Our Courses | BCTC

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 problem-solving 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 one-variable 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 pre-calculus 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

  1. State the geometric interpretation of the solution to a linear programming problem
  2. Determine whether two events are independent or not
  3. Determine whether two events are mutually exclusive or not
  4. Use proper matrix notation to organize arrays of numbers and represent equations
  5. Write and understand permutations and combinations in their standard notation
  6. Write and understand probabilities in standard notation
  7. Write and understand set notation for unions, intersections, and complements
  8. Represent sets within Venn Diagrams and understanding such representations
  9. Perform matrix operations
  10. Find the inverse of a matrix
  11. Find the simple, compound, or conditional probability
  12. Determine unions, intersections, and complements of sets and events
  13. Determine the number of ways a task can be performed using counting principles
  14. Solve a system of linear equations by substitution, elimination, using matrix row operations, and using matrix equations
  15. Solve a linear programming problem graphically and by the simplex method
  16. Determine whether a problem involves permutations, combinations, or basic counting methods
  17. Determine whether a problem involves simple, compound, or conditional probability
  18. Set up and solve an application involving systems of equations
  19. Set up and solve an application involving linear programming
  20. Solve multi-step problems that contain simple, compound and conditional probabilities

OFFICIALCOURSE OUTLINE (Approved Spring 2003)

  1. Linear Systems
    1. Solve linear systems of two or more variables by graphing, substitution, elimination or Gauss-Jordan methods.
    2. Recognize consistent, inconsistent, and dependent systems
    3. Write solutions in parametric form
    4. Set up and solve applied problems
  2. Matrix Operations
    1. Recognize and be able to write coefficient matrices and augmented matrices
    2. Be able to define and identify square matrices, equal matrices, and matrices dimensions.
    3. Add and subtract matrices
    4. Perform scalar multiplication
    5. Perform matrix multiplication
    6. Find inverses
    7. Use inverses to solve systems
  3. Linear Inequalities
    1. Graph inequalities
    2. Graph systems of inequalities
    3. Identify corner points and feasible regions
    4. Solve optimization problems by substituting corner points into objectivefunctions.
    5. Identify standard maximization and minimization problems.
    6. Solve standard maximization simplex problems
    7. Solve duality problems using simplex
    8. Convert non-standard optimization problems to standard maximum problems:
      1. Problems with constraints
      2. Problems with = constraints
      3. Problems with negative numbers on the right-hand side of constraints
      4. Problems with a minimized objective function.
    9. Identify simplex problems without a single solution
      1. Multiple solutions
      2. Unbounded solutions
      3. No solutions
    10. Solve applied optimization problems using simplex and/or graphing methods.
  4. Sets
    1. Use, define and identify set builder notation, empty or null set, universal set, equal sets, subsets, proper subsets, elements, union, intersection, complements, disjoint sets
    2. Use and solve applied problems with Venn Diagrams
    3. Identify the number of elements in sets
  5. Combinatorics
    1. Define and use the Multiplication Rule on applied counting problems
    2. Define and use the Addition Rule on applied counting problems
    3. Solve applied permutation problems
    4. Solve applied combination problems
  6. Probability
    1. Identify and define experiment, outcome, trial, sample space, event, empirical probability, randomoutcomes
    2. Find probabilities of equally likely events in applied problems
    3. Find probabilities of compound events in applied problems
      1. union
      2. intersection
      3. complement
    4. Define and identify mutually exclusive events and independent events
    5. Solve applied conditional probability problems
    6. Solve applied probability problems using Baye’s Rule
  7. Markov Chains (OPTIONAL)
    1. Identify and define state matrices, transition matrices, markov chains, and steady-state matrices
    2. Solve applied problems involving Markov Chains
    3. Find steady-state matrices
    4. Identify regular matrices
  8. Solve applied problems using Bernouilli’s Formula (OPTIONAL)

GENERAL EDUCATION COMPETENCIES

  1. 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
  2. Intellectual and practical skills, including
    1. inquiry and analysis
    2. critical and creative thinking
    3. written and oral communication
    4. quantitative literacy
    5. information literacy
    6. teamwork and problem solving
  3. Personal and social responsibility, including
    1. civic knowledge and engagement (local and global)
    2. intercultural knowledge and competence
    3. ethical reasoning and action
    4. foundations and skills for lifelong learning
  4. 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:

  1. 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
  2. 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
  3. 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.
  4. 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 multi-step problems that contain simple, compound and conditional probabilities.
  5. 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) (1-2) - Course Information

Laboratory offered (only) as an adjunct to certain mathematics lecture courses. Offered only on a pass/fail basis.
Co-requisite: Set by instructor.

