Course Descriptions

MATH 087 Quantitative Literacy

• Demonstrate quantitative reasoning to analyze problems, critique arguments, and draw and justify conclusions
• Accurately perform arithmetic operations involving fractions, decimals, percents, and signed numbers
• Recall and apply the standard order of operations
• Use proportional reasoning in solving applied problems
• Use statistical and probabilistic reasoning in solving applied problems
• Explain how quantities change, including multiplicative vs. additive and relative vs. absolute
• Use estimation skills to solve problems, detect errors, and check accuracy
• Interpret and use scientific notation
• Make comparisons of relative magnitudes and work with various representations of quantitative information: ratios, rates, percentages, conversions, indices, scales, etc.
• Organize and summarize data using a variety of representations, such as tables, graphs, and formulas
• Use variables to represent quantities
• Solve simple algebraic equations
• Read and interpret quantitative information from a variety of real-world sources
• Analyze and use quantitative information to support an argument
• Recognize, make, and evaluate quantitative assumptions
• Communicate quantitative results both in writing and orally using appropriate language, symbolism, data, and graphs
• Use technology appropriately as a tool for calculations and to gather, research, and analyze quantitative information
• Apply logical and time-effective study skills to mathematics

MATH 090 Introduction to Algebra for STEM

• Apply properties of the real number system to both numeric and algebraic problems
• Apply the rules of exponents
• Add, subtract, multiply, and divide polynomials
• Solve first degree equations algebraically
• Identify key characteristics of linear functions
• Create linear equation models and apply those equations to making predictions
• Compare and contrast methods to solve and graph equations with methods needed to solve and graph inequalities
• Solve formulas for a specified variable
• Describe linear functions in multiple forms including: tables, graphs, and equations
• Solve systems of equations with two variables
• Use factoring to solve second degree equations
• Use the mathematical critical thinking skills of problem solving, pattern recognition, substitution, following structural rules, and quantitative modeling to solve problems involving basic algebra

MATH 093 Applied Math and Computing Fundamentals

• Compute with fractions, decimals, ratios, proportions, and percents
• Read and interpret graphs of linear, quadratic, and exponential functions
• Use scientific notation during computation
• Distinguish between exact and approximate solutions
• Solve both symbolic and word problems involving linear and quadratic equations
• Add and multiply polynomial expressions
• Solve and graph problems involving inequalities
• Simplify and solve equations involving radicals and complex numbers
• Describe the algorithmic steps in solving simple algebraic problems
• Use a symbolic computing program to solve algebraic problems
• Apply the mathematical skills of computational problem solving, pattern recognition, substitution, following structural rules, discrete modeling, and formal logic to solve problems requiring reasoning, critical thinking, and computation 

MATH 098 Essentials of Intermediate Algebra

• Use dimensional analysis to make calculations
• Interpret and move flexibly between multiple formats, including graphs, tables, equations, and words
• Solve applied problems involving linear, quadratic, exponential, rational, and radical equations
• Calculate the slope of linear data and interpret slope within the context of the problem
• Distinguish between linear and exponential growth models
• Apply exponent rules to simplify expressions with exponents
• Solve formulas for a specified variable
• Use geometric concepts of area and volume in solving applied problems
• Create and use models (tables, words, graphs, equations) of real-world situations
• Analyze and use quantitative information to support an argument
• Communicate quantitative results both in writing and orally using appropriate language, symbolism, data, and graphs
• Demonstrate quantitative reasoning to analyze problems, critique arguments, and draw and justify conclusions
• Use technology appropriately as a tool for calculations and to gather, research, and analyze quantitative information

MATH 099 Intermediate Algebra for STEM

• Identify and apply the rules of algebra to solve algebraic problems
• Demonstrate the use of rational, irrational, and complex numbers in problem solving
• Solve problems involving linear, quadratic, logarithmic,  and exponential equations and functions
• Differentiate among linear, quadratic, and exponential functions by emphasizing key characteristics and graphs
• Simplify rational expressions and solve rational equations, using factoring when necessary
• Identify functions and use functional notation and terminology
• Solve problems involving inequalities
• Simplify radical expressions and solve radical equations
• Apply technology appropriately as a tool for calculations
• Research and analyze quantitative information using technology
• Use the mathematical critical thinking skills of problem solving, pattern recognition, substitution, following structural rules, and quantitative modeling to solve problems involving intermediate algebra

