Mathematics and Statistics

Upon completion of this course, the student will be able to:

• analyze causes of math anxiety.
• examine myths about mathematics.
• describe the experiences in mathematics which have influenced personal attitudes towards math.
• compare personal learning experiences, as related to mathematics.
• apply skills to overcome fear and achieve success in mathematics.
• create a study plan for mathematics courses.
• apply learning strategies to achieve success in mathematics.

Upon completion of this course, the student will be able to:

• evaluate problems using addition, subtraction, multiplication, and division of whole numbers, fractions, and decimals.
• use the order of operations to simplify expressions.
• read, write, and round whole numbers and decimals.
• identify and use factors and prime factorization of whole numbers.
• identify types of fractions.
• simplify fractions.
• demonstrate the relationships between fractions and decimals.
• set up and solve application problems using computational arithmetic.

Upon completion of this course, the student will be able to:

• evaluate numerical expressions that contain integers, fractions, and decimals using the order of operations.
• evaluate algebraic expressions for given value(s) of the variable(s).
• simplify variable expressions by using the distributive property and combining similar terms.
• solve elementary linear equations.
• set up and solve elementary application problems, including problems involving percents, ratios, and proportions.
• convert between percents, decimals, and fractions.
• convert units of measurement, including U.S. and metric systems.
• evaluate numerical square root expressions.
• calculate area, perimeter, and volume of geometric figures.

Upon completion of this course, the student will be able to:

• evaluate problems using addition, subtraction, multiplication, and division of whole numbers, fractions, and decimals, without the use of a calculator.
• use the order of operations to simplify expressions without the use of a calculator.
• read, write, and round whole numbers and decimals.
• identify and use factors and prime factorizations of whole numbers.
• analyze and simplify fractions without the use of a calculator.
• demonstrate the relationships between fractions, decimals, and percents.
• analyze and estimate problems involving whole numbers, fractions, and decimals.
• set up and solve application problems using computational arithmetic without the use of a calculator.

Upon completion of this course, the student will be able to:

• evaluate expressions that contain addition, subtraction, multiplication, and division of real numbers without the use of a calculator.
• solve numerical and applied percent problems.
• simplify algebraic expressions using order of operations without the use of a calculator.
• evaluate and simplify exponential and square root expressions.
• solve linear equations, including those with signed numbers, fractions, and/or decimals without the use of a calculator.
• set up and solve elementary application problems using algebraic techniques without the use of a calculator.
• compute perimeter and area of geometric figures.
• translate words into symbols and equations without the use of a calculator.
• perform operations on signed fractions without the use of a calculator.
• graph linear equations without the use of a calculator.

Upon completion of this course, the student will be able to:

• simplify expressions using the basic operations and properties of real numbers.
• solve one-variable equations and inequalities.
• combine polynomials using the basic operations of polynomials.
• factor polynomials.
• simplify rational expressions.
• solve rational equations.
• solve linear equations.
• graph linear equations.
• find the equation of a line given (a) the slope and a point on the line, and (b) two points on the line.
• solve and graph systems of linear equations.
• simplify expressions containing integer exponents.
• simplify expressions containing second and third degree roots.
• solve quadratic equations.
• graph quadratic equations.
• develop an appropriate equation or system of equations and use the resulting equation(s) to solve application problems.

Upon completion of this course, the student will be able to:

• compute lengths, areas, and volumes of geometric objects.
• apply algebraic skills to geometric problems.
• solve mathematical and logical problems which require geometric skills.
• prove geometric theorems using direct proof structures.
• construct geometric loci using a straightedge and compass.
• select the appropriate trigonometric identity to find angles and sides of right triangles.
• identify theorems that relate angles, arcs, intercepted arcs in circles and polygons.

