# 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.

### BCTC Courses

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.

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can:

- Read pictorial representations and charts to solve fair division problems and/or voting method problems
- Interpret apportionment information given in charts
- Organize information in preference schedules for use in discussing various voting methods and apportionment problems
- Create graphs to illustrate graph theory problems and/or geometric concepts
- Find appropriate modified divisors for different apportionment methods
- Solve equations involving consumer finance formulas
- Select the appropriate formula to use when solving problems involving consumer finance
- Use circuits and paths to model situations involving graph theory
- Compare advantages and disadvantages of different voting methods and different apportionment methods
- Estimate the relative error using an approximate algorithm to solve graph theory problems
- Compare results of consumer finance problems and evaluating assumptions applicable to different formulas

##### OFFICIAL COURSE OUTLINE (Approved February 2016)

Include parts I, II, III, and IV, plus at least one section from part V.

- Voting Methods
- Methods
- Plurality
- Elimination
- Borda Count
- Pairwise Comparison

- Fairness Criteria

- Methods
- Fair Division
- Equal Division
- Fair Shares
- Divider-Chooser Method
- Sealed Bids

- Proportional Division
- Quota Methods
- Hamilton
- Lowndes’

- Divisor Methods
- Jefferson
- Adams’
- Webster
- Huntington-Hill

- Quota Methods

- Equal Division
- Financial Math
- Percent Increase/Decrease
- Simple Interest
- Compound Interest
- Systematic Savings Plans
- Amortized Loans

- Graph Theory
- Euler Paths and Circuits
- Euler’s Theorems
- Graph Modelling
- Eulerization

- Hamilton Paths and Circuits
- Travelling Salesman Problem
- Approximate Algorithms
- Nearest Neighbor
- Cheapest Link

- Euler Paths and Circuits
- Additional Topics (Choose 1)
- Growth Modelling
- Geometry
- Scheduling
- Logic
- Number Theory
- Statistics

##### 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)

Upon completion of this course, the student can:

- Interpret information presented in mathematical and/or statistical forms by:
- reading pictorial representations and charts to solve fair division problems and/or voting method problems
- interpreting apportionment information given in charts

- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by:
- organizing information in preference schedules for use in discussing various voting methods and apportionment problems
- creating graphs to illustrate graph theory problems and/or geometric concepts

- Determine when computations are needed and execute the appropriate computations by:
- finding appropriate modified divisors for different apportionment methods
- solving equations involving consumer finance formulas

- Apply an appropriate model to the problem to be solved by:
- selecting the appropriate formula to use when solving problems involving consumer finance
- using circuits and paths to model situations involving graph theory
- comparing advantages and disadvantages of different voting methods and different apportionment methods

- Make inferences, evaluate assumptions, and assess limitations in
- estimation modeling and/or statistical analysis by:estimating the relative error using an approximate algorithm to solve graph theory problems
- comparing results of consumer finance problems and evaluating assumptions applicable to different formulas

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.

Note: MAT 055 has been replaced by MAT 011 Modules 1 – 4.

**Delivery Mode:** OnlineOnly

**Components:** Lecture: 3.0 credits (45contact hours)

**Implementation:** n/a

**Attributes:** Remedial -Mathematics

**Advising Note:** None

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can:

- State and use the properties of real numbers.
- Perform basic operations on integers, fractions, and decimals.
- Determine the absolute value of an integer, a fraction, or a decimal.
- Determine prime factorization of whole numbers.
- State and use the order of operations on integers, fractions, and decimals.
- Round whole numbers and decimals to an indicated place value.
- Evaluate whole number powers of integers, fractions, and decimals.
- Evaluate square roots of perfect squares of integers, fractions, and decimals.
- Evaluate algebraic expressions.
- Simplify algebraic expressions.
- Use both the addition and multiplication properties to solve a linear equation.
- Solve problems involving ratio and proportion.
- Solve problems involving percents.
- Convert among fractions, decimals, and percents.
- Determine the length of the unknown side of a right triangle using the Pythagorean Theorem.
- Determine the perimeter, circumference, area, surface area, and volume of basic plane figures and solids.
- Solve applied problems using these competencies with real world applications.

##### OFFICIAL COURSE OUTLINE

- Integers

- Properties of Real Numbers
- Basic Operations
- Absolute Value
- Prime Factorization
- Divisibility Tests
- Order of Operations
- Rounding
- Whole Number Powers of Integers
- Square Roots of Perfect Squares

- Fractions

- Common Denominators
- Basic Operations
- Absolute Value
- Order of Operations
- Ordering Fractions
- Whole Number Powers of Fractions
- Square Roots of Perfect Squares

- Decimals

- Basic Operations
- Absolute Value
- Order of Operations
- Ordering Decimals
- Rounding
- Whole Number Powers of Decimals
- Square Roots of Perfect Squares

- Algebraic Expressions and Equations

- Evaluating Algebraic Expressions
- Simplifying Algebraic Expressions
- Solving Linear Equations Using the Addition and Multiplication Properties
- Solving Linear Equations containing fractions (without clearing fractions).

- Ratios and Proportions

- Simplifying Ratios
- Solving Proportions

- Percents

- Converting among fractions, decimals, and percents
- Problems Involving Percents

- Geometry

- Perimeter and Circumference
- Area
- Surface Area
- Volume
- Pythagorean Theorem

- Applications

- Real Number Applications
- Ration and Proportion Applications
- Percent Applications
- Geometry Applications

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.

Note: MAT 062 has been replaced by MAT 011 Modules 1 – 6.

