Mathematics and Statistics

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

• SLO 1: CORRECTLY USE THE ORDER OF OPERATIONS TO EVALUATE EXPRESSIONS. ACCURATELY COMPUTE PROBLEMS INVOLVING THE BASIC OPERATIONS OF ARITHMETIC (ADDITION, SUBTRACTION, MULTIPLICATION, DIVISION, EXPONENTS, ORDER OF OPERATIONS) ON WHOLE NUMBERS, FRACTIONS, AND DECIMALS.
• 1a: identify the prime numbers from 2 to 50. Use divisibility tests, factorization, and the concept of prime and composite to construct the least common multiple. Understand the process of rewriting a given number as the product of all distinct prime numbers.
• 1b: express numeric information in one of the following three forms: fraction, percent, decimal.
• 1c: incorporate concepts of prime factorization and greatest common factor to simplify fractions.
• 1d: evaluate problems involving ratios, proportions, and percents.
• 1e: perform unit conversions for American measurements which involve length, capacity, weight, and times. Use the method of unit conversions to solve application problems.
• 1f: demonstrate concepts of rounding and estimation of whole numbers and decimals to nearest place value.
• SLO 2: DEMONSTRATE THE ABILITY TO TRANSLATE MATHEMATICAL PROBLEMS IN WORD FORM TO AN EXPRESSION OR SINGLE VARIABLE EQUATION, AND SOLVE SINGLE VARIABLE ONE-STEP EQUATIONS.
• 2a: translate simple English phrases and sentences into simple algebraic expressions and equations.
• 2b: construct equations by translating information from word form to symbolic form with the use of a variable.
• 2c: set up applied problems involving ratios, proportions, and percent.
• 2d: calculate solutions of one-step single variable equations.
• 2e: solve applications problems involving whole numbers, fractions, decimals, ratios, proportions, and percent.
• 2f: find perimeter and area of basic Euclidean and compound shapes.
• SLO 3: ANALYZE PATTERNS AND ORGANIZE MATHEMATICAL THOUGHTS TO INCREASE THE LEVEL OF ABSTRACT THINKING THAT IS ESSENTIAL FOR REAL-LIFE PROBLEM-SOLVING.
• ~ Apply mathematical concepts and patterns to new problems and new situations.
• ~ Demonstrate ability to communicate mathematically by writing and presenting the work of the problems in an organized way.

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

• SLO 1: CORRECTLY USE THE ORDER OF OPERATIONS TO EVALUATE EXPRESSIONS. ACCURATELY COMPUTE PROBLEMS INVOLVING THE BASIC OPERATIONS OF ARITHMETIC (ADDITION, SUBTRACTION, MULTIPLICATION, DIVISION, EXPONENTS, ORDER OF OPERATIONS) ON WHOLE NUMBERS, FRACTIONS, AND DECIMALS.
• ~Identify the prime numbers from 2 to 50. Use divisibility tests, factorization, and the concept of prime and composite to construct the least common multiple. Understand the process of rewriting a given number as the product of all distinct prime numbers.
• ~Express numeric information in one of the following three forms: fraction, percent, decimal.
• ~Incorporate concepts of prime factorization and greatest common factor to simplify fractions.
• ~Evaluate problems involving ratios, proportions, and percents.
• ~Perform unit conversions for American measurements which involve length, capacity, weight, and times. Use the method of unit conversions to solve application problems.
• ~Demonstrate concepts of rounding and estimation of whole numbers and decimals to nearest place value.
• SLO 2: DEMONSTRATE THE ABILITY TO TRANSLATE MATHEMATICAL PROBLEMS IN WORD FORM TO AN EXPRESSION OR SINGLE VARIABLE EQUATION, AND SOLVE SINGLE VARIABLE ONE-STEP EQUATIONS.
• ~Translate simple English phrases and sentences into simple algebraic expressions and equations.
• ~Construct equations by translating information from word form to symbolic form with the use of a variable.
• ~Set up applied problems involving ratios, proportions, and percents.
• ~Calculate solutions of one-step single variable equations.
• ~Solve applications problems involving whole numbers, fractions, decimals, ratios, proportions, and percents.
• ~Find perimeter and area of basic Euclidean and compound shapes.
• SLO 3: ANALYZE PATTERNS AND ORGANIZE MATHEMATICAL THOUGHTS TO INCREASE THE LEVEL OF ABSTRACT THINKING THAT IS ESSENTIAL FOR REAL-LIFE PROBLEM-SOLVING.
• ~Apply mathematical concepts and patterns to new problems and new situations.
• ~Demonstrate ability to communicate mathematically by writing and presenting the work of the problems in an organized way.