MATH 099X Accelerated Intermediate Algebra for STEM

• Demonstrate the use of integers, rational, irrational, and complex numbers in problem solving
• Solve problems involving linear, quadratic, logarithmic, and exponential equations and functions
• Differentiate between linear, quadratic, and exponential functions by emphasizing key characteristics and graphs
• Apply the rules of exponents
• Add, subtract, multiply, and divide polynomials
• Use factoring to solve second degree equations
• Simplify rational expressions and solve rational equations, using factoring when necessary
• Identify functions and use functional notation and terminology
• Simplify radical expressions and solve radical equations
• Compare and contrast methods to solve and graph equations with methods needed to solve and graph inequalities
• Solve formulas for a specified variable
• Solve systems of equations with two variables
• Create linear and quadratic equation models and apply those equations to making predictions
• Apply technology appropriately as a tool for calculations
• Research and analyze quantitative information using technology
• Use the mathematical critical thinking skills of problem solving, pattern recognition, substitution, following structural rules, and quantitative modeling to solve problems involving basic and intermediate algebra

MATH 105 Applied Math

• Apply problem-solving skills to real-world problems
• Apply and adapt a variety of appropriate strategies and mathematical procedures to interpret and solve technical problems
• Use the language of mathematics to express mathematical ideas precisely
• Estimate and check answers to mathematical problems in order to determine reasonableness, identify alternatives, and select optimal results
• Interpret mathematical models such as formulas, graphs, tables, and schematics
• Draw inferences from mathematical models
• Communicate mathematical information symbolically, visually, numerically, and verbally

MATH 111 College Algebra with Applications

• Solve, graph, and interpret linear and quadratic equations, functions, and inequalities
• Graph, transform, and compose functions
• Solve systems of equations in two and three variables
• Use trigonometric and inverse trigonometric functions to solve problems
• Use vector analysis to solve problems in physics
• Use quantitative modeling to solve problems involving functions, linear algebra, geometry, and  trigonometry

MATH 147 Digital Mathematics

• Apply counting techniques to solve simple problems in probability
• Explain the integer system expressed in various bases
• Identify logical elements in artificial languages
• Determine tautological, contradictory, and contingent logical forms
• Differentiate between functions and relations
• Appreciate the inductive structure of mathematics
• Solve simple problems using recursion
• Explain the fundamental rules of graph and tree data structures
• Construct simple algorithms for computation
• Express problems using a variety of different data structures
• Write simple computer programs in very high-level software languages
• Describe the use of logic and recursion in semiconductor circuitry
• Apply the mathematical skills of computational problem solving, pattern recognition, substitution, following structural rules, discrete modeling, and formal logic to solve problems requiring reasoning, critical thinking, and computation

MATH 220 Linear Algebra

• Perform matrix operations, calculate determinants, find inverses for matrices (where possible), and find the transpose of a matrix
• Use elementary row operations to solve systems of linear equations using Gaussian Elimination and Gauss-Jordan reduction methods
• Identify a system of linear equations as independent, inconsistent, or dependent
• Perform vector operations, use properties of vector operations, and determine vector subspaces, spanning sets, and bases of vector spaces
• Show that a set of vectors forms the basis for a set, and find the dimension of a subspace
• Find inner products and find a basis for a given inner product space
• Use matrices to perform transformations between vector spaces and to identify isomorphisms
• Find the kernel, range, rank, and nullity of a linear transformation
• Find the standard matrix for a given linear transformation and use this matrix to find the image of a given vector
• Find real eigenvalues and eigenvectors of a square matrix
• Diagonalize symmetric matrices
• Use the mathematical critical thinking skills of problem solving, pattern recognition, substitution, following structural rules, and quantitative modeling to solve problems requiring reasoning, critical thinking, and computation