##### MA162 FINITE MATHEMATICS AND 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 multi-step 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 Gauss-Jordan 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 non-standard optimization problems to standard maximum problems:

- Problems with ≥ constraints
- Problems with = constraints
- Problems with negative numbers on the right-hand 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 steady-state matrices
- Solve applied problems involving Markov Chains
- Find steady-state 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 multi-step 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.

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.

Note: MAT 075 is equivalent to MAT 011 Modules 5 – 8.

**Delivery Mode:** Online Only

**Components:** Lecture: 3.0 credits (45contact hours)

**Implementation:** n/a

**Attributes:** Remedial -Mathematics

**Advising Note:** None

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can:

- Convert between units of measurement.
- Use significant digits to show the accuracy and precision of a measurement.
- Use and interpret scientific notation.
- Simplify algebraic expressions using the properties of algebra, including the distributive law and combining like terms.
- Solve linear equations in one variable.
- Translate verbal statements into algebraic expressions.
- Solve literal equations for a given variable.
- Solve variation problems with percentages, ratios, and proportions.
- Plot points on a rectangular coordinate system.
- Graph lines from their equation.
- Find the intercepts of a line from the graph or equation.
- Calculate the slope of a line from the graph, equation, or two given points.
- Interpret slope as a rate of change in applications.
- Simplify algebraic expressions using the rules of exponents.
- Use technology appropriately to solve application problems.
- Solve applied problems using the above competencies within appropriate contexts.

##### OFFICIAL COURSE OUTLINE

- Studying Mathematics

- Learning Styles
- Study Skills
- Test Taking
- Real Number Arithmetic Skills
- Effective Calculator Use
- Calculation with Basic Geometric Formulas

- Measurement

- Unit Conversion
- Significant Digits
- Scientific Notation
- Accuracy and Precision of Measurements

- Formulas

- Introduction to Formulas
- Writing Formulas from Verbal Information
- Formulas and Applications

- Properties of Algebra

- Basic Properties of Algebra
- Simplifying Algebraic Expressions
- Properties of Equality

- Equations

- Interpreting Equations
- Guidelines for Solving Equations
- Solving Linear Equations
- Solving Formulas for a Variable

- Ratios, Proportions, and
- Variation
- Ratios
- Proportions
- Percent
- Direct Variation
- Inverse Variation
- Joint Variation

- Graphing

- Plotting Points
- Graphing Lines
- Slope
- Rates of Change
- Intercepts of a Line

- Exponents

- Algebraic Rules of Exponents
- Integer Exponents
- Simplifying Algebraic Expressions with Exponents

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.

Note: MAT 085 is equivalent to MAT 011 Modules 9 – 12.

**Delivery Mode:** In-Person and Online

**Components:** Lecture: 3 credit hours (45 contact hours)

**Implementation:** Fall 2012

**Advising Note:** None

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student will:

- Write equations of lines from given data, verbal descriptions, and graphs.
- Write the equation of a line parallel or perpendicular to a given line.
- Solve absolute value equations.
- Solve compound inequalities.
- Solve and graph absolute value inequalities.
- Graph linear inequalities in two variables.
- Simplify rational expressions.
- Add, subtract, multiply, and divide rational expressions.
- Solve equations involving rational expressions.
- Convert between radical and rational exponent form.
- Simplify radicals.
- Add, subtract, multiply, and divide radicals.
- Solve equations involving radicals.
- Solve quadratic equations with complex solutions using completing the square and the quadratic formula.
- Parabolas by finding the vertex, finding the axis of symmetry, and plotting points.
- Evaluate a function using function notation.
- Determine whether a given correspondence or graph representsfunction.

Determine the domain of a function. - Identify the range of a function.
- Model and solve applications based on linear, quadratic, and exponential functions.

##### OFFICIAL COURSE OUTLINE

- Equations of Lines

- Writing Equations of Lines Given Data, Verbal Descriptions, and Graphs
- Writing Equations of Parallel or Perpendicular Lines

- Absolute Value and Inequalities

- Absolute Value Equations
- Compound Inequalities
- Absolute Value Inequalities
- Graphing Linear Inequalities in Two Variables

- Rational Expressions

- Simplifying Rational Expressions
- Basic Operations
- Solving Equations

- Radicals

- Converting Between Radical and Rational Exponent Form
- Simplifying Radicals
- Basic Operations
- Solving Equations

- Quadratics

- Completing the Square
- Quadratic Formula
- Complex Solutions
- Graphing Parabolas

- Functions

- Function Notation
- Evaluating Functions

Approved: March 2012 - Identifying Functions
- Domain and Range

##### LEARNING RESOURCES

Martin-Gay, E. (2009). *Intermediate Algebra* (5th ed.). Boston, MA: Pearson

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]

##### OFFICIAL COURSE COMPETENCIES

Upon completion of this course, the student can:

- Solve for the unknown quantity in a percentage, rate, and base problem.
- Determine percent increase and decrease using markup and markdown applications.
- Apply use of annual percentage rate and annual percentage yield to problems in finance.
- Solve problems which involve the simple interest formula.
- Calculate compound interest and compound amount.
- Determine present and future values of an annuity.
- Calculate periodic payment for a sinking fund.
- Set up an amortization schedule and calculate the early payoff of a loan.
- Solve problems involving installment buying and credit card usage.
- Determine mortgage payment amount, closing costs, and total cost of a loan.
- Compute annual and accumulated depreciation and book value using various depreciation methods.
- Solve application problems involving the above competencies.

