Computer Mathematics notes

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Number of Pages: 210 Pages
File size: 4.5 MB
Suitable for: Certificate, KNEC Diploma, KASNEB, University and Professional Courses

Topics Covered:

Topic 1: Data representation and number systems.
Topic 2: Binary arithmetic
Topic 3: Set theory
Topic 4: Logic and truth tables
Topic 5: Elementary matrices
Topic 6: Linear equations
Topic 7: Elementary statistics
Topic 8: Introduction to probability
Topic 9: Emerging issues and trends




2.1       Data representation and number systems

  • Computer codes: BCD, ASCII. EBCDIC
  • Bit, byte, nibble, word
  • Number systems: Decimal numbers, Binary numbers. ‘Octal numbers. Hexadecimal numbers
  • Number conversions

2.2       Binary arithmetic

  • Addition, subtraction
  • Multiplication, division
  • Complements

2 :3      Set theory

  • Introduction: definitions and purpose
  • Types of sets: Universal set. empty null set, sub-sets, finite, infinite, power sets, partition
  • Description of sets; enumeration method and descriptive method
  • Operations: Union and intersection, complements, difference
  • Duality
  • Sets and elements
  • Venn diagrams
  • Ordered pairs, product sets, relations

2.4       Logic and truth tables

  • Introduction
  • Conjunction and disjunction
  • Negation
  • Proportions and truth tables
  • Tautology and contradiction
  • Logical equivalence

2.5       Elementary matrices

  • Introduction to matrices: definitions and importance of matrices
  • Matrix addition and subtraction
  • Dimensions/order of matrices
  • Types of matrices
  • Identity matrix
  • Matrix operations: addition, subtraction. multiplication, inversion of 2×2 matrices
  • Applications of matrices to business problems

2 5       Linear equations

  • Linear equations in one unknown
  • System of two linear equations in two unknowns

2.7       Elementary statistics

  • Sources of data: primaries are and secondary
  • Methods of collecting primary data: observation. interviews, questionnaires Sampling methods: probabilistic and non-probabilistic
  • Data presentation: frequency tables and histograms
  • Measures of central tendency: arithmetic mean, mode, median
  • Measures of dispersion: range. mean deviation. standard deviation, variance, coefficient of variation

2.8       Introduction to probability

  • Definitions: events, outcome, experiment, sample space
  • Types of events: simple, elementary. mutually exclusive, mutually inclusive, dependent and independent
  • Laws of probability addition and multiplication
  • Basic probability trees
  • Finite probability spaces and conditional probability

2.8 Emerging issues and trends

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