MATH 230 Matrix Algebra with Applications

• Perform matrix operations, calculate determinants, find inverses for matrices (where possible), and find the transpose of a matrix
• Use elementary row operations to solve systems of linear equations using Gaussian Elimination and Gauss-Jordan reduction methods
• Apply LU decomposition methods to factorize a matrix
• Identify a system of linear equations as independent, inconsistent, or dependent
• Identify properties of Euclidean vector spaces and the effects of linear transformations
• Perform vector operations; use properties of vector operations; and determine vector subspaces, spanning sets, and bases of vector spaces
• Show that a set of vectors forms the basis for a set, and find the dimension of a subspace
• Find inner products and find a basis for a given inner product space
• Use matrices to perform transformations between vector spaces and to identify isomorphisms
• Find the kernel, range, rank, and nullity of a linear transformation
• Find the standard matrix for a given linear transformation and use this matrix to find the image of a given vector
• Use Gram-Schmidt orthogonalization to find orthonormal vectors
• Apply QR decomposition methods to factorize a matrix
• Find real eigenvalues and eigenvectors of a square matrix
• Diagonalize symmetric matrices
• Apply matrix algebra to data fitting and least squares analysis
• Use the mathematical critical thinking skills of problem solving, pattern recognition, substitution, following structural rules, and quantitative modeling to solve problems requiring reasoning, critical thinking, and computation

MATH 238 Differential Equations

• Describe differential equations using appropriate mathematical notation, symbols, and graphs
• Classify differential equations by order, linearity, and homogeneity
• Solve first and second order linear differential equations
• Solve linear equations with constant coefficients
• Use separation of variables, method of undermined coefficients, and variation of parameters to solve differential equations
• Use power series methods to solve differential equations
• Determine whether a system of functions is linearly independent using the Wronksian
• Use Laplace transforms and their inverses to solve differential equations
• Solve systems of linear differential equations using matrix techniques and eigenvalues
• Use numerical methods to solve differential equations
• Model real-life applications using differential equations
• Use technology for finding solutions and data visualization
• Use the mathematical critical thinking skills of problem solving, pattern recognition, substitution, following structural rules, and quantitative modeling to solve problems requiring reasoning, critical thinking, and computation

MATH 246 Business Statistics

• Identify and implement statistically valid business data collection methods, and perform detailed statistical analysis using Excel and/or PASW
• Present analytics for business applications using descriptive statistics and visualization
• Apply linear regression to business data using Excel and/or PASW, and express how multiple regression can be utilized to improve upon linear regression
• Apply probability distributions and statistical tools used for analysis and decision making in a business management context
• Calculate and interpret measures of statistical inference, and apply these measures to  decision-making in a business management context
• Interpret the results of hypothesis tests and Chi-square analyses using business related examples
• Define the Central Limit Theorem, and apply its principles to Control Charts

• exhibit the analytical thought, informed judgment, ethical behavior, and appreciation for diversity required by management positions in the transportation and logistics management industries

MATH 335 Computational Design

MATH 351 Biostatistics

• Apply statistical and other quantitative analysis tools and techniques to issues in public health
• Evaluate and analyze data as it relates to health outcomes and prevention, management, and treatment strategies

MATH& 107 Math in Society

• Use proportions and ratios to interpret quantities and estimate the relative size of quantities
• Apply proportionality to solve and analyze a variety of multi-step contextual problems
• Use formulas and perform relevant calculations pertaining to personal finance to solve context-based scenarios
• Analyze and critique claims related to personal finance (i.e. loans, mortgages, annuities, etc.) to make informed decisions
• Calculate and interpret probabilities, including conditional probabilities, and use those calculations to make informed decisions
• Analyze and critique statements about probability and risk that appear in the media (i.e. advertisements, odds, medical test results, etc.)
• Recognize and categorize methods for obtaining data, discuss possible sources of bias, and use this information to make an informed decision given a scenario
• Use appropriate tools and strategies to describe and display authentic data (including boxplots, histograms, pie charts, and other graph types)
• Calculate, interpret, analyze, and critique numerical summaries of data (including measures of center and spread), and use these values to compare and contrast two or more samples or populations
• Analyze data and/or scenarios to determine if they describe linear or exponential growth
• Create linear and exponential models for an authentic situation
• Use, interpret, and analyze linear and exponential models to make predictions, discussing appropriateness and limitations of the model
• Read a complex problem requiring quantitative and/or symbolic analysis, use flexibility in selecting a solution strategy, and impose an appropriate mathematical structure or mathematical procedure in solving the problem
• Determine the reasonableness and implications of mathematical solutions, recognize the limitations of the methods used in context, and then apply those methods to making personal and societal choices