##### MAT 105 COURSE OUTLINE

- Percents

- Percentage, Base and Rate
- Percent Increase and Decrease
- Markup and Markdown

- Simple Interest

- Ordinary and Exact Methods
- Appropriate Use of Simple Interest Formula

- Compound Interest

- Annual Percentage Rate
- Annual Percentage Yield
- Present and Future Value of Money

- Consumer Savings

- Annuity
- Sinking Fund

- Fixed Installment Loans

- Amount of Periodic Payment, Finance Charge and Total Amount Paid
- Unearned Interest on Early Payoff

- Credit Cards

- Average Daily Balance Method
- Unpaid Balance Method

- Mortgages

- Closing Costs
- Truth in Lending Statements
- Amortization Schedule
- Total Cost of Loan

- Depreciation

- Straight-Line Method
- Declining-Balance Method
- Sum-of –the-Year’s Digits Method
- Accelerated Cost Recovery System

##### 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 105, students will learn to:

- Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):

- Determine percent increase and decrease using markup and markdown applications.

- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by

(Gen Ed Comp A, B, C):

- Set up an amortization schedule and calculate the early payoff of a loan.
- Compute annual and accumulated depreciation and book value using various depreciation methods.

- Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):

- Solve for the unknown quantity in a percentage, rate, and base problem
- Solve problems which involve the simple interest formula.
- Calculate compound interest and compound amount.
- Determine present and future values of an annuity.
- Calculate periodic payment for a sinking fund.

- Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):

- Solve application problems involving compound interest, annuities and sinking funds.
- Determine mortgage payment amount, closing costs, and total cost of a loan.

- Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis

by (Gen Ed Comp A, D):

- Apply use of annual percentage rate and annual percentage yield to problems in finance.

##### LEARNING RESOURCES

Miller, C. D. et al. (2008). Business mathematics (11th ed.). Boston, MA: Addison-Wesley, Inc.

##### MAT 105S Co-requisite Remediation for Business Mathematics (1)

Provides supplementary instruction for students who do not meet college readiness
standards for MAT 105. Covers content necessary for student success in MAT 105.

Note: Concurrent Enrollment in MAT 105 Required.

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]

##### OFFICIAL COURSE COMPETENCIES

Upon completion of this course, the student can:

- Write the equation of a given line and graph linear equations in two variables;
- Solve systems of linear equations in two variables;
- Set up and solve ratios and proportions;
- Use and interpret scientific notation;
- Convert between various units of measure;
- Solve problems involving percents;
- Solve problems involving significant digits, and accuracy and precision of measurements;
- Solve problems involving simple and compound interest;
- Calculate and interpret basic descriptive statistical measures such as mean, median, mode, range, variance, and standard deviation and use the normal distribution.
- Use logic to determine the validity of arguments.
- Solve application problems involving the above competencies.

##### MAT 110 COURSE OUTLINE

- Number Theory and the Real Number System

- Prime Numbers and Divisibility
- Least Common Multiple and Greatest Common Divisor
- Rules of Exponents
- Scientific Notation
- Operations with Square Roots
- Applications

- Measurements and Units

- Significant Digits
- Precision and Accuracy
- Metric Units of Measurement
- Conversions to and from U.S. Customary (“Standard”) System of Measurement
- Applications

- Algebra and Graphs

- Solving Linear Equations in One Variable
- Solving Proportions
- Graphing Lines
- Writing the Equation of a Given Line
- Applications

- Inequalities and Systems of Linear Equations

- Solving Systems of Linear Equations
- Solving Inequalities
- Applications

- Consumer Mathematics

Percents

Simple and Compound Interest

Applications - Statistics

- Sampling Techniques
- Statistical Graphs and Charts
- Measures of Central Tendency (Mean, Median, Mode)
- Measures of Dispersion (Range, Variance, Standard Deviation)
- Using the Normal Distribution Curve
- Applications

- Logic

- Conjunction, Disjunction, and Conditionals
- Truth Tables
- Categorical Propositions
- Fallacies and Valid
- Applications

##### 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 Spring 2018

Upon completion of MAT 110, the student can:

- Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):

- Use and interpret scientific notation;

- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by

(Gen Ed Comp A, B, C):

- Calculate and interpret basic descriptive statistical measures such as mean, median,
mode, range, variance,

and standard deviation and use the normal distribution.

- Calculate and interpret basic descriptive statistical measures such as mean, median,
mode, range, variance,
- Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):

- Solve problems involving percents;
- Solve problems involving simple and compound interest;

- Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):

- Convert between various units of measure;
- Solve application problems involving the above competencies.

- Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis

by (Gen Ed Comp A, D):

- Use logic to determine the validity of arguments.

##### LEARNING RESOURCES

- Angel, A. and Porter, S. (2001). A Survey of Mathematics with Applications (6th ed.)
New York: Addison

Wesley Longman. - Aufmann, R.N. Lockwood, J.S., Nation, R.D., & Clegg, D.K. (2004). Mathematical Excursions
Boston, MA:

Houghton Mifflin Co. - Setek, Gallo (2002). Fundamentals of Mathematics (9th ed) New Jersey: Prentice Hall.
- Smith, R. D. (2002). Technical Mathematics (4th ed.). Albany, NY: Delmar-Thompson Learning.

##### MAT 110S Co-requisite Remediation for Applied Mathematics (1)

Provides supplementary instruction for students who do not meet college readiness
standards for MAT 110. Covers content necessary for student success in MAT 110.

Note: Concurrent Enrollment in MAT 110 Required.