Upon completion of this course, the student will be able to:

• graph and solve linear inequalities.
• graph systems of linear inequalities.
• solve equations and inequalities containing absolute values.
• solve and graph linear equations and systems of linear equations.
• create linear equations that pass through a given point and are parallel to a given line.
• create linear equations that pass through a given point and are perpendicular to a given line.
• simplify polynomial expressions.
• choose and apply appropriate techniques to factor a variety of polynomials.
• state whether a mathematical relation is a function and find its domain and range.
• construct the inverse of a given function.
• sketch graphs of basic exponential functions.
• utilize the properties of exponents to simplify exponential expressions and to solve exponential equations.
• sketch graphs of basic logarithmic functions.
• utilize the properties of logarithms to simplify logarithmic expressions and to solve logarithmic equations.
• simplify expressions containing radicals, using complex numbers where appropriate.
• solve quadratic equations for real and complex solutions.
• solve equations containing radicals.
• simplify rational expressions and solve rational equations for real and complex solutions.
• sketch graphs of basic conic sections.
• solve and graph systems of non-linear equations.
• develop an appropriate equation or system of equations and use the resulting equation(s) to solve application problems.

Upon completion of this course, the student will be able to:

• identify and solve various types of equations and systems of equations.
• factor a variety of polynomials.
• collect like terms in simplifying polynomial, exponential, and logarithmic functions.
• create graphs of lines, parabolas, exponential, and logarithmic functions.
• associate equations and information from tables or charts with their corresponding graphs.
• explain the concept of a mathematical function/relation and use functional notation appropriately to formulate solutions.
• construct and compare inverse functions with their original functions.
• explain what a logarithm is and solve logarithmic equations and applications.

Upon completion of this course, the student will be able to:

• recognize and solve various types of equations, inequalities, and systems of equations, and related applications.
• factor a variety of polynomials.
• collect like terms in simplifying polynomial, rational, exponential, and logarithmic expressions.
• sketch graphs of lines and conics and functions.
• associate equations and information from tables or charts with their corresponding graphs.
• recognize and explain the concept of a mathematical function/relation and use functional notation appropriately to formulate solutions.
• compare and contrast the properties of a mathematical function and its inverse function.
• analyze and solve applications related to linear, rational, and radical equations.
• define what a logarithm is and solve logarithmic equations and applications.
• define what an exponential function is and solve exponential equations and applications.

Upon completion of this course, the student will be able to:

• solve linear equations and inequalities.
• graph linear equations and inequalities.
• apply appropriate solving techniques to solve systems of linear equations.
• demonstrate addition, subtraction, and multiplication of polynomials.
• apply properties of exponents.
• set up and solve application problems using appropriate algebraic methods.

Upon completion of this course, the student will be able to:

• apply appropriate factoring techniques to polynomials.
• demonstrate factoring and algebraic techniques to solve quadratic equations.
• simplify rational expressions and solve equations with rational expressions.
• identify and solve variation applications.
• use roots, radicals, and exponents in simplifying expressions.
• solve equations with radical expressions.
• set up and solve application problems using appropriate algebraic methods.

Upon completion of this course, the student will be able to:

• differentiate between a mathematical function and relation.
• evaluate functions using function notation.
• solve quadratic equations using a variety of algebraic methods.
• analyze and graph quadratic functions.
• analyze and graph exponential and logarithmic functions.
• solve exponential and logarithmic equations using algebraic properties.
• classify and construct graphs of conic sections.
• set up and solve application problems using appropriate algebraic methods.

Upon completion of this course, the student will be able to:

• solve application problems which require basic algebraic skills.
• evaluate problems using addition, subtraction, multiplication, and division of whole numbers.
• evaluate problems using addition, subtraction, multiplication, and division of fractions.
• evaluate problems using addition, subtraction, multiplication, and division of decimals.
• apply basic geometric formulas and properties to solve problems.
• apply and use trigonometric ratios of right triangles to solve application problems.
• apply dimensional analysis in performing technical calculations.
• use units and dimensions in measurement problems involving customary units and metric terms.
• demonstrate problem-solving techniques of applications using ratio and proportions.

Upon completion of this course, the student will be able to:

• define the vocabulary of a given mathematical topic.
• translate open-ended problems into the given mathematical topic.
• apply techniques (processes or algorithms) to manipulate, illustrate or compute the mathematical objects of the given mathematical topic.
• generalize the techniques (processes or algorithms) of the given mathematical topic to other settings.

