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Course Outline

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Lecture 1 Learning Objectives To use set notations To apply operations (union, intersection) on sets To define de Morgan’s Laws for sets To define relations on sets To define set partitions RMIT University, Taylor's College

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Lecture 2 Learning Objectives: To describe functions To define a “one-to-one” and “onto” function To apply and distinguish special kinds of functions (i.e. absolute value, floor and ceiling, logarithmic, exponential and polynomial) RMIT University; Taylor's College

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Lecture 3 Learning Objectives To apply the summation and product notation To define a matrix To solve problems on matrix summation, subtraction and multiplication To find the transpose of a matrix To calculate the inverse of a matrix RMIT University; Taylor's College

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Lecture 4 Learning Objectives To define a proposition To form a compound proposition using connectives To determine the truth values of compound propositions based on the truth values of their constituent propositions To use the different ways of expressing implication To determine the equivalence of two propositions RMIT University; Taylor's College

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Lecture 5 Learning Objectives To apply the division algorithm To apply the Euclidean algorithm RMIT University; Taylor's College

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Lecture 6 To apply the Principle of Mathematical Induction To solve the Towers of Hanoi puzzle To define a recurrence relation 7RMIT University; Taylor's College

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Lecture 7 To combine propositions using connectives To construct the truth table of a given compound proposition To define de Morgan Law for logic To define the difference between a predicate and a proposition To use a quantifier in a predicate 8RMIT University; Taylor's College

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Lecture 8 To apply quantifiers on predicates To apply the de Generalized de Morgan’s Laws To determine the truth value of predicates involving combination of two quantifiers RMIT University; Taylor's College

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Lecture 9 To apply the sum rule and product rule in solving problems To apply the principles of counting (i.e. combination, permutation) in solving problems 10RMIT University; Taylor's College

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Lecture 10 To define the Binomial Theorem To understand the relationship between Pascal’s Triangle and the Binomial Theorem To apply the Pigeonhole Principle in counting 11RMIT University; Taylor's College

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Lecture 11 To define probabilities To calculate probabilities of events To calculate conditional probabilities To apply Bayes’ Theorem in calculating probabilities 12RMIT University; Taylor's College

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Lecture 12 To define a random variable To construct probability distribution function and cumulative probability distribution function To apply some special kinds of probability distributions, i.e. finite uniform distribution and binomial distribution RMIT University; Taylor's College

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Lecture 13 To calculate the mean, median and mode To calculate and interpret the measure of spread To distinguish between population parameter and sample statistic RMIT University; Taylor's College

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