## Mathematics (MTH)

### MTH 1 - Developmental Mathematics

### Course Description

Effective: 1992-05-01

### MTH 111 - Basic Technical Mathematics

### Course Description

Effective: 2017-08-01

### General Course Purpose

This course is intended for students who are in career and technical fields/degree programs requiring technical math components including trigonometry.

### Course Prerequisites/Corequisites

Prerequisites: MTE 1-3 Prereq OR Corequisite: MCR 1.

### Course Objectives

- Communication
- Interpret and communicate quantitative information and mathematical and statistical concepts using language appropriate to the context and intended audience.
- Problem Solving
- Make sense of problems, develop strategies to find solutions, and persevere in solving them
- Reasoning
- Reason and draw conclusions or make decisions with quantitative information.
- Evaluation
- Critique and evaluate quantitative arguments that utilize mathematical, statistical, and quantitative information.
- Technology
- Use appropriate technology in a given context.
- Students will engage in all course content described below in context to the technical fields being supported.
- Basic Skills
- Use a scientific calculator.
- Round-off numbers correctly.
- Identify significant digits.
- Use scientific notation
- Convert between units in both standard and metric
- Perform operations with signed numbers
- Basic Algebra
- Apply and interpret ratios and proportions
- Compute values in direct, indirect and inverse variation
- Solve single variable equations
- Locate and plot points on the xy plane
- Interpret the concept of slope using real world examples (including vertical and horizontal lines)
- Graph lines using a table of values with and without the domain provided
- Graph lines using the slope-intercept method when lines are in y=mx+b form and Ax+By=C form
- Write the equation of a line in slope-intercept form that models a real world situation when given the rate of change and initial value
- Make predictions using the equation of a line
- Geometry
- Classify triangles by their sides/angles.
- Calculate the perimeter and circumference
- Calculate the area of a polygon and circle
- Apply concepts of sector and arc length of a circle
- Recognize various geometric solids such as cylinder, cone, pyramid, prism and sphere.
- Calculate surface area and volume of various geometric solids
- Use the properties of inscribed and circumscribed polygons and circles to find unknown amounts
- Apply the concept of similar triangles
- Apply the Pythagorean theorem
- Convert between decimal degrees and DMS notation.
- Interpret and apply line and angle relationships.
- Trigonometry
- Properly use terms related to an angle(s).
- Define the trigonometric functions and their values
- Solve right triangles and their applications
- Identify the signs of the trigonometric function of angles greater than 90?
- Determine trigonometric functions of any angle

### Major Topics to be Included

- Basic Skills
- Basic Algebra
- Geometry
- Trigonometry

### MTH 130 - Fundamentals of Reasoning

### Course Description

Effective: 2017-08-01

### General Course Purpose

The Fundamental of Reasoning course is organized around big mathematical concepts. The course?s nontraditional treatment of content will help students develop conceptual understanding by supporting them in making connections between concepts and applying previously learned material to new contexts. The course will help to prepare students for success in future courses, gain skills for the workplace, and participate as productive citizens in our society. Encourage students to do mathematics with real data. This includes recognizing the real world often has less than perfect data, ambiguities and multiple possible solutions. It also means equipping students to be intelligent consumers of quantitative data and reports. Encourage students to engage in productive struggle to learn mathematics and make connections to the world in which they live.

### Course Prerequisites/Corequisites

Prerequisites: Competency in MTE 1-3 as demonstrated through placement or unit completion or equivalent or Corequisite: MCR 2

### Course Objectives

- Communication
- Interpret and communicate quantitative information and mathematical and statistical concepts using language appropriate to the context and intended audience.
- Use appropriate mathematical language in oral, written and graphical forms.
- Read and interpret real world advertisements, consumer information, government forms and news articles containing quantitative information.
- Use quantitative information from multiple sources to make or critique an argument.
- Problem Solving
- Make sense of problems, develop strategies to find solutions, and persevere in solving them.
- Use multiple calculations to develop an answer to an open-ended question requiring analysis and synthesis of data.
- Develop personal problem solving processes and apply them to applications studied over an extended period of time.
- Reasoning
- Reason and draw conclusions or make decisions with quantitative information.
- Draw conclusions or make decisions in quantitatively based situations that are dependent upon multiple factors.
- Analyze how different situations would affect the decisions.
- Present written or verbal justifications of decisions that include appropriate discussion of the mathematics involved.
- Recognize when additional information is needed or the appropriate times to simplify a problem
- Evaluation
- Critique and evaluate quantitative arguments that utilize mathematical, statistical, and quantitative information.
- Evaluate the validity and possible biases in arguments presented in real world contexts based on multiple sources of quantitative information for example; advertising, internet postings, or consumer information.
- Technology
- Use appropriate technology in a given context
- Use a computer or calculator to organize quantitative information and make repeated calculations using simple formulas. This would include using software like Excel or internet-based tools appropriate for a given context for example, an online tool to calculate credit card interest.
- Basic Algebra

### MTH 131 - Technical Mathematics

### Course Description

Effective: 2017-08-01

### General Course Purpose

This course is intended for students entering degree programs in Engineering Design Technology (CAD), Electrical/Instrumentation/Electronics (EIE), Machine Technology or similar fields.

### Course Prerequisites/Corequisites

Prerequisites: Competency in MTE 1-6 as demonstrated through placement or unit completion or equivalent or Corequisite: MCR 3

### Course Objectives

- Communication
- Interpret and communicate quantitative information and mathematical and statistical concepts using language appropriate to the context and intended audience.
- Problem Solving
- Make sense of problems, develop strategies to find solutions, and persevere in solving them.
- Reasoning
- Reason and draw conclusions or make decisions with quantitative information.
- Evaluation
- Critique and evaluate quantitative arguments that utilize mathematical, statistical, and quantitative information.
- Technology
- Use appropriate technology in a given context.
- Students will engage in all course content described below in context to the technical fields being supported.
- Basic Skills
- Use a scientific calculator.
- Round-off numbers correctly.
- Identify significant digits.
- Use scientific and engineering notation
- Convert between units in both standard and metric
- Apply basic algebraic principles
- Geometry
- Apply and interpret line and angle relationships.
- Classify triangles by their sides/angles.
- Calculate the perimeter of a polygon
- Calculate the circumference and chord length on a circle
- Calculate the area of a polygon
- Calculate the area of a circle
- Apply concepts of sector and arc length of a circle
- Recognize various geometric solids such as cylinder, cone, pyramid, prism, sphere and conic sections.
- Calculate surface area and volume of various geometric solids
- Apply the concept of similar triangles
- Trigonometry
- Properly use terms related to an angle(s).
- Classify triangles by their sides/angles.
- Know/apply the radian as a measure of an angle, convert between degrees and radians
- Define the trigonometric functions and their values
- Solve right triangles and their applications
- Identify the signs of the trigonometric function of angles greater than 90?
- Determine trigonometric functions of any angle
- Vectors
- Describe vectors and their components.
- Solve applications involving vectors.
- Perform addition and scalar multiplication with vectors
- Complex Numbers
- Interpret complex numbers and perform basic operations
- Convert between forms of rectangular, and polar complex numbers
- Perform basic operations with polar complex numbers

### Major Topics to be Included

- Basic Skills
- Geometry
- Trigonometry
- Vectors
- Complex Numbers

### MTH 132 - Business Mathematics

### Course Description

Effective: 2017-08-01

### General Course Purpose

This course is intended for students entering degree and certificate programs in accounting, administrative support, business management, marketing or similar fields. It provides instruction of business concepts dependent on mathematical skills for understanding and application.

### Course Prerequisites/Corequisites

Prerequisites: Competency in MTE 1-3 or as demonstrated through placement or unit completion or equivalent or Corequisite: MCR 8

### Course Objectives

- Communication
- Problem Solving
- Make sense of problems, develop strategies to find solutions, and persevere in solving them.
- Reasoning
- Reason and draw conclusions or make decisions with quantitative information.
- Evaluation
- Technology
- Use appropriate technology in a given context.
- Communication and Basic Skills
- Solve application problems by interpreting the materials presented, including determining the nature and extent of the information needed, and present the answer in standard English.
- Estimate and consider answers to mathematical problems in order to determine reasonableness.
- Correctly calculate sums, differences, products and quotients of whole numbers, fractions and mixed numbers, and decimal numbers without the use of a calculator.
- Perform basic calculator operations.
- Solve a formula for any specified variable.
- Convert decimal numbers and fractions to and from percents.
- Banking Applications
- Solve word problems using the basic percentage formula.
- Identify the component parts of a check, check stub and deposit slip.
- Perform simple banking transactions, rectify bank statements.
- Calculate simple interest, compound interest and simple discount.
- Use the formulas for maturity value and present value for simple interest loans.
- Use tables to calculate present value and future value.
- Find the monthly mortgage payment, interest and PITI and prepare a partial amortization schedule.
- Calculate sales, property, loans with closed-end credit and open-end credit.
- Taxes
- Calculate Payroll, income taxes.
- Calculate gross earnings based on salaries, commissions and wages.
- Calculate overtime earnings for wages, salaries, and commissions.
- Calculate State withholding taxes.
- Calculate FICA and Medicare taxes for employees and self-employed individuals.
- Calculate Federal withholding taxes using the wage bracket and percentage methods.
- Calculate an employer's Federal Tax Liability.
- Business Applications
- Complete an invoice.
- Calculate the selling price for an item using markup and markdown.
- Use the basic percentage formula to calculate trade, chain, quantity and cash discounts, and net cost.
- Use complements to calculate net cost.
- Calculate the equivalent single discount for a series discount.
- Determine the last date of a discount period.
- Calculate the selling price for an item using markup and markdown.
- Determine the break-even point and the amount of a profit/loss.

### Major Topics to be Included

- Communication and Basic Skills
- Banking Applications
- Taxes
- Business Applications

### MTH 133 - Mathematics for Health Professions

### Course Description

Effective: 2017-08-01

### General Course Purpose

This course is intended for students entering degree and certificate programs in a health professions field such as radiography, diagnostic medical sonography, and nursing.

### Course Prerequisites/Corequisites

Prerequisites: Competency in MTE 1-3 as demonstrated through placement or unit completion or equivalent or Corequisite: MCR 9

### Course Objectives

- Communication
- Problem Solving
- Make sense of problems, develop strategies to find solutions, and persevere in solving them.
- Reasoning
- Reason and draw conclusions or make decisions with quantitative information.
- Evaluation
- Technology
- Use appropriate technology in a given context.
- Students will engage in all course content described below in context to the health professions fields being supported.
- Topics in Arithmetic
- Interpret relative value of decimals and perform basic arithmetic of decimals.
- Interpret relative value of fractions and perform basic arithmetic of fractions.
- Simplify arithmetic expressions using the order of operations
- Calculate powers and roots of numbers
- Topics in Measurement and Conversions
- Solve linear equations.
- Solve problems involving percents and ratio proportions.
- Simplify and solve basic exponential and logarithmic expressions and equations. Include applications pertaining to health professions.
- Graph linear equations.
- Recognize the characteristics of linear, quadratic, and exponential functions as presented in their graphs.
- Topics in Statistics
- Interpret data presented in frequency distribution tables, bar graphs or histograms, pie charts, or line graphs.
- Compute mean, median, mode, and standard deviation for a data set.
- Topics in Geometry
- Use geometric formulas to calculate perimeter, area, surface area, volume.
- Be able to measure angles with a protractor.
- Solve problems involving angle measure.
- Topics in Health Professions
- Solve problems involving dilutions and dosages.
- Solve problems involving reconstituting solutions.
- Solve problems involving IV flow rates.