MATH& 131 Math for Elementary Education 1

• Use problem-solving models and apply them to concepts introduced throughout the course
• Explore counting, place value, and numeration through a study of historical number systems
• Identify and distinguish among different methods for addition, subtraction, multiplication, and division
• Explore math operations using manipulatives, pictorial arrays, and different bases
• Apply a variety of algorithms and mental computations to solve problems dealing with whole numbers, fractions, decimals, ratios, proportions, and percentages
• Incorporate basic number theory concepts including primes, factors, divisibility, and equality as problem-solving strategies
• Identify common student errors and learning difficulties related to the course topics
• Develop and practice teaching strategies for mathematical concepts
• Self-assess learning and teaching experiences, and modify strategies as needed

MATH& 141 Pre-Calculus I

• Apply the principles of basic algebra and coordinate geometry to solve math problems
• Analyze and solve equations verbally, algebraically, graphically, and numerically
• Use mathematical modeling to solve application problems and interpret the solution in the context of the problem
• Simplify and evaluate combined functions and composite functions
• Describe how transformations of functions affect their graphs
• Determine key features of functions, such as domain, range, asymptotes, and intercepts
• Graph linear, absolute value, piecewise, radical, polynomial, rational, exponential and logarithmic functions
• Find an equation of a function from its graph
• Find the inverse of a one-to-one function
• Apply the properties and laws of logarithms
• Interpret and analyze linear and non-linear data to develop appropriate models

MATH& 142 Pre-Calculus II

• Measure angles in degrees and radians and relate them to arc length 
• Identify reference angles and coterminal angles
• Solve applied problems involving arc length, linear/angular speed, and the area of a circular sector
• Link the graphical, numeric, and symbolic definitions of the trigonometric functions in terms of the unit circle
• Solve problems involving right triangles and unit circles using the definitions of the trigonometric functions
• Apply the law of sines and law of cosines to solve for unknown sides and angles of triangles, and solve applied problems associated with these laws
• Graph the trigonometric functions and their transformations
• Identify key features including amplitude, period, and horizontal shifts from a graph, formula, table, or verbal description
• Use trigonometric functions to model periodic behavior described numerically or verbally
• Use the inverse trigonometric functions to solve equations
• Prove trigonometric identities and use identities to algebraically solve trigonometric equations
• Perform operations with vectors and use them to solve problems both graphically and component-wise
• Relate coordinates in polar form to coordinates in rectangular form
• Write clear, correct, and complete solutions to mathematical problems utilizing proper mathematical notation and appropriate language 
• Use exact and approximate solutions when appropriate
• Use problem solving skills, pattern recognition, substitution, structural rules, and quantitative modeling to solve problems involving trigonometric functions, vectors, and alternative coordinate systems

MATH& 146 Introduction to Statistics

• Organize and graph data using scatterplots, histograms, and boxplots
• Calculate mean, standard deviation, z-scores, and percentile values
• Solve problems using the basic elements of probability theory, such as sample spaces, the addition rule, and the multiplication rule
• Calculate the mean and standard deviation of a probability distribution
• Calculate expected value
• Calculate probabilities using the binomial probability formula
• Calculate probabilities and find percentile values using the normal distribution and the central limit theorem
• Construct and interpret confidence intervals
• Perform hypothesis tests
• Measure and test for correlation
• Use regression equations to make predictions