MA 194 Supplementary Mathematics Workshop II: (Subtitle required) (1-2) - Course Information

Laboratory offered (only) as an adjunct to certain mathematics lecture courses. Offered only on a pass/fail basis.
Co-requisite: 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.
Pre-requisite: 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
representations of a given function and
determine their intervals of convergence.

7. Represent curves by parametric equations, and
apply the methods of calculus to parametric
curves.

8. Determine the slope of a tangent line to and the
arc length of the graph of a parametric function.

9. Calculate the slope of a tangent line to and the arc
length of a polar graph, and determine the volume
and surface area of solids formed by revolving
regions bound by polar functions.

OFFICIAL COURSE OUTLINE (Approved Fall 2017) 

  1. Applications of Integrals
    1. Area Between Curves
    2. Volumes of Revolution
      1. Disks
      2. Washers
      3. Shells
      4. Average Value
      5. Work
      6. Arc Length
  2. Integration Techniques/Strategies
    1. Integration by Parts
    2. Trigonometric Integrals
      1. Powers of sin(x), cos(x), sec(x) & tan(x)
      2. Products of sin(x) & cos(x)
      3. Products of sec(x) & tan(x)
      4. Arbitrary Combinations of Trigonometric Functions
    3. Trigonometric Substitution
    4. Partial Fractions
      1. Long Division
      2. Completing the Square
      3. Rationalizing Substitutions
      4. Tables
  3. Improper Integrals
    1. Infinite Intervals
    2. Discontinuous Integrands
  4. Sequences
    1. Definition
      1. Convergent
      2. Divergent
  5. Series
    1. Definition
      1. Convergence
      2. Divergence
      3. Absolute Convergence
      4. Conditional Convergence
    2. Geometric Series
    3. P-Series
    4. Alternating Series
    5. Tests
      1. Test for Divergence
      2. Integral Test
      3. Comparison Tests
        1. Direct Comparison Test
        2. Limit Comparison Test
      4. Alternating Series Test
      5. Ratio Test
      6. Root Test
    6. Power Series
      1. Radius of Convergence
      2. Interval of Convergence
      3. Properties
        1. Derivative
        2. Integral
      4. 4. Expressing Functions as Power Series
        1. Taylor Series
        2. Maclaurin Series
  6. Parametric Equations
    1. Conversion to Cartesian Equation
    2. Parametric Curves
      1. Graphing
      2. Tangents
      3. Areas
      4. Arc Length
  7. Polar Coordinates
    1. Conversions
      1. Polar to Cartesian
      2. Cartesian to Polar
    2. Polar Curves
      1. Graphing
      2. Tangents
      3. Areas
      4. Arc Length

GENERAL EDUCATION COMPETENCIES

  1. 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.
  2. Intellectual and practical skills, including
    • inquiry and analysis
    • critical and creative thinking
    • written and oral communication
    • quantitative literacy
    • information literacy
    • teamwork and problem solving
  3. 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
  4. 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:

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.

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:

  1. Develop an understanding of fundamental concepts of geometry including point, line, angle, and plane.
  2. Describe data and its characteristics including dispersion and central tendency, and solve problems involving these concepts.
  3. Understand concepts of symmetry such as congruence, similarity, proportionality, and isometries as they relate to various plane shapes.
  4. 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. 
  5. Practice the process of measurement and identify units in the standard systems of measurement. 
  6. Calculate the perimeter and area of various different shapes and the volume of various solids. 
  7. Draw reasonable conclusions based on the characteristics of a data set, and solve problems that involve finding the probability of an event.
  8. Demonstrate an understanding of and solve application problems involving the concepts of permutations and combinations.
  9. Identify projections, cross sections, and decompositions of common two dimensional and three dimensional figures. 
  10. Use deductive reasoning and counter examples to prove or disprove statements about two dimensional and three dimensional figures.
  11. Develop notions about probability of events empirically through simulations and calculate these probabilities.