### Major Topics to be Included

- Basic Arithmetic
- Measurement and Conversions
- Algebra and Graphing
- Statistics
- Geometry
- Health Professions Applications

### MTH 154 - Quantitative Reasoning

### Course Description

Effective: 2019-08-01

### General Course Purpose

The Quantitative Reasoning course is organized around big mathematical concepts. The course's nontraditional treatment of content will help students develop conceptual understanding by supporting them in making connections between concepts and applying previously learned material to new contexts. The course will help to prepare students for success in future courses, gain skills for the workplace, and participate as productive citizens in our society. * Encourage students to do mathematics with real data. This includes recognizing the real world often has less than perfect data, ambiguities and multiple possible solutions. It also means equipping students to be intelligent consumers of quantitative data and reports. * Encourage students to engage in productive struggle to learn mathematics and make connections to the world in which they live.

### Course Prerequisites/Corequisites

Prerequisites: Competency in MTE 1-5 as demonstrated through placement or unit completion or equivalent or Corequisite: MCR 4: Learning Support for Quantitative Reasoning

### Course Objectives

- Communication
- Use appropriate mathematical language in oral, written and graphical forms.
- Read and interpret real world advertisements, consumer information, government forms and news articles containing quantitative information.
- Use quantitative information from multiple sources to make or critique an argument.
- Problem Solving
- Share strategies to find solutions to life application problems to make sense of the mathematical content and persevere in solving them.
- Apply strategies for solving open-ended questions requiring analysis and synthesis of multiple calculations, data summaries, and/or models.
- Apply problem solving strategies to applications requiring multiple levels of engagement.
- Reasoning
- Reason, model, and draw conclusions or make decisions with quantitative information.
- Draw conclusions or make decisions in quantitatively based situations that are dependent upon multiple factors. Students will analyze how different situations would affect the decisions.
- Present written or verbal justifications of decisions that include appropriate discussion of the mathematics involved.
- Recognize when additional information is needed.
- Recognize the appropriate ways to simplify a problem or its assumptions.
- Evaluation
- Evaluate the validity and possible biases in arguments presented in real world contexts based on multiple sources of quantitative information - for example; advertising, internet postings, consumer information, political arguments.
- Technology
- Use appropriate technology in a given context.
- Use a spreadsheet to organize quantitative information and make repeated calculations using simple formulas.
- Search for and apply internet-based tools appropriate for a given context - for example, an online tool to calculate credit card interest or a scheduling software package.
- Financial Literacy
- Simple Interest
- Define interest and its related terminology.
- Develop simple interest formula.
- Use simple interest formulas to analyze financial issues
- Compound Interest
- Compare and contrast compound interest and simple interest.
- Explore the mechanics of the compound interest formula addressing items such as why the exponent and (1+r/n) is used by building the concept of compounding interest through manual computation of a savings or credit account.
- Apply compound interest formulas to analyze financial issues
- Create a table or graph to show the difference between compound interest and simple interest.
- Borrowing
- Compute payments and charges associated with loans.
- Identify the true cost of a loan by computing APR
- Evaluate the costs of buying items on credit
- Compare total loan cost using varying lengths and interest rates.
- Investing
- Calculate the future value of an investment and analyze future value and present value of annuities (Take into consideration possible changes in rate, time, and money.)
- Compare two stocks and justify your desire to buy, sell, or hold stock investment.
- Explore different types of investment options and how choices may impact one's future such as in retirement.
- Perspective Matters - Number, Ratio, and Proportional Reasoning
- Solve real-life problems that include interpretation and comparison of summaries which extend beyond simple measures, such as weighted averages, indices, or ranking and evaluate claims based on them.
- Solve real-life problems requiring interpretation and comparison of various representations of ratios (i.e., fractions, decimals, rates, and percentages including part to part and part to whole, per capita data, growth and decay via absolute and relative change).
- Distinguish between proportional and non-proportional situations and, when appropriate, apply proportional reasoning leading to symbolic representation of the relationship. Recognize when proportional techniques do not apply.
- Solve real-life problems requiring conversion of units using dimensional analysis.
- Apply scale factors to perform indirect measurements (e.g., maps, blueprints, concentrations, dosages, and densities).
- Order real-life data written in scientific notation. The data should include different significant digits and different magnitudes.
- Modeling
- Observation
- Through an examination of examples, develop an ability to study physical systems in the real world by using abstract mathematical equations or computer programs
- Collect measurements of physical systems and relate them to the input values for functions or programs.
- Compare the predictions of a mathematical model with actual measurements obtained
- Quantitatively compare linear and exponential growth
- Explore behind the scenes of familiar models encountered in daily life (such as weather models, simple physical models, population models, etc.)
- Mathematical Modeling and Analysis
- Collect measurements and data gathered (possibly through surveys, internet, etc.) into tables, displays, charts, and simple graphs.
- Create graphs and charts that are well-labeled and convey the appropriate information based upon chart type.
- Explore interpolation and extrapolation of linear and non-linear data. Determine the appropriateness of interpolation and/or extrapolation.
- Identify and distinguish linear and non-linear data sets arrayed in graphs. Identifying when a linear or non-linear model or trend is reasonable for given data or context.
- Correctly associate a linear equation in two variables with its graph on a numerically accurate set of axes
- Numerically distinguish which one of a set of linear equations is modeled by a given set of (x,y) data points
- Identify a mathematical model's boundary values and limitations (and related values and regions where the model is undefined). Identify this as the domain of an algebraic model.
- Using measurements (or other data) gathered, and a computer program (spreadsheet or GDC) to create different regressions (linear and non-linear), determine the best model, and use the model to estimate future values.
- Application
- Starting with a verbally described requirement, generate an appropriate mathematical approach to creating a useful mathematical model for analysis
- Explore the graphical solutions to systems of simultaneous linear equations, and their real world applications
- Numerically analyze and mathematically critique the utility of specific mathematical models: instructor-provided, classmate generated, and self-generated
- Validity Studies
- Identify logical fallacies in popular culture: political speeches, advertisements, and other attempts to persuade
- Analyze arguments or statements from all forms of media to identify misleading information, biases, and statements of fact.
- Develop and apply a variety of strategies for verifying numerical and statistical information found through web searches.
- Apply the use of basic symbolic logic, truth values, and set theories to justify decisions made in real-life applications, such as if-then-else statements in spreadsheets, Venn Diagrams to organize options, truth values as related to spreadsheet and flow-chart output. (Students must have experience with both symbolic logic and basic truth tables to meet this standard.)

### Major Topics to be Included

- Financial Literacy (Interest, Borrowing, and Investing)
- Perspective (Complex Numeric Summaries, Ratios, Proportions, Conversions, Scaling, Scientific Notation)
- Modeling (Observation, Mathematical Modeling and Analysis, Application)
- Validity Studies (Statements, Conclusions, Validity, Bias, Logic, Set Theory)

### MTH 155 - Statistical Reasoning

### Course Description

Effective: 2019-08-01

### General Course Purpose

Statistical Reasoning is a first course in statistics for students whose college and career paths require knowledge of the fundamentals of the collection, analysis, and interpretation of data. Emphasis is placed on the development of statistical thinking, simulation, and the use of statistical software. Students should develop an appreciation of the need for data to make good decisions and an understanding of the dangers inherent in basing decisions on anecdotal evidence rather than data. To that end, students will use appropriate data-collection methods and statistical techniques to support reasonable conclusions through the following content learning outcomes: Data Exploration, Statistical Design, Probability and Simulation, and Statistical Inference.

### Course Prerequisites/Corequisites

Prerequisite: Competency in MTE 1-5 as demonstrated through placement or unit completion or equivalent or Co-requisite: MCR 5Learning Support for Statistical Reasoning.

### Course Objectives

- Communication
- Use appropriate statistical language in oral, written, and graphical terms.
- Read and interpret graphs and descriptive statistics.
- Problem Solving
- Make sense of problems, develop strategies to find solutions, and persevere in solving them.
- Understand what statistical question is being addressed, use appropriate strategies to answer the question of interest, and state conclusions using appropriate statistical language.
- Reasoning
- Reason, model, and draw conclusions or make decisions with quantitative information.
- Use probability, graphical, and numerical summaries of data, confidence intervals, and hypothesis testing methods to make decisions.
- Support conclusions by providing appropriate statistical justifications.
- Evaluation
- Identify errors such as inappropriate sampling methods, sources of bias, and potentially confounding variables, in both observational and experimental studies.
- Identify mathematical or statistical errors, inconsistencies, or missing information in arguments.
- Technology
- Use appropriate technology in a given context.
- Use some form of spreadsheet application to organize information and make repeated calculations using simple formulas and statistical functions.
- Use technology to calculate descriptive statistics and test hypotheses.
- Graphical and Numerical Data Analysis
- Identify the difference between quantitative and qualitative data
- Identify the difference between discrete and continuous quantitative data
- Construct and interpret graphical displays of data, including (but not limited to) box plots, line charts, histograms, and bar charts
- Construct and interpret frequency tables
- Compute measures of center (mean, median, mode), measures of variation, (range, interquartile range, standard deviation), and measures of position (percentiles, quartiles, standard scores)
- Sampling and Experimental Design
- Recognize a representative sample and describe its importance
- Identify methods of sampling
- Explain the differences between observational studies and experiments
- Recognize and explain the key concepts in experiments, including the selection of treatment and control groups, the placebo effect, and blinding
- Probability Concepts
- Describe the difference between relative frequency and theoretical probabilities and use each method to calculate probabilities of events
- Calculate probabilities of composite events using the complement rule, the addition rule, and the multiplication rule.
- Use the normal distribution to calculate probabilities
- Identify when the use of the normal distribution is appropriate.
- Recognize or restate the Central Limit Theorem and use it as appropriate.
- Statistical Inference
- Explain the difference between point and interval estimates.
- Construct and interpret confidence intervals for population means and proportions.
- Interpret the confidence level associated with an interval estimate.
- Conduct hypothesis tests for population means and proportions.
- Interpret the meaning of both rejecting and failing to reject the null hypothesis.
- Use a p-value to reach a conclusion in a hypothesis test.
- Identify the difference between practical significance and statistical significance.
- Correlation and Regression
- Analyze scatterplots for patterns, linearity, and influential points
- Determine the equation of a least-squares regression line and interpret its slope and intercept.
- Calculate and interpret the correlation coefficient and the coefficient of determination.
- Categorical Data Analysis
- Conduct a chi-squared test for independence between rows and columns of a two-way contingency table.

### Major Topics to be Included

- Graphical and Numerical Data Analysis
- Sampling and Experimental Design
- Probability
- Statistical Inference
- Correlation and Regression
- Categorical Data Analysis

### MTH 156 - Elementary Geometry

### Course Description

Effective: 2018-01-01

### General Course Purpose

To present the fundamentals of plane and solid geometry and introduce non-Euclidean geometries and current topics while modeling sound pedagogy to support students in presenting these concepts to their own students

### Course Prerequisites/Corequisites

Prerequisite: MTE 1-9 or placement.