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]

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can:

- Perform conversions using U. S. customary and SI (metric) measures.
- Apply basic plane geometric principles of lines, angles, triangles and other polygons, circles and arcs, congruency and similarity.
- Calculate surface area and volume of basic geometric solids.
- Solve problems involving significant digits and accuracy and precision of numbers.
- Solve problems involving ratio, proportion, direct, inverse and joint variation.
- Perform conversions between coordinate systems.
- Apply fundamentals of trigonometric functions and co-functions to right triangles.
- Apply the law of sines and the law of cosines to oblique triangles.
- Solve problems involving compound angles.
- Identify the vector concept, the components of vectors and add vectors.
- Use a scientific calculator.
- Solve application problems involving the above competencies.

##### OFFICIAL COURSE OUTLINE

- Measurement

- Precision
- Accuracy
- Significant Digits
- Conversion US customary – Metric

- Variation

- Ratio
- Proportion
- Direct Variation
- Inverse Variation
- Joint Variation

- Geometry

- Lines
- Angles
- Triangles and Other Polygons
- Circles and Arcs
- Congruency and Similarity
- Solids – Surface and Volume

- Trigonometry

- Trigonometric Functions for Right Triangles
- Law of Sines
- Law of Cosines
- Compound Angles
- Conversions between Coordinate Systems
- Vector Concepts, Components and Addition

##### 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 Spring 2018

Upon completion of MAT 116, the student can:

- Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):

- Perform conversions using U. S. customary and SI (metric) measures.
- Identify the vector concept, the components of vectors and add vectors.

- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by

(Gen Ed Comp A, B, C):

- Calculate surface area and volume of basic geometric solids.
- Solve problems involving significant digits and accuracy and precision of numbers.
- Solve problems involving compound angles.

- Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):

- Perform conversions between coordinate systems.

- Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):

- Apply basic plane geometric principles of lines, angles, triangles and other polygons,
circles and arcs,

congruency and similarity. - Apply fundamentals of trigonometric functions and co-functions to right triangles.
- Apply the law of sines and the law of cosines to oblique triangles.

- Apply basic plane geometric principles of lines, angles, triangles and other polygons,
circles and arcs,
- Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis

by (Gen Ed Comp A, D):

- Solve application problems involving the course competencies.

##### LEARNING RESOURCES

- Tan, S.T. (2004). Applied Mathematics (3rd ed.). Belmont, CA: Wadsworth-Thomson Learning.
- Smith, Karl J. (2003). Mathematics Its Power and Utility (7th ed.). Pacific Grove,
CA: Brooks/Cole-Thomson

Learning. - Smith (2002). Technical Mathematics (4th ed.). Albany, NY: Delmar/Thomson Learning.
- Kramer, A. D. (2002). Mathematics for Electricity & Electronics (2nd ed.). Albany,
NY: Delmar-Thompson

Learning.

##### MAT 116S Co-requisite Remediation for Technical Mathematics (1)

Provides supplementary instruction for students who do not meet college readiness
standards for MAT 116. Covers content necessary for student success in MAT 116.

Note: Concurrent Enrollment in MAT 116 Required.

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]

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can:

- Solve problems involving ratio, proportion, direct, inverse, and joint variation.
- Solve rational equations.
- Define trigonometric functions and use them to solve right triangles.
- Solve triangles using the law of sines and the law of cosines.
- Identify the vector concept and the components of vectors, and add vectors.
- Determine the solutions to simultaneous linear equations using determinants.
- Solve quadratic equations by the processes of factoring, completing the square, and the quadratic formula.
- Apply radians and radian measurements including their applications to rotating objects.
- Utilize Phasor algebra to perform basic operations on complex numbers.
- Utilize exponent and logarithmic equations such as population growth, time constants and pH scale.
- Perform conversions between number systems such as decimal, binary, octal, and hexadecimal.
- Use a scientific calculator.
- Solve occupation specific application problems using the above competencies.

##### OFFICIAL COURSE OUTLINE

- Algebra

- Variation
- Quadratic Equations

- Factoring
- Completing the square
- Quadratic formula

- Rational Equations
- Ratio and Proportion
- Rectangular Coordinate Plane
- Phasor Form
- Systems of Linear Equation Solution by Determinants
- Exponential Equations
- Logarithmic Equations
- Complex Numbers

- Trigonometry

- Basic Definitions of Functions
- Radians
- Law of Sines
- Law of Cosines
- Polar Coordinates

- Number systems

- Decimal
- Binary
- Octal
- Hexadecimal

##### 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)

Upon completion of MAT 126, the student can:

- Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):

- Define trigonometric functions and use them to solve right triangles.
- Identify the vector concept and the components of vectors, and add vectors.

- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by

(Gen Ed Comp A, B, C):

- Solve problems involving ratio, proportion, direct, inverse, and joint variation.
- Utilize Phasor algebra to perform basic operations on complex numbers.
- Solve triangles using the law of sines and the law of cosines.

- Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):

- Solve quadratic and rational equations.
- Perform conversions between number systems such as decimal, binary, octal, and hexadecimal.

- Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):

- Apply radians and radian measurements including their applications to rotating objects.
- Utilize exponent and logarithmic equations such as population growth, time constants and pH scale.

- Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis

by (Gen Ed Comp A, D):

- Solve occupation specific application problems using course competencies.

##### LEARNING RESOURCES

- Cleaves and Hobbs (2004). College Mathematics for Technology (6rd ed.). Upper Saddle
River, NJ: Prentice

Hall - Deem, B. R., & Zannini, T. (2003). Electronics and Computer Math (7th ed.). Upper Saddle River, NJ: Prentice Hall

##### MAT 126S Co-requisite Remediation for Technical Algebra and Trigonometry (2)

Provides supplementary instruction for students who do not meet college readiness
standards for MAT 126. Covers content necessary for student success in MAT 126.

