Foundations of Mathematics 120

Unit 1: Statistics

The normal distribution with standard deviation and z-scores, and interpreting statistical data using confidence intervals, confidence levels, and margin of error.

• Standard deviation and the bell curve
• z-scores

• Confidence intervals and levels
• Margin of error

Unit 2: Logical Reasoning

Puzzles and games involving numerical and logical reasoning, the application of set theory, and problems involving conditional statements.

• Strategies for logic puzzles and games
• Justifying puzzle and game reasoning

• Sets, unions and intersections
• Counting with set theory

• Conditional statements and their related forms
• Truth values and biconditionals

Unit 3: Probability

Odds and probability statements, the probability of mutually exclusive and non-mutually-exclusive events and of two events, the fundamental counting principle, permutations, combinations, and the binomial theorem.

• Interpreting odds and probability
• Assessing the validity of probability claims

• Mutually exclusive events
• Non-mutually-exclusive events

• Independent events
• Dependent events

• Applying the fundamental counting principle
• Counting with restrictions

• Permutations of distinct objects
• Permutations with restrictions or repeated objects

• Combinations of objects
• Choosing combinations or permutations

• Expanding binomials with Pascal's triangle
• The binomial theorem and general term

Unit 4: Relations and Functions

Representing data using polynomial functions, exponential and logarithmic functions, and sinusoidal functions to solve problems.

• Fitting a polynomial model to data
• Solving problems with a polynomial model

• Modelling with exponential functions
• Modelling with logarithmic functions and scales

• Building a sinusoidal model
• Solving problems with a sinusoidal model