UNIVERSITY OF COLOMBO SCHOOL OF COMPUTING

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UNIVERSITY OF COLOMBO SCHOOL OF COMPUTING (UCSC)
DEGREE OF BACHELOR OF INFORMATION
TECHNOLOGY (EXTERNAL) WEB SITE www.bit.lk
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IT1102 Mathematics for Computing I

• NEW SYLLABUS
• NEW STUDENTS
• SYLLABUS REVISION
• TEACHERS REPEATERS
• IT1101 ? IT1102

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LEARNING OBJECTIVE

• After successfully completing this module
  students should be able to
• Translate problem into mathematical language and
  to obtain solutions.
• Exploit the versatile nature of the Mathematical
  method of problem solving.
• Understand and use the mathematical concepts and
  techniques for the study of IT.

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TOPICS

• Minimum No.
• Of Hours
• Indices and logarithms 03
• Sets 07
• Logic 15
• Relations and Functions 12
• Boolean Algebra 03
• Techniques of Counting 10
• Probability 10
• Total 60

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MAIN READING

• Elementary Algebra for School, Metric Edition by
  H.S. Hall and R.S. Knight, A.I.T.B.S. Publishers
  Distributors India, 2000.
• Schaums Outline series Discrete Mathematics,
  2nd Edition by Seymour Lipshutz Marc Lipson,
  Tata McGraw-Hill India, 2003.
• Discrete Mathematics by Olympia Nicodemi, CBS
  publishers and Distributors India, 2001.
• Schaums Outline SeriesProbability by Seymour
  Lipshutz Marc Lipson, McGraw-Hill International
  Edition, 2000.

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SUPPLEMENTARY READING(OPTIONAL)

• Mathematics for Computing by K.R.M.T.
  Karunaratna, Tharangee Printers Sri Lanka, 2002.

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Indices and logarithms

• OBJECTIVES
• Transform expressions with indices and
  logarithmic expressions into forms which are more
  manageable.
• Represent graphically the basic expressions
  involving indices and logarithms.

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Indices and logarithms ..

• Example

How to simplify expressions with indices
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Indices and logarithms ..

• Example

How to simplify logarithmic expressions
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Indices and logarithms ..

• Index laws (for integral indices and rational
  indices), surds, ex
• Logarithms Definition, laws of logarithms,
  change of base (log b c log a c . log b a)
• Graphs of ax, log a x

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Sets

• OBJECTIVE
• Illustrate properties of set algebra using
  Venn-diagrams.
• Prove various useful results of set algebra.

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Sets..

• Introduction to sets (sets of numbers (N, Z, Q
  etc)), subsets, proper subsets, power sets,
  universal set, null set, equality of two sets,
  Venn diagrams .
• Set operations (union, intersection, complement
  and relative complement)

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Sets..

• Laws of algebra of sets (The idempotent laws, the
  associative laws, the commutative laws, the
  identity laws, the complement laws, De Morgan's
  laws) proofs of the laws using labelled general
  Venn diagram, proofs of results using the laws.

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Logic

• OBJECTIVE
• Grasp the language of mathematical logic starting
  from the language of sets.
• Construct Propositions and to evaluate truth
  values.
• Use quantifiers.
• Identify appropriate methods and applying them in
  the proof of mathematical statements.

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Logic..

• Propositions and Propositional Logic
• Negation, conjunction, disjunction defined by
  truth tables
• Truth - tables of compound propositions
• Tautologies and contradictions
• Logical equivalence
• Algebra of propositions
• The conditionals p gt q and p ltgt q and their
  truth - tables
• Arguments

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Logic..

• Predicates and Quantifiers .
• Predicates involving one or more variables
• The quantifiers ?, ?
• Propositions involving unmixed and simple mixed
  quantifiers (for example ?x?Z, ?y?N, ygtx)
• Types of Proofs
• Direct proofs and proofs by contradiction
• Counter example
• Mathematical induction

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Relations and Functions

• OBJECTIVE
• Define and work with functions and relations

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Relations and Functions

• Relations
• Definition of a relation
• Relation from a set A to a set B
• Relation on a set A
• Relations as sets of ordered pairs
• Inverse of a relation
• Directed graph
• Equivalence Relations

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Relations and Functions

• Functions
• Function as a mapping from a set A to a set B
• One to one functions
• Bijections
• Inverse functions
• Composite functions

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Boolean Algebra (03hrs) (New Section)

• Boolean algebra defines an abstract mathematical
  structure and based on laws of sets and
  propositions.
• Knowledge in Boolean Algebra is an essential
  prerequisite to understand logic gates and
  circuits.

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Boolean Algebra .

• Basic definitions
• Duality
• Basic theorems
• Sum of products form of Boolean algebras
• Minimal Boolean expression, prime implications

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Technique of Counting

• OBJECTIVE
• Count the number of elements in certain
  mathematically defined sets where ordinary
  methods of counting are tedious.

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Technique of Counting

• Example
• How many three-digit integers from 100 to 999,
  including these two numbers, are divisible by 5?
  
• How many different 3 letter words are possible if
  each letter is selected from letters A-Z?

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Technique of Counting

• Permutations
• Binomial theorem and the binomial coefficients
• Combinations
• Tree diagrams
• Pigeon hole principle

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Probability

• OBJECTIVE
• Solve typical probabilistic problems.
• Explain the basic concept of probability

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Probability..

• Sample space and events
• Axioms of probability and basic theorems
• Finite probability spaces
• Conditional probability and the multiplication
  rule
• Tree diagrams
• Bayes theorem
• Independent events

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Sections Removed

• Functions
• Graph of a function as a set of ordered pairs
• Special functions and sketching their graphs.
• The quadratic functions
• Trigonometric functions
• Sketching the graphs of simple rational functions

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Sections Removed

• Probability
• Stochastic processes

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LEARNING PROCESS

• THERE WOULD BE CONTINUOUS ASSIGNMENTS, QUIZES
  AND GROUP WORK
• IN ADDITION TO THE FINAL EXAMINATION WHICH IS
  BASED
• ON MULTIPLE CHOICE QUESTIONS