Note: Concurrent Enrollment in MAT 126 Required.

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.

Note: Prerequisites may also be met by MAT 075 or MAT 011 Modules 5 - 8

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can:

- Read pictorial representations and charts to solve fair division problems and/or voting method problems
- Interpret apportionment information given in charts
- Organize information in preference schedules for use in discussing various voting methods and apportionment problems
- Create graphs to illustrate graph theory problems and/or geometric concepts
- Find appropriate modified divisors for different apportionment methods
- Solve equations involving consumer finance formulas
- Select the appropriate formula to use when solving problems involving consumer finance
- Use circuits and paths to model situations involving graph theory
- Compare advantages and disadvantages of different voting methods and different apportionment methods
- Estimate the relative error using an approximate algorithm to solve graph theory problems
- Compare results of consumer finance problems and evaluating assumptions applicable to different formulas

##### OFFICIAL COURSE OUTLINE(Approved February 2016)

Include parts I, II, III, and IV, plus at least one section from part V.

- Voting Methods
- Methods
- Plurality
- Elimination
- Borda Count
- Pairwise Comparison

- Fairness Criteria

- Methods
- Fair Division
- Equal Division
- Fair Shares
- Divider-Chooser Method
- Sealed Bids

- Proportional Division
- Quota Methods
- Hamilton
- Lowndes’

- Divisor Methods
- Jefferson
- Adams’
- Webster
- Huntington-Hill

- Quota Methods

- Equal Division
- Financial Math
- Percent Increase/Decrease
- Simple Interest
- Compound Interest
- Systematic Savings Plans
- Amortized Loans

- Graph Theory
- Euler Paths and Circuits
- Euler’s Theorems
- Graph Modelling
- Eulerization

- Hamilton Paths and Circuits
- Travelling Salesman Problem
- Approximate Algorithms
- Nearest Neighbor
- Cheapest Link

- Euler Paths and Circuits
- Additional Topics (Choose 1)
- Growth Modelling
- Geometry
- Scheduling
- Logic
- Number Theory
- Statistics

##### 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)

Upon completion of this course, the student can:

- Interpret information presented in mathematical and/or statistical forms by:
- reading pictorial representations and charts to solve fair division problems and/or voting method problems
- interpreting apportionment information given in charts

- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by:
- organizing information in preference schedules for use in discussing various voting methods and apportionment problems
- creating graphs to illustrate graph theory problems and/or geometric concepts

- Determine when computations are needed and execute the appropriate computations by:
- finding appropriate modified divisors for different apportionment methods
- solving equations involving consumer finance formulas

- Apply an appropriate model to the problem to be solved by:
- selecting the appropriate formula to use when solving problems involving consumer finance
- using circuits and paths to model situations involving graph theory
- comparing advantages and disadvantages of different voting methods and different apportionment methods

- Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis by:
- estimating the relative error using an approximate algorithm to solve graph theory problems
- comparing results of consumer finance problems and evaluating assumptions applicable to different formulas

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:

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

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can:

- Recognize functions and specify the domain and the range of a given function.
- Graph linear, quadratic, polynomial, rational, exponential, logarithmic and piecewise functions.
- Write expressions from data, verbal descriptions or graph.
- Solve polynomial, rational, exponential and logarithmic equations.
- Solve application problems using linear, quadratic, exponential, and logarithmic functions.
- Perform operations with functions and find inverse functions.
- Solve linear and nonlinear systems of equations.
- 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
- Piecewise-defined 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.

Provides parallel and supplemental review of algebra skills needed for success in college algebra for students with a Math ACT of 19-21. (Credit not available by special exam; withdrawal from MAT 100 requires withdrawal from MAT 150; can be offered pass/fail or letter grade basis.) Lecture: 2.0 credits (30 contact hours).

**Prerequisite:** Concurrent enrollment in MAT 150.

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:** One of the following:

- Math ACT score of 22 or above,
- Math ACT score of 19-21 with concurrent MAT150,
- Successful completion of Intermediate Algebra, MAT 126, or equivalent, or
- KCTCS placement examination recommendation.

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can:

- State the definition of the six trigonometric functions in their multiple forms.
- Compute trigonometric function values using the definitions.
- State basic trigonometric identities.
- Apply the trigonometric function definitions to right triangles.
- Find trigonometric values of angles.
- Solve right triangle application problems.
- Solve problems involving vectors and right triangles.
- Use radian and degree measure.
- Solve application problems using radian measure.
- Graph the six trigonometric functions.
- Determine the amplitude and period of the trigonometric functions.
- Determine the inverse functions for the six trigonometric functions.
- Prove trigonometric identities.
- Solve problems using the sum and difference and double-angle formulas.
- Solve trigonometric equations.
- Solve general triangles using the Law of Sines and the Law of Cosines.
- Put complex numbers into trigonometric form.
- Calculate complex roots of numbers.
- Plot points in polar coordinates.
- Graph equations in polar coordinates.

