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Course Content Summary
Course Prefix and Number -- Course Title
MTH 120: Introduction to Mathematics (3 cr.)
VCCS Course Description
Introduces number systems, logic, basic algebra, and descriptive statistics. Includes systems of
equations, basic geometry. Lecture 3 hours per week.
General Course Purpose
To provide the mathematical background necessary for the student pursuing the A.A.S. degree.
Course Prerequisites/Corequisites
Prerequisite: MTH 120 eligible or MTE 1-3 (two-year shelf life and ENG 111 eligible.
General Education Outcomes
Degree graduates will demonstrate the ability to:
GEO2.6
GEO 6.1
GEO 6.2
GEO 6.3
GEO 6.4
GEO 6.5
GEO 6.6
Use problem solving skills
Use logical and mathematical reasoning within the context of various
disciplines
Interpret and use mathematical formulas
Interpret mathematical models such as graphs, tables, and schematics, and
draw inferences from them
Use graphical, symbolic, and numerical methods to analyze, organize, and
interpret data
Estimate and consider answers to mathematical problems in order
to determine reasonableness
Represent mathematical information numerically, symbolically, and
visually using graphs and charts
Course Outcomes
Upon completing the course, the student will be able to:
1. Demonstrate and apply the properties of the real number system
a. Determine the classification of numbers.
Departmental Approval: Spring 2014
b.
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i. Natural numbers (counting numbers) 1, 2, 3, …
ii. Whole numbers – 0, 1, 2, 3, …
iii. Integers -- …, -3, -2, -1, 0, 1, 2, 3, …
Determine whether an integer is divisible by another integer.
Distinguish between prime and composite numbers.
Determine the prime factorization of a natural number.
Apply the Fundamental Theorem of Arithmetic.
Find the greatest common divisor of a set of numbers.
Find the least common multiple of a set of numbers.
Distinguish between rational and irrational numbers.
Perform operations involving irrational numbers.
Simplify expressions involving rational and irrational numbers.
Express a decimal as a fraction.
Perform operations with fractions (without the use of a calculator).
Apply the fundamental law of rational numbers.
Express fractions in percent notation and vice versa.
Perform operations with rational and irrational numbers using a scientific
calculator.
Simplify exponential and radical expressions.
Convert numbers expressed in scientific notation on the calculator to standard
decimal notation.
2. Express numbers and perform operations with numbers in bases other than ten
a. Express Hindu-Arabic (base ten) numerals in expanded exponential notation.
b. Understand and interpret place value systems of numeration.
c. Express Hindu-Arabic numerals (base ten) as a numeral in in bases other than ten,
including binary, octal, and hexadecimal bases.
d. Convert a numeral in a base other than ten into a base ten numeral.
e. Perform addition and subtraction in number systems of base other than ten.
f. Perform multiplication and division in number systems of base other than ten.
3. Recognize logical forms.
a. Identify and write simple logic statements.
b. Utilize connectives to create compound logic statements.
i. Conjunctions.
ii. Disjunctions (Exclusive Or and Inclusive Or).
iii. Negations.
iv. Conditionals (If, Then).
v. Biconditionals (If and only if).
c. Use quantifiers in connection with logic statements.
d. Express logic statements symbolically.
e. Translate an English language statement into a symbolic statement.
f. Translate a symbolic logic statement into an English language statement.
g. Create the negation of quantitative logic statements.
h. Construct truth tables to determine the truth values of logic statements.
i. Use truth tables to determine equivalency of logic statements.
j. Apply De’Morgan’s Laws to create equivalent logic statements.
k. Understand and use variations of conditional logic statements.
Departmental Approval: Spring 2014
i. Converse
ii. Inverse
iii. Contrapositive
4. Apply the concepts of basic algebra to solve linear equations and inequalities.
a. Perform arithmetic operations with variables
b. Apply the order of operations principles to simplify and evaluate algebraic
expressions.
c. Solve linear equations in one variable by applying:
i. Addition property
ii. Multiplication property.
d. Use ratios and proportions to solve application problems.
e. Use formulas to solve application problems.
f. Solve an equation (or formula) for a specified variable in terms of the other
variables in the equation.
g. Create and solve mathematical models (linear equations in one variable) to solve
application problems.
h. Create and solve variation models to solve application problems.
i. Solve and graph linear inequalities in one variable.
j. Graph linear equations in one variable by:
i. Plotting points
ii. Using x-axis and y-axis intercepts
iii. Using the slope-intercept form of a linear equation
5. Solve Systems of equations by:
a. Graphing
b. Linear combinations
c. Substitution
6. Apply and interpret the tools of descriptive statistics.
a. Understand the language (terms) of statistical data analysis.
b. Differentiate among the various statistical sampling techniques.
c. Create and interpret statistical tables and frequency distributions.
d. Use and interpret graphical displays of statistical data:
i. Circle graphs
ii. Histograms
iii. Frequency polygons
e. Calculate measures of central tendencies:
i. mean,
ii. median,
iii. mode
iv. Mid-range
v. Measures of position
f. Calculate measures of dispersion:
i. variance
ii. standard deviation
iii. Range
Departmental Approval: Spring 2014
g. Apply the normal distribution.
i. 68% - 95%-99.7% rule
ii. Calculate and apply the Z-score
7. Apply the concepts of Euclidean geometry.
a. Classify geometric figures.
b. Calculate measurements associated with geometric figures:
i. Perimeter
ii. Area
iii. Angle measurements
c. Calculate measurements in the metric system.
d. Convert measurements between the English system and metric system of
measurement.
e. Solve problems involving angles.
f. Apply the Pythagorean Theorem.
g. Identify specific special polygons.
Major Topics to be Included
1. Properties of the Real Number System
2. Number Systems
3. Logic
4. Linear Equations and Inequalities
5. Systems of Equations
6. Statistics
7. Geometry
Departmental Approval: Spring 2014