OFFICIAL COURSE OUTLINE (Approved Fall 2007)

  1. Geometry and Measurement
    1. Develop visualization skills:
      1. Be familiar with projections, cross-sections, and decomposition of common two- and three-dimensional figures.
      2. Represent three-dimensional shapes in two dimensions and constructing three-dimensional objects from two-dimensional representations.
      3. Manipulate mentally physical representations of two- and three-dimensional shapes.
      4. Determine the rotational and line symmetries for two-dimensional shapes.
    2. Develop familiarity with basic shapes and their properties:
      1. Know fundamental objects of geometry, including point, ray, line, and line segment.
      2. Develop an understanding of angles and how they are measured.
      3. Be familiar with plane isometries - reflections (flips), rotations (turns), and translations (slides).
      4. Understand congruence, similarity, and proportional reasoning via similarity.
      5. Learn technical vocabulary and understanding the importance of definition.
      6. Be familiar with currently available manipulatives and software that allow exploration of shapes.
    3. Understanding the process of measurement and measurement techniques:
      1. Recognize different aspects of size.
      2. Understand the idea of unit and the need to select a unit appropriate to the attribute being measured.
      3. Know the standard (English and metric) system of units.
      4. Use measurement tools such as rulers and meter sticks to make measurements.
      5. Estimate using common units of measurement.
      6. Compare units and relate measurements within each of the two common systems of measure, English and metric.
      7. Understand that measurements are approximate and that different units affect precision.
      8. Understand role of in measurement.
      9. Understand and use Pythagorean Theorem.
    4. Understand length, area, and volume:
      1. Know what is meant by one-, two-, and three-dimensions.
      2. See rectangles as arrays of squares and rectangular solids as arrays of cubes.
        Updated 11-17-2017
      3. Recognize the behavior of measure (length, area, and volume) under uniform dilations.
      4. 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 three-dimensional objects.
      5. Decompose and recompose non-regular shapes to find area or volume.
      6. Understand the independence of perimeter and area; surface area and volume.
  2. Data Analysis, Statistics, and Probability
    1. Design data investigations (optional):
      1. Understanding the kinds of questions that can be addressed by data.
      2. Make decisions on what and how to measure.
      3. Be familiar with how surveys and statistical experiments are designed and what can be learned from them.
      4. Understand what constitutes a random sample and how bias is reduced.
    2. Describe data:
      1. Describe shape: symmetric versus skewed data distribution and what this indicates about the question being addressed by the data. (optional)
      2. Describe spread: range, outliers, clusters (optional), gaps (optional), and what these indicate about the question being addressed by the data.
      3. Describe center: mean, median, and mode and what these indicate about the question being addressed by the data.
      4. Be familiar with different forms of graphical data representation, e.g. line plots, histograms, line graphs, bar graphs, box plots, pie charts, stem-and-leaf 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.
      5. Comparing two sets of data (not always of the same size).
    3. Draw conclusions:
      1. Choose among representations and summary statistics to communicate conclusions.
      2. Understand variability and the role it plays in decision making. (optional)
      3. Understand some of the difficulties that arise in sampling and inference.
      4. Recognize some of the ways that statistics and graphical displays of data can be misleading.
    4. Develop notions of probability:
      1. Making judgements under uncertainty.
      2. Assign numbers as a measure of likelihood to single-stage and multi-stage events.
      3. Understand conditional probability and some of its applications.
      4. Be familiar with the idea of randomness.
      5. Develop empirical probabilities through simulations; relate to theoretical probability.
      6. Understand the notions of expected value and fairness and use probability to determine fairness. (optional)

GENERAL EDUCATION COMPETENCIES

  1. 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.
  2. Intellectual and practical skills, including
    • inquiry and analysis
    • critical and creative thinking
    • written and oral communication
    • quantitative literacy
    • information literacy
    • teamwork and problem solving
  3. 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
  4. 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:

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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 19-21 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 Pre-calculus course. Credit not available on the basis of special exam.)