##### OFFICIAL COURSE OUTLINE

- Six Trigonometric Functions

- Angles, Degrees, and Special Triangles
- The Rectangular System
- Definitions of the Trigonometric Functions
- Introduction to Identities

- Right Triangle Trigonometry

- Right Triangle Trigonometric Definitions
- Calculator and Trigonometric Functions of an Acute Angle
- Solving Right Triangles
- Applications
- Vectors

- Radian Measure

- Reference Angle
- Radians and Degrees
- Definitions of the Circular Functions
- Arc Length and Area of a Sector Formulas
- Linear and Angular Velocities

- Graphing and Inverse Functions

- Basic Graphs
- Amplitude and Period
- Phase Shift
- Inverse Trigonometric functions

- Identities and Formulas

- Proving Identities
- Sum and Difference Formulas
- Double-Angle Formulas
- Half-Angle Formulas
- Other Identities

- Trigonometric Equations

- Solving Trigonometric Equations
- Trigonometric Equations Involving Multiple Angles
- Parametric Equations and Further Graphing

- General Triangles

- Law of Sines
- Law of Cosines
- Area of a General Triangle

- Complex Numbers and Polar Coordinates

- Complex Numbers
- Trigonometric Form for Complex Numbers
- Products and Quotients in Trigonometric Form
- Roots of a Complex Number
- Polar Coordinates
- Equations in Polar Coordinates

##### 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 155, students will learn to:

- Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):

- Stating the definition of the six trigonometric functions in their multiple forms.
- Stating basic trigonometric identities.
- Using radian and degree measure.
- Determining the inverse functions for the six trigonometric functions.

- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by (Gen Ed Comp A, B, C):

- Solving problems involving vectors and right triangles.
- Graphing the six trigonometric functions.
- Determining the amplitude and period of the trigonometric functions.

- Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):

- Computing trigonometric function values using the definitions.
- Finding trigonometric values of angles.
- Solving trigonometric equations.

- Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):

- Applying the trigonometric function definitions to right triangles.
- Solving right triangle application problems.
- Solving application problems using radian measure.

- Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis by (Gen Ed Comp A, D):

- Proving trigonometric identities.
- Solving problems using the sum and difference and double-angle formulas.
- Solving general triangles using the Law of Sines and the Law of Cosines

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, MAT 150, or equivalent.

Note: MAT 150 is equivalent to MA 109.

##### 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 multi-step 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 Gauss-Jordan 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 non-standard optimization problems to standard maximum problems:

- Problems with ≥ constraints
- Problems with = constraints
- Problems with negative numbers on the right-hand 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 steady-state matrices
- Solve applied problems involving Markov Chains
- Find steady-state 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 multi-step 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.

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, cross-sections, and decomposition of common two- and three-dimensional figures.
- Represent three-dimensional shapes in two dimensions and constructing three-dimensional objects from two-dimensional representations.
- Manipulate mentally physical representations of two- and three-dimensional shapes.
- Determine the rotational and line symmetries for two-dimensional 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 three-dimensions.
- See rectangles as arrays of squares and rectangular solids as arrays of cubes.

Updated 11-17-2017 - 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 three-dimensional objects.
- Decompose and recompose non-regular 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, 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.
- 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 single-stage and multi-stage 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

##### 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.

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).

##### 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, cross-sections, and decomposition of common two- and three-dimensional figures.
- Represent three-dimensional shapes in two dimensions and constructing three-dimensional objects from two-dimensional representations.
- Manipulate mentally physical representations of two- and three-dimensional shapes.
- Determine the rotational and line symmetries for two-dimensional 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 three-dimensions.
- See rectangles as arrays of squares and rectangular solids as arrays of cubes.
- 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

three-dimensional objects. - Decompose and recompose non-regular 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, 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. - Comparing two sets of data (not always of the same size).

- Describe shape: symmetric versus skewed data distribution and what this indicates
about the
- 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 single-stage and multi-stage 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.

- Developing an understanding of fundamental concepts of geometry including point, line,
angle,
- 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.

- Understanding concepts of symmetry such as congruence, similarity, proportionality,
and
- 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.

- Practicing the process of measurement and identify units in the standard
- 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.

- Drawing reasonable conclusions based on the characteristics of a data
- 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.

- Identifying projections, cross sections, and decompositions of common

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.

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can:

- Approximate limits graphically and numerically and evaluate limits analytically.
- List the conditions for the continuity of a function at a point and determine if a function is continuous or discontinuous at a point.
- Determine the intervals of continuity of a function.
- Evaluate infinite limits and limits at infinity.
- Define the derivative of a function and evaluate the derivative of a function using the definition.
- Evaluate the derivative of a function using differentiation rules for algebraic functions as well as product, quotient, and chain rules.
- Use the derivative of a function to find the equation of the line tangent to the graph of the function at a given point.
- Sketch the graph of a function using the first and second derivatives to determine the critical points, intervals on which the function is either increasing or decreasing, relative extrema, intervals on which the graph is either concave up or concave down, and inflection points of the graph.
- Perform implicit differentiation.
- Use derivatives to solve application problems including problems involving related rates and optimization for biological sciences, social sciences, physical sciences, or business.
- Define the differential and use differentials to approximate function values.
- Find indefinite and definite integrals of a function using integration rules for algebraic functions.
- Find definite and indefinite integrals using substitution.
- Find the average value of a function on an interval.
- Use definite integrals to find the area under a curve and the area between two curves.
- Determine if a function is differentiable or nondifferentiable at a point.
- Find the derivative and integral of functions including polynomial, rational, root, exponential, and logarithmic functions.
- Solve application problems using integrals for biological sciences, social sciences, physical sciences, or business.

