STATISTICS

Course Credits: 3 Units

Prerequisites: Math 18

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STAT 117 - Mathematics for Statistics

Course Description

This course covers principles of logic; methods of proofs; fields, sigma fields, and sequence of sets; the real number system; summation of series; combinatorial analysis.

Course Learning Outcomes

After completion of the course, the student should be able to:

  1. Prove or disprove mathematical statements
  2. Perform operations and prove properties of sets, Cartesian products, fields, and sigma-fields
  3. Perform operations and prove properties of functions, sequences, and summations
  4. Calculate the cardinality of a finite set using combinatorial analysis
Course Outline

UNIT 1. Logic

  1. Introduction to Logic
  2. Logical Connectives
  3. Truth Tables
  4. Logical Equivalence
  5. Quantifiers

UNIT 2. Proving Validity of Arguments

  1. Arguments
  2. Truth Table Method
  3. Direct Proof
  4. Indirect Proof

UNIT 3. Proving Mathematical Statements

  1. Direct Method
  2. Indirect Method
  3. Proving Biconditional Statements
  4. Disproving Statements
  5. Mathematical Induction

UNIT 4. Set Theory

  1. Sets and Subsets
  2. Set Operations
  3. Classes of Sets and Cartesian Products
  4. Sequences of Sets
  5. Generalized Operations
  6. Fields and Sigma-Fields
  7. Real Number System

UNIT 5. Relations and Functions

  1. Representation of Relations
  2. Types of Functions
  3. Special Types of Functions

UNIT 6. Sequences and Series

  1. Sequences
  2. The Summation Notation
  3. Series and Expansions
  4. Special Sums

UNIT 7. Counting Techniques

  1. Cardinality
  2. The Fundamental Principle of Counting
  3. Permutation
  4. Combination
  5. Binomial Theorem

UNIT 8. Other Topics

  1. Statistical Experiment
  2. Sample Space and Sample Points
  3. Event Space and Events