College Course Content Summary
MTH 151: Mathematics for the Liberal Arts I (3 cr.)
VCCS Course Description
Presents topics in sets, logic, numeration systems, geometric systems, and elementary computer
concepts. Lecture 3 hours per week.
General Course Purpose
The general purpose of this course is to give the student an appreciation for the uses of
mathematics in the contemporary world and to develop ability by the student to solve certain
mathematical problems in a logical manner.
Course Prerequisites/Corequisites
Prerequisites: MTE 1-5 or satisfactory score on an appropriate proficiency examination.
MTH 151 and MTH 152 do not have to be taken in sequence.
General Education Objectives
Degree graduates will demonstrate the ability to:
GEO 2.6:
GEO 6.1:
GEO 6.2:
GEO 6.3:
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
GEO 6.4: Use graphical, symbolic, and numerical methods to analyze, organize, and interpret
data
GEO 6.5: Estimate and consider answers to mathematical problems in order to determine
reasonableness
GEO 6.6: Represent mathematical information numerically, symbolically, and visually using
graphs and charts
Departmental Approval: Spring 2014
Course Outcomes
"MTH 151 and 152 provide a liberal arts based study of mathematics and are intended to connect
mathematics to the world. In this light, great effort should be made to provide students
opportunity to explore and apply the mathematics content throughout the course."
Upon the completion of the course, the student should be able to:
A. Perform operations on sets and solve problems utilizing set operations
1. Designate a set by word description, listing or set builder notation.
2. Define and recognize the empty set.
3. Find the cardinal number of a set.
4. Determine whether a set is finite or infinite.
5. Determine if two sets are equal.
6. Determine if two sets are equivalent.
7. Use the symbols  and  appropriately.
8. Determine the number of subsets and proper subsets of a given set.
9. Use the following symbols appropriately: , , and  .
10. Draw Venn diagrams to illustrate relationships among sets.
11. Find the complement of a set and the intersection, union, or difference of two
sets.
12. Find the Cartesian product of two sets.
13. Use the cardinal number formula to find the number of elements in the union of
two sets.
14. Find the number of elements in the Cartesian product of two sets.
15. Draw and shade Venn diagrams with 2 or 3 sets.
16. Use Venn diagrams to prove the equality of sets.
17. Solve survey problems with a Venn diagram.
B. Analyze logical structures for truth value and validity
1. Identify English sentences that are mathematical statements.
2. Express simple and compound statements with symbols.
3. Use the following symbols appropriately: ∧, ∨, ~, →, and ↔.
4. Form the negation of a simple, compound or quantified statement.
5. Construct truth tables for negation, conjunction, disjunction, conditional, and
biconditional.
6. Determine the validity of arguments using truth tables
7. Apply DeMorgan's Laws to negate conjunctions and disjunctions.
8. Recognize a tautology.
9. Given a conditional statement be able to construct its converse, inverse and
contrapositive.
10.
Use truth tables to show that two statements are equivalent.
11. Use Euler diagrams to analyze arguments.
C. Demonstrate the relationship between place values and number bases
1. Evaluate an exponential expression.
2. Write a Hindu-Arabic numeral in expanded form and expanded form as a HinduArabic numeral.
Departmental Approval: Spring 2014
3. Convert numbers from the ancient Egyptian and/or traditional Chinese
numeration systems into the Hindu-Arabic system and vice versa.
4. Perform computations using the Egyptian algorithm, the Russian peasant
method, the lattice method and/or an abacus.
5. Convert a number from base ten to another base and from another base into base
ten.
D. Explore Euclidean geometry and non-Euclidean geometry
*Any questions that require the use of factoring, solving quadratics, or the use of rules of
exponents are not required as these concepts are not part of the course prerequisite
content.
1. Solve application problems by applying basic concepts of Euclidean geometry.
2. Discuss the differences between Euclidean and non-Euclidean geometries.
3. Classify objects topologically by genus.
4. Apply Euler's method for determining if a path is traversable.
E. Personal Finance
1. Calculate simple/compound interest, and future/present value.
2. Determine the annual effective yield.
3. Calculate payments for installment loans and revolving loans.
4. Determine the APR for loans.
5. Calculate the regular monthly payment for a fixed rate mortgage.
6. Explain the differences between stocks and bonds.
7. Discuss the advantages and disadvantages of credit cards.
F. Apply computer concepts (do one of the following)
1. Research a math topic on the Internet.
2. Use Blackboard to complete quizzes and/or other assignments.
3. Use a math software package to solve an application problem.
Major Topics to be Included
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Perform operations on sets and solve problems utilizing set operations
Analyze logical structures for truth value and validity
Demonstrate the relationship between place values and number bases
Explore Euclidean geometry and non-Euclidean geometry
Apply computer concepts
Personal Finance
Departmental Approval: Spring 2014