# FIT 302: Mathematics for ICT

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1 FIT 302: Mathematics for ICT INTRODUCTION This is one of the three courses designed for the Foundation in Information Technology (FIT) programme. This course consists of two parts which play an important role in Information Technology. The aim of this course is to introduce basic mathematical and statistical concepts as well as to develop analytical thinking. Practical skills, problem solving and computational techniques are also emphasized throughout the course. After the successful completion of this course the learner will possess problem solving and analytical skills together with the required mathematical and statistical knowledge necessary for day to day life as well as in computing. LEARNING OUTCOMES After successfully completing this course, students will be able to: Apply basic mathematical and statistical concepts to real-world situations Illustrate mathematical intuition and abstract reasoning Apply probabilistic concepts for prediction in the face of uncertainty ASSESSMENT CRITERIA The formative evaluation procedure consists of 4 LMS based on-line self assessments. The summative evaluation which is two hours computer based e-test. Structure of Exams Formative Assessmentso 4 assessments consist of multiple-choice questions Summative Assessmentso One computer based e-test of two hours Mathematics for ICT Detailed Syllabus Page 1/10

2 OUTLINE OF SYLLABUS Part I Topic Average learning hours * 1. Introduction to Numbers and Arithmetic Introduction to Basic Algebra Solving Equations Fundamentals of Measurements Introduction to Ratios and Proportions Introduction to Percentages and Interest Rates Time Related Problems 05 Total 40 Part II Topic Average learning hours * 8. Indices and Logarithms Introduction to Sets Logic and Truth tables Relations and Functions Techniques of Counting Fundamentals of Statistics Introduction to Probability Fundamentals of Sequences and Series Introduction to Differentiation Introduction to Integration 06 Total 80 * Depending on the students capability this could vary. Mathematics for ICT Detailed Syllabus Page 2/10

3 REQUIRED MATERIALS Supplementary Reading Ref 1: New comprehensive mathematics for O level by Greer, 2 nd edition, Stanley Thornes (Publishers) Ltd. Ref 2: Schaum s Outline series: Basic mathematics with application to science and technology by Kruglak H, Moore J.T, Mata-Toledo R. 2 rd edition, MC Graw Hill. Ref 3: Mathematics for computing by K.M.R.T. Karunaratna, Tharangee Printers Sri Lanka, Ref 4: Schaum s Outline series: Theory and problems of statistics by Murray R. Spiegel, 2 nd edition. Ref 5: Schaum s Outline series: Probability by Seymour Lipshutz & Marc Lipson, McGraw-Hill International Edition, Ref 6: Schaum s Outline series: Set theory and related topics by Seymour Lipshutz, 2 rd edition, MC Graw Hill. Note: Under the detailed syllabus, book numbers of relevant text are given for each topic only as a guideline for minimal references based on the recommended supplementary reading. These references are generally sufficient to understand the concepts and measure the expected depth of the content. DETAILED SYLLABUS PART I 1. Introduction to Numbers and Arithmetic (6 hrs.) [Ref 1: pg 1-17, pg 62-71, pg 83-86], [Ref 2 : pg 1-8, pg 36-50, pg 61-94, pg , pg ] Identify types of numbers, arithmetic operations, prime numbers, fractions, indices, square roots and surds Estimate, approximate and use appropriate degrees of accuracy Explain what the number line is and what the absolute value of a number is Apply operations on different types of numbers, apply the laws of indices, and simplify surds State the basic rules involving the order of operations Recognize the need for such rules in mathematics 1.1 Types of numbers 1.2 The number line and the ordering of numbers 1.3 Basic mathematical operations 1.4 The order of operations 1.5 The absolute value of a number 1.6 Prime numbers and factors 1.7 Estimation of numbers 1.8 Introduction to exponents 1.9 Square roots and surds Mathematics for ICT Detailed Syllabus Page 3/10