### Course Objectives

- Basic Properties, Definitions, Symbols, and Proof
- Demonstrate geometric properties: intersecting lines, shortest distance between a point and a line, congruence of vertical angles, the seven basic Euclidean constructions, the polygon sum formula, the relationships between the base angles of an isosceles triangle and between its legs, intersecting planes, congruent segments, congruent angles, and congruent polygons
- Understand relevant geometry terminology
- Recognize relevant conventional geometric symbols
- Use definitions and postulates in two-column (deductive) proofs to prove basic theorems
- Apply properties learned to solve problems
- Properties of Quadrilaterals, Circles, and Congruent Triangles
- Demonstrate geometric properties: relationships between sides, angles, and diagonals of parallelograms, relationships between diagonals in rhombi and in rectangles, relationships between special angles, arcs, chords, secants, and tangents in circles, and conditions sufficient to prove or dispute congruence of triangles
- Understand relevant geometry terminology
- Recognize relevant conventional geometric symbols
- Use definitions, postulates, and proven theorems to prove triangles congruent in two-column proofs
- Apply properties learned to solve problems
- Transformations, Symmetry, and Area
- Demonstrate, investigate, and discover geometric properties using inductive reasoning: basic transformations including translations, rotations, reflections, two reflections over parallel lines and two reflections over intersecting lines, distances between relevant points and lines in these transformations, numbers of reflection symmetries of regular polygons and numbers and degrees of the rotational symmetries of regular polygons, formulae for the areas of parallelograms, triangles, trapezoids, and circles
- Demonstrate understanding of relevant geometry terminology
- Recognize relevant conventional geometric symbols
- Apply properties learned to solve problems

### Major Topics to be Included

- Basic Properties, Definitions, Symbols, and Proof
- Properties of Quadrilaterals, Circles, and Congruent Triangles
- Transformations, Symmetry, and Area
- Theorem of Pythagoras, Solid Geometry, Non-Euclidean Geometries and Topology

### MTH 161 - PreCalculus I

### Course Description

Effective: 2021-08-01

### General Course Purpose

The general purpose of this one-semester course is to prepare students for a course in statistics or applied calculus sequence by providing them with the necessary competencies in algebra and functions. Precalculus I can also be applied in conjunction with Precalculus II in preparation for a course in calculus with analytic geometry.

### Course Prerequisites/Corequisites

Prerequisites: Competency in MTE 1-9 as demonstrated through placement or unit completion or equivalent or Corequisite: MCR 6: Learning Support for Precalculus I

### Course Objectives

- Relations and Functions
- Distinguish between relations and functions.
- Evaluate functions both numerically and algebraically.
- Determine the domain and range of functions in general, including root and rational functions.
- Perform arithmetic operations on functions, including the composition of functions and the difference quotient.
- Identify and graph linear, absolute value, quadratic, cubic, and square root functions and their transformations.
- Determine and verify inverses of one-to-one functions.
- Polynomial and Rational Functions
- Determine the general and standard forms of quadratic functions.
- Use formula and completing the square methods to determine the standard form of a quadratic function.
- Identify intercepts, vertex, and orientation of the parabola and use these to graph quadratic functions.
- Identify zeros (real-valued roots) and complex roots, and determine end behavior of higher order polynomials and graph the polynomial, and graph.
- Determine if a function demonstrates even or odd symmetry.
- Use the Fundamental Theorem of Algebra, Rational Root test, and Linear Factorization Theorem to factor polynomials and determine the zeros over the complex numbers.
- Identify intercepts, end behavior, and asymptotes of rational functions, and graph.
- Solve polynomial and rational inequalities.
- Interpret the algebraic and graphical meaning of equality of functions (f(x) = g(x)) and inequality of functions (f(x) > g(x))
- Exponential and Logarithmic Functions
- Identify and graph exponential and logarithmic functions and their transformations.
- Use properties of logarithms to simplify and expand logarithmic expressions.
- Convert between exponential and logarithmic forms and demonstrate an understanding of the relationship between the two forms.
- Solve exponential and logarithmic equations using one-to-one and inverse properties.
- Solve application problems involving exponential and logarithmic functions.
- Systems of Equations
- Solve three variable linear systems of equations using the Gaussian elimination method.

### Major Topics to be Included

- Relations and Functions
- Polynomial and Rational Functions
- Exponential and Logarithmic Functions
- Systems of Equations

### MTH 162 - PreCalculus II

### Course Description

Effective: 2021-08-01

### General Course Purpose

The general purpose of this one-semester course, in conjunction with Precalculus I, is to prepare students for the skills and level of rigor needed for successful study in a sequence of courses in calculus with analytic geometry.

### Course Prerequisites/Corequisites

Prerequisites: Placement or completion of MTH 161: Precalculus I or equivalent with a grade of C or better

### Course Objectives

- Trigonometric Functions
- Identify angles in standard form in both degree and radian format and convert from one to the other.
- Find the arc length.
- Find the value of trigonometric functions of common angles without a calculator using the unit circle and right triangle trigonometry.
- Use reference angles to evaluate trig functions.
- Find the value of trigonometric functions of angles using a calculator.
- Use fundamental trigonometric identities to simplify trigonometric expressions.
- Graph the six trigonometric functions using the amplitude, period, phase and vertical shifts.
- Use trig functions to model applications in the life and natural sciences.
- Analytic Trigonometry
- Use the fundamental, quotient, Pythagorean, co-function, and even/odd identities to verify trigonometric identities.
- Use the sum and difference, double angle, half-angle formulas to evaluate the exact values of trigonometric expressions.
- Determine exact values of expressions, including composite expressions, involving inverse trigonometric functions.
- Solve trigonometric equations over restricted and non-restricted domains.
- Applications of Trigonometry
- Solve right triangles and applications involving right triangles.
- Use the Law of Sines and Cosines to solve oblique triangles and applications.
- Conics
- Identify the conic sections of the form:Ax^2+By^2+Dx+Ey+F=0.
- Write the equations of circles, parabolas, ellipses, and hyperbolas in standard form centered both at the origin and not at the origin.
- Identify essential characteristics unique to each conic.
- Graph equations in conic sections, centered both at the origin and not at the origin.
- Solve applications involving conic sections.
- Sequences and Series (Optional unit at the discretion of the department, not required for transfer.)
- Identify the terms of geometric sequences.
- Find a particular term of geometric sequence.
- Determine the formula for the an term of geometric sequences.
- Find the sum of first n terms of finite geometric series.
- Find the sum of infinite geometric series.
- Introduce arithmetic concepts as time allows.

### Major Topics to be Included

- Trigonometric Functions
- Analytic Trigonometry
- Applications of Trigonometry
- Conics

### MTH 165 - Finite Math

### Course Description

Effective: 2018-01-01

### General Course Purpose

The general purpose is to expose students to the use of mathematics as a tool (applications and mathematical modeling), as well as developing problem solving and critical thinking abilities.

### Course Prerequisites/Corequisites

Prerequisite: MTE 1-9 or placement.

### Course Objectives

- Systems of Equations
- Set-up and solve business applications modeled by systems of equations by various methods.
- Find inverse matrices, row reduced matrices and perform matrix operations. For 3x3 matrices or larger, a graphing calculator may be used to find inverses.
- Write matrix equations and use them to solve "Input-Output" problems from economics (Leontief Models) with the calculator.
- Finance
- Explain the differences between the formulas for simple, compound, and continuous interest related to investments, annuities, and loans, with an emphasis on the role and appropriate use of exponential growth and summation.
- Investigate loan and investment options and utilize the appropriate formulas to solve a variety of problems.
- Linear Programming
- Solve simple linear programming problems applying the geometric method.
- Solve standard maximization and minimization linear programming problems by the Simplex Method.
- Model business case studies applying linear program concepts and applying appropriate methods to draw conclusions and make recommendations.
- Probability
- Use simple counting methods: multiplicative, additive principle, permutations and combinations to answer counting theory questions.
- Form and solve probability problems with "and" and "or", intersection and union.
- Identify and solve conditional probability problems with probability trees and use them with Bayes? Theorem to solve applied problems in business.
- Form probability distributions for simple random variables and use ?mathematical expectation? to solve decision analysis problems from sentence descriptions.
- Markov Chains
- Construct "transition" matrices to describe a stochastic process and use them to solve problems about states after transition periods.
- Find "steady state" or long-range predictions for regular transition matrices and applications (use the powers of matrices on the calculator to find).
- Application
- Complete a semester project demonstrating broad knowledge of course content and applying appropriate technology in project development. (Instructors see pedagogical notes in course docs.)

### Major Topics to be Included

- Systems of Equations
- Finance
- Linear Programming
- Probability
- Markov Chains
- Applications

### MTH 167 - PreCalculus with Trigonometry

### Course Description

Effective: 2021-08-01

### General Course Purpose

The general purpose of this one-semester course is to prepare students for the skills and level of rigor needed for successful study in a sequence of courses in calculus with analytic geometry.

### Course Prerequisites/Corequisites

Prerequisites: Competency in MTE 1-9 as demonstrated through placement or unit completion or equivalent or Corequisite: MCR 7: Learning Support for Precalculus w/ Trigonometry

### Course Objectives

- Relations and Functions
- Distinguish between relations and functions.
- Evaluate functions both numerically and algebraically.
- Determine the domain and range of functions in general, including root and rational functions.
- Perform arithmetic operations on functions, including the composition of functions and the difference quotient.
- Identify and graph linear, absolute value, quadratic, cubic, and square root functions and their transformations.
- Determine and verify inverses of one-to-one functions.
- Polynomial and Rational Functions
- Determine the general and standard forms of quadratic functions.
- Use formula and completing the square methods to determine the standard form of a quadratic function.
- Identify intercepts, vertex, and orientation of the parabola and use these to graph quadratic functions.
- Identify zeros (real-valued roots) and complex roots, and determine end behavior of higher order polynomials and graph the polynomial, and graph.
- Determine if a function demonstrates even or odd symmetry.
- Use the Fundamental Theorem of Algebra, Rational Root test, and Linear Factorization Theorem to factor polynomials and determine the zeros over the complex numbers.
- Identify intercepts, end behavior, and asymptotes of rational functions and graph.
- Solve polynomial and rational inequalities.
- Interpret the algebraic and graphical meaning of equality of functions (f(x) = g(x)) and inequality of functions (f(x) > g(x))
- Exponential and Logarithmic Functions
- Identify and graph exponential and logarithmic functions and their transformations.
- Use properties of logarithms to simplify and expand logarithmic expressions.
- Convert between exponential and logarithmic forms and demonstrate an understanding of the relationship between the two forms.
- Solve exponential and logarithmic equations using one-to-one and inverse properties.
- Solve application problems involving exponential and logarithmic functions.
- Systems of Equations
- Solve three variable linear systems of equations using the Gaussian elimination method.
- Trigonometric Functions
- Identify angles in standard form in both degree and radian format and convert from one to the other.
- Find the arc length.
- Find the value of trigonometric functions of common angles without a calculator using the unit circle and right triangle trigonometry.
- Use reference angles to evaluate trig functions.
- Find the value of trigonometric functions of angles using a calculator.
- Use fundamental trigonometric identities to simplify trigonometric expressions.
- Graph the six trigonometric functions using the amplitude, period, phase and vertical shifts.
- Use trig functions to model applications in the life and natural sciences.
- Analytic Trigonometry
- Use the fundamental, quotient, Pythagorean, co-function, and even/odd identities to verify trigonometric identities.
- Use the sum and difference, double angle, half-angle formulas to evaluate the exact values of trigonometric expressions.
- Determine exact values of expressions, including composite expressions, involving inverse trigonometric functions.
- Solve trigonometric equations over restricted and non-restricted domains.
- Applications of Trigonometry
- Solve right triangles and applications involving right triangles.
- Use the Law of Sines and Cosines to solve oblique triangles and applications.
- Conics
- Identify the conic sections of the form:Ax^2+By^2+Dx+Ey+F=0.
- Write the equations of circles, parabolas, ellipses, and hyperbolas in standard form centered both at the origin and not at the origin.
- Identify essential characteristics unique to each conic
- Graph equations in conic sections, centered both at the origin and not at the origin.
- Solve applications involving conic sections.
- Sequences and Series (Optional unit at the discretion of the department. Not required for transfer.)
- Identify the terms of geometric sequences.
- Find a particular term of geometric sequence.
- Determine the formula for the an term of geometric sequences.
- Find the sum of first n terms of finite geometric series.
- Find the sum of infinite geometric series.
- Introduce arithmetic concepts as time allows.