Upon completion of this course, the student will be able to:

• discuss several branches of mathematics, including their history and uses beyond mathematics.
• identify appropriate procedures and solve exercises from selected mathematical topics.
• apply critical thinking skills to solve exercises in new settings.
• explain the process and results of several mathematical procedures.

Upon completion of this course, the student will be able to:

• research the fundamental concepts of calculus and their applications.
• employ the derivative to compute slopes and evaluate rates of change.
• apply the integral to compute areas under curves and interpret their meaning.
• recognize that differential and integral calculus are inverse operations.
• apply fundamental calculus techniques in slopes (rates of change) and areas (under curves) involving elementary functions.
• analyze the role of calculus in finding speeds, area, volumes, and optimal values.

Upon completion of this course, the student will be able to:

• explore and discover mathematical patterns and relations for a variety of problems from number theory, statistics, and geometry.
• formulate conjectures based on exploration in a variety of problems from number theory, geometry, and statistics.
• prove or find a counterexample for proposed conjectures.
• analyze statistical data.
• calculate probabilities by applying appropriate statistical concepts.

Upon completion of this course, the student will be able to:

• represent statements of English in well-formed sentences of predicate logic.
• prove the validity of statements and arguments in predicate logic using formal proof techniques.
• apply truth table or truth tree methods to determine semantic properties such as invalidity and consistency.
• construct interpretations that satisfy statements and sets of statements.
• distinguish classical first order logical systems from other logical systems.

Upon completion of this course, the student will be able to:

• analyze and investigate properties of functions.
• synthesize results from the graphs and/or equations of functions.
• solve and apply equations including linear, absolute value, polynomial, radical, rational, exponential, and logarithmic equations.
• solve linear and nonlinear systems of equations and inequalities.
• apply functions and other algebraic techniques to model real world applications.
• recognize the relationship between functions and their inverses graphically and algebraically.
• apply transformations to the graphs of functions.

Upon completion of this course, the student will be able to:

• evaluate and explore functions that represent quantities important in business, including profit, average cost, supply, and demand.
• compute limits graphically, numerically, and analytically.
• find derivatives of various functions, including polynomial, rational, exponential, and logarithmic functions using the Power, Product, Quotient, and Chain Rules.
• find the equation of the tangent line to a polynomial, rational, exponential, or logarithmic function, using derivatives.
• sketch the graph of functions using horizontal and vertical asymptotes, intercepts, first and second derivatives to determine intervals of increase and decrease, maximum and minimum values, intervals of concavity, and points of inflection.
• recognize and solve business applications that call for derivatives of single or multivariable functions including implicit differentiation, related rates, and optimization problems.
• find antiderivatives of various functions using substitution, integration by parts, and other methods.
• evaluate definite integrals using the Fundamental Theorem of Calculus.
• recognize and solve business applications that call for antiderivatives of single variable or multivariable functions.

Upon completion of this course, the student will be able to:

• simplify algebraic expressions and solve algebraic equations related to business and economics problems.
• evaluate limits and derivatives of algebraic, exponential, and logarithmic functions, and apply them to business and economics situations.
• formulate solutions to applications in business and economics using definite and indefinite integrals.
• analyze functions of several variables and their relevance to business and economics applications.

Upon completion of this course, the student will be able to:

• analyze formulas, tables, graphs, and data sets in order to form conclusions or make predictions.
• identify and graph linear, quadratic, rational, polynomial, exponential, and logarithmic functions.
• formulate and apply exponential growth or decay functions pertaining to business applications.
• calculate both present and future values involving simple interest, compound interest, and annuities.
• analyze applications of annuities involving loan amortization and sinking funds, applying necessary formulas.
• evaluate rates of change for a variety of elementary functions and apply them to marginal analysis.
• find and interpret optimum values related to business applications.
• solve linear programming problems by the graphical approach.

Upon completion of this course, the student will be able to:

• differentiate polynomial, radical, trigonometric, logarithmic, and exponential functions.
• graph and analyze the curves of elementary functions.
• calculate maxima and minima of elementary functions.
• apply derivatives to applications in biology and medicine.
• integrate basic elementary functions.
• apply the Fundamental Theorem of Calculus to the evaluation of definite integrals.

