Introduction to Mathematics I - DSU-108

Course Description: This six-week online course develops a rudimentary understanding of mathematical processes. Problem solving, sets, logic, numeration systems, real number systems and other mathematical systems and topics in algebra are addressed in this course that seeks to utilize real-world examples and problem solving to introduce mathematical concepts. This course, and its companion, Introduction to Mathematics II (IIEI-109) create a strong foundation in basic mathematical concepts.

Prerequisite: None

Course Credit: 3 Credit Hours

Major Course Topics & Course Outcomes

As a result of the group and individual activities included in this course, the student will acquire the following knowledge and skills that can be applied to the workplace:

Problem Solving

• Explain the two types of mathematics
• Explain the difference between inductive and deductive reasoning
• State the steps for the basic problem-solving procedure
• Solve problems using the basic problem-solving procedures
• Solve problems using estimation.

Sets

• Define set, element and null set.
• Designate sets in three different ways
• Classify sets as finite or infinite
• Identify equal sets and equivalent sets
• Find subsets and proper subsets of a set
• Find the union and intersection of two sets
• Find the complement of a set
• Draw Venn diagrams for set operations
• Solve survey and classification problems using sets
• Find the general term of an infinite set
• Determine whether or not a set is infinite

Logic

• Determine whether or not a sentence is a statement
• Classify statements as simple or compound
• Write compound statements in symbols using the four basic connectives
• Write symbolic statements in words
• Construct truth tables for statements
• Identify the type of statement according to the hierarchy of connectives
• Determine whether or not two statements are logically equivalent
• Write the converse, inverse or contrapositive of a statement
• Determine the validity of arguments by using truth tables
• Determine whether or not an argument is valid using Euler circles 

Numeration Systems

• Define a numeration system
• Convert Egyptian numerals to Hindu-Arabic numerals and Hindu-Arabic numerals to Egyptian numerals
• Perform addition and subtraction using Egyptian numerals
• Convert Babylonian numerals to Hindu-Arabic numerals and Hindu-Arabic numerals to Babylonian numerals
• Convert Hindu-Arabic numerals to Roman numerals and Roman numerals to Hindu-Arabic numerals
• Determine the place value of a digit in a Hindu-Arabic numeral
• Write a Hindu-Arabic numeral in expanded notation
• Convert a base ten number to a base five number and vice versa
• Perform addition and subtraction using base five numbers
• Convert base ten numbers to numbers written in other bases, such as base two and base three and vice versa

Real Number Systems

• Distinguish between a prime number and a composite number
• Find the factors of a number
• Find a prime factorization of a number
• Find the greatest common factor of two or more numbers
• Find the multiples of a number
• Find the least common multiple of two or more numbers
• Add, subtract, multiply and divide integers
• Use the order of operations to simplify expressions
• Add, subtract, multiply and divide rational numbers
• Change fractions to decimals and decimals to fractions
• Add, subtract, multiply and divide irrational numbers
• Identify the properties of real numbers
• Simplify expressions using the properties of exponents
• Convert large and small decimal numbers into numbers in scientific notation
• Convert numbers in scientific notation into numbers in decimal notation.
• Perform multiplication and division with numbers written in scientific notation
• Write the terms of an arithmetic or geometric sequence
• Find specific terms of an arithmetic or geometric sequence
• Find the sum of n terms of an arithmetic or geometric sequence

Other Mathematical Systems

• Identify the structure of a mathematical system.
• Perform addition, subtraction, and multiplication on the 12-hour clock.
• Determine which properties, such as closure, commutativity, etc. are true for the operation on the 12-hour clock.
• Perform operations and determine which properties are true for modular systems.
• Perform operations and determine which properties are true for mathematical systems without numbers.

Topics in Algebra

• Simplify algebraic expressions by combining like terms and using the distributive property
• Evaluate algebraic expressions and formulas
• Solve linear equations in one variable
• Identify equations that have no solution or infinitely many solutions
• Translate verbal expressions into mathematical symbols
• Solve real-world problems using linear equations
• Solve linear inequalities and graph the solutions on the number line
• Solve real-world problems using linear inequalities
• Write ratios as fractions
• Simplify ratios
• Solve proportions
• Solve real-world problems using proportions and variations
• Solve quadratic equations using factoring or quadratic formula
• Solve real-world problems using quadratic equations

Course Texts:

There is one textbook required for this course. You can obtain it through your favorite bookstore.

Mathematics in Our World
Allan G. Bluman
McGraw Hill Publishers
ISBN: 0-07-245107-6

 

Please note that textbooks are subject to change. Please contact your advisor before purchasing the textbook for your class to confirm.