##### OFFICIAL COURSE OUTLINE

- Limits

- Finding limits graphically
- Approximating limits numerically
- Finding limits analytically
- One-sided limits
- Continuity
- Infinite limits (f(x)→±∞)
- Limits as x→±∞
- Horizontal asymptotes
- Vertical asymptotes

- Differentiation

- Definition of the derivative
- Finding derivatives using the definition
- Finding the tangent line to the graph of a function
- Basic differentiation rules for algebraic functions, product and quotient rules, chain rule
- Finding the tangent line to a graph
- Implicit Differentiation

- Applications of Differentiation

- Related rate applications
- Finding critical numbers
- First derivative test/increasing/decreasing
- Finding relative maxima and minima
- Concavity and inflection points
- Second derivative test
- Curve sketching
- Optimization applications
- Differentials

- Integration

- Fundamental theorem of calculus
- Finding the average value of a function
- Properties of definite integrals
- Integration using substitution

- Applications of Integration

- Area under curve
- Area between two curves

##### 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 170, students will learn to:

- Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):

- Approximating limits graphically and numerically and evaluating limits analytically.
- Defining the derivative of a function and evaluating the derivative of a function using the definition.

- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by (Gen Ed Comp A, B, C):

- Listing the conditions for the continuity of a function at a point and determining if a function is continuous or discontinuous at a point.
- Determining the intervals of continuity of a function.
- Sketching the graph of a function using the first and second derivatives to determine the critical points, intervals on which the function is either increasing or decreasing, relative extrema, intervals on which the graph is either concave up or concave down, and inflection points of the graph.

- Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):

- Evaluating infinite limits and limits at infinity.
- Evaluating the derivative of a function using differentiation rules for algebraic functions as well as product, quotient, and chain rules.
- Performing implicit differentiation.
- Finding indefinite and definite integrals of a function using integration rules for algebraic functions.
- Finding definite and indefinite integrals using substitution.
- Determining if a function is differentiable or non-differentiable at a point.
- Finding the derivative and integral of functions including polynomial, rational, root, exponential, and logarithmic functions.

- Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):

- Using the derivative of a function to find the equation of the line tangent to the
graph of the function at a given

point.

Make inferences, evaluate assumptions, and assess limitations in estimation modeling and/or statistical analysis

by (Gen Ed Comp A, D): - Using derivatives to solve application problems including problems involving related
rates and optimization for biological sciences, social sciences, physical sciences,
or business.

Using definite integrals to find the area under a curve and the area between two curves. - Solving application problems using integrals for biological sciences, social sciences, physical sciences, or business.

- Using the derivative of a function to find the equation of the line tangent to the
graph of the function at a given

##### LEARNING RESOURCES

- Berresford, G. & Rockett, A. (2004). Brief applied calculus (3rd ed.). Boston, MA: Houghton/Mifflin
- Lial, M. L., Greenwell, R. N., & Ritchey, N. P. (2005). Calculus with applications, brief version (8th ed.). Boston, MA: Pearson/Addison Wesley.

Serves as the entry-level mathematics class for students in STEM fields. Prepares students for success in Calculus I. Develops fluency in the manipulation of polynomial, rational, radical, exponential, logarithmic, and trigonometric functions in order to solve equations, inequalities, and application problems. Familiarizes students with the graphs of the aforementioned functions. Includes linear and nonlinear systems of equations. Students may not receive credit for both MAT 171 and any other College Algebra, Trigonometry, or Precalculus course. Credit not available on the basis of special examination.

**Prerequisite:** ACT Math of 23 or equivalent

Examines one-variable calculus including limits, differentiation and integration of algebraic, trigonometric, exponential, logarithmic, hyperbolic, and inverse trigonometric functions with applications.

**Prerequisite:** 1. College Algebra and Trigonometry, or equivalent, with grades of “C” or higher;
2. Math ACT 27 or above; 3. Placement exam recommendation; or 4. Consent of instructor.

Includes applications of integration, advanced integration techniques, sequences and infinite series, and parametric and polar equations.

**Prerequisite:** Calculus I, or equivalent, with grade of “C” or higher, or consent of instructor.

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.

##### COURSE OBJECTIVES (Approved Fall 2017)

Upon completion of this course, the student can:

- Perform the operations of addition, subtraction,

dot product, and cross product on vectors. - Find directional derivatives and the gradient of

functions of several variables. - Find relative extrema of functions of several

variables. - Evaluate line integrals within vector fields.
- Identify various surfaces, including quadric

surfaces, by their equations and their graphs. - Determine the equations of lines and planes and

find distances in space. - Find derivatives and integrals of vector valued

functions and tangent lines to space curves. - Determine the arc length, unit tangent vector,

principal unit normal vector, and curvature of a

vector-valued function. - Find partial derivatives of and apply chain rule derivative techniques to multivariable functions.
- Find iterated integrals, double integrals over

regions, and double integrals in polar coordinates. - Evaluate triple integrals in polar, spherical, and

cylindrical coordinates. - Use Green's Theorem and the principle of path

independence to evaluate line integrals within

conservative vector fields. - Interpret derivatives of vector valued functions as

velocity and acceleration functions. - Find the equations of planes tangent to surfaces

and total differentials of functions of several

variables. - Use multiple integration to solve problems

involving volume, surface area, and center of

mass.

##### OFFICIAL COURSE OUTLINE (Approved Fall 2017)

- Vectors and Geometry in R2 and R3
- Three-Dimensional Coordinate System
- Vectors
- The Dot and Cross Products
- Equations of Lines and Planes
- Surfaces in R3

- Parametric Equations in R3

- Curves Defined by Parametric Equations
- Tangents and Area
- Arc Length

- Vector-Valued Functions

- Vector Functions and Space Curves
- Derivatives and Integrals of Vector Functions
- Arc Length and Curvature
- Velocity and Acceleration

- Partial Derivatives

- Functions of Several Variables
- Limits and Continuity
- Partial Derivatives
- Tangent Planes and the Total Differential
- The Chain Rules
- Directional Derivatives and Gradient Vectors
- Extrema
- Lagrange Multipliers

- Multiple Integration

- Double Integrals over Rectangles
- Iterated Integrals
- Introduction to Polar Coordinates
- Double Integrals in Polar Coordinates
- Applications of Double Integrals
- Triple Integrals
- Introduction to Cylindrical and Spherical Coordinates
- Triple Integrals in Cylindrical and Spherical Coordinates

- Vector Calculus

- Vector Fields
- Line Integrals and the Fundamental Theorem
- Green's Theorem
- Curl and Divergence

##### 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 213, students will learn to:

- Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):

- Performing the operations of addition, subtraction, dot product, and cross product on vectors.
- Finding directional derivatives and the gradient of functions of several variables.
- Finding relative extrema of functions of several variables.
- Evaluating line integrals within vector fields.

- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically

by (Gen Ed Comp A, B, C):

- Identifying various surfaces, including quadric surfaces, by their equations and their graphs.
- Determining the equations of lines and planes and find distances in space.

- Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):

- Finding derivatives and integrals of vector valued functions and tangent lines to space curves.
- Determining the arc length, unit tangent vector, principal unit normal vector, and
curvature of a vectorvalued

function. - Finding partial derivatives of and apply chain rule derivative techniques to multivariable functions.
- Finding iterated integrals, double integrals over regions, and double integrals in polar coordinates.
- Evaluating triple integrals in polar, spherical, and cylindrical coordinates.
- Using Green's Theorem and the principle of path independence to evaluate line integrals
within

conservative vector fields.

- Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):

- Interpreting derivatives of vector valued functions as velocity and acceleration functions.
- Finding the equations of planes tangent to surfaces and total differentials of functions of several variables.

- Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical

analysis by (Gen Ed Comp A, D):

- Using multiple integration to solve problems involving volume, surface area, and center of mass.

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)

- 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
- 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
- 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

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 common-sense 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 non-sampling variability.
- Identify strategies for understanding non-sampling 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 on-line poll, a CBS Evening News call-in poll, a Gallup random-dialing poll, and a door-to-door 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 hands-on repeated sampling.
- 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.

- 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
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.

- Explain if and how hidden or confounding variables can or did affect the associated
common-sense 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 hands-on 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 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 220 Statistics (3) – Course Information

Examines statistical description of sample data including frequency distributions,
measures of central tendency, and measures of dispersion. Includes theoretical distributions,
statistical estimation, and hypothesis testing. Introduces simple linear regression
and correlation.

**Prerequisite:** MAT 150 or equivalent.

**Official Course Description**

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.**Prerequisites:** MA 113, MA 123, MA 137 or equivalent.

##### OFFICAL COURSE COMPENTENCIES/OBJECTIVES

Upon completion of this course, the student can:

- Demonstrate understanding of p-value, margins of error and confidence intervals, formal hypothesis tests through their creation or evaluation.
- Generate and/or analyze critically quantitative and graphic data summaries in their real-world contexts.
- Integrate knowledge from huge reservoir of available data and illustrate their comprehension of that knowledge through individual summarization.

##### OFFICIAL COURSE OUTLINE (Approved Fall 2014)

- Data

- Data Collection
- Sample Designs
- Categorical vs.
- Quantitative Data

- Descriptive Statistics

- Summarizing Categorical Data
- Summarizing Quantitative Data
- Measures of Center
- Measures of Spread
- Standard Deviation
- Sensitivity and Specificity

- Probability

- Probability Rules
- Joint Probability and Contingency Tables
- Conditional Probability

- Random Variables

- Discrete Random Variables
- Binomial Probability Distributions
- Continuous Probability Distributions
- Normal Distributions
- t-Distributions

- Sampling Distributions

- Sampling Distribution for Proportions
- Central Limit Theorem
- Sampling Distribution for Means

- Confidence Intervals

- Confidence Intervals for Proportions
- Confidence Intervals for Means
- Margin of Error
- Assumptions
- Sample Size

- Hypothesis Testing

- Hypotheses
- P-values
- Reasoning
- Testing Hypotheses about the Mean
- Testing Hypotheses about the Proportion

- Comparing Means

- Difference between Two Means – Dependent Samples
- Difference between Two Means – Independent Samples

- Comparing Proportions

- Goodness of Fit Tests
- Chi-Square Interpretation
- Chi-Square Test of Homogeneity
- Chi-Square Test of Independence

- Linear Regression

- Correlation
- Linear Model
- Assumptions
- Test for the Regression Slope

##### 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

##### STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING (Approved Fall 2017)

- Interpret Information presented in mathematical and/or statistical forms. (B)

- Summarize data with measures of center and measures of spread.
- Identify and explain sensitivity and specificity.

- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically.

(A, B and C)

- Summarize categorical data in graphical form.
- Summarize quantitative data in graphical form.

- Determine when computations are needed and execute the appropriate computations. (B)

- Properly apply rules of probability.
- Calculate joint and conditional probability.
- Find the probability, mean and standard deviation for discrete and continuous probability distributions.

- Apply an appropriate model to the problem to be solved. (A, C and D)

- Construct a linear model for a regression problem.
- Predict an outcome within the range of a linear model.

- Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis.

(B, C and D)

- Construct and interpret confidence intervals for a mean and proportion.
- Conduct hypothesis testing for a mean and proportion.
- Construct and interpret confidence intervals for the difference between two means.
- Conduct hypothesis testing for the difference between two means.

##### LEARNING RESOURCES

- Rayens, William (2013 or latest edition). Making Sense of Uncertainty: Activities
for Teaching Statistical

Reasoning. Van-Griner Publishing. ISBN-13: 978-1-61740-106-0 - My Stat Lab