Dual Enrollment Program DE Course: Math 1100 The Nature of Mathematics

Not for science, engineering or mathematics majors. For students who desire an exposure to mathematics as part of a liberal education.

Using mathematics to solve problems and reason quantitatively. Topics include set theory, logic, personal finance, and elementary number theory.

This is an LSU Integrative Learning Core (ILC) course that awards general education credit.

Note: Math 1100 is designed for fine arts, liberal arts, political science, communication studies, and most social science majors. It covers topics that students on these career paths will need, such as problem solving and critical thinking, set theory, logic statements and arguments, personal finance, and elementary number theory. Topics may vary. This course is offered only in the fall semester and should be followed by Math 1029 in the spring semester. Students can use the same MyLab Math access code for this course and for Math 1029.

Course Details

High School Code: 160350 Discrete Math
Louisiana Common Course Numbering: CMAT 1204 The Nature of Mathematics
Number of Credit Hours: 3
Course Offered: Fall
Student Prerequisite: Student must meet one of the three options for BOR student eligibility listed in the LSU DE Catalog.
Teacher Prerequisite: Teacher must complete summer training prior to the school year in which the course is planned to be taught.

Topics and Objectives

Chapter and section numbers refer to Thinking Mathematically, 8th edition

1.1 Inductive and Deductive Reasoning

(14 exercises)

Find a counterexample
Use inductive reasoning to identify a pattern
Use deductive reasoning to prove a conjecture

2.1 Basic Set Concepts

(26 exercises)

Determine whether a collection is a set
Use three methods to represent sets
Identify and name special sets
Use symbols to represent “is an element of” and “is not an element of”
Determine a set's cardinal number
Identify and give examples of equivalent and equal sets

2.2 Subsets

(21 exercises)

Identify subsets and use the notation for subsets
Identify proper subsets and use the notation for proper subsets
List the subsets of a given set

2.3 Venn Diagrams and Set Operations

(28 exercises)

Use Venn diagrams to visualize relationships between two sets
Identify universal sets for given sets
Find the complement of a set
Perform operations with sets, including unions or complements
Determine sets involving set operations from a Venn diagram
Solve applications involving Venn diagrams and set operations

2.4 Set Operations and Venn Diagrams with Three Sets

(22 exercises)

Perform set operations with three sets
Use Venn diagrams to represent three sets
Use Venn diagrams to prove equality of sets

3.1 Statements, Negations, and Quantified Statements

(25 exercises)

Identify English sentences that are statements
Form the negation of a statement
Express negations using symbols
Translate a negation represented by symbols into English
Write negations of quantified statements

3.2 Compound Statements and Connectives

(35 exercises)

Express compound statements in symbolic form given two simple statements
Express symbolic statements with parentheses in English
Express compound statements in symbolic form given three simple statements
Express statements in words or symbolic form using the dominance of connectives

3.3 Truth Tables for Negation, Conjunction, and Disjunction

(25 exercises)

Determine truth values using the definitions of negation, conjunction, and disjunction
Construct truth tables
Indicate the conditions that make a compound statement true using truth tables
Determine the truth value of a compound statement for a specific case

3.4 Truth Tables for the Conditional and the Biconditional

(11 exercises)

Construct truth tables for conditional statements
Construct truth tables for biconditional statements
Determine whether a statement is a tautology, a self-contradiction, or neither
Determine the truth value of a conditional or biconditional statement for a specific case

3.5 Equivalent Statements and Variations of Conditional Statements

(10 exercises)

Show that statements are equivalent using a truth table
Write the converse, inverse, and contrapositive for a conditional statement

3.6 Negations of Conditional Statements and De Morgan’s Laws

(12 exercises)

Write the negation of a conditional statement
Use De Morgan's laws to write equivalent statements

5.1 Number Theory: Prime and Composite Numbers

(23 exercises)

Use rules of divisibility to determine if one number is divisible by another number
Write the prime factorization of a composite number
Find the greatest common divisor of two numbers
Find the least common multiple of two numbers
Determine whether or not given numbers are perfect numbers
Determine whether or not given numbers are prime number

5.2 The Integers; Order of Operations

(24 exercises)

Use the symbols $\lt$ and $\gt$ to compare values
Find the absolute value of an integer
Perform operations with integers
Use the order of operations to simplify expressions

5.3 The Rational Numbers

(14 exercises)

Reduce rational numbers
Convert between mixed numbers and improper fractions
Convert between rational numbers and decimals
Perform operations with rational numbers

5.4 The Irrational Numbers

(18 exercises)

Simplify or evaluate square roots
Perform operations with square roots

8.1 Percent, Sales Tax, and Discounts

(20 exercises)

Express a fraction as a percent
Express a decimal as a percent
Express a percent as a decimal
Use the percent formula A=PB to find the unknown

8.3 Simple Interest

(16 exercises)

Calculate simple interest
Use the future value formula to calculate the value of an unknown
Solve applications involving simple interest

8.4 Compound Interest