MAT 100 - Introduction to College Mathematics - Textbook

Learning Objectives

• Describe memberships of sets, including the empty set, using proper notation, and decide whether given items are members and determine the cardinality of a given set.
• Describe the relations between sets regarding membership, equality, subset, and proper subset, using proper notation.
• Perform the operations of union, intersection, complement, and difference on sets using proper notation.
• Be able to draw and interpret Venn diagrams of set relations and operations and use Venn diagrams to solve problems.
• Recognize when set theory is applicable to real-life situations, solve real-life problems, and communicate real-life problems and solutions to others

This module is divided into four sections/sub-modules:

Sub-Module 1: Basics of Set. 

• What is set?
• Three ways to write a set: "verbal description", "roster form" , "set builder notation"
• Empty set, element of a set and the corresponding notation
• Subset and proper subset and its corresponding notation

Sub-Module 2: Union, intersection, complement and universal set. 

• Union of sets
• Intersection of sets
• Complement of sets
• Universal sets
• Operation involving all of the above

Sub-Module 3: Venn diagram. 

• What is Venn diagram and how to draw it
• How to represent different section in Venn diagram using set notation
• How to represent set operation using Venn diagram

Sub-Module 4: Survey problem. 

• Survey questions involving two sets
• Survey questions involving three sets
• Advance survey questions

Reading Notes

Assessments

Reading Notes

Videos

Assessments

Reading Notes

Videos

Please watch these videos in the order they are given.

Assessments

Reading Notes

Videos

Please watch the videos in the order they are listed. 

Assessments

Complete this assessment after you finish all sub-modules in Module 1.

CC Licensed Content, Original Content

• Three ways to write a set. Authored by: Tanvir Prince At: Hostos Community College. License: CC BY 4.0.

• Empty Set Elements of Set. Authored by: Tanvir Prince At: Hostos Community College. License: CC BY 4.0.

• Subset Proper Subset. Authored by: Tanvir Prince At: Hostos Community College. License: CC BY 4.0.

• Assessment Sub-Module 2: Operation on Set. - Questions. Authored by: David Lippman. License: IMathAS Community License (GPL + CC-BY).

• Assessment Sub-Module 3: Venn Diagram. - Questions. Authored by: David Lippman. License: IMathAS Community License (GPL + CC-BY).

• Assessment Sub-Module 4: Survey. Authored by: David Lippman. License: IMathAS Community License (GPL + CC-BY).

CC Licensed Content, Shared Previously

• Sets. Authored by: David Lippman. Located at: http://www.opentextbookstore.com/mathinsociety/. Project: Math in Society. License: CC BY-SA.

• Language of sets. Authored by: Timothy Peil, Ph.D. License: CC BY-SA.

• Universal set and Venn diagrams. Authored by: Timothy Peil, Ph.D. License: CC BY-SA.

• Set operations – unions. Authored by: Timothy Peil, Ph.D. License: CC BY-SA.

• Set operations – Intersection. Authored by: Timothy Peil, Ph.D. License: CC BY-SA.

• Sets: union, intersection, and complement. Authored by: David Lippman. Located at: https://youtu.be/qTUWzBvI9bk. License: CC BY-SA.

• Venn diagram. Found in: Sets. Authored by: David Lippman. Located at: http://www.opentextbookstore.com/mathinsociety/. Project: Math in Society. License: CC BY-SA.

• Sets: Drawing a Venn diagram. Authored by: David Lippman. Located at: https://youtu.be/CPeeOUldZ6M. License: CC BY-SA.

• Sets: Writing an expression for a Venn diagram region. Authored by: David Lippman. Located at: https://youtu.be/VfC8rhLdYYg. License: CC BY-SA.

• Sets: Cardinality. Authored by: David Lippman. Located at: https://youtu.be/wErcETeKvrU. License: CC BY-SA.

• Survey Question. Found in: Sets. Authored by: David Lippman. Located at: http://www.opentextbookstore.com/mathinsociety/. Project: Math in Society. License: CC BY-SA.

• Sets: Surveys with two sets. Authored by: David Lippman. Located at: https://youtu.be/SKc-gIfPv9o. License: CC BY-SA.

• Sets: Surveys with three sets. Authored by: David Lippman. Located at: https://youtu.be/iCDJsOXoySY. License: CC BY-SA.

• Review Exercises for Module 1 - Set Theory. Found in: Sets. Authored by: David Lippman. Located at: http://www.opentextbookstore.com/mathinsociety/. Project: Math in Society. License: CC BY-SA.