### Major Topics to be Included

- Relations and Functions
- Polynomial and Rational Functions
- Exponential and Logarithmic Functions
- Systems of Equations and Inequalities
- Trigonometric Functions
- Analytic Trigonometry
- Applications of Trigonometry
- Conics

### MTH 245 - Statistics I

### Course Description

Effective: 2019-08-01

### General Course Purpose

To serve as a first course in data collection and analysis, applied probability, and statistical inference for students needing greater depth in preparation for application of content to workforce task or further study in statistical research methods.

### Course Prerequisites/Corequisites

Prerequisite: Completion of MTH 154 or MTH 161 or equivalent with a grade of C or better.

### Course Objectives

- Graphical and Numerical Data Analysis
- Identify the difference between qualitative, discrete quantitative, and continuous quantitative data.
- Construct and interpret graphical displays of data, including (but not limited to) frequency tables, box plots, line charts, histograms, and bar charts.
- Compute measures of center (mean, weighted mean, median, mode), measures of variation, (range, interquartile range, standard deviation, variance), and measures of position (percentiles, quartiles, standard scores).
- Apply the Empirical Rule
- Sampling/Experimental Design
- Recognize a representative sample and describe its importance.
- Identify methods of sampling.
- Explain the differences between observational studies and experiments.
- Recognize and explain the key concepts in experiments.
- Probability Concepts
- Describe the difference between relative frequency and theoretical probabilities and use each method to calculate probabilities of events.
- Determine whether two events are mutually exclusive or independent.
- Determine probabilities of composite events using the complement rule, the addition rule, and the multiplication rule.
- Apply the Law of Large Numbers.
- Distinguish between discrete and continuous random variables.
- Use the binomial, normal, and t distributions to calculate probabilities.
- Recognize or restate the Central Limit Theorem and use it as appropriate.
- Identify when the use of the normal distribution is appropriate.
- Identify when the t distribution is preferable to the normal distribution in statistical inference.
- Distinguish between the distribution of a random variable and the sampling distributions of its associated sample statistics.
- Identify the sampling distributions of the sample mean and the sample proportion and use them to make statistical inferences.
- Univariate Statistical Inference
- Explain the difference between point and interval estimates.
- Describe the concepts of best estimate and margin of error.
- Construct confidence intervals for population means and proportions.
- Interpret the confidence level associated with an interval estimate.
- Distinguish between a two-tailed, left-tailed, and right-tailed hypothesis tests.
- Conduct hypothesis tests for population means and proportions.
- Interpret the meaning of both rejecting and failing to reject the null hypothesis.
- Describe Type I and Type II errors in the context of specific hypothesis tests.
- Use a p-value to reach a conclusion in a hypothesis test.
- Identify the interrelationship between hypothesis tests and confidence intervals.
- Two-Sample Statistical Inference
- Construct and interpret a confidence interval for the difference between two population means where the samples are independent and the population variances are assumed unequal.
- Construct and interpret a confidence interval for the difference between two population means where the data consists of matched pairs.
- Conduct a hypothesis test for the equality of two population means where the samples are independent and the population variances are assumed unequal.
- Conduct a hypothesis test for the equality of two population means where the data consists of matched pairs.
- Correlation and Regression
- Analyze scatterplots for patterns, linearity, and influential points.
- Determine the equation of a least-squares regression line and interpret its slope and intercept.
- Calculate and interpret the correlation coefficient and the coefficient of determination.
- Conduct a hypothesis test for the presence of correlation.
- Technology Application
- Construct statistical tables, charts, and graphs using appropriate technology.
- Calculate descriptive and inferential statistics using an appropriate statistical software package.
- Complete statistical project. Students are required to complete some form of semester project in their course that is worth a significant portion of the student's grade. This could be either an individual or group effort, and could be completed in stages through the semester or as a single, stand-alone exercise. As a minimum, the project should require students to manipulate and draw statistical inferences from a large, realistic data set using a statistical software package.

### Major Topics to be Included

- Graphical and Numerical Data
- Sampling and Experimental Design
- Probability
- Univariate Statistical Inference
- Two-Sample Statistical Inference
- Correlation and Regression

### MTH 246 - Statistics II

### Course Description

Effective: 2017-08-01

### General Course Purpose

To serve as a second course in statistics that focuses on multivariate and nonparametric techniques useful to business, science, and social science majors.

### Course Prerequisites/Corequisites

Prerequisite: Completion of MTH 245 or equivalent with a grade of C or better.

### Course Objectives

- Review of Hypothesis Testing
- Conduct hypothesis tests for population means and proportions.
- Conduct a hypothesis test for the equality of two population means where:
- The samples are independent and the population variances are assumed unequal.
- The data consists of matched pairs.
- Conduct a hypothesis test for the presence of correlation.
- Experimental Design
- Define and apply the basic principles of design, including randomization, replication, and treatment/control groups.
- Explain single and double blinding.
- Describe the placebo and experimenter effects and describe how they can be countered using blinding.
- Design experiments using the following methods:
- Completely randomized.
- Randomized block.
- Matched pairs.
- Explain the concept of confounding.
- Correlation and Regression
- Construct and interpret the residual plot related to a simple least-squares regression model.
- Conduct hypothesis tests related to the coefficients of a simple least-squares regression model.
- Construct and Apply a logistic regression model.
- Calculate the coefficient of determination, the adjusted coefficient of determination, and overall P-value for a multiple regression model and use them to construct a best-fit multiple regression equation.
- Categorical Data Anaylsis
- Conduct chi-squared tests for:
- Goodness of fit.
- Independence between rows and columns of a two-way contingency table.
- Homogeneity of population proportions.
- Analysis of Variance (ANOVA)
- Conduct one-way ANOVA to test the equality of two or more population means for both equal and unequal sample sizes and recognize its relationship to the pooled two sample t-test.
- Conduct a multiple comparison test, such as Tukey's HSD, to determine which of the three or more population means differs from the others.
- Conduct two-way ANOVA on sample data categorized with two fixed factors.
- Nonparametric Methods
- Determine the rank of each element of a sorted data set.
- Identify the relationship between a nonparametric test and its corresponding parametric technique.
- Conduct a Wilcoxon signed-ranks test for a single sample.
- Conduct a Wilcoxon signed-ranks test for matched pairs.
- Technology Application
- Construct statistical tables, charts, and graphs using appropriate technology.
- Perform statistical calculations using an appropriate statistical software package.
- Complete statistical project. Students are required to complete some form of semester project in their course that is worth a significant portion of the student's grade. This could be either an individual or group effort, and could be completed in stages through the semester or as a single, stand-alone exercise. As a minimum, the project should require students to manipulate and draw statistical inferences from a large, realistic data set using a statistical software package.

### Major Topics to be Included

- Hypothesis Testing
- Experimental Design
- Correlation and Regression
- Categorical Data Analysis
- Analysis of Variance
- Nonparametric Methods

### MTH 261 - Applied Calculus I

### Course Description

Effective: 2019-08-01

### General Course Purpose

The general purpose of this one-semester course is to prepare students in business, social sciences and life sciences to apply concepts of differentiation and integration of algebraic, exponential and logarithmic functions in future mathematics and degree coursework.

### Course Prerequisites/Corequisites

Prerequisite: Completion of MTH 161 or equivalent with a grade of C or better.

### Course Objectives

- Limits and Continuity
- Calculate and interpret limits at particular x-values and as x approaches infinity.
- Determine whether a function is continuous at a given point and over open/closed intervals.
- Derivatives
- Find the derivative of a function applying the limit definition of the derivative.
- Interpret the derivative as both the instantaneous rate of change of a function and the slope of the tangent line to the graph of a function.
- Use the Power, Product, Quotient, and Chain rules to find the derivatives of algebraic, exponential, and logarithmic functions
- Applications of the Derivative
- Find the relative extreme values for a continuous function using the First and Second Derivative Tests.
- Apply derivatives to solve problems in life sciences, social sciences, and business.
- Find higher order derivatives and interpret their meaning.
- Use derivatives to model position, velocity, and acceleration.
- Apply First and Second Derivative Tests to determine relative extrema, intervals of increase and decrease, points of inflection, and intervals of concavity.
- Graph functions, without the use of a calculator, using limits, derivatives and asymptotes.
- Use derivatives to find absolute extrema and to solve optimization problems in life sciences, social sciences, and business.
- Perform implicit differentiation and apply the concept to related rate problems.AND/OR
- Evaluate partial derivatives and interpret their meaning.
- Integration and Its Applications
- Use basic integration formulas to find indefinite integrals of algebraic, exponential, and logarithmic functions.
- Develop the concept of definite integral using Riemann Sums.
- Evaluate definite integrals using Fundamental Theorem of Calculus.
- Use the method of integration by substitution to determine indefinite integrals.
- Evaluate definite integrals using substitution with original and new limits of integration.
- Calculate the area under a curve over a closed interval [a, b].
- Calculate the area bounded by the graph of two or more functions by using points of intersections.
- Use integration to solve applications in life sciences such as exponential growth and decay.
- Use integration to solve applications in business and economics, such as future value and consumer and producer's surplus

### Major Topics to be Included

- Limits and Continuity
- Derivatives
- Applications of the Derivative
- Integration and Its Applications

### MTH 262 - Applied Calculus II

### Course Description

Effective: 2017-08-01

### General Course Purpose

The general purpose of this second course in Applied Calculus is to extend the study of the techniques and applications of calculus and prepare students in business, social sciences and life sciences to apply these concepts in future mathematics and degree coursework. This course is intended for those who will transfer to an institution requiring two semesters of applied calculus in one of these disciplines.

### Course Prerequisites/Corequisites

Prerequisite: Completion of MTH 261 or equivalent with a grade of C or better.

### Course Objectives

- Integration and Its Applications
- Use basic integration formulas to find indefinite integrals of algebraic, exponential, and logarithmic functions.
- Develop the concept of definite integral using Reimann Sums.
- Evaluate definite integrals using Fundamental Theorem of Calculus.
- Use the method of integration by substitution to determine indefinite integrals.
- Evaluate definite integrals using substitution with original and new limits of integration.
- Calculate the area under a curve over a closed interval [a, b].
- Calculate the area bounded by the graph of two or more functions by using points of intersections.
- Use integration to solve applications in business and economics, such as future value and consumer and producer?s surplus.
- Techniques of Integration ? Differential Equations
- Use the method of integration by parts to find antiderivatives and evaluate definite integrals.
- Integrate using tables of integrals.
- Approximate integrals using numerical integration (Trapezoidal and Simpson's rules).
- Evaluate improper integrals.
- Solve basic first order differential equations.
- Use simple integration and separation of variables to solve differential equations.
- Multivariable Calculus
- Evaluate functions of several variables and sketch three-dimensional surfaces.
- Calculate partial derivatives of functions of several variables.
- Calculate maxima and minima of functions of several variables.
- Calculate constrained maxima and minima using the Method of LaGrange Multipliers.
- Evaluate multiple integrals.

