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Paper 7

MATHEMATICAL CONCEPTS IN DATA SCIENCE

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This unit specifies competencies required to apply mathematical concepts in data science. It enables the learner to perform linear algebra operations, handle operations involving calculus, predict occurrences using probability theory and manage data using statistical methods.

On completion, a candidate should be able to

  • Perform Linear Algebra operations
  • Handle operations involving calculus
  • Predict occurrences using probability theory
  • Manage data using statistical methods

Content

  1. 1

    Perform Linear algebra operations

    Perform Linear algebra operations

    1. ❑ Linear Equations ❑ Linear equation in one variable ❑ Equation of a line ❑ Forms of linear equation ✓ General form ✓ Slope intercept form ✓ Point form ✓ Intercept form ✓ Two-point form ❑ Standard form of linear equation ✓ Slope intercept form ✓ Point slope form ✓ Intercept form ✓ Two-point form ❑ How to solve linear equations ❑ Solution of linear equations in

      1. ne variable ✓ Solution of linear equations in two variables ❑ System of two linear equations in two unknowns Vector operations ❑ Operations on vectors ❑ External ❑ Vector subtraction ❑ Properties of vector addition and scalar multiplication ❑ Unit vectors

  2. 2

    Handle operations involving calculus

    Handle operations involving calculus

    1. ❑ Definition of calculus ❑ Limits and continuity ❑ Functions, domain and range ❑ Evaluating limits ✓ Graphically ✓ Numerically ✓ Algebraically ❑ Definition of derivative ❑ Derivative as a function ❑ Derivative rules ❑ Applications of derivatives ❑ Approximating areas ❑ The definite integral ❑ The fundamental theorem of calculus ❑ Applications of integration

  3. 3

    Predict occurrences using probability theory

    Predict occurrences using probability theory

    1. ❑ Definition of terms ✓ Events ✓ Outcome ✓ Experiment ✓ Sample space ✓ ❑ Types of events ✓ Simple ✓ Elementary, ✓ Mutually exclusive, ✓ Mutually inclusive, ✓ Dependent ✓ Independent ❑ Laws of probability ✓ Addition ✓ Multiplication ❑ Basic probability trees ❑ Finite probability spaces and conditional probability

  4. 4

    Manage data using statistical methods

    Manage data using statistical methods

    1. ❑ Sources of data: ✓ Primary ✓ Secondary ❑ Methods of collecting primary data: ✓ observation ✓ interviews ✓ questionnaires ❑ Sampling methods ✓ Probabilistic ✓ Non-probabilistic ❑ Data presentation: ✓ Frequency tables ✓ Histograms ❑ Measures of central tendency: ✓ Arithmetic mean ✓ Mode, ✓ Median ❑ Measures of dispersion/Spread ✓ Range, ✓ Mean deviation, ✓ Standard deviation,