4 2. Introduction to Basic Algebra (7 hrs.) [Ref 1: pg 72-86, pg, pg , pg ], [Ref 2: pg 61-94, pg ] Identify variables, numerical expressions and algebraic expressions Evaluate algebraic expressions when values for the variables are given Solve problems in which verbal phrases are translated into algebraic expressions Solve equations involving absolute values, and simplify algebraic expressions Identify rules of inequalities and solve problems 2.1 Introduction to algebraic expressions 2.2 Expanding and factorizing algebraic expressions 2.3 Working with formulas 2.4 Solutions of equations involving absolute values 2.5 Intervals on the number line 2.6 Rules of inequalities, solutions of inequalities 3. Solving Equations (5 hrs.) [Ref 1: pg ], [Ref 2: pg ] Recognize the need to use the quadratic formula to solve quadratic equations Solve quadratic equations using the techniques of factorizing Identify methods of solving simultaneous equations Imparting skills of applying quadratic and simultaneous equations to solve day-to-day life problems 3.1 Solving quadratic equations 3.2 Solving simultaneous equations Elimination method Substitution method 4. Fundamentals of Measurements (6 hrs.) [Ref 1: pg , pg ], [Ref 2: pg ] Determine the perimeter, area and volume of some geometric shapes Determine heights and distances using angles Solve problems involving the concepts length, area and volume 4.1 Introduction to perimeter, area and volume of objects of different shapes 4.2 Introduction to trigonometry 4.3 Problems involving angles of elevation and depression Mathematics for ICT Detailed Syllabus Page 4/10

5 5. Introduction to Ratios and Proportions (4 hrs.) [Ref 1: pg 24-28], [Ref 2: pg ] Define ratios and proportions Solve problems involving ratios and proportions Apply proportions to solve percentage problems 5.1 Ratios 5.2 Proportions 5.3 Solving problems 6. Introduction to Percentages and Interest Rates (7 hrs.) [Ref 1: pg 29-34, pg 47-53], [Ref 2: pg 51-60] Define percentage, original price, discount, profit, loss, sales tax, tax rate, selling price, interest, interest rate and time Describe and apply procedures for finding discount, profit or loss, selling price and tax Analyze percentage problems Describe and apply formulas for finding simple interests and compound interests 6.1 Calculation of profit and loss 6.2 Percentage profit and discount 6.3 Working with tax 6.4 Calculation of simple interest and compound interest 7. Time Related Problems (5 hrs.) [Ref 1: pg ] Describe the change in distance, volume with respect to time and work done with respect to time Calculate change in distance, volume with respect to time and work done 7.1 Distance and time 7.2 Work and time 7.3 Volume and time Mathematics for ICT Detailed Syllabus Page 5/10

6 DETAILED SYLLABUS PART II 8. Indices and Logarithms (6 hrs.) [Ref 1: pg ], [Ref 2: pg ], [Ref 3 pg 1-25] Identify and use index notation to solve problems Explain what logarithm is and solve problems with different bases of logarithms Summarize uses of logarithms and identify laws of logarithms 8.1 Indices Integral and rational indices Index laws x a The graph of 8.2 Logarithms Definition Laws of logarithm Changing the base of logarithms The graph of log a x 9. Introduction to Sets (5 hrs.) [Ref 1: pg ], [Ref 3: pg 27-61], [Ref 6] Identify different methods of denoting sets Illustrate properties of set algebra using labeled Venn-diagrams Solve problems involving sets; for example finding the number of elements of sets 9.1 The concept of a set 9.2 Operations on sets (union, intersection, complement & relative complement) 9.3 Relations between sets (subset, equality, proper subset) 9.4 Introduction to power sets 9.5 Introduction to the laws of algebra of sets 9.6 Venn diagrams (Including labeled Venn diagrams) 9.7 Special Venn diagrams 10. Logic and Truth Tables (12 hrs.) [Ref 3 pg ] Grasping the language of logic and constructing compound propositions Construct truth tables to determine the truth values of given compound propositions containing any combination of connectives (conjunction, disjunction and negation) Discuss logical operations, tautologies, contradictions, logical equivalence and laws of algebra of propositions Solve problems involving predicates and quantifiers Mathematics for ICT Detailed Syllabus Page 6/10