Prerequisites: One of the following:

  1. Math ACT score of 22 or above;
  2. Math ACT score of 19 – 21 with concurrent MAT 100 workshop;
  3. Successful completion of Intermediate Algebra, MAT 126, or equivalent; or
  4. KCTCS placement exam recommendation.

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 

  1. Functions
    1. Functions, relations, domain, and range
    2. Properties of functions
    3. Operations with functions
    4. Inverse functions
  2. Graphs and Applications
    1. Linear functions
    2. Quadratic functions
    3. Exponential functions
    4. Logarithmic functions
    5. Polynomial functions
    6. Rational Functions
    7. Piecewise-defined functions
  3. Equations and Inequalities
    1. Polynomial equations
    2. Rational equations
    3. Exponential equations
    4. Logarithmic equations
    5. Nonlinear inequalities
    6. Systems of linear equations
    7. Systems of nonlinear equations

GENERAL EDUCATION COMPETENCIES

  1. 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.
  2. Intellectual and practical skills, including
    • inquiry and analysis
    • critical and creative thinking
    • written and oral communication
    • quantitative literacy
    • information literacy
    • teamwork and problem solving
  3. 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
  4. 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:

  1. 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
  2. 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
  3. 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.
  4. 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.
  5. 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. 1. Identify and classify differential equations.
  2. Solve differential equations by separation of variables.
  3. Solve homogeneous, exact, and linear differential equations.
  4. Solve differential equations with constant coefficients.
  5. Solve differential equations using reduction of order and variation of parameters.
  6. Solve application problems using differential equations of first order.
  7. Solve application problems using differential equations involving simple and damped harmonic motion.
  8. Find the Laplace transforms of common functions, and use Laplace Transforms to solve differential equations.
  9. Find series solutions to differential equations.
  10. Solve linear systems of differential equations.

OFFICIAL COURSE OUTLINE (Approved Fall 2017)

  1. Classification of Differential Equations
  2. First Order Differential Equations
    1. A. Linear Equations with Variable Coefficients
    2. Separable Equations
    3. Exact Equations and Integrating Factors
    4. Existence and Uniqueness of Solutions
    5. Applications of First Order Equations
  3. Second Order Linear Differential Equations
    1. Homogeneous Equations with Constant Coefficients
    2. Fundamental Solutions of Linear Homogeneous Equations
    3. Linear Independence and the Wronskian
    4. Complex Roots of the Characteristic Equation
    5. Repeated Roots of the Characteristic Equation
    6. Solution of Nonhomogeneous Equations using Method of Undetermined Coefficients
    7. Variation of Parameters Method
      H. Applications of Second Order Equations
    8. Series Solutions near an Ordinary Point
  4. Higher Order Linear Differential Equations
    1. General Theory of nth Order Linear Equations
    2. Homogeneous Equations with Constant Coefficients
    3. Method of Undetermined Coefficients
  5. Laplace Transforms
    1. Definition of Laplace Transform
    2. Solution of Initial Value Problems using Laplace Transforms
    3. Step Functions
    4. Differential Equations with Discontinuous Forcing Functions
    5. Impulse Functions
  6. Eigenvalues and Eigenvectors
    1. Linear Dependence / Independence of Vectors
    2. Definition of Eigenvalues and Eigenvectors
    3. Solve Linear Systems with Constant Coefficients
    4. Complex Eigenvalues

GENERAL EDUCATION COMPETENCIES

  1. 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.
  2. Intellectual and practical skills, including
    • inquiry and analysis
    • critical and creative thinking
    • written and oral communication
    • quantitative literacy
    • information literacy
    • teamwork and problem solving
  3. 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
  4. 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:

  1. Interpret information presented in mathematical and/or statistical forms by (Gen Ed Comp B):
    • Identifying and classifying differential equations.
  2. 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.
  3. 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.
  4. 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.
  5. 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.

 

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 multi-variable calculus. Topics include vectors and geometry of space, three-dimensional 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, mastery-level progression through entry-level 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 entry-level college mathematics courses have been met.
Prerequisite: KCTCS placement examination.