Upon completion of this course, the student will be able to:

• solve systems of linear equations with matrix techniques.
• compute eigenvalues and eigenvectors for square matrices.
• solve systems of linear differential equations.
• apply systems of linear differential equations to problems in biology and medicine.
• compute partial derivatives of functions of several variables.
• compute double integrals.
• identify absolute and local extrema of functions of two variables.
• calculate equations of tangent planes to graphs of functions of two variables.

Upon completion of this course, the student will be able to:

• analyze and investigate properties of functions.
• synthesize connections between equations of functions and their graphs, including asymptotic behavior, intercepts, and vertices.
• apply transformations to the graphs of functions, including quadratic, absolute value, radical, rational, logarithmic, and exponential functions.
• recognize the relationship between a function and its inverse both graphically and algebraically.
• solve equations and applications involving rational, linear, polynomial, radical, absolute value, exponential, and logarithmic equations.
• solve systems of equations and inequalities.
• apply techniques for determining zeros of polynomials and roots of equations.
• apply functions and other algebraic techniques to model real world STEM applications.
• analyze conics algebraically and graphically.
• use formulas to find the sum of both finite and infinite series.

Upon completion of this course, the student will be able to:

• convert between degree measure and radian measure of angles.
• graph angles in the coordinate plane and identify the reference angle.
• define the six trigonometric functions in terms of right triangles, the rectangular coordinate system, and the unit circle.
• apply the right triangle definitions of the six trigonometric functions to solve right triangles.
• evaluate trigonometric functions of angles in both degrees and radians.
• evaluate trigonometric functions of special angles in both degrees and radians without a calculator.
• recognize and create the graphs of the basic trigonometric functions.
• graph transformations of the basic trigonometric functions by thinking about amplitude, period, phase shift, and vertical shift.
• simplify expressions using trigonometric identities.
• find function values by making use of identities.
• prove a variety of identities.
• evaluate and graph inverse trigonometric functions.
• evaluate compositions of trigonometric and inverse trigonometric functions.
• solve a variety of trigonometric equations.
• use the Laws of Sines and Cosines to solve oblique triangles.
• solve application problems that involve right and oblique triangles.
• represent a vector both graphically and in ai+bj form.
• perform basic vector operations: addition, subtraction, and scalar multiplication, as well as represent these operations graphically and algebraically.
• calculate powers and roots of complex numbers using De Moivre's Theorem.
• convert between polar and rectangular coordinates and equations.
• graph polar equations.

Upon completion of this course, the student will be able to:

• graph functions and relations and investigate their properties.
• synthesize connections between equations of functions and their graphs, including asymptotic behavior, intercepts, and vertices.
• apply transformations to the graphs of functions and relations, including quadratic, absolute value, radical, rational, logarithmic, and exponential functions.
• recognize the relationship between a function and its inverse both graphically and algebraically.
• solve equations and applications involving linear, absolute value, polynomial, rational, radical, exponential, and logarithmic equations.
• apply techniques for determining zeros of polynomials and roots of equations.
• apply functions to model real world applications.
• identify special triangles and their related angle and side measures.
• evaluate the trigonometric function at an angle whose measure is given in degrees and radians.
• graph the basic trigonometric functions and apply changes in period, amplitude, vertical shift, and horizontal shift to generate new graphs.
• evaluate and graph inverse trigonometric functions.
• solve trigonometric equations, triangles, and applications.
• manipulate and simplify trigonometric expressions and prove trigonometric identities.
• convert between polar and rectangular coordinates and graph polar equations.
• calculate powers and roots of complex numbers using DeMoivre's Theorem.
• represent a vector (a quantity with magnitude and direction) in the form <a, b> and ai+bj.
• solve systems of equations and inequalities.
• analyze conics algebraically and graphically.
• use formulas to find the sum of both finite and infinite series.
• use the Binomial Theorem to expand (a+b)^n.

Upon completion of this course, the student will be able to:

• graph functions and relations and investigate their properties.
• apply transformations to the graphs of functions and relations, including quadratic, absolute value, radical, rational, logarithmic and exponential functions.
• recognize the relationship between a function and its inverse both graphically and algebraically.
• solve equations and applications involving linear, absolute value, polynomial, rational, radical, exponential, and logarithmic equations.
• apply techniques for determining zeros of polynomials and roots of equations.
• identify special triangles and their related angle and side measures.
• evaluate trigonometric functions at an angle whose measure is given in degrees and radians.
• graph the basic trigonometric functions and apply changes in period, amplitude, vertical shift, and horizontal shift to generate new graphs.
• solve trigonometric equations, triangles, and applications.
• manipulate and simplify trigonometric expressions and prove trigonometric identities.

Upon completion of this course, the student will be able to:

• evaluate limits graphically, analytically, and by using L'Hopital's Rule.
• compute derivatives using the definition of derivative.
• apply differentiation rules to various types of functions.
• recognize and solve application problems that require use of derivatives.
• apply antidifferentiation rules to various types of functions.
• compute definite integrals using the Fundamental Theorem of Calculus.
• recognize and solve application problems that require use of antiderivatives.

Upon completion of this course, the student will be able to:

• identify and use properties of logarithmic, exponential, and inverse trigonometric functions to evaluate integrals.
• evaluate integrals using the techniques of integration by parts, trig substitution, partial fractions, and rationalizing substitutions.
• recognize and evaluate limits in indeterminate forms and improper integrals.
• determine the convergence or divergence of sequences and series, find power series representations for certain transcendental functions, and apply appropriate Calculus techniques to evaluate derivatives and integrals of power series.
• rewrite, analyze and graph equations in three forms: rectangular, parametric, and polar; using appropriate calculus techniques.
• use various integration techniques to solve applications, including area, volume, and arc length.
• solve separable differential equations to determine growth and decay functions.

Upon completion of this course, the student will be able to:

• analyze and graph two- and three-dimensional functions, vectors, vector-valued functions, and geometric surfaces and solids in order to solve for various geometric quantities and to represent motion in space.
• perform vector operations: addition, subtraction, scalar multiplication, dot products, and cross products.
• determine the equations of lines and planes in space, including tangent planes to a surface.
• find the limit of a multivariate function at a point and determine the differentiability of a multivariate function.
• evaluate partial derivatives and apply them to find local extrema and test for saddle points of multivariate functions.
• apply Lagrange multipliers to solve optimization problems with constraints.
• compute the arc length of a curve.
• set up and evaluate iterated integrals in rectangular, cylindrical, and spherical coordinates to calculate the area, volume, mass, and center of mass for a surface or solid.
• find the gradient of a scalar field and the divergence and curl of a vector field.
• set up and evaluate line and surface integrals using Green's, Gauss', and Stokes' Theorems and use results to solve application problems involving vector fields.

Upon completion of this course, the student will be able to:

• solve systems of linear equations by reducing an augmented matrix to row-echelon or reduced row-echelon form.
• determine whether a linear system is consistent or inconsistent; for consistent systems, characterize solutions as unique or infinitely many and write parametric solutions for systems with infinitely many solutions.
• evaluate matrix expressions using properties of matrix algebra.
• compute the transpose, determinant, adjoint, and inverse of matrices if defined for a given matrix.
• determine if a subset of a vector space is a vector space, and if so, prove that the subset is a subspace.
• determine if a given set of vectors is linearly independent, and if so, prove that this determination is correct.
• determine if a given set of vectors is a basis for a vector space, and if so, prove that this determination is correct and find the basis and dimension of spaces such as those associated with matrices and linear transformations or the intersection of two subspaces.
• calculate inner products, use properties of inner products to determine angle and orthogonality, and use an orthonormal basis to to find the projection of a vector on a space.
• determine if a function that maps two vectors from a vector space to a scalar is an inner product on that vector space.
• construct orthogonal and orthonormal bases using the Gram-Schmidt Process for a given basis.
• construct the orthogonal diagonalization of a symmetric matrix.
• determine the matrix for a linear transformation on Euclidean 2-space or 3-space, and for a given linear transformation, determine kernel, range, rank, nullity, and whether the linear transformation is an isomorphism.
• compute the characteristic polynomial, eigenvalues, eigenvectors, and eigenspaces for both matrices and linear transformations.
• use eigenvalues and eigenvectors in applications and diagonalization.
• prove basic results in linear algebra using accepted proof-writing techniques including linear independence of vectors, properties of subspaces, linearity, injectivity, surjectivity, properties of eigenvectors, and properties of eigenvalues.

Upon completion of this course, the student will be able to:

• formulate and analyze mathematical models using ordinary differential equations.
• categorize a given differential equation by type, order, and linearity.
• determine existence and uniqueness of solutions of an initial value problem for the first-order ordinary differential equation.
• solve elementary first-order and second-order ordinary differential equations (linear and nonlinear) using analytical methods.
• solve ordinary differential equations using power series.
• solve higher order ordinary differential equations with constant coefficients using analytical techniques.
• solve systems of linear ordinary differential equations with constant coefficients using analytical methods.
• assess situations in which a differential equation can be solved more efficiently with the Laplace Transform or the Inverse Laplace Transform and apply the transform to the equation when appropriate.

Upon completion of this course, the student will be able to:

• perform critical analysis and exploration when confronted with a nonstandard challenging mathematics problem by constructing models and developing cogent strategies to find a solution.
• demonstrate mastery and understanding of various mathematical topics from pre-calculus.
• present work in a seminar to a critical audience.
• explore and attack mathematics problems with depth and significance.

Upon completion of this course, the student will be able to:

• analyze and investigate properties of functions.
• choose and apply appropriate techniques to factor a variety of polynomials.
• synthesize results from the graphs and/or equations of functions.
• solve and apply equations including linear, absolute value, polynomial, radical, rational, exponential, and logarithmic equations.
• solve linear and nonlinear systems of equations and inequalities.
• apply functions and other algebraic techniques to model real-world applications.
• recognize the relationship between functions and their inverses graphically and algebraically.
• apply transformations to the graphs of functions.

Upon completion of this course, the student will be able to:

• apply learning strategies to achieve success in Calculus for Business and Economics or Modern Business Mathematics.
• use real numbers to perform arithmetic operations in the evaluation of algebraic functions.
• simplify expressions and solve equations involving polynomial, rational, radical, exponential, and logarithmic functions.
• analyze the structure of multivariable equations utilizing graphs, tables, and algebraic methods.
• utilize algebraic techniques and problem solving strategies to solve application problems.

Upon completion of this course, the student will be able to:

• apply learning strategies to achieve success in Calculus I.
• apply appropriate support methods to evaluate limits.
• apply appropriate support methods to solve algebraic and trigonometric equations in calculus problems.
• apply appropriate support methods to assist with differentiation of various functions.
• apply appropriate support methods when using derivatives to sketch curves and solve optimization problems.
• apply appropriate support methods to recognize and solve application problems that require the use of derivatives.
• apply appropriate support methods to find antiderivatives and evaluate definite integrals.
• apply appropriate support methods to recognize and solve application problems that require the use of antiderivatives.

Upon completion of this course, the student will be able to:

• use technology appropriately to achieve success in Calculus II.
• apply appropriate support methods in the evaluation of integrals using the integration techniques of partial fractions, trigonometric substitution, and rationalizing substitutions.
• apply appropriate support methods when estimating definite integrals using numerical integration.
• use appropriate support methods to assist in the evaluation of improper integrals.
• apply appropriate support methods to help determine mathematical models and find solutions to applications of integration.
• apply appropriate support methods to solve separable differential equations.
• use appropriate support methods to assist in determining convergence or divergence of sequences and series.
• apply mathematical support techniques to find intervals of convergence of power series and to determine power series representations of functions.
• apply appropriate support techniques to find the area inside polar curves and determine tangents to polar curves.

Upon completion of this course, the student will be able to:

• apply learning strategies to achieve success in Calculus for Biology and Medicine I.
• apply appropriate support methods to solve algebraic and trigonometric equations in calculus problems.
• apply appropriate support methods to assist with differentiation of various functions.
• apply appropriate support methods when using derivatives to sketch curves and solve optimization problems.
• apply appropriate support methods to find appropriate mathematical models to solve calculus application problems in biology and medicine.
• apply appropriate support methods to find antiderivatives and evaluate definite integrals.
• apply appropriate support methods to solve first-order differential equations.

Upon completion of this course, the student will be able to:

• use technology appropriately to achieve success in Calculus for Biology and Medicine II.
• apply appropriate support methods to calculate eigenvalues and eigenvectors.
• apply appropriate support methods to find the parametric equations for the tangent line to a surface at a point on the surface in the direction of the y-axis.
• apply appropriate support methods to find the equation of a tangent plane to a surface at a point on the surface.
• apply appropriate support methods to solve optimization problems for functions of two variables that model applications in biology.
• apply appropriate support methods to compute probabilities in a binomial experiment.
• apply Bayes' Theorem appropriately to solve applications in biology and medicine.
• apply appropriate support methods to sketch Type 1 or Type 2 regions and determine the center of mass of a lamina that occupies the region using double integrals.
• apply appropriate support methods to solve linear systems of ordinary differential equations.

Upon completion of this course, the student will be able to:

• use mathematics support skills to solve equations and inequalities and manipulate expressions.
• use mathematics support skills to solve systems of equations and inequalities.
• use mathematics support skills to demonstrate a deep understanding of functions and their properties.
• apply learning strategies to achieve success in College Algebra for Calculus.

Upon completion of this course, the student will be able to:

• recall the methods from arithmetic necessary to be successful in Trigonometry for Calculus
• review the methods from algebra necessary to be successful in Trigonometry for Calculus
• demonstrate an understanding of the methods from geometry necessary to be successful in Trigonometry for Calculus
• apply learning strategies to achieve success in Trigonometry for Calculus

Upon completion of this course, the student will be able to:

• apply learning strategies to achieve success in Pre-Calculus.
• recall the methods from arithmetic necessary to be successful in Pre-Calculus.
• review the methods from algebra necessary to be successful in Pre-Calculus.
• demonstrate an understanding of the methods from geometry necessary to be successful in Pre-Calculus.

Upon completion of this course, the student will be able to:

• apply appropriate support methods to achieve success in Preparation for Calculus.
• apply appropriate support methods to solve equations and inequalities, and manipulate expressions.
• apply appropriate support methods to develop a deep understanding of functions and their properties.
• apply appropriate support methods to graph functions.
• apply appropriate support methods to solve exponential and logarithmic equations.
• demonstrate an understanding of the methods from geometry necessary to learn trigonometry.
• apply appropriate support methods to evaluate and algebraically manipulate trigonometric functions.
• apply appropriate support methods to graph trigonometric functions.

Upon completion of this course, the student will be able to:

• apply learning strategies to achieve success in Introduction to Mathematical Ideas (MATH 300).
• use support mathematics skills to identify appropriate procedures and solve exercises from selected mathematical topics.
• use support mathematics skills to apply critical thinking skills to solve exercises in new settings.
• use support mathematics skills to explain the process and results of several mathematical procedures.

Upon completion of this course, the student will be able to:

• apply learning strategies to achieve success in statistics.
• use problem solving techniques in the context of data analysis and statistical methods.
• demonstrate relevant arithmetic, algebraic, and geometric skills in the context of statistics.
• apply mathematical and statistical skills in real-world settings and interpret the results in context.