7 10.1 Propositions Propositions and compound propositions Basic logical operations (conjunction, disjunction and negation defined by truth tables) Tautologies and contradictions Logical equivalence Laws of algebra of propositions 10.2 Predicates and quantifiers 11. Relations and Functions (8 hrs.) [Ref 1: pg ], [Ref 3: pg ] Describe relations Discuss types of relations and work with the different types of relations Explain what a function is and express functions using different notations Describe different types of functions and solve problems involving functions Construct new functions from given functions 11.1 Introduction to relations Relations Binary relations Order relations (partial order and total order) and Equivalence relations 11.2 Introduction to functions Functions Functions as relations One-to-one functions and onto functions Bijections Inverse functions Composite functions 12. Techniques of Counting (7 hrs.) [Ref 2: pg ], [Ref 3: pg ] Define permutations and combinations Calculate the number of possible outcomes of elementary combinatorial processes such as permutations and combinations Use techniques of counting as tools in probability for large sample spaces 12.1 Introduction to counting 12.2 Basic counting principles (sum rule and product rule) 12.3 Introduction to permutations Introduction Permutations with repetitions 12.4 Introduction to combinations 12.5 Tree-diagrams Mathematics for ICT Detailed Syllabus Page 7/10

8 13. Fundamentals of Statistics (12 hrs.) [Ref 1: pg ], [Ref 2: pg ], [Ref 4] Apply underlying statistical concepts and definitions Identify methods of summarization and organization of data numerically and graphically Apply different types of frequency distributions in problem solving Define the measures of central tendency, measures of dispersion and measures of position Identify the normal curve 13.1 Introduction to Statistics 13.2 Descriptive Statistics Types of data (qualitative, quantitative, continuous, discrete); Scales of measurement (nominal, ordinal, interval, ratio,) 13.3 Organization and summarization of data Frequency table, cumulative frequency table, histogram, frequency polygon, cumulative frequency polygon Bar charts, pie-charts, percentiles, 5- number summary, Box plot 13.4 Measures of location Mean Median Mode 13.5 Measures of dispersion Range Inter quartile range Variance Standard deviation 14. Introduction to Probability (10 hrs.) [Ref 1: pg ], [Ref 2: pg ], [Ref 5 pg ], [Ref 3: ] Define sample space and events related to random experiments. Introduce concept of probability and discuss ways to assign probabilities to events. Explain combined events and ways to find probabilities of such events. Discuss relative probabilities with respect to reduced sample space. Describe a convenient graphical tool to compute probabilities in a (finite) sequence of experiments. Explain methods to find probabilities of events (and related conditional events) for a given a partition of the sample space is available. Introduce two commonly encountered distributions and relate them to real life problems Introduction to probability 14.2 Sample space and events 14.3 Some basic theorems on probability space Mathematics for ICT Detailed Syllabus Page 8/10

9 14.4 Mutually exclusive events 14.5 Conditional probability and tree diagrams 14.6 Independent events 14.7 Total probability law and Bayes theorem 14.8 The binomial distribution 15. Fundamentals of Sequences and Series (7 hrs.) [Ref 1: pg ] Define sequences and series Identify the sequence of terms in a series Identify arithmetic progression and geometric progression, and use formulas to find the n th term and the sum of the first n terms Find the sum to infinity of a series and convergence and divergence of series 15.1 The idea of a sequence 15.2 The idea of a series and the sequence of terms of a series 15.3 The sum of the first n terms of a series 15.4 Arithmetic progressions Formulae for the n th term Formulae for the sum of the first n terms 15.5 Geometric progressions The formula for the n th term The formula for the sum of the first n terms 15.6 The sum to infinity of a series and the convergence and divergence of a series 16. Introduction to Differentiation (7 hrs.) [Ref 1: pg ] Explain what differentiation is Describe the properties of differentiation Solve problems involving differentiation 16.1 Introduction to differentiation 16.2 Properties and examples Mathematics for ICT Detailed Syllabus Page 9/10

10 17. Introduction to Integration (6 hrs.) [Ref 1: pg ] Explain integration Know and apply the integrals of standard functions Explain the relation between integration and the area under a curve Solve problems involving integration 17.1 Integration as the inverse of differentiation 17.2 Integration of standard functions ( e x, log x, sin x, cos x, tan x, sec x, cosec x, cot x ) 17.3 The relation between integration and the area under the curve Mathematics for ICT Detailed Syllabus Page 10/10

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