifically a Our company brought three packages with very _ applications: payroll, accounts receivable and accounts payable b And applications program is designed to a _ type of work, such as calculating the stress factor on a roof c Did the analyst give the new programmer the necessary to start on the project? 7a Content review Match the following words in column A with the corresponding information in column B A source program high-level languages applications program software packages object program compiler systems program operating systems linkage editor 10 load module B a to solve a particular problem b can be executed by the computer directly c program translated to machine code d connects routines with programs in memory e examples are COBOL and PASCAL f directs the processes of the computer CPU, and peripherals Tieáng Anh – Toaùn Tin - 67 – g groups of programs designed to solve a specific problem h written in a high-level language i computer needs one for each highlevel language j deals with the running of the actual computer not with programming problems 7b Content review Summarize the information on different high-level computer languages by completing the table below LANGUAGE FORTRAN DEVELOPED FUNCTION CHARACTERISTIC FUNCTION CHARACTERISTIC 1959 LANGUAGE DEVELOPED Mathematical and scientific purpose Tiếng Anh – Toán Tin - 68 – Combines features of COBOL and ALGOL BASIC 1962 Tiếng Anh – Toán Tin - 69 – Focus review Read paragraphs and of ‘Programs and Programming Languages againthey are re-written below What the words in italics signify? Computers can deal with different kinds of problems if they are given the right instructions for what to Instructions are first written in one of the high-level languages, e.g FORTRAN, COBOL, ALGOL, PL/1, PASCAL, OR BASIC, depending on the type of problem to be solved A program written in one of these languages is often called a source program, and it cannot be directly processed by the computer until it has been compiled, which means interpreted into machine code Usually a single instruction written in a high-level language, when transformed to machine code, results in several instructions Here is a brief description of some of the many high-level languages… The program produced after the source program has been converted into machine code is referred to as and object program or object module This is done by a computer program called the compiler, which is unique for each computer Consequently, a computer needs its own compiler for the various high-level languages if it is expected to accept programs written in those languages For example, in order that and IBM system 370 may process a program in FORTRAN, it needs to have a compiler that would understand that particular model and the FORTRAN language as well a Cause-effect b c d e f g h i j k l Cause -effect m Tiếng Anh – Toán Tin A Acceleration Analog computer Algorithm Algebra theâm - 70 – GLOSSARY gia tốc máy tính vật lý thuật toán đại số Application program Arithmetic Argument Augment trình ứng dụng số học đối số-góc cực tăng thêm-bổ sung sơ đồ khối biên Branch ngành Compact Compile Circuits Cores Curve Curve surface thu gọn biên dịch vi mạch cốt lõi đường cong mặt cong B Block diagram Boundary C Calculate tính toán Calculation tính toán Calculus phép tính vi tích phân Card reader phận đọc phiếu Chance ngẫu nhiên Combinatorics toán học tổ hợp Coefficient hệ số (Leading coefficient Central processing unit hệ số số hạng cao nhất) đơn vị xử lý trung taâm D Data Decimal Decompose Decisor Definite integral Derivative Device liệu thập phân phân tích số chia, ước số tích phân xác định đạo hàm thiết bị Digit Digital computer Dimension Discrete Disk Disk drive Display screen chữ số máy tính kỹ thuật số số chiều, chiều rời rạc đóa ỗ đóa hình hiển thị toán sơ cấp vi mạch điện tử xung điện Equal Equation Exponent phương trình số mũ, phương trình thừa số tập hợp hữu hạn lưu đồ Foundation Fraction Function sở phân số hàm số E Elementary math Electronic circuit Electric pulses mũ F Factor Finite set Flow chart Tiếng Anh – Toaùn Tin - 71 – G Geometry Graph hình học đồ thị Group theory lý thuyết nhóm H Hardware component High-level language Hypothesis phận phần cứng ngôn ngữ bậc cao giã thuyết I Input Installation Instruction Integers nhập vào cài đặt thị số nguyên Internal memory Inventory Investigate nhớ kiểm kê khảo sát giới hạn trình giới hạn tuyến tính Linkage editor Load module biên tập nốt kết trình nạp L Limit Limitting process Linear M Magnetic tape Mainframe Manipulate Maximun Medium băng từ máy điện toán lớn thao tác cực đại phương tiện-trung bình Minimum cực tiểu Mixed number of integer hỗn số Moment of inertia mô-men quán tính Multiple bội số chương trình đối tượng toán tử-thao tác Operating system Optimization hệ điều hành tối ưu hoá Prime number Probability Process Processor Proper fraction Proportion Punched card số nguyên tố xác xuất xữ lý xữ lý phân số thực tỉ lệ thức phiếu đục lỗ Rational fraction Rectangle phân thức hữu tỉ hình chữ nhật O Object program Operations P Packages Partial fraction Pentagon Periodic Peripheral devices Point Polynomial chương trình soạn sẵn phân thức tối giản hình ngũ giác tuần hoàn thiết bị ngoại vi điểm đa thức R Random Ratio ngẫu nhiên tỉ lệ Tiếng Anh – Toaùn Tin - 72 – S Sample space Secondary memory Semi-circle Software Source program không gian mẫu nhớ phụ hình bán nguyệt phần mềm chương trình nguồn Storage device Subset of Statistics System program thiết bị lưu trữ hợp thống kê trình hệ thống tiếp tuyến phận đọc băng từ số hạng Terminal Trigonometry trạm cuối lượng giác biến thiên vận tốc Versatility tính đa T Tangent line Tape drive Term V Variation Velocity W Whole number số nguyên BEST WISHES TO YOU ... 63 GLOSSARY 70 Tieáng Anh – Toán Tin -3– LỜI TỰA Nhằm đáp ứng kịp thời nhu cầu học Tiếng Anh chuyên ngành sinh viên Toán – Tin, biên soạn, biên tập số học có liên quan... space, arrivals and departures - 29 – Tiếng Anh – Toán Tin - 30 – Tiếng Anh – Toán Tin - 31 – UNIT 5: STATISTICS Statistics is the scientific method of collecting information in a form of numerical... Building _ is usually required before starting any renovations to a building for a computer department continuation, continue, continuing, continuously a If microcomputer sales to