MATH& 148 Business Calculus

• Construct and transform the graphs of common functions
• Solve simple exponential equations
• Use the product, quotient and chain rules to differentiate simple functions
• Construct equations for tangents and find average and instantaneous rates of change
• Apply the concepts, techniques and vocabulary of limits, continuity, and first and second derivatives to solve simple problems
• Use simple substitutions and appropriate software to find antiderivatives of simple functions
• Determine the values of definite integrals using the Fundamental Theorem of Calculus
• Apply the ideas of definite and indefinite integrals to solve problems
• Recognize applications of differential and integral calculus to business problems

MATH& 151 Calculus I

• Describe a function verbally, algebraically, graphically, and numerically
• Define and calculate limits
• Define the derivative of a function
• Interpret derivatives as slopes of tangent lines and rates of change
• Differentiate polynomial, exponential, logarithmic, and trigonometric functions
• Apply the product, quotient, and chain rules to differentiate functions
• Use implicit differentiation
• Graph functions and their derivatives
• Use linear approximation to estimate the value of a function
• Calculate the maximum and minimum values of a function
• Apply L’Hospital’s rule for solving indeterminate forms
• Approximate solutions using curve sketching
• Define antiderivative and find the antiderivative of a function
• Solve application problems using differential calculus
• Use problem solving skills, pattern recognition, substitution, structural rules, and quantitative modeling to solve problems involving differential calculus and limits

MATH& 152 Calculus II

• Calculate antiderivatives, areas and distances, and the definite integral
• Solve and evaluate functions using The Fundamental Theorem of Calculus
• Solve and evaluate indefinite integrals
• Compute the average value of a function
• Integrate trigonometric functions
• Solve equations using numerical integration and approximation of integrals
• Evaluate improper integrals
• Integrate by parts
• Calculate the length of a curve, the area between curves, the volume of washers and shells, and center of mass
• Use problem solving skills, pattern recognition, substitution, structural rules, and quantitative modeling to solve problems involving integral calculus

MATH& 163 Calculus III

• Use appropriate convergence tests to discuss the behavior of infinite series
• Compute the Maclaurin and Taylor series expansions of basic and transcendental functions, and use them to solve relevant applications
• Define vector-valued functions, and identify their key characteristics and graphs
• Evaluate and interpret algebraic and calculus operations on vector functions and functions of two or more variables graphically, numerically, and analytically
• Describe curves in planes and space using polar, parametric, and vector-valued forms, and identify situations where these alternate coordinate systems can simplify calculations
• Calculate a path of motion, and describe its curvature, arc length, velocity, and acceleration
• Differentiate and integrate parametric equations, polar equations, and vector-valued functions
• Use double integrals in multiple coordinate systems, and apply principles to finding centers of mass and moments of inertia, volumes of solids, and other applications
• Calculate partial derivatives for functions of several variables, using the chain rule as necessary, and use them to solve relevant applications
• Use mathematical critical thinking skills, problem solving, pattern recognition, and substitution, following structural rules and quantitative modeling to solve problems requiring reasoning, critical thinking, and computation

MATH& 264 Calculus IV

• Identify key features of multivariable functions (local and absolute maximums and minimums, as well as saddle points)
• Find the domain and range of a multivariable function, and sketch its typical level curve or level surface
• Find both first-order and second-order partial derivatives of a multivariable function
• Compute the gradient and apply it to finding equations of tangent lines and planes, as well as to computing directional derivatives of multivariable functions
• Evaluate double and triple integrals, and apply these multiple integration principles to solving area, volume and average-value applications
• Compute line and surface integrals, and use them to solve relevant applications
• Use alternative coordinate systems (including polar, cylindrical, and spherical) to simplify multiple integration problems
• Compute gradient, curl, and divergence, using vector and scalar fields appropriately
• Apply Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem
• Introduce first-order differential equations, including initial value problems
• Use mathematical critical thinking skills, problem solving, pattern recognition, and substitution, following structural rules and quantitative modeling to solve problems requiring reasoning, critical thinking, and computation