Upon completion of this course, the student will be able to:

• identify methods of obtaining data and related advantages and disadvantages of each.
• organize and display data using appropriate tables and graphs.
• summarize a given data set using appropriate numerical summaries.
• analyze data by computing measures of central tendency, measures of dispersion, and measures of position.
• make meaningful and appropriate comparisons of distributions of data collected from two or more different groups.
• analyze bivariate data for linear trends using the least-squares regression model and the correlation coefficient.
• develop and apply the concept of numeracy to investigate and describe quantitative relationships and solve problems in a variety of contexts.
• solve problems that require the use of ratios, rates, proportions, and scaling.
• express real-world and quantitative situations with equations, inequalities, expressions, tables, verbal descriptions, symbols, and graphs.
• solve application problems involving equations, systems of equations, and inequalities and explain how results relate to the original context.
• apply functions as a way of modeling a correspondence between two variables in linear, quadratic, exponential, and logarithmic situations.
• solve problems involving exponential growth and decay in formulas, graphs, tables, and applications.
• calculate and interpret probabilities.
• estimate probabilities (including conditional probabilities) empirically and using simulation.
• use statistical software or graphing calculator to calculate single variable and analyze the results.
• apply learning strategies to achieve success in mathematics.

Upon completion of this course, the student will be able to:

• Assess how data were collected and recognize how data collection affects what conclusions can be drawn from the data.
• Identify appropriate graphs and summary statistics for variables and relationships between them and correctly interpret information from graphs and summary statistics.
• Describe and apply probability concepts and distributions.
• Demonstrate an understanding of, and ability to use, basic ideas of statistical processes, including hypothesis tests and confidence interval estimation.
• Identify appropriate statistical techniques and use technology-based statistical analysis to describe, interpret, and communicate results.
• Evaluate ethical issues in statistical practice.
• Analyze bivariate data for linear trends using linear regression and the correlation coefficient.
• Analyze and interpret applications using data from various disciplines such as administration of justice, business, economics, education, health science, information technology, life science, physical science, political science, psychology, and social science.
• Use a statistical software package such as, but not limited to, StatCrunch, R, SAS, SPSS, EXCEL, Minitab, Desmos, and/or graphing calculators to perform a variety of statistical analysis.

Upon completion of this course, the student will be able to:

• identify methods of obtaining data and related advantages and disadvantages of each.
• distinguish between types of data as well as their different scales of measurement and corresponding implications.
• organize and display data appropriately using tables and graphs.
• analyze data by computing measures of central tendency, measures of dispersion, and measures of position.
• analyze bivariate data for linear trends using the least-squares regression model and the correlation coefficient.
• analyze both discrete and continuous probability distributions, including binomial probability and normal distribution, by examining and interpreting areas under the graph of a histogram or a normal curve.
• apply inferential statistical methods to compare population parameters, make predictions, and draw conclusions about hypothesis.
• apply the concept of numeracy to investigate and describe quantitative relationships and solve problems in a variety of contexts.
• select the appropriate hypothesis test, perform the necessary computations and comparisons for the test (including significance of p-values and type I/II errors), and explain the conclusion of the test.
• test the significance of correlation and make prediction based on linear trends using the least-squares regression model.
• create and interpret confidence interval estimates for population parameters based on appropriate probability models.
• analyze and interpret applications using data from various disciplines including business, social sciences, psychology, life sciences, health science, and education.
• use statistical software or graphing calculator to calculate single variable and two-variable statistics and analyze the results.
• make conjectures about the behavior of a function in a given context.
• apply learning strategies to achieve success in mathematics.

Upon completion of this course, the student will be able to:

• Assess how data were collected and recognize how data collection affects what conclusions can be drawn from the data.
• Identify appropriate graphs and summary statistics for variables and relationships between them and correctly interpret information from graphs and summary statistics.
• Describe and apply probability concepts and distributions.
• Demonstrate an understanding of, and ability to use, basic ideas of statistical processes, including hypothesis tests and confidence interval estimation.
• Identify appropriate statistical techniques and use technology-based statistical analysis to describe, interpret, and communicate results.
• Evaluate ethical issues in statistical practice.
• Analyze bivariate data for linear trends using linear regression and the correlation coefficient.
• Analyze and interpret applications using data from various disciplines such as administration of justice, business, economics, education, health science, information technology, life science, physical science, political science, psychology, and social science.
• Use a statistical software package such as, but not limited to, StatCrunch, R, SAS, SPSS, EXCEL, Minitab, Desmos, and/or graphing calculators to perform a variety of statistical analysis.
• Analyze and critique the use and misuse of statistics in popular and academic media.