### Major Topics to be Included

- Integration and Its Applications
- Techniques of Integration - Differential Equations
- Multivariable Calculus

### MTH 263 - Calculus I

### Course Description

Effective: 2019-08-01

### General Course Purpose

The general purpose of this first course in a three course sequence is to prepare students for further study in calculus with analytic geometry by providing them with the necessary competencies in finding limits, differentiation and integration.

### Course Prerequisites/Corequisites

Prerequisite: Completion of MTH 167 or MTH 161/162 or equivalent with a grade of C or better.

### Course Objectives

- Limits
- Differentiate between the limit and the value of a function at a point
- Find the limit of a function by numerical, graphical and analytic methods
- Apply Limit Laws
- Calculate one-sided limit of a function
- Prove the existence of a limit using precise definition of the limit
- Determine the continuity of a function
- Calculate Vertical and Horizontal asymptotes using limits
- Derivatives and Differentiation Rules
- Define Derivatives and Rates of Change
- Compute derivatives of basic functions using the definition of the derivative
- Differentiate polynomial, rational, radical, exponential and logarithmic functions
- Find equation of a tangent line using derivative
- Differentiate trigonometric functions
- Apply product, quotient, chain rules
- Apply implicit differentiation and find derivatives of inverse trigonometric functions
- Apply concept of rates of change to natural and social sciences
- Apply the concept of related rates
- Define hyperbolic functions and their derivatives
- Find linear approximation of a function at a given point
- Applications of Differentiation
- Calculate local and absolute maximum and minimum values of a function
- Apply Rolle's Theorem and Mean Value Theorem to study properties of a function
- Find critical points, and intervals of increasing and decreasing values of a function
- Find points of inflection and intervals of different concavities
- Sketch a curve for a given function
- Apply rules of differentiation to solve optimization problems
- Find antiderivatives for basic functions using knowledge of derivatives
- Integrals
- Relate areas to definite integrals using sigma notation, Riemann Sums, and limits. [Note: L?Hopital?s Rule is in Calc II but may be used for instructional purposes here.]
- Apply Fundamental Theorem of Calculus to find definite integrals and derivatives
- Find indefinite integrals of polynomials and basic trigonometric and exponential function
- Apply Net Change Theorem
- Perform integration using substitution
- Find areas between curves
- Find average value of a function

### Major Topics to be Included

- Limits
- Derivatives and Differentiation Rules
- Applications of Differentiation
- Integrals

### MTH 264 - Calculus II

### Course Description

Effective: 2019-08-01

### General Course Purpose

The general purpose of this second course in a three course sequence is to prepare students for further study in calculus with analytic geometry as well as topics such as linear algebra and differential equations so that they meet the necessary competencies in integration, algebraic and transcendental functions, graphing, power series and their applications.

### Course Prerequisites/Corequisites

Prerequisite: Completion of MTH 263 or equivalent with a grade of C or better.

### Course Objectives

- Applications of Integration
- Compute Volumes by cross-section
- Compute Volumes by disk-washer
- Compute Volumes by shells
- Compute Work (spring, rope)
- Compute Work (pumping liquids)
- Compute Arc length
- Compute Areas of surfaces of revolution
- Compute Application (center of mass)
- Techniques of Integration
- Integrate by parts
- Calculate trigonometric integrals
- Calculate integrals by trigonometric substitution
- Define the indeterminate form and apply L'Hopital's Rule.
- Calculate improper integrals
- Integrate by partial fractions
- Integrate using Tables and Software
- Approximate integrals (Trapezoidal, Simpson) with error estimation.
- Infinite Sequences and Series
- Write definition of and understand Sequences
- Write definition of and understand Series (intro)
- Determine convergence by integral test
- Determine convergence by comparison test
- Determine convergence of alternating series
- Determine absolute convergence (ratio, root tests)
- Apply strategies for testing series
- Work with power series
- Represent functions as power series
- Find Taylor, Maclaurin series & polynomials
- Calculate Taylor and Maclaurin series
- Parametric Curves and Polar Coordinates
- Represent curves by parametric equations
- Perform calculus with parametric curves
- Use and graph with polar system
- Calculate areas and lengths in polar coordinates
- Define the conic forms in polar form

### Major Topics to be Included

- Applications of Integration
- Techniques of Integration
- Infinite Sequences and Series
- Parametric Curves and Polar Coordinates

### MTH 265 - Calculus III

### Course Description

Effective: 2017-08-01

### General Course Purpose

The general purpose of this third course in a three course sequence is to prepare students for further study in mathematics, engineering and science programs by providing the necessary competencies in calculus concepts in the three dimensional space.

### Course Prerequisites/Corequisites

Prerequisite: Completion of MTH 264: Calculus II or equivalent with a grade of C or better

### Course Objectives

- Vectors and the Geometry of Space
- Identify and apply the parts of the three-dimensional coordinate system, distance formula and the equation of the sphere
- Compute the magnitude, scalar multiple of a vector, and find a unit vector in the direction of a given vector
- Calculate the sum, difference, and linear combination of vectors
- Calculate the dot product and cross product of vectors, use the products to calculate the angle between two vectors, and to determine whether vectors are perpendicular or parallel
- Determine the scalar and vector projections
- Write the equations of lines and planes in space
- Draw various quadric surfaces and cylinders using the concepts of trace and cross-section
- Vectors and the Geometry of Space
- Sketch vector valued functions
- Determine the relation between these functions and the parametric representations of space curves
- Compute the limit, derivative, and integral of a vector valued function
- Calculate the arc length of a curve and its curvature; identify the unit tangent, unit normal and binormal vectors
- Calculate the tangential and normal components of a vector
- Describe motion in space
- Partial Derivatives
- Define functions of several variables and know the concepts of dependent variable, independent variables, domain and range.
- Calculate limits of functions in two variables or prove that a limit does not exist;
- Test the continuity of functions of several variables;
- Calculate partial derivatives and interpret them geometrically, calculate higher partial derivatives
- Determine the equation of a tangent plane to a surface; calculate the change in a function by linearization and by differentials,
- Determine total and partial derivatives using chain rules,
- Calculate directional derivatives and interpret the results
- Identify the gradient, interpret the gradient, and use it to find directional derivative
- Apply intuitive knowledge of concepts of extrema for functions of several variables, and apply them to mathematical and applied problems. Lagrange multipliers.
- Multiple Integrals
- Define double integral, evaluate a double integral by the definition and the midpoint rule and describe the simplest properties of them.
- Calculate iterated integrals by Fubini'sTheorem
- Calculate double integrals over general regions and use geometric interpretation of double integral as a volume to calculate such volumes. Some applications of double integrals may include computing mass, electric charge, center of mass and moment of inertia
- Evaluate double integrals in polar coordinates to calculate polar areas, evaluate Cartesian double integrals of a particular form by transforming to polar double integrals
- Define triple integrals, evaluate triple integrals, and know the simplest properties of them. Calculate volumes by triple integrals
- Transform between Cartesian, cylindrical, and spherical coordinate systems; evaluate triple integrals in all three coordinate systems; make a change of variables using the Jacobian
- Vector Calculus
- Describe vector fields in two and three dimensions graphically; determine if vector fields are conservative, directly and using theorems
- Identify the meaning and set-up of line integrals and evaluate line integrals
- Apply the connection between the concepts of conservative force field, independence of path, the existence of potentials, and the fundamental theorem for line integrals. Calculate the work done by a force as a line integral
- Apply Green's theorem to evaluate line integrals as double integrals and conversely
- Calculate and interpret the curl, gradient, and the divergence of a vector field
- Evaluate a surface integral. Understand the concept of flux of a vector field
- State and use Stokes Theorem
- State and use the Divergence Theorem

### Major Topics to be Included

- Vectors and the Geometry of Space
- Vector Functions
- Partial Derivatives
- Multiple Integrals
- Vector Calculus

### MTH 266 - Linear Algebra

### Course Description

Effective: 2017-08-01

### General Course Purpose

The general purpose is to give the student a solid grasp of the methods and applications of linear algebra, and to prepare the student for further coursework in mathematics, engineering, computer science and the sciences.

### Course Prerequisites/Corequisites

Prerequisite: Completion of MTH 263 or equivalent with a grade of B or better or MTH 264 or equivalent with a grade of C or better.

### Course Objectives

- Matrices and Systems of Equations
- Use correct matrix terminology to describes various types and features of matrices (triangular, symmetric, row echelon form, et.al.)
- Use Gauss-Jordan elimination to transform a matrix into reduced row echelon form
- Determine conditions such that a given system of equations will have no solution, exactly one solution, or infinitely many solutions
- Write the solution set for a system of linear equations by interpreting the reduced row echelon form of the augmented matrix, including expressing infinitely many solutions in terms of free parameters
- Write and solve a system of equations modeling real world situations such as electric circuits or traffic flow
- Matrix Operations and Matrix Inverses
- Perform the operations of matrix-matrix addition, scalar-matrix multiplication, and matrix-matrix multiplication on real and complex valued matrices
- State and prove the algebraic properties of matrix operations
- Find the transpose of a real valued matrix and the conjugate transpose of a complex valued matrix
- Identify if a matrix is symmetric (real valued)
- Find the inverse of a matrix, if it exists, and know conditions for invertibility.
- Use inverses to solve a linear system of equations
- Determinants
- Compute the determinant of a square matrix using cofactor expansion
- State, prove, and apply determinant properties, including determinant of a product, inverse, transpose, and diagonal matrix
- Use the determinant to determine whether a matrix is singular or nonsingular
- Use the determinant of a coefficient matrix to determine whether a system of equations has a unique solution
- Norm, Inner Product, and Vector Spaces
- Perform operations (addition, scalar multiplication, dot product) on vectors in Rn and interpret in terms of the underlying geometry
- Determine whether a given set with defined operations is a vector space
- Basis, Dimension, and Subspaces
- Determine whether a vector is a linear combination of a given set; express a vector as a linear combination of a given set of vectors
- Determine whether a set of vectors is linearly dependent or independent
- Determine bases for and dimension of vector spaces/subspaces and give the dimension of the space
- Prove or disprove that a given subset is a subspace of Rn
- Reduce a spanning set of vectors to a basis
- Extend a linearly independent set of vectors to a basis
- Find a basis for the column space or row space and the rank of a matrix
- Make determinations concerning independence, spanning, basis, dimension, orthogonality and orthonormality with regards to vector spaces
- Linear Transformations
- Use matrix transformations to perform rotations, reflections, and dilations in Rn
- Verify whether a transformation is linear
- Perform operations on linear transformations including sum, difference and composition
- Identify whether a linear transformation is one-to-one and/or onto and whether it has an inverse
- Find the matrix corresponding to a given linear transformation T: Rn -> Rm
- Find the kernel and range of a linear transformation
- State and apply the rank-nullity theorem
- Compute the change of basis matrix needed to express a given vector as the coordinate vector with respect to a given basis
- Eigenvalues and Eigenvectors
- Calculate the eigenvalues of a square matrix, including complex eigenvalues.
- Calculate the eigenvectors that correspond to a given eigenvalue, including complex eigenvalues and eigenvectors.
- Compute singular values
- Determine if a matrix is diagonalizable
- Diagonalize a matrix

### Major Topics to be Included

- Matrices and Systems of Equations
- Matrix Operations and Matrix Inverses
- Determinants
- Norm, Inner Product, and Vector Spaces
- Basis, Dimension, and Subspaces
- Linear Transformations
- Eigenvalues and Eigenvectors

### MTH 267 - Differential Equations

### Course Description

Effective: 2017-08-01

### General Course Purpose

The general purpose is to give the student a solid grasp of the methods solving and applying differential equations and to prepare the student for further coursework in mathematics, engineering, computer science and the sciences.

### Course Prerequisites/Corequisites

Prerequisite: Completion of MTH 264 or equivalent with a grade of C or better.

### Course Objectives

- First Order Differential Equations
- Classify a differential equation as linear or nonlinear.
- Understand and create a directional field for an arbitrary first-order differential equation.
- Determine the order, linearity or nonlinearity, of a differential equation.
- Solve first order linear differential equations.
- Solve Separable differential equations.
- Solve initial value problems.
- Numerical Approximations
- Use the Euler or tangent line method to find an approximate solution to a linear differential equation.
- Higher Order Differential Equations
- Solve second order homogenous linear differential equations with constant coefficients including those with complex roots and real roots.
- Determine the Fundamental solution set for a linear homogeneous equation.
- Calculate the Wronskian.
- Use the method of Reduction of order.
- Solve nonhomogeneous differential equations using the method of undetermined coefficients.
- Solve nonhomogeneous differential equations using the method of variation of parameters.
- Applications of Differential Equations, Springs-Mass-Damper, Electrical Circuits, Mixing Problems
- Solve applications of differential equations as applied to Newton's Law of cooling, population dynamics, mixing problems, and radioactive decay. (1st order)
- Solve springs-mass-damper, electrical circuits, and/or mixing problems (2nd order)
- Solve application problems involving external inputs (non-homogenous problems).
- Laplace Transforms
- Use the definition of the Laplace transform to find transforms of simple functions
- Find Laplace transforms of derivatives of functions whose transforms are known
- Find inverse Laplace transforms of various functions.
- Use Laplace transforms to solve ODEs.

### Major Topics to be Included

- First Order Differential Equations
- Numerical Approximations
- Higher Order Differential Equations
- Applications of Differential Equations, Springs-Mass-Damper, Electrical Circuits, Mixing Problems
- Laplace Transforms

### MTH 280 - College Geometry

### Course Description

Effective: 2018-01-01

### General Course Purpose

Presents topics in Euclidean and non-Euclidean geometries chosen to prepare individuals for teaching geometry at the high school level or to other areas of study applying geometric principles.

### Course Prerequisites/Corequisites

Prerequisite: Completion of MTH 263 with a grade of C or better or equivalent.

### Course Objectives

- Historic Overview of Euclidean Geometry
- Describe the historic role of Euclid's Elements in the development of modern geometry
- State the axioms ("postulates" and "common notions") that are the foundation of Euclid's geometry
- Upon reviewing familiar results of "high school" Euclidean geometry, write basic proofs using the Elements as the source (focus on definitions and theorems of Book One)
- Introduction to Logic and Proof
- Identify the hypothesis and conclusion of a conditional statement
- Write the inverse, converse, and contrapositive of a conditional
- Identify argument structures/rules of inference (e.g. modus ponens)
- Recognize styles of direct and indirect proof, proof by contradiction, proof by cases
- Axiomatic Systems
- Define an axiomatic system and identify its parts
- Determine if a set of axioms is consistent, independent, complete
- Prove theorems using rules of inference within an abstract axiomatic system, given a list of the available definitions, axioms and theorems
- Construct models that satisfy the given axioms of a system and determine if the system is categorical
- State and apply the axioms that define finite projective and affine geometries (e.g. Fano Plane)
- Neutral Geometry
- Progress through the development of a neutral geometry based on Hilbert's (or similar) axioms, starting with incidence, metric, and betweenness axioms, incorporating the SAS Postulate of congruence, and to the proof of the Saccheri-Legendre Theorem
- Write proofs of results within neutral geometry, correctly identifying and citing axioms, definitions, and theorems established within the system as justifications
- Apply the above outcomes in the context of results about congruent triangles and quadrilaterals (including Saccheri quadrilaterals), and circles (including the tangent and secant theorems)
- Illustrate geometric concepts and results by construction through the use of appropriate software
- Parallel Postulates
- Articulate the history and development of various forms of a parallel postulate (Euclid, Riemann, Lobechevski)
- State the parallel postulates that define Euclidean, hyperbolic, and spherical geometries
- State equivalent forms of the Euclidean parallel postulate
- Euclidean Geometry
- Write proofs of results within Euclidean geometry, correctly identifying and citing axioms, definitions, and theorems established within the system as justifications
- Apply the above outcomes in the context of results about congruence and similarity for triangles and quadrilaterals
- Apply the Side-Splitting Theorem to compute segment lengths in triangles
- State, prove, and apply results about circles in Euclidean geometry (e.g. arc and angle measures, Secant-Tangent Theorem)
- Apply terminology related to polygons to classify and describe; compute angle measures and area of polygons
- Hyperbolic Geometry
- State and prove key theorems of hyperbolic geometry, recognizing where the results differ from Euclidean (e.g. angle sum of triangle less than 180, AAA similarity implies congruence)
- Construct segments and angles and measure distances and angle sums within the Poincare disk model of hyperbolic geometry (note this objective assumes the continued existence of the hyperbolic geometry construction application Non-Euclid or comparable)
- Compute the defect and area of a polygon in hyperbolic geometry
- Spherical Geometry
- Define spherical geometry in terms of its parallel postulate
- Contrast spherical geometry with Euclidean and hyperbolic geometries, and identify key theorems of neutral geometry which do not hold in spherical geometry
- Topics in Geometry/Modern Geometry
- Trigonometry (instructors may wish to review trigonometry, but knowledge of definitions and techniques is assumed as prerequisite knowledge):
- Demonstrate a deep understanding of the foundations of trigonometry through derivation of key results, including Law of Sines and Law of Cosines
- Solid figures:
- Define, identify and classify convex polyhedra (Platonic solids, Archimedean solids)
- Compute volume and surface area for selected examples of the above ((instructors may also wish to review volume and surface area formulas for sphere, cone, prism, etc.):
- Transformations:
- Describe transformations as functions that take points in the plane as inputs, and give other points as outputs
- Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

### Major Topics to be Included

- Historic Overview of Euclidean Geometry
- Introduction to Logic and Proof
- Axiomatic Systems
- Neutral Geometry
- Parallel Postulates
- Euclidean Geometry
- Hyperbolic Geometry
- Spherical Geometry
- Topics in Geometry/Modern Geometry

### MTH 281 - Introductory Abstract Algebra

### Course Description

Effective: 2018-01-01

### General Course Purpose

To provide an introduction to abstract mathematics and rigorous proof in the context of algebraic structures to students seeking endorsement to teach mathematics at the secondary level.

### Course Prerequisites/Corequisites

Prerequisite: Completion of MTH 263 with a grade of C or better or equivalent.

### Course Objectives

- Introduction to Logic and Proof
- Demonstrate the proof writing strategies of direct proof, indirect proof (proof of contrapositive), and proof by contradiction in the context of proving basic results about integers (e.g. "Prove that the product of two odd integers is odd.")
- State and apply the Well Ordering Principle (for the naturals) and General Well Ordering Principle (for sets of integers bounded below) to conclude whether a given set is guaranteed a smallest element.
- Write induction proofs in the context of proving basic results about integers
- Operations and Relations
- State and apply the definition of an equivalence relation on a set and determine which properties (reflexive, symmetric, transitive) a defined relation on a given set passes or fails.
- State and apply the definition of a partial order, and determine if a defined relation on a given set is anti-symmetric
- Construct equivalence classes given a set and equivalence relation
- Determine if a given operation on a set is well defined
- Illustrate the construction of integers as equivalence classes of ordered pairs of natural numbers with defined operations of addition and multiplication
- Divisibility and Prime Numbers
- State and apply the definition of divides and prove basic results about divisibility of integers (e.g. "if a|b and b|c, then a|c")
- Given two integers a and b, apply the Division Algorithm to express a = bq + r, 0 <= r < b
- Use the Euclidean Algorithm to find the greatest common divisor of a pair of integers
- Obtain integer solutions to Diophantine equations and write the general form of the solution
- Write the prime factorization of a given natural number
- State and prove the Fundamental Theorem of Arithmetic
- State and prove results about prime numbers
- Apply the definition of the Euler phi-function to determine the number of numbers relatively prime to a given integer
- State and apply Euler's Theorem and Fermat's Little Theorem
- Modular Arithmetic, Congruence, and an Introduction to Zm
- State and apply the definition of congruence modulo m
- State and prove fundamental properties of the congruence relation
- Perform modular arithmetic on congruence classes of integers
- State and prove results about solutions to linear congruences, and apply them to determine solutions
- Solve systems of linear congruences
- Define Zm and its operations and perform arithmetic within Zm for a given m
- Prove that the operations on Zm satisfy the properties of commutativity and associativity of addition and multiplication, and the distributive property of multiplication over addition
- Solve linear equations within Zm for a given m
- Rings, Fields, and Integral Domains
- State the definitions of ring, commutative ring, ring with unity, integral domain, and field
- Given a set and two binary operations, determine which of the above structures it falls under by verifying algebraic properties (examples including integer/rational/real/complex numbers with addition and multiplication, Zm rings, and sets and operations in the abstract as defined by Cayley tables)
- Determine if an element of a ring is a zero divisor, a unit, or neither
- Perform algebraic operations in the complex field, including applying De Moivre's Theorem to compute powers and nth roots
- Polynomials
- Perform algebraic operations on polynomials in Q[x] and Z[x] (rational and integer coefficients), and also in Zm[x] (coefficients in a Zm ring with arithmetic modulo m).
- Perform long division of polynomials in F[x] (F a field, including Q, Z, C, and Zm, m prime) and express in the form of the Division Algorithm
- Use the Euclidean algorithm to find the greatest common divisor of two polynomials in F[x]
- State, prove, and apply the Remainder/Root Theorems for polynomials
- State and prove the Unique Factorization Theorem for polynomials in F[x]
- Determine if a polynomial is reducible in F[x] (apply relevant theorems such as Eisenstein's Criterion); if so, factor completely
- State the Fundamental Theorem of Algebra, and display an understanding of the concepts underlying the proof
- Groups, Isomorphism, and Homomorphism
- State the definitions of group and Abelian group, and state and prove additional basic properties of groups (e.g. (xy)^-1=y^-1x^-1)
- Given a set and a binary operation, determine whether it is a group (and if Abelian) by verifying algebraic properties (examples including integer/rational/real/complex numbers with addition or multiplication, the Klein-4 group, and sets and operations in the abstract as defined by Cayley tables)
- Construct Cayley tables for the groups Um formed from the units of Zm with the operation of multiplication and perform arithmetic in Um
- Define the dihedral groups of symmetries of the triangle and the square and implement operations on elements within the groups
- State and apply the definitions of subgroup, proper subgroup, and cyclic subgroup
- Construct direct (Cartesian) product groups
- State the definition of an isomorphism between two groups and be able to determine if one exists by identifying an operation preserving bijection
- State the definition of a homomorphism between two groups and be able to determine if one exists by identifying an operation preserving map

### Major Topics to be Included

- Introduction to Logic and Proof
- Operations and Relations
- Divisibility and Prime Numbers
- Modular Arithmetic, Congruence, and an Introduction to Zm
- Rings, Fields, and Integral Domains
- Polynomials
- Groups, Isomorphism, and Homomorphism

### MTH 283 - Probability and Statistics

### Course Description

Effective: 2018-01-01

### General Course Purpose

The first part of the content provides understanding of the basic concepts of probability required for further study in statistics. The statistics content provides a solid foundation and training in some of the fundamental tools used by statistical practitioners.

### Course Prerequisites/Corequisites

Prerequisite: Completion of MTH 264 with a grade of C or better or equivalent.

### Course Objectives

- Basic Concepts of Probability
- Relate the probability of an event to the likelihood of this event occurring.
- Explain how relative frequency is used to estimate the probability of an event.
- Determine the sample space of a given random experiment, including by using methods of enumeration.
- Demonstrate probabilities through simulations.
- Find the probability of events in the case in which all outcomes are equally likely.
- State and apply the laws of probability concerning these events.
- Use tools such as Venn Diagrams or probability tables as aids for finding probabilities.
- Explain the reasoning behind conditional probability, and how this reasoning is expressed by the definition of conditional probability.
- Find conditional probabilities and interpret them.
- Determine whether two events are independent or not.
- Use the general multiplication rule to find the probability that two events occur (p(a and b)).
- Use probability trees as a tool for finding probabilities.
- Understand the total probability and Bayes' theorem.
- Discrete Distributions
- Identify discrete random variable.
- Find the probability distribution of discrete random variables, and use it to find the probability of events of interest.
- Compute the expected value and variance of a discrete random variable, and apply these concepts to solve real-world problems.
- Explain the concepts of Bernoulli Trials and discrete models such as binomial distribution, geometric, negative binomial distribution, hypergeometric distribution, and Poisson Distribution.
- Recognize the situations to which each of the distributions is applicable, and solve applied problems.
- Find the mean and variance using the moment generating function.
- Continuous Distributions
- Distinguish between discrete and continuous random variables
- Explain how a density function is used to find probabilities involving continuous random variables.
- Compute the expected value and variance of each of the distributions studied.
- Find probabilities associated with the normal distribution.
- Perform probabilities associated with uniform, exponential distributions, gamma, chi-square distributions, Weibull Distribution, joint probability distributions, and mixed type distributions.
- Recognize the situations to which each of the distributions is applicable, and solve applied problems.
- Bivariate Distributions
- Compute probabilities, marginal densities, conditional densities and conditional probabilities for multivariate probability distributions.
- Compute the expected value, variance and covariance of each of the multivariate distributions studied.
- Apply the rules of means and variances to find the mean and variance of a linear transformation of a random variable and the sum of two independent random variables.
- Graphically display the relationship between two quantitative variables and describe: a) the overall pattern, and b) striking deviations from the pattern.
- Interpret the value of the correlation coefficient, and be aware of its limitations as a numerical measure of the association between two quantitative variables.
- Perform bivariate normal distribution problems
- Distributions of Functions of Random Variables
- Use transformation of a random variable to find probability distributions for functions of one random variable.
- Use moment generating functions to find the probability distributions for sums of random variables.
- Use transformations of two random variables to find the probability distribution.
- Compute with several independent random variables.
- Derive random functions associated with normal distribution
- Estimation
- Use basic statistical techniques in the analysis and interpretation of data in the various disciplines and physical phenomena.
- Determine point estimates in simple cases, and make the connection between the sampling distribution of a statistic, and its properties as a point estimator.
- Define and calculate maximum likelihood estimators of various distributions.
- Explain the application of the Central Limit Theorem to sampling distributions.
- Explain what a confidence interval represents and determine how changes in sample size and confidence level affect the precision of the confidence interval.
- Find confidence intervals for the mean, the difference between two means, a proportion, Perform simple regression analysis.
- Tests of Statistical Hypotheses
- Explain the logic behind and the process of hypotheses testing. Explain what the p-value is and how it is used to draw conclusions.
- Specify (in a given context) the null and alternative hypotheses for the appropriate population parameters.
- Carry out hypothesis testing for the population parameters, and draw conclusions in context.
- Apply the concepts of sample size, statistical significance vs. practical importance, and the relationship between hypothesis testing and confidence intervals.
- Determine the likelihood of making type i and type ii errors, and explain how to reduce them, in context.
- Determine confidence intervals for the least squares estimators.
- Estimate the regression coefficients.
- Find confidence intervals for the parameters of a regression model.
- Identify and distinguish among cases where use of calculations specific to independent samples, matched pairs, and ANOVA appropriate.
- Perform ANOVAs.(one-way)
- Nonparametric Methods
- Perform Chi-Square goodness of fit tests and Chi-square test for independence. (Chop 10)
- Technology Applications
- Demonstrate the application of statistics through a comprehensive project. [Instructors see pedagogical notes for details.]
- Use a statistical package to investigate and analyze data and to generate statistical information. [Instructors see pedagogical notes for details.]

### Major Topics to be Included

- Basic Concepts of Probability
- Discrete Distributions
- Continuous Distributions
- Bivariate Distributions
- Distributions of Functions of Random Variables
- Estimation
- Tests of Statistical Hypotheses
- Nonparametric Methods
- Technology Applications

### MTH 288 - Discrete Mathematics

### Course Description

Effective: 2018-01-01

### General Course Purpose

The goal is to give the student a solid grasp of the methods and applications of discrete mathematics to prepare the student for higher level study in mathematics, engineering, computer science, and the sciences.

### Course Prerequisites/Corequisites

Prerequisite: Completion of MTH 263 with a grade of C or better or equivalent.

### Course Objectives

- Note: Methods of proofs and applications of proofs are emphasized throughout the course.
- Logic - Propositional Calculus
- Use statements, variables, and logical connectives to translate between English and formal logic.
- Use a truth table to prove the logical equivalence of statements.
- Identify conditional statements and their variations.
- Identify common argument forms.
- Use truth tables to prove the validity of arguments.
- Logic - Predicate Calculus
- Use predicates and quantifiers to translate between English and formal logic.
- Use Euler diagrams to prove the validity of arguments with quantifiers.
- Logic - Proofs
- Construct proofs of mathematical statements - including number theoretic statements - using counter-examples, direct arguments, division into cases, and indirect arguments.
- Use mathematical induction to prove propositions over the positive integers.
- Set Theory
- Exhibit proper use of set notation, abbreviations for common sets, Cartesian products, and ordered n-tuples.
- Combine sets using set operations.
- List the elements of a power set.
- Lists the elements of a cross product.
- Draw Venn diagrams that represent set operations and set relations.
- Apply concepts of sets or Venn Diagrams to prove the equality or inequality of infinite or finite sets.
- Create bijective mappings to prove that two sets do or do not have the same cardinality.
- Functions and Relations
- Identify a function's rule, domain, codomain, and range.
- Draw and interpret arrow diagrams.
- Prove that a function is well-defined, one-to-one, or onto.
- Given a binary relation on a set, determine if two elements of the set are related.
- Prove that a relation is an equivalence relation and determine its equivalence classes.
- Determine if a relation is a partial ordering.
- Counting Theory
- Use the multiplication rule, permutations, combinations, and the pigeonhole principle to count the number of elements in a set.
- Apply the Binomial Theorem to counting problems.
- Graph Theory
- Identify the features of a graph using definitions and proper graph terminology.
- Prove statements using the Handshake Theorem.
- Prove that a graph has an Euler circuit.
- Identify a minimum spanning tree.
- Boolean Algebra
- Define Boolean Algebra.
- Apply its concepts to other areas of discrete math.
- Apply partial orderings to Boolean algebra.
- Recurrence Relations
- Give explicit and recursive descriptions of sequences.
- Solve recurrence relations.

### Major Topics to be Included

- Logic - Propositional Calculus
- Logic - Predicate Calculus
- Logic - Proofs
- Set Theory
- Functions and Relations
- Counting Theory
- Graph Theory
- Boolean Algebra
- Recurrence Relations

### MTH 289 - Differential Equations Extended

### Course Description

Effective: 2018-01-01

### General Course Purpose

The purpose of the course is to provide for a smooth transition of STEM students to 4-year colleges and introduce them to advanced topics of mathematics, physics and engineering: numerical methods for solving differential equations, classical partial differential equations, methods for solving PDEs and boundary-value problems (BVPs).

### Course Prerequisites/Corequisites

Prerequisite: Completion of MTH 267 with a grade of C or better or equivalent.

### Course Objectives

- System of Linear First Order Differential Equations
- Define system of linear first-order differential equations, Initial value problem (IVP) and its solution vector, linear dependence/independence, fundamental set of solutions
- Check that a vector of functions is a solution of a system or an initial value problem (IVP)
- Apply criterion for linearly independent solutions and find general solution for homogeneous and nonhomogeneous systems (for the 3 types of eigenvalues: distinct real, complex, repeated)
- Solve nonhomogeneous linear systems by the methods of undetermined coefficients and variation of parameters
- Numerical solutions of Ordinary Differential Equations
- Understand the concept of local and global truncation errors, stability of numerical method
- Use single-step and multistep methods( Euler's Method, Improved Euler's Method, 1st, 2nd and 4th-order Runge-Kutta Method, Adams-Bashforth-Moulton Method) and finite difference method to approximate ivp and bvp solutions
- Plane Autonomous Systems
- Explain the concept of autonomous systems of first-order des (linear and nonlinear)
- Find critical points and classify critical points of linear and nonlinear systems (stable/unstable nodes, saddle point, degenerate unstable node, center, stable/unstable spiral points), identify equilibrium solution and periodic solution
- Use stability criterion for plane autonomous systems
- Apply the concept of linearization of differentiable function and classify stable and unstable critical points
- Perform stability analysis for linear/nonlinear systems for various applications
- Orthogonal Functions
- Define orthogonal functions and sets of orthogonal functions
- Write the definition of the Fourier Series and expansion of functions in a Fourier Series
- Define Sturm-Liouville problem and solve it
- Write the definitions and expand the function in Fourier-Bessel Series
- Boundary-Value Problems in Rectangular Coordinates
- Define linear/nonlinear, homogeneous/nonhomogeneous partial differential equations
- Classify the linear second-order pdes as hyperbolic, parabolic or elliptic
- Use the method of separation of variables to find particular solution of pdes
- Identify classical and modified pdes and bvps (1d heat equation, 1d wave equation and 2d form of Laplace?s Equation) and solve them
- Use the concept of orthogonal series expansions or generalized Fourier Series and solve bvps by using orthogonal series expansions
- Integral Transforms
- Find the Laplace transform of partial derivatives of functions of two variables, use Laplace transform to solve bvps
- Define a Fourier integral of function and conditions for convergence, the Fourier integral of even/odd functions
- Use the definitions of three Fourier transform pairs (direct and inverse integral transforms)
- Solve bvps using the Fourier transform

### Major Topics to be Included

- System of Linear First Order Differential Equations
- Numerical solutions of Ordinary Differential Equations
- Plane Autonomous Systems
- Orthogonal Functions
- Boundary-Value Problems in Rectangular Coordinates
- Integral Transforms

### MTH 3 - Bundle 1-3 - Operations with Fractions, Decimals, and Percents and Algebra Basics

### Course Description

Effective: 2017-08-01

### General Course Purpose

To prepare students for successful entry into credit mathematics courses as well as other credit courses requiring basic math competencies as prerequisites.

### Course Prerequisites/Corequisites

Prerequisites: Qualifying placement score

### Course Objectives

- Operations with Fractions
- Identify, write and graph fractions and mixed numbers.
- Represent information with fractions and mixed numbers.
- Express parts of a whole using fraction notation.
- Convert between improper fractions and mixed numbers.
- List the factors of a number.
- Find the prime factorization of a given number.
- Write equivalent fractions.
- Write fractions in simplest form.
- Multiply and divide fractions.
- Express repeated factors using exponents.
- Find reciprocals.
- Add and subtract fractions with like and unlike denominators.
- Find the least common multiple (LCM) of two or more whole numbers.
- Find the least common denominator (LCD) of two or more fractions.
- Simplify expressions involving fractions using order of operation.
- Add, subtract, multiply, and divide mixed numbers.
- Using U.S. Customary Units of Measure to solve application problems.
- Operations with Decimals and Percents
- Convert decimals between standard notation and word notation.
- Identify place values in decimals.
- Round decimals to a specific place value.
- Add, subtract, multiply and divide decimals.
- Estimate sums, differences, products, and quotients with decimals.
- Demonstrate the relationship among fractions, decimals, and percents.
- Convert among fractions, decimals, and percents.
- Order a list of fractions and decimals from smallest to largest.
- Order of Operations: Simplify expressions using order of operations.
- Write parts of a whole using percent notation.
- Solve percent problems using proportions
- Calculate all values in the basic percent problem (percent, amount /part, and base).
- Calculate percent increase and percent decrease.
- Read and interpret information from graphs (bar, line, pie).
- Calculate the percentage denoted by a pie graph.
- Convert within and between the U.S. and metric systems.
- Solve application problems using U.S. customary and metric units of measurement.
- Convert units of time.
- Convert between Fahrenheit and Celsius temperatures.
- Algebra Basics
- Classify real numbers.
- Determine the absolute value of a number.
- Find the principal square root of a perfect square.
- Add, subtract, multiply, and divide integers.
- Express repeated factors using exponents.
- Demonstrate proper use of exponents.
- Evaluate powers of numbers.
- Simplify numeric expressions using the order of operations.
- Identify the properties of real numbers (Commutative, Associative, Distributive, Identity and Inverse Properties).
- Simplify an algebraic expression by combining like terms.
- Verify solutions to equations
- Translate solutions into equations
- Solve equations using the Addition and Multiplication Properties.
- Solve one-step equations using rational numbers.
- Translate word statements into percent equations
- Solve application problems including finding perimeter, area and volume and calculate sales tax or simple interest.
- Convert between integer powers of 10 and equivalent decimal numbers.
- Convert numbers between scientific notation and standard notation.

### Major Topics to be Included

- Fractions
- Decimals
- Percents
- Algebra Basics

### MTH 5 - Bundle 4-5 - First Degree Equations and Inequalities and Systems of Linear Equations

### Course Description

Effective: 2017-08-01

### General Course Purpose

To prepare students for successful entry into credit mathematics courses as well as other credit courses requiring basic math competencies as prerequisites.

### Course Prerequisites/Corequisites

Prerequisites: MTE 1-3 or qualifying placement score

### Course Objectives

- Equations and Inequalities
- Solve first degree equations in one variable using the Addition and/or Multiplication Property of Equality.
- Solving Linear Equations in One Variable that contain parentheses and/or the variable on both sides of the equal sign.
- Solve first degree equations in one variable and identify the solution to an equation as finite, the empty set or all real numbers.
- Solve application problems using a single first degree equation or inequality.
- Solve a formula or equation for one of its variables using the Addition and/or Multiplication Property of Equality.
- Solve first degree inequalities in one variable stating the solution using inequality notation.
- Solve first degree inequalities in one variable and graph the solution on a real number line.
- Solve first degree absolute value equations containing a single absolute value.
- Graphing
- Determine the coordinates of a point plotted on the coordinate plane.
- Graphing Linear Equations in Two Variables
- Identify the x and y intercepts of a graph.
- Graph a linear equation by plotting intercepts.
- Graph a horizontal and vertical line given its equation.
- Find the slope of a line given two points on the line.
- Find the slope of a line given its graph.
- Find the slope of horizontal and vertical lines.
- Write an equation of a line in slope-intercept form given the slope and the y-intercept.
- Use point-slope form to write an equation of a line in slope intercept form given the slope and a point on the line.
- Use point-slope form to write an equation of a line in slope intercept form given two points on the line.
- Find the equation of a line that is parallel or perpendicular to a given line and passes through a given point.
- Write the equation of a vertical line and horizontal line.
- Find the slope of a line given its equation in slope-intercept form.
- Find the slope of a line given its equation by converting to slope-intercept form.
- Graph a linear inequality in two variables.
- Solve Systems of Linear Equations by Graphing
- Determine if an ordered pair is a solution of system of equations in two variables.
- Graph a linear equation by finding and plotting ordered pair solutions.
- Graph an equation given in slope-intercept form.
- Solve systems of linear equations by graphing, substitution, and elimination. Identify a system of linear equations as consistent and independent, consistent and dependent, or inconsistent.
- Solve applications problems that require linear equations, inequalities and systems of linear equations in two variables.
- Identify independent and dependent variables.
- Evaluate y = f(x) for specific values of x.
- Given the graph of y = f(x), evaluate f(x)
- Given the graph of y = f(x), find x for specific values of f(x).

### Major Topics to be Included

- Solving and Graphing First Degree Equations
- Solving and Graphing First Degree Inequalities
- Solving Systems of Equations

### MTH 9 - Bundle 6-9 - Exponents, Factoring, Poly Equations, Rational Expressions and ...

### Course Description

Effective: 2017-08-01

### General Course Purpose

To prepare students for successful entry into credit mathematics courses as well as other credit courses requiring basic math competencies as prerequisites.

### Course Prerequisites/Corequisites

Prerequisites: MTE 1-5 or qualifying placement score.

### Course Objectives

- Exponents
- Evaluate the product of two exponential expressions.
- Evaluate the quotient of two exponential expressions.
- Evaluate the power of a power of an exponential expression.
- Evaluate exponential expressions that contain combinations of products, quotients, power of a power and negative exponents.
- Polynomials
- Identify an expression as a monomial, binomial, trinomial or polynomial.
- Add and subtract monomials using the rules of exponents.
- Add and subtract binomials.
- Add and subtract trinomials.
- Multiply monomials using the rules of exponents.
- Multiply combinations of binomials and trinomials.
- Evaluate exponential expressions that contain negative exponents.
- Multiply and divide numbers in Scientific Notation.
- Divide polynomials.
- Factoring
- Find the greatest common factor from a list of terms.
- Find the greatest common factor from a polynomial.
- Factor a polynomial by grouping.
- Factor trinomials of the form x2 + bx + c.
- Factor trinomials of the form ax2 + bx + c, trials and ac method.
- Factor a difference of squares.
- Factor a sum of two cubes.
- Factor a difference of two cubes.
- Solve equations using factoring techniques.
- Solve application problems involving polynomial equations and factoring.
- Rational Expressions and Equations
- Identify the real value of the variable for which a rational algebraic expression having a denominator of the form ax + b is undefined.
- Identify all real values of the variable for which a rational algebraic expression having a denominator of the form ax2 + bx + c is undefined.
- Simplify a rational algebraic expression.
- Evaluate a rational algebraic expression given specific integral values for each variable.
- Perform multiplication of rational algebraic expressions and express the product in simplest terms.
- Use factorization to divide rational algebraic expressions and express the quotient in simplest terms.
- Divide a polynomial by a monomial.
- Perform polynomial long division.
- Find the Least Common Denominator (LCD) of two or more rational algebraic expressions.
- Perform addition and subtraction of rational algebraic expressions having like denominators.
- Perform addition and subtraction of rational algebraic expressions having denominators that have no common factors.
- Perform addition and subtraction of rational algebraic expressions having denominators that have a common monomial factor.
- Perform addition and subtraction of rational algebraic expressions having denominators that have a common binomial factor.
- Simplify complex fractions.
- Solve rational algebraic equations.
- Write a rational equation to match the information given in an application problem.
- Solve an application problem using rational equations.
- Radical Expressions and Rational Exponents
- Convert between square root and a1/2 forms.
- Simplify square roots.
- Simplify nth roots of variable expressions.
- Compute and estimate radicals.
- Calculate square roots via calculator.
- Estimate square roots.
- Calculate nth roots via calculator.
- Simplify using the properties of rational exponents.
- Simplify radicals by using the multiplication property of radicals.
- Simplify radicals by using the division property of radicals.
- Convert between nth root and a1/n forms.
- Convert between combinations of nth root and mth power and am/n forms.
- Define like radicals.
- Combine and simplify like radicals.
- Multiply and simplify radicals.
- Rationalize the denominator (one term and two terms).
- Simplify radicals by rationalizing a denominator with one term.
- Simplify radicals by rationalizing a denominator with two terms.
- Solve radical equations.
- Solve application problems involving radicals.
- Solve problems involving right triangles.
- Solve problems involving the Pythagorean Theorem.
- Solve problems involving the distance formula.
- Define the imaginary unit i and imaginary numbers.
- Simplify square roots of negative numbers using the imaginary unit.
- Functions
- Determine if a relation is a function and identify the domain and range of the function.
- Determine if a list of ordered pairs, graph, or equation is a function.
- Determine the domain and range of a function given as a list of ordered pairs.
- Determine the domain and range of a function given as a graph.
- Determine the domain of a function given as an equation.
- Evaluate for constant values of and for specific monomials and binomials.
- Quadratics
- Find all roots of quadratic equations using both the square root method and the quadratic formula.
- Find the roots of quadratic equations of the form.
- Find the roots of quadratic equations of the form when the discriminant is a positive perfect square, (i.e. the quadratic is factorable).
- Find the roots of quadratic equations of the form when the discriminant is positive, but not a perfect square.
- Find the roots of quadratic equations of the form when the discriminant is zero.
- Find the roots of quadratic equations of the form when the discriminant is negative.
- Describe the roots of a quadratic based upon the discriminant in all cases.
- Analyze a quadratic function to determine its vertex by completing the square and using the formula.
- Write a quadratic function in vertex form by completing the square for quadratics with and identify the vertex.
- Find the vertex of a quadratic equation using the formula method.
- Graph a quadratic function, using the vertex form, indicating the intercepts and vertex.
- Determine whether the parabola opens upward or downward.
- Plot the vertex of the parabola.
- Determine the axis of symmetry for the parabola.
- Plot the -intercepts of the parabola, if they exist.
- Plot the -intercept of the parabola and complete the graph with additional points as needed.
- Apply knowledge of quadratic functions to solve application problems from geometry, economics, applied physics, and other disciplines.
- Solve problems involving area optimization.
- Solve problems involving revenue optimization.
- Solve problems involving the motion of falling objects.

### Major Topics to be Included

- Exponents, Factoring, and Polynomial Equations
- Rational Expressions and Equations
- Rational Exponents and Radicals
- Functions, Quadratic Equations, and Parabolas