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Paper prepared by Prof. Omar Hasan Kasule Sr. MB ChB (MUK), MPH (Harvard) DrPH (Harvard) Chairman, Institutional Review Board - KFMC
DEFINITION AND CLASSIFICATION:
• Mathematics is the language of science.
• Science is closely related to mathematics because of its need for an exact description that can only be made using the exact language of mathematics.
• Equations and graphs represent the results of observations and experimentation in a precise and concise manner.
HISTORICAL DEVELOPMENT:
BASIC PRINCIPLES AND PARADIGMS: RANDOM VARIABLE:
• Natural variation is random. A variable is a characteristic of a sample or a population that can take on various values. A random event is a change of state. If the change is expressed numerically it becomes a random variable. A random variable maps outcomes on a number line.
• A random variable results when numerical values are assigned to results of experiments that involve either measurement or counting. The value of a random variable is governed by a random unpredictable selection. A random variable probability can also be assigned to the different values of the random variable.
• A random variable can alternatively be defined as a numerical variable whose value is not perfectly predictable.
• A constant is the opposite of a variable. It has only one unvarying value under all circumstances. Constants are few and reflect basic laws laid down by the creator. Examples of constants are: the speed of light, the value of p, etc. In statistics, an observation is looked at as a random variable.
BASIC PRINCIPLES AND PARADIGMS: PROBABILITY:
• Probability is the modeling of chance random events and a measure of the likelihood of their occurrence.
• The concept of pure chance is not absolutely true from a tauhidi perspective. All events are pre-determined by Allah. Humans use chance or probability estimates because of limited knowledge. Wh at appears random or the chance to humans has an underlying deterministic order known only to Allah.
• The consistency of probabilities and predictions is based on sunan al Ilaah. Probability is classified as theoretical and empirical.
RESEARCH METHODS:
ISLAMIC EPISTEMOLOGICAL CRITIQUE:
ISLAMIC INTRODUCTION TO THE DISCIPLINE: