Our Courses
The Mathematics and Statistics Division at Bluegrass Community and Technical College offers a broad range of mathematics and statistics courses that meet the varied needs of students who are pursuing their academic goals.
Courses range from basic arithmetic to college algebra, contemporary mathematics, geometry, trigonometry, elementary calculus, calculus, finite mathematics, mathematics for business, applied mathematics, and statistics.
Through such coursework, students acquire the ability to think logically and abstractly, as well as develop the problemsolving and computational skill necessary in all fields of study. Most of the courses within the mathematics curriculum fulfill general education and transfer requirements.
Math & Stats Flowchart
BCTC Courses
MA 111 Introduction to Contemporary Mathematics (3)  Course Information
An introduction to concepts and applications of mathematics, with examples drawn from
such areas as voting methods, apportionment, consumer finance, graph theory, tilings,
polyhedra, number theory and game theory. This course is not available for credit
to persons who have received credit in any mathematics course of a higher number with
the exceptions of MA 112, 123, 162, 201 and 202. This course does not serve as a prerequisite
for any calculus course. Credit not available on the basis of special examination.
Prerequisite: Two years of high school algebra and a Math ACTE score of 19 or above, or MA 108R,
or math placement test.
MA 113 Calculus I (4)  Course Information
A course in onevariable calculus, including topics from analytic geometry. Derivatives
and integrals of elementary functions (including the trigonometric functions) with
applications. Lecture, three hours; recitation, two hours per week. Students may not
receive credit for MA 113 and MA 137.
Prerequisite: Math ACT of 27 or above, or math SAT of 620 or above, or MA 109 and MA 112, or MA
110, or consent of the department. Students who enroll in MA 113 based on their test
scores should have completed a year of precalculus study in high school that includes
the study of the trigonometric function.
Note: Math placement test recommended.
MA 114 Calculus II (4)  Course Information
A second course in Calculus. Applications of the integral, techniques of integration,
convergence of sequence and series, Taylor series, polar coordinates. Lecture, three
hours; recitation, two hours per week.
Prerequisite: A grade of C or better in MA 113, MA 137, or MA 132.
Finite mathematics with applications to business, biology, and the social sciences.
Linear functions and inequalities, matrix algebra, linear programming, probability.
Emphasis on setting up mathematical models from stated problems.
Prerequisite: MA 109 or equivalent.
MA162FINITE MATHEMATICSAND ITS APPLICATIONS (UK Course) (3credit hours)
Official Course Description  Finite mathematics with applications to business, biology, and the social sciences. Linear functions and inequalities, matrix algebra, linear programming, probability. Emphasis on setting up mathematical models from stated problems.Prerequisites: MA 109 or equivalent. 
OFFICIAL COURSE COMPETENCIES/OBJECTIVES
 State the geometric interpretation of the solution to a linear programming problem
 Determine whether two events are independent or not
 Determine whether two events are mutually exclusive or not
 Use proper matrix notation to organize arrays of numbers and represent equations
 Write and understand permutations and combinations in their standard notation
 Write and understand probabilities in standard notation
 Write and understand set notation for unions, intersections, and complements
 Represent sets within Venn Diagrams and understanding such representations
 Perform matrix operations
 Find the inverse of a matrix
 Find the simple, compound, or conditional probability
 Determine unions, intersections, and complements of sets and events
 Determine the number of ways a task can be performed using counting principles
 Solve a system of linear equations by substitution, elimination, using matrix row operations, and using matrix equations
 Solve a linear programming problem graphically and by the simplex method
 Determine whether a problem involves permutations, combinations, or basic counting methods
 Determine whether a problem involves simple, compound, or conditional probability
 Set up and solve an application involving systems of equations
 Set up and solve an application involving linear programming
 Solve multistep problems that contain simple, compound and conditional probabilities
OFFICIALCOURSE OUTLINE (Approved Spring 2003)
 Linear Systems
 Solve linear systems of two or more variables by graphing, substitution, elimination or GaussJordan methods.
 Recognize consistent, inconsistent, and dependent systems
 Write solutions in parametric form
 Set up and solve applied problems
 Matrix Operations
 Recognize and be able to write coefficient matrices and augmented matrices
 Be able to define and identify square matrices, equal matrices, and matrices dimensions.
 Add and subtract matrices
 Perform scalar multiplication
 Perform matrix multiplication
 Find inverses
 Use inverses to solve systems
 Linear Inequalities
 Graph inequalities
 Graph systems of inequalities
 Identify corner points and feasible regions
 Solve optimization problems by substituting corner points into objectivefunctions.
 Identify standard maximization and minimization problems.
 Solve standard maximization simplex problems
 Solve duality problems using simplex
 Convert nonstandard optimization problems to standard maximum problems:
 Problems with ≥ constraints
 Problems with = constraints
 Problems with negative numbers on the righthand side of constraints
 Problems with a minimized objective function.
 Identify simplex problems without a single solution
 Multiple solutions
 Unbounded solutions
 No solutions
 Solve applied optimization problems using simplex and/or graphing methods.
 Sets
 Use, define and identify set builder notation, empty or null set, universal set, equal sets, subsets, proper subsets, elements, union, intersection, complements, disjoint sets
 Use and solve applied problems with Venn Diagrams
 Identify the number of elements in sets
 Combinatorics
 Define and use the Multiplication Rule on applied counting problems
 Define and use the Addition Rule on applied counting problems
 Solve applied permutation problems
 Solve applied combination problems
 Probability
 Identify and define experiment, outcome, trial, sample space, event, empirical probability, randomoutcomes
 Find probabilities of equally likely events in applied problems
 Find probabilities of compound events in applied problems
 union
 intersection
 complement
 Define and identify mutually exclusive events and independent events
 Solve applied conditional probability problems
 Solve applied probability problems using Baye’s Rule
 Markov Chains (OPTIONAL)
 Identify and define state matrices, transition matrices, markov chains, and steadystate matrices
 Solve applied problems involving Markov Chains
 Find steadystate matrices
 Identify regular matrices
 Solve applied problems using Bernouilli’s Formula (OPTIONAL)
GENERAL EDUCATION COMPETENCIES
 Knowledge of human cultures and the physical and natural worlds through study in the sciences and mathematics,social sciences, humanities, histories, languages, and the arts
 Intellectual and practical skills, including
 inquiry and analysis
 critical and creative thinking
 written and oral communication
 quantitative literacy
 information literacy
 teamwork and problem solving
 Personal and social responsibility, including
 civic knowledge and engagement (local and global)
 intercultural knowledge and competence
 ethical reasoning and action
 foundations and skills for lifelong learning
 Integrative and applied learning, including synthesis and advanced accomplishment across general and specializedskills.
STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING (Approved Fall 2017)
In MA162, students will learn to:
 Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):
 Determining whether a problem involves permutations, combinations, or basic counting methods
 Determining whether a problem involves simple, compound, or conditional probability
 Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by(Gen Ed Comp A, B, C):
 Stating the geometric interpretation of the solution to a linear programming problem.
 Using proper matrix notation to organize arrays of numbers and represent equations.
 Writing and understanding probabilities in standard notation.
 Representing sets within Venn Diagrams and understanding such representations
 Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):
 Performing matrix operations.
 Finding the simple, compound, or conditional probability.
 Determining unions, intersections, and complements of sets and events.
 Determining the number of ways a task can be performed using counting principles.
 Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):
 Solving a system of linear equations by substitution, elimination, using matrix row operations, and using matrix equations.
 Solving a linear programming problem graphically and by the simplex method.
 Solving multistep problems that contain simple, compound and conditional probabilities.
 Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis by (Gen Ed Comp A, D):
 Setting up and solving an application involving systems of equations.
 Setting up and solving an application involving linear programming.
MA 193 Supplementary Mathematics Workshop I: (Subtitle required) (12)  Course Information
Laboratory offered (only) as an adjunct to certain mathematics lecture courses. Offered
only on a pass/fail basis.
Corequisite: Set by instructor.
MA 194 Supplementary Mathematics Workshop II: (Subtitle required) (12)  Course Information
Laboratory offered (only) as an adjunct to certain mathematics lecture courses. Offered
only on a pass/fail basis.
Corequisite: Set by instructor.
Sets, numbers and operations, problem solving and number theory. Recommended only
for majors in elementary and middle school education.
Prerequisite: MA 109 or MA 111 or consent of department.
A second course in Calculus. Applications of the integral, techniques of integration, convergence of sequence and series, Taylor series, polar coordinates. Lecture, three hours; recitation, two hours per week.
Prerequisite: A grade of C or better in MA 113, MA 137, or MA 132.
MA 114 CALCULUS II (UK Course) (4 credit hours)
Official Course Description  A second course in Calculus. Applications of the integral, techniques of integration,
convergence of sequence and series, Taylor series, polar coordinates. Lecture, three hours; recitation, two hours per week. Prerequisite: A grade of C or better in MA113, MA137, or MA132. 
OFFICIAL COURSE COMPETENCIES/OBJECTIVES (Approved Fall 2017)
Upon completion of this course, the student can:
1. Use integration to find the area between curves, volume of solids of revolution, and the arc length of graphs of a function. 2. Use integration to solve application problems involving average value and work. 3. Compute integrals using various techniques including the methods of substitution, integration by parts, trigonometric substitution, partial fractions, and tables. 4. Evaluate improper integrals. 5. Determine and compute convergence/divergence of sequences and series. 
6. Find power series and Taylor and Maclaurin series 7. Represent curves by parametric equations, and 8. Determine the slope of a tangent line to and the 9. Calculate the slope of a tangent line to and the arc 
OFFICIAL COURSE OUTLINE (Approved Fall 2017)
 Applications of Integrals
 Area Between Curves
 Volumes of Revolution
 Disks
 Washers
 Shells
 Average Value
 Work
 Arc Length
 Integration Techniques/Strategies
 Integration by Parts
 Trigonometric Integrals
 Powers of sin(x), cos(x), sec(x) & tan(x)
 Products of sin(x) & cos(x)
 Products of sec(x) & tan(x)
 Arbitrary Combinations of Trigonometric Functions
 Trigonometric Substitution
 Partial Fractions
 Long Division
 Completing the Square
 Rationalizing Substitutions
 Tables
 Improper Integrals
 Infinite Intervals
 Discontinuous Integrands
 Sequences
 Definition
 Convergent
 Divergent
 Definition
 Series
 Definition
 Convergence
 Divergence
 Absolute Convergence
 Conditional Convergence
 Geometric Series
 PSeries
 Alternating Series
 Tests
 Test for Divergence
 Integral Test
 Comparison Tests
 Direct Comparison Test
 Limit Comparison Test
 Alternating Series Test
 Ratio Test
 Root Test
 Power Series
 Radius of Convergence
 Interval of Convergence
 Properties
 Derivative
 Integral
 4. Expressing Functions as Power Series
 Taylor Series
 Maclaurin Series
 Definition
 Parametric Equations
 Conversion to Cartesian Equation
 Parametric Curves
 Graphing
 Tangents
 Areas
 Arc Length
 Polar Coordinates
 Conversions
 Polar to Cartesian
 Cartesian to Polar
 Polar Curves
 Graphing
 Tangents
 Areas
 Arc Length
 Conversions
GENERAL EDUCATION COMPETENCIES
 Knowledge of human cultures and the physical and natural worlds through study in the sciences and mathematics, social sciences, humanities, histories, languages, and the arts.
 Intellectual and practical skills, including
 inquiry and analysis
 critical and creative thinking
 written and oral communication
 quantitative literacy
 information literacy
 teamwork and problem solving
 Personal and social responsibility, including
 civic knowledge and engagement (local and global)
 intercultural knowledge and competence
 ethical reasoning and action
 foundations and skills for lifelong learning
 Integrative and applied learning, including synthesis and advanced accomplishment across general and specialized skills.
STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING (Approved Fall 2017)
In MA 114, students will learn to:
 Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):
 Determining and computing convergence/divergence of sequences and series.
 Finding power series and Taylor and Maclaurin series representations of a given function
and determining
their intervals of convergence.
 Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by (Gen Ed Comp A, B, C):
 Representing curves by parametric equations, and applying the methods of calculus to parametric curves.
 Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):
 Computing integrals using various techniques including the methods of substitution,
integration by parts,
trigonometric substitution, partial fractions, and tables.  Evaluating improper integrals.
 Determining the slope of a tangent line to and the arc length of the graph of a parametric function.
 Calculating the slope of a tangent line to and the arc length of a polar graph, and
determining the volume
and surface area of solids formed by revolving regions bound by polar functions.
 Computing integrals using various techniques including the methods of substitution,
integration by parts,
 Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):
 Using integration to solve application problems involving average value and work.
 Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis by (Gen Ed Comp A, D):
 • Using integration to find the area between curves, volume of solids of revolution,
and the arc length of
graphs of a function.
 • Using integration to find the area between curves, volume of solids of revolution,
and the arc length of
Sets, numbers and operations, problem solving and number theory. Recommended only for majors in elementary and middle school education.
Prerequisite: MA 109 or MA 111 or consent of department.
MA 202 MATHEMATICS FOR ELEMENTARY TEACHERS (UK Course) (3 credit hours)
Official Course Description  Algebraic reasoning, introduction to statistics and probability, geometry, and measurement. Prerequisites: A grade of “C” or better in MA 201. Also recommended: a course in logic (e.g. PHI 120) or a course in calculus (e.g. MA 123). 
OFFICIAL COURSE COMPETENCIES/OBJECTIVES
Upon completion of this course, the student can:
 Develop an understanding of fundamental concepts of geometry including point, line, angle, and plane.
 Describe data and its characteristics including dispersion and central tendency, and solve problems involving these concepts.
 Understand concepts of symmetry such as congruence, similarity, proportionality, and isometries as they relate to various plane shapes.
 Select the appropriate representation for data display and interpret information presented in such graphical displays including bar graphs, line plots, circle graphs, and stem and leaf plots.
 Practice the process of measurement and identify units in the standard systems of measurement.
 Calculate the perimeter and area of various different shapes and the volume of various solids.
 Draw reasonable conclusions based on the characteristics of a data set, and solve problems that involve finding the probability of an event.
 Demonstrate an understanding of and solve application problems involving the concepts of permutations and combinations.
 Identify projections, cross sections, and decompositions of common two dimensional and three dimensional figures.
 Use deductive reasoning and counter examples to prove or disprove statements about two dimensional and three dimensional figures.
 Develop notions about probability of events empirically through simulations and calculate these probabilities.
OFFICIAL COURSE OUTLINE (Approved Fall 2007)
 Geometry and Measurement
 Develop visualization skills:
 Be familiar with projections, crosssections, and decomposition of common two and threedimensional figures.
 Represent threedimensional shapes in two dimensions and constructing threedimensional objects from twodimensional representations.
 Manipulate mentally physical representations of two and threedimensional shapes.
 Determine the rotational and line symmetries for twodimensional shapes.
 Develop familiarity with basic shapes and their properties:
 Know fundamental objects of geometry, including point, ray, line, and line segment.
 Develop an understanding of angles and how they are measured.
 Be familiar with plane isometries  reflections (flips), rotations (turns), and translations (slides).
 Understand congruence, similarity, and proportional reasoning via similarity.
 Learn technical vocabulary and understanding the importance of definition.
 Be familiar with currently available manipulatives and software that allow exploration of shapes.
 Understanding the process of measurement and measurement techniques:
 Recognize different aspects of size.
 Understand the idea of unit and the need to select a unit appropriate to the attribute being measured.
 Know the standard (English and metric) system of units.
 Use measurement tools such as rulers and meter sticks to make measurements.
 Estimate using common units of measurement.
 Compare units and relate measurements within each of the two common systems of measure, English and metric.
 Understand that measurements are approximate and that different units affect precision.
 Understand role of in measurement.
 Understand and use Pythagorean Theorem.
 Understand length, area, and volume:
 Know what is meant by one, two, and threedimensions.
 See rectangles as arrays of squares and rectangular solids as arrays of cubes.
Updated 11172017  Recognize the behavior of measure (length, area, and volume) under uniform dilations.
 Devise area formulas for triangles, parallelograms, and trapezoids; knowing the formula for the area of a circle; be familiar with volume and surface area formulas for prisms, cylinders, and other threedimensional objects.
 Decompose and recompose nonregular shapes to find area or volume.
 Understand the independence of perimeter and area; surface area and volume.
 Develop visualization skills:
 Data Analysis, Statistics, and Probability
 Design data investigations (optional):
 Understanding the kinds of questions that can be addressed by data.
 Make decisions on what and how to measure.
 Be familiar with how surveys and statistical experiments are designed and what can be learned from them.
 Understand what constitutes a random sample and how bias is reduced.
 Describe data:
 Describe shape: symmetric versus skewed data distribution and what this indicates about the question being addressed by the data. (optional)
 Describe spread: range, outliers, clusters (optional), gaps (optional), and what these indicate about the question being addressed by the data.
 Describe center: mean, median, and mode and what these indicate about the question being addressed by the data.
 Be familiar with different forms of graphical data representation, e.g. line plots, histograms, line graphs, bar graphs, box plots, pie charts, stemandleaf plots, among others; recognize that different forms of representation communicate different features of the data and that some representations are more appropriate than others for a given data set.
 Comparing two sets of data (not always of the same size).
 Draw conclusions:
 Choose among representations and summary statistics to communicate conclusions.
 Understand variability and the role it plays in decision making. (optional)
 Understand some of the difficulties that arise in sampling and inference.
 Recognize some of the ways that statistics and graphical displays of data can be misleading.
 Develop notions of probability:
 Making judgements under uncertainty.
 Assign numbers as a measure of likelihood to singlestage and multistage events.
 Understand conditional probability and some of its applications.
 Be familiar with the idea of randomness.
 Develop empirical probabilities through simulations; relate to theoretical probability.
 Understand the notions of expected value and fairness and use probability to determine fairness. (optional)
 Design data investigations (optional):
GENERAL EDUCATION COMPETENCIES
 Knowledge of human cultures and the physical and natural worlds through study in the sciences and mathematics, social sciences, humanities, histories, languages, and the arts.
 Intellectual and practical skills, including
 inquiry and analysis
 critical and creative thinking
 written and oral communication
 quantitative literacy
 information literacy
 teamwork and problem solving
 Personal and social responsibility, including
 civic knowledge and engagement (local and global)
 intercultural knowledge and competence
 ethical reasoning and action
 foundations and skills for lifelong learning
 Integrative and applied learning, including synthesis and advanced accomplishment across general and specialized skills.
STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING (Approved Fall 2017)
In MA 202, students will learn to:
 Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):
 Developing an understanding of fundamental concepts of geometry including point, line, angle, and plane.
 Describing data and its characteristics including dispersion and central tendency, and solve problems involving these concepts.
 Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by (Gen Ed Comp A, B, C):
 Understanding concepts of symmetry such as congruence, similarity, proportionality, and isometries as they relate to various plane shapes.
 Selecting the appropriate representation for data display and interpret information presented in such graphical displays including bar graphs, line plots, circle graphs, and stem and leaf plots.
 Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):
 Practicing the process of measurement and identify units in the standard systems of measurement.
 Calculating the perimeter and area of various different shapes and the volume of various solids.
 Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):
 Drawing reasonable conclusions based on the characteristics of a data set, and solve problems that involve finding the probability of an event.
 Demonstrating an understanding of and solve application problems involving the concepts of permutations and combinations.
 Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis by (Gen Ed Comp A, D):
 Identifying projections, cross sections, and decompositions of common two dimensional and three dimensional figures.
 Using deductive reasoning and counter examples to prove or disprove statements about two dimensional and three dimensional figures.
 Developing notions about probability of events empirically through simulations and calculate these probabilities.
Includes selected topics in algebra and analytic geometry. Develops manipulative skills and concepts required for further study in mathematics. Includes linear, quadratic, polynomial, rational, exponential, logarithmic, and piecewise functions; systems of equations; and an introduction to analytic geometry. (Students may not receive credit for MAT 150 and any other College Algebra or Precalculus course. Credit not available on the basis of special exam.)
Prerequisite: 1. Math ACT score of 22 or above, 2. Math ACT score of 1921 with concurrent MAT 100 workshop, 3. Successful completion of Intermediate Algebra, MAT 126, or equivalent, or 4. KCTCS placement examination recommendation.
MAT 150 COLLEGE ALGEBRA (3 credit hours)
KCTCS Course Information
Official Course Description 
Includes selected topics in algebra and analytic geometry. Develops manipulative skills and concepts required for further study in mathematics. Includes linear, quadratic, polynomial, rational, exponential, logarithmic and piecewise functions; systems of equations; and an introduction to analytic geometry. (Students may not receive credit for both MAT150 and any other College Algebra or Precalculus course. Credit not available on the basis of special exam.) Prerequisites: One of the following:

OFFICIAL COURSE COMPETENCIES/OBJECTIVES
Upon completion of this course, the student can:
1. Recognize functions and specify the domain and the range of a given function. 2. Graph linear, quadratic, polynomial, rational, exponential, logarithmic and piecewise functions. 3. Write expressions from data, verbal descriptions or graph. 4. Solve polynomial, rational, exponential and logarithmic equations. 
5. Solve application problems using linear, quadratic, exponential, and logarithmic functions. 6. Perform operations with functions and find inverse functions. 7. Solve linear and nonlinear systems of equations. 8. Solve nonlinear inequalities 
OFFICAL COURSE OUTLINE
 Functions
 Functions, relations, domain, and range
 Properties of functions
 Operations with functions
 Inverse functions
 Graphs and Applications
 Linear functions
 Quadratic functions
 Exponential functions
 Logarithmic functions
 Polynomial functions
 Rational Functions
 Piecewisedefined functions
 Equations and Inequalities
 Polynomial equations
 Rational equations
 Exponential equations
 Logarithmic equations
 Nonlinear inequalities
 Systems of linear equations
 Systems of nonlinear equations
GENERAL EDUCATION COMPETENCIES
 Knowledge of human cultures and the physical and natural worlds through study in the
sciences and
mathematics, social sciences, humanities, histories, languages, and the arts.  Intellectual and practical skills, including
 inquiry and analysis
 critical and creative thinking
 written and oral communication
 quantitative literacy
 information literacy
 teamwork and problem solving
 Personal and social responsibility, including
 civic knowledge and engagement (local and global)
 intercultural knowledge and competence
 ethical reasoning and action
 foundations and skills for lifelong learning
 Integrative and applied learning, including synthesis and advanced accomplishment
across general and
specialized skills.
STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING (Approved Fall 2017)
In MAT 150, students will learn to:
 Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):
 Recognizing functions and specify the domain and the range of a given function
 Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by
(Gen Ed Comp A, B, C): Graphing linear, quadratic, polynomial, rational, exponential, logarithmic and piecewise functions
 Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):
 Solving polynomial, rational, exponential and logarithmic equations.
 Performing operations with functions and find inverse functions.
 Solving nonlinear inequalities.
 Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):
 Writing expressions from data, verbal descriptions or graph.
 Solving application problems using linear, quadratic, exponential, and logarithmic functions.
 Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis
by (Gen Ed Comp A, D): Solving linear and nonlinear systems of equations
LEARNING RESOURCES
Bittinger, M. L. et al. (2009). Algebra & trigonometry: Graphs & models (4th ed.). Boston, MA: Pearson
Education, Inc.
A course in ordinary differential equations. Emphasis is on first and second order equations and applications. The course includes series solutions of second order equations and Laplace transform methods.
Prerequisite: MA 213 or equivalent.
MA 214 CALCULUS IV (UK Course) (3 credit hours)
Official Course Description  MA 214 is a course in ordinary differential equations. Emphasis is on first and second order equations and applications. The course includes series solutions of second order equations and Laplace transform methods. Prerequisites: MA 213 or equivalent. 
OFFICIAL COURSE COMPETENCIES/OBJECTIVES (Approved Fall 2017)
 1. Identify and classify differential equations.
 Solve differential equations by separation of variables.
 Solve homogeneous, exact, and linear differential equations.
 Solve differential equations with constant coefficients.
 Solve differential equations using reduction of order and variation of parameters.
 Solve application problems using differential equations of first order.
 Solve application problems using differential equations involving simple and damped harmonic motion.
 Find the Laplace transforms of common functions, and use Laplace Transforms to solve differential equations.
 Find series solutions to differential equations.
 Solve linear systems of differential equations.
OFFICIAL COURSE OUTLINE (Approved Fall 2017)
 Classification of Differential Equations
 First Order Differential Equations
 A. Linear Equations with Variable Coefficients
 Separable Equations
 Exact Equations and Integrating Factors
 Existence and Uniqueness of Solutions
 Applications of First Order Equations
 Second Order Linear Differential Equations
 Homogeneous Equations with Constant Coefficients
 Fundamental Solutions of Linear Homogeneous Equations
 Linear Independence and the Wronskian
 Complex Roots of the Characteristic Equation
 Repeated Roots of the Characteristic Equation
 Solution of Nonhomogeneous Equations using Method of Undetermined Coefficients
 Variation of Parameters Method
H. Applications of Second Order Equations  Series Solutions near an Ordinary Point
 Higher Order Linear Differential Equations
 General Theory of nth Order Linear Equations
 Homogeneous Equations with Constant Coefficients
 Method of Undetermined Coefficients
 Laplace Transforms
 Definition of Laplace Transform
 Solution of Initial Value Problems using Laplace Transforms
 Step Functions
 Differential Equations with Discontinuous Forcing Functions
 Impulse Functions
 Eigenvalues and Eigenvectors
 Linear Dependence / Independence of Vectors
 Definition of Eigenvalues and Eigenvectors
 Solve Linear Systems with Constant Coefficients
 Complex Eigenvalues
GENERAL EDUCATION COMPETENCIES
 Knowledge of human cultures and the physical and natural worlds through study in the
sciences and
mathematics, social sciences, humanities, histories, languages, and the arts.  Intellectual and practical skills, including
 inquiry and analysis
 critical and creative thinking
 written and oral communication
 quantitative literacy
 information literacy
 teamwork and problem solving
 Personal and social responsibility, including
 civic knowledge and engagement (local and global)
 intercultural knowledge and competence
 ethical reasoning and action
 foundations and skills for lifelong learning
 Integrative and applied learning, including synthesis and advanced accomplishment
across general and
specialized skills.
STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING (Approved Fall 2017)
In MA 214, students will learn to:
 Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):
 Identifying and classifying differential equations.
 Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by
(Gen Ed Comp A, B, C): Solving application problems using differential equations involving simple and damped harmonic motion.
 Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):
 Solving differential equations by separation of variables.
 Solving homogeneous, exact, and linear differential equations.
 Solving differential equations with constant coefficients.
 Solving differential equations using reduction of order and variation of parameters.
 Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):
 Solving application problems using differential equations of first order.
 Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis by
(Gen Ed Comp A, D): Finding the Laplace transforms of common functions, and use Laplace transforms to
solve differential
equations.
 Finding the Laplace transforms of common functions, and use Laplace transforms to
solve differential
MA 202 Mathematics for Elementary Teachers (3)  Course Information
Algebraic reasoning, introduction to statistics and probability, geometry, and measurement.
Prerequisite: A grade of "C" or better in MA 201.
Also recommended: a course in logic (e.g. PHI 120) or a course in calculus (e.g. MA 123).
MA 213 Calculus III (4)  Course Information
A course in multivariable calculus. Topics include vectors and geometry of space,
threedimensional vector calculus, partial derivatives, double and triple integrals,
integration on surfaces, Green's theorem. Optional topics include Stokes' theorem
and the Gauss' divergence theorem. Lecture, three hours; recitation, two hours per
week.
Prerequisite: MA 114 or MA 138 or equivalent.
MA 214 Calculus IV (3)  Course Information
A course in ordinary differential equations. Emphasis is on first and second order
equations and applications. The course includes series solutions of second order equations
and Laplace transform methods.
Prerequisite: MA 213 or equivalent.
MAT 011 Transitional Algebra (3)  Course Information
Provides individualized, accelerated, masterylevel progression through entrylevel
college mathematics prerequisite competencies as defined by KY Council of Postsecondary
Education. Note: A passing grade in this course does not necessarily indicate that
all prerequisites for all entrylevel college mathematics courses have been met.
Prerequisite: KCTCS placement examination.
MAT 055 PreAlgebra (3)  Course Information
Includes operations on integers, decimals and fractions. Introduces exponents, square
roots, percents, ratios, proportions, prime factorization, basic geometry, algebraic
expressions, basic linear equations, and applications.
Prerequisite: KCTCS placement examination.
MAT 062 Intro to Workplace Mathematics (3)  Course Information
Prepares students for Business Mathematics, Applied Mathematics, and Technical Mathematics.
Includes properties of algebra, using formulas, solving linear equations, percentages,
ratios, proportions, plotting points, graphing lines, exponents, and measurement.
Encourages applications of algebra and effective use of technology.
Prerequisite: MAT 055 or equivalent as determined by KCTCS placement examination.
MAT 075 Mathematical Literacy (4)  Course Information
Designed to develop the mathematical thinking skills and understanding needed for
nonmath and nonscience majors, this onesemester course integrates numeracy, proportional
reasoning, algebraic reasoning, and functions. This course provides an alternate path
to collegelevel math courses other than college algebra.
Prerequisite: MAT 055 or equivalent as determined by KCTCS placement examination.
MAT 085 Intermediate Algebra (3)  Course Information
Includes rational expressions, radical expressions, rational exponents, graphing parabolas,
inequalities, equations of lines, functions and applications, with emphasis on solving
quadratic, rational, and radical equations.
Prerequisite: MAT 065 or MAT 075 or equivalent as determined by KCTCS placement examination.
MAT 105 Business Mathematics (3)  Course Information
Covers basic mathematical concepts as applied to finance. Includes percentages, simple
and compound interest, annuities, sinking funds, depreciation, and consumer debt,
including installment buying, credit cards, and mortgages.
Prerequisite: MAT 062 or MAT 065 or equivalent as determined by KCTCS placement examination. [AAS
degrees only]
MAT 110 Applied Mathematics (3)  Course Information
Includes the concepts of ratio and proportion, units and conversions, linear equations
in two variables, inequalities, graphing and writing equation of a line, percents,
interest, descriptive statistics, and logical symbolism. Emphasizes applications in
the various technologies.
Prerequisite: MAT 062 or MAT 065 or equivalent as determined by KCTCS placement examination. [AAS
degrees only]
MAT 116 Technical Mathematics (3)  Course Information
Includes some mathematical concepts from algebra, geometry, and trigonometry and applications
relevant to these topics. Includes unit conversions, variation, measurement of geometric
figures, vectors, and solving right and oblique triangles using trigonometry. Emphasizes
applications in the various technologies.
Prerequisite: MAT 062 or MAT 065 or equivalent as determined by KCTCS placement examination. [AAS
degrees only]
MAT 126 Technical Algebra and Trigonometry (3)  Course Information
Examines mathematical concepts from algebra and trigonometry. Includes vectors, phasor
algebra, variation, trigonometric functions, coordinate systems, system of linear
equations, quadratic, rational, exponential and logarithmic equations.
Prerequisite: MAT 065 or equivalent as determined by KCTCS placement examination. [AAS degrees
only]
xMAT 150 College Algebra (3)  Course Information
Includes selected topics in algebra and analytic geometry. Develops manipulative skills
and concepts required for further study in mathematics. Includes linear, quadratic,
polynomial, rational, exponential, logarithmic, and piecewise functions; systems of
equations; and an introduction to analytic geometry. (Students may not receive credit
for MAT 150 and any other College Algebra or Precalculus course. Credit not available
on the basis of special exam.)
Prerequisite: 1. Math ACT score of 22 or above, 2. Math ACT score of 1921 with concurrent MAT 100
workshop, 3. Successful completion of Intermediate Algebra, MAT 126, or equivalent,
or 4. KCTCS placement examination recommendation.
MAT 155 Trigonometry (3)  Course Information
Includes the trigonometric functions, identities, multiple analytic formulas, laws
of sines and cosines, graphs of trigonometric functions in rectangular and polar coordinates,
and solving trigonometric equations. Emphasizes applications in each topic. (Students
may not receive credit for both MAT155 and any other trigonometry or precalculus course.)
Prerequisite: 1. Math ACT score of 22 or above, 2. Math ACT score of 1921 with concurrent MAT150,
3. Successful completion of Intermediate Algebra, MAT 126, or equivalent, or 4. KCTCS
placement examination recommendation.
MAT 160 Precalculus (5)  Course Information
Prepares students to enroll in a calculus sequence. Includes trigonometric functions,
exponentials and logarithms, graphs, polar coordinates, conic sections, and systems
of nonlinear equations. Students may not receive credit for both MAT 160 and either
College Algebra or Trigonometry. Credit is not available by special examination. Lecture:
5 credits (75 contact hours).
Prerequisite: 1. Math ACT score of 23 or above, 2. Placement examination recommendation, or 3. Consent
of instructor.
MAT 170 Brief Calculus with Applications (3)  Course Information
Provides an introduction to differential and integral calculus with applications in
biological sciences, social sciences, physical sciences, or business with an analysis
of algebraic, exponential, and logarithmic functions. (Students may not receive credit
for both MAT 170 and MAT 175.)
Prerequisite: 1. Math ACT score of 27 or above or 2. Successful completion of College Algebra,
MAT 150, or equivalent.
MAT 195 Mathematics Workshop (12)  Course Information
Promotes student success in mathematics by providing supplemental instruction in the form of extra class sessions.
The goal of this course is to help students develop or refine their statistical literacy
skills. Both the informal activity of human inference arising from statistical constructs,
as well as the more formal perspectives on statistical inference found in confidence
intervals and hypothesis tests are studied. Throughout, the emphasis is on understanding
what distinguishes good and bad inferential reasoning in the practical world around
us.
Prerequisites: Quantitative Reasoning College Readiness Indicators as defined by CPE
(ACT 19 or higher, or equivalent as determined by placement examination)
OFFICIAL COURSE COMPETENCIES/OBJECTIVES
Upon completion of this course, the student can:
 Begin to absorb common statistical information appropriately and form associated human inferences carefully.
 Develop an evolved sense of what statistical confidence means and doesn't mean by involving students in real surveys they will enjoy discussing.
 Juxtapose the concepts and language of hypothesis testing with the more easily accessible ideas of sensitivity and specificity
OFFICIAL COURSE OUTLINE
 Begin to absorb common statistical information appropriately and form associated human
inferences carefully.
 Identify categorically good or bad statistical summaries, charts and graphs, and explain the reasons they are so categorized.
 Identify categorically good or bad statistical arguments based on statistical summaries, charts, and graphs, and explain the reasons they are so categorized.
 Distinguish the concepts of correlation and causation and explain how they offer different types of evidence.
 Identify hidden or confounding variables in studies reported by the media or in the literature.
 Explain if and how hidden or confounding variables can or did affect the associated commonsense inferences.
 Define what is meant by Simpson's Paradox.
 Explain how a misinterpretation of randomness leads to poor human inferences.
 Explain how not having enough or the right information leads to poor human inference.
 Present examples relative to each of parts E, F, G, and H.
 Identify and present at least one argument from psychology or neuroscience that supports the contention that poor human inferences are common.
 Develop an evolved sense of what statistical confidence means and doesn't mean by
involving students in real surveys they will enjoy discussing.
 Identify categorically good or bad surveys and explain the reasons they are so categorized.
 Identify a push poll from the news and explain the reasons such a poll is likely not a source of useful information.
 Explain the difference between sampling variability and nonsampling variability.
 Identify strategies for understanding nonsampling variability.
 Identify a margin of error that is in the news, but not discussed in class, from the associated confidence interval and use statistical language to explain the sort of confidence that is being offered, and the type of risk that is being quantified.
 Compare and contrast the information contained in a Cosmopolitan online poll, a CBS Evening News callin poll, a Gallup randomdialing poll, and a doortodoor political campaign poll.
 Define sampling variability and explain the role it plays in the construction of a confidence interval.
 Define sampling distribution and demonstrate the Central Limit Theorem by handson repeated sampling.
 Produce a non95% confidence interval for a proportion or mean, based on data from a simple random sample.
 Explain what happens to a confidence interval as the confidence level changes and/or the sample size changes.
 Juxtapose the concepts and language of hypothesis testing with the more easily accessible
ideas of sensitivity and specificity in an effort to demystify these more difficult
ideas and facilitate a discussion of the related statistical Issues.
 Define sensitivity and specificity.
 Read about a dichotomous decision process that is in the news, not discussed in class, and explain the roles for sensitivity and specificity in assessing the integrity of that process.
 Identify the structure of a test of hypothesis and explain the purpose of the null and the alternative hypotheses, and the way in which the evidence that is gathered is used.
 Define significance and power and explain the roles each play in assessing the integrity of dichotomous significance test.
 Read about a test of significance associated with an experiment that is in the news,
but not discussed in class,
and use the language of statistics to explain and evaluate the nature of the evidence that is presented.  Explain the role of modeled error in a simple test of hypothesis for a simple experimental design.
 Define the Prosecutor's Fallacy.
 Explain the importance of the Prosecutor's Fallacy to interpreting specificity and sensitivity.
 Explain the importance of the Prosecutor's Fallacy to describing the results of null hypothesis testing.
 Read a news story and identify and demonstrate the difference between various conditional
events and
unconditional events discussed in that story.
GENERAL EDUCATION COMPETENCIES
 Knowledge of human cultures and the physical and natural worlds through study in the
sciences and mathematics,
social sciences, humanities, histories, languages, and the arts.  Intellectual and practical skills, including
 inquiry and analysis
 critical and creative thinking
 written and oral communication
 quantitative literacy
 information literacy
 teamwork and problem solving
 Personal and social responsibility, including
 civic knowledge and engagement (local and global)
 intercultural knowledge and competence
 ethical reasoning and action
 foundations and skills for lifelong learning
 Integrative and applied learning, including synthesis and advanced accomplishment
across general and specialized
skills.
STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING (Approved Fall 2017)
 Interpret information presented in mathematical and/or statistical forms. (B)
 Explain if and how hidden or confounding variables can or did affect the associated
commonsense inferences.
Explain the difference between sampling variability and nonsampling variability.  Define significance and power and explain the roles each play in assessing the integrity
of dichotomous significance
test.
 Explain if and how hidden or confounding variables can or did affect the associated
commonsense inferences.
 Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically. (A, B and C)
 Identify categorically good or bad statistical summaries, charts and graphs, and explain
the reasons they are so
categorized.  Identify categorically good or bad statistical arguments based on statistical summaries,
charts, and graphs, and
explain the reasons they are so categorized.
 Identify categorically good or bad statistical summaries, charts and graphs, and explain
the reasons they are so
 Determine when computations are needed and to execute the appropriate computations.
(B)
 Define sampling distribution and demonstrate the Central Limit Theorem by handson repeated sampling.
 Define sensitivity and specificity.
 Apply an appropriate model to the problem to be solved. (A, C and D)
 Distinguish the concepts of correlation and causation and explain how they offer different types of evidence.
 Identify the structure of a test of hypothesis and explain the purpose of the null
and the alternative hypotheses, and
the way in which the evidence that is gathered is used.
 Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis. (B, C and D)
 Produce a non95% confidence interval for a proportion or mean, based on data from a simple random sample.
 Explain what happens to a confidence interval as the confidence level changes and/or the sample size changes.
 Explain the role of modeled error in a simple test of hypothesis for a simple experimental design.
LEARNING RESOURCES
Beyond the Numbers: StudentCentered Activities for Learning Statistical Reasoning, current edition, by William Rayens,
VanGriner Publishers
StatCrunch Student 6Month Access Code
STA 296 Statistical Methods (3)  Course Information
Introduction to principles of statistics with emphasis on conceptual understanding.
Students will articulate results of statistical description of sample data (including
bivariate), application of probability distributions, confidence interval estimation
and hypothesis testing to demonstrate properly contextualized analysis of realworld
data.
Prerequisite: MA 113, MA 123, MA 137 or equivalent.