## Topical Outline with Specific Course Objectives

- Inductive and Deductive Reasoning
- Use inductive reasoning to reason to a general conclusion through observations of specific cases.
- Use deductive reasoning to reason to a specific conclusion from a general statement.

- Sets and Venn Diagrams
- Indicate sets by description, roster form, and set-builder notation.
- Categorize equal and equivalent sets.
- Use symbols to illustrate the relationship between sets and to distinguish elements from subsets.
- Construct Venn diagrams to illustrate set relationships.
- Determine new sets from old using any combination of the set operations complement, intersection, and union. (The difference of two sets and the Cartesian product are optional.)
- Use Venn diagrams to determine if statements involving sets are equal.
- Solve practical problems using sets.

- Logic
- Write negations of statements, including ones that contain quantifiers such as
*all, none,*and*some*. - Translate verbal compound statements (
*not, and, or, if-then,*and*if and only if*) into symbolic form, and vice versa. - Construct truth tables for compound statements.
- Determine if statements are logically equivalent.
- Use De Morgan’s laws to write equivalent statements.
- Use variations of the conditional (converse, inverse, and contrapositive) to write equivalent statements.
- Determine whether symbolic arguments are valid or invalid.
- Use Euler diagrams to determine whether syllogistic arguments are valid or invalid.

- Write negations of statements, including ones that contain quantifiers such as
- Geometry
- Classify lines (intersecting, parallel, perpendicular, skew) and angles (right, acute, obtuse, straight).
- State and apply the basic relationships between special pairs of angles such as complementary, supplementary, vertical, alternate interior, alternate exterior, and corresponding.
- Classify polygons including special types of triangles (acute, obtuse, right, isosceles, equilateral, scalene) and quadrilaterals (trapezoid, parallelogram, rhombus, rectangle, square).
- Use proportions to find missing lengths in similar figures.
- Calculate the perimeter and area of two-dimensional figures such as triangles, squares, rectangles, trapezoids, and circles.
- State and apply the Pythagorean theorem.
- Classify three-dimensional figures including special types of polyhedra (platonic solids, prisms, pyramids).
- Calculate the volume of three-dimensional figures such as rectangular solids, cubes, cylinders, cones, and spheres.
- Calculate the surface area of three-dimensional figures such as rectangular solids, cubes, cylinders, and spheres.

- Probability
- Determine empirical probabilities.
- Determine theoretical probabilities using the definition.
- Use the fact that the sum of the probabilities of all possible outcomes of an experiment is 1.
- Write the sample space for an experiment.
- Use tree diagrams to determine probabilities.
- Find the probability of event A
*or*event B. - Find the probability of event A
*and*event B. - Solve probability problems by using combinations.

- Counting Principles
- Use the formula
*n(A ∪ B) = n(A) + n(B) - n(A ∩ B)*. - Count the number of items or events by listing them.
- State and apply the Fundamental Counting Principle.

- Use the formula
- Permutations and Combinations
- Evaluate factorials.
- Define the terms permutation and combination.
- Count permutations.
- Calculate a specified permutation.
- Count combinations
- Calculate a specified combination

- Descriptive Statistics
- Organize and display data using tools such as frequency distributions, histograms, frequency polygons, and stem-and-leaf displays.
- Find and interpret measures of central tendency such as mean, median, and mode. Midrange is optional.
- Find and interpret measures of dispersion such as range and standard deviation.
- Apply the empirical rule which states the following. In any normal distribution,
- Approximately 68% of all the data lies within one standard deviation of the mean (in both directions).
- Approximately 95% of all the data lies within two standard deviations of the mean (in both directions).
- Approximately 99.7% of all the data lies within three standard deviations of the mean (in both directions).

- Determine the relative relationships between the mean, median, and mode for various distributions.

## Department Policies

- Comprehensive Final Assessment