MAT 055 Pre-Algebra (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 non-math and non-science majors, this one-semester course integrates numeracy, proportional reasoning, algebraic reasoning, and functions. This course provides an alternate path to college-level 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 19-21 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 19-21 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 (1-2) - 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:

  1. Begin to absorb common statistical information appropriately and form associated human inferences carefully.
  2. Develop an evolved sense of what statistical confidence means and doesn't mean by involving students in real surveys they will enjoy discussing.
  3. Juxtapose the concepts and language of hypothesis testing with the more easily accessible ideas of sensitivity and specificity

OFFICIAL COURSE OUTLINE

  1. Begin to absorb common statistical information appropriately and form associated human inferences carefully.
    1. Identify categorically good or bad statistical summaries, charts and graphs, and explain the reasons they are so categorized.
    2. Identify categorically good or bad statistical arguments based on statistical summaries, charts, and graphs, and explain the reasons they are so categorized.
    3. Distinguish the concepts of correlation and causation and explain how they offer different types of evidence.
    4. Identify hidden or confounding variables in studies reported by the media or in the literature.
    5. Explain if and how hidden or confounding variables can or did affect the associated common-sense inferences.
    6. Define what is meant by Simpson's Paradox.
    7. Explain how a misinterpretation of randomness leads to poor human inferences.
    8. Explain how not having enough or the right information leads to poor human inference.
    9. Present examples relative to each of parts E, F, G, and H.
    10. Identify and present at least one argument from psychology or neuroscience that supports the contention that poor human inferences are common.
  2. Develop an evolved sense of what statistical confidence means and doesn't mean by involving students in real surveys they will enjoy discussing.
    1. Identify categorically good or bad surveys and explain the reasons they are so categorized.
    2. Identify a push poll from the news and explain the reasons such a poll is likely not a source of useful information.
    3. Explain the difference between sampling variability and non-sampling variability.
    4. Identify strategies for understanding non-sampling variability.
    5. 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.
    6. Compare and contrast the information contained in a Cosmopolitan on-line poll, a CBS Evening News call-in poll, a Gallup random-dialing poll, and a door-to-door political campaign poll.
    7. Define sampling variability and explain the role it plays in the construction of a confidence interval.
    8. Define sampling distribution and demonstrate the Central Limit Theorem by hands-on repeated sampling.
    9. Produce a non-95% confidence interval for a proportion or mean, based on data from a simple random sample.
    10. Explain what happens to a confidence interval as the confidence level changes and/or the sample size changes.
  3. 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.
    1. Define sensitivity and specificity.
    2. 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.
    3. 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.
    4. Define significance and power and explain the roles each play in assessing the integrity of dichotomous significance test.
    5. 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.
    6. Explain the role of modeled error in a simple test of hypothesis for a simple experimental design.
    7. Define the Prosecutor's Fallacy.
    8. Explain the importance of the Prosecutor's Fallacy to interpreting specificity and sensitivity.
    9. Explain the importance of the Prosecutor's Fallacy to describing the results of null hypothesis testing.
    10. Read a news story and identify and demonstrate the difference between various conditional events and
      unconditional events discussed in that story.

GENERAL EDUCATION COMPETENCIES

  1. 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.
  2. Intellectual and practical skills, including
    • inquiry and analysis
    • critical and creative thinking
    • written and oral communication
    • quantitative literacy
    • information literacy
    • teamwork and problem solving
  3. 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
  4. Integrative and applied learning, including synthesis and advanced accomplishment across general and specialized
    skills.

STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING (Approved Fall 2017)

  1. Interpret information presented in mathematical and/or statistical forms. (B)
    • Explain if and how hidden or confounding variables can or did affect the associated common-sense inferences.
      Explain the difference between sampling variability and non-sampling variability.
    • Define significance and power and explain the roles each play in assessing the integrity of dichotomous significance
      test.
  2. 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.
  3. Determine when computations are needed and to execute the appropriate computations. (B)
    • Define sampling distribution and demonstrate the Central Limit Theorem by hands-on repeated sampling.
    • Define sensitivity and specificity.
  4. 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.
  5. Make inferences, evaluate assumptions, and assess limitations in estimation modeling and/or statistical analysis. (B, C and D)
    • Produce a non-95% 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: Student-Centered Activities for Learning Statistical Reasoning, current edition, by William Rayens,
Van-Griner Publishers

StatCrunch Student 6-Month 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 real-world data.
Prerequisite: MA 113, MA 123, MA 137 or equivalent.