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

• SLO 1: ARTICULATE THE IMPORTANCE OF THE ORDER OF OPERATIONS AND HOW THEY RELATE TO THE REAL NUMBER SYSTEM, EXPRESSIONS, EQUATIONS AND EVALUATION OF MATHEMATICAL FORMULAS.
• ~ Compute with accuracy problems involving the basic operations of arithmetic (addition, subtraction, multiplication, division, exponents, order of operations) on signed numbers.
• ~ Multiply and divide numbers expressed in scientific notation.
• ~ Simplify expressions involving variables by adding, subtracting, multiplying, dividing, or reducing.
• ~ Use and evaluate formulas with more than one variable.
• ~ Demonstrate accurate use of the properties of real numbers and the exponent rules in addition, subtraction, and multiplication of polynomials.
• SLO 2: DEMONSTRATE THE ABILITY TO RECOGNIZE KEY WORDS OR PHRASES THAT WOULD GUIDE ONE THROUGH THE TRANSLATION OF A MATHEMATICAL PROBLEM IN WORD FORM TO AN ALGEBRAIC EXPRESSION OR EQUATION.
• ~ Solve applied problems using signed numbers, variable expressions, scientific notation, and equations.
• ~ Solve linear equations in one variable involving signed numbers, fractions, and decimals.
• ~ Directly translate equations in word form to symbolic form with the use of variables and solve them.
• SLO 3: INVESTIGATE AND MODEL REAL LIFE PHENOMENA THROUGH THE USE OF LINEAR EQUATIONS IN TWO VARIABLES AND THEIR CORRESPONDING GRAPHS (ALGEBRAICALLY AND GEOMETRICALLY), AND THINK CRITICALLY ABOUT HOW THE MATHEMATICS IS RELEVANT TO ONE’S LIFE.
• ~ Find solutions to linear equations in two variables and plot these points on the two-dimensional coordinate system.
• ~ Interpret graphs of two-dimensional data, such as bar graphs, line graphs, and pie charts.
• SLO 4: UTILIZE AND APPLY THE METHOD OF DIMENSIONAL ANALYSIS (OR UNIT ANALYSIS) TO COMPARE AND CONVERT QUANTITIES.
• ~ Solve applied problems using measurement conversions, proportions, and percent.
• ~ Perform accurate computations involving measurement conversion.
• SLO 5: DEMONSTRATE THE ABILITY TO RECOGNIZE PATTERNS, ORGANIZE MATHEMATICAL THOUGHTS, AND INCREASE THE LEVEL OF ABSTRACT THINKING THAT IS ESSENTIAL FOR REAL-LIFE PROBLEM-SOLVING.

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

• SLO#1: Use increased computational skills and number sense, recognize the order of operations and properties of real numbers; include evaluating various mathematical formulas and extending operations to variable expressions and combining like terms
• ~ Simplify expressions using the order of operations and basic properties of real numbers.
• ~ Compute with accuracy problems involving the basic operations of arithmetic (addition, subtraction, multiplication, division, exponents, order of operations) on signed numbers.
• ~ Multiply and divide numbers expressed in scientific notation.
• ~ Use and evaluate formulas with more than one variable.
• SLO#2: Solve first-degree equations, inequalities, and applications.
• ~ Identify the types of equations including conditional equations, contradiction, and identity and techniques for their solution.
• ~ Solve linear inequalities and write the solution in both set-builder and interval notation.
• ~ Apply problem-solving skills to construct equations and inequalities for application problems and solve the applications by solving the equations or inequalities and appropriately interpreting the results.
• SLO#3: Identify and analyze linear equations, and graphs of linear equations and linear inequalities.
• ~ Interpret the slope of a line as a rate of change and graph a line.
• ~ Generate an algebraic model for data that follows linear behavior and interpret the result of this model. Applications of linear models include linear growth, linear depreciations, and rates.
• SLO#4: Apply mathematical terminology, symbols and operations to develop and extend arithmetic operations on polynomials and to evaluate polynomial expressions.
• ~ Evaluate and expand polynomial expressions and expressions written in scientific notation.
• ~ Apply rules of exponents (including negative exponents) to simplify algebraic expressions.
• ~ Demonstrate proficiency in all arithmetic operations on polynomials, particularly multiplying using FOIL.
• ~ Use operations on polynomials to solve certain polynomial equations and applications.
• SLO#5: Identify prime polynomials and factor polynomials into primes using various techniques.
• ~ Factor out common factors and factor by grouping.
• ~ Factor the difference of two squares and factor trinomials including perfect square trinomials.
• ~ Solve polynomial equations by factoring and using the zero factor property.
• ~ Think critically and abstractly by modeling an application problem using a polynomial equation to solve and interpret the result.
• SLO#6: Simplify, combine and evaluate rational expressions using the operations of arithmetic.
• ~ Multiply and divide rational expressions and incorporate factoring to simplify to lowest terms.
• ~ Add and subtract rational expressions using the algebraic method and least common denominator.
• ~ Solve rational equations by multiplying by the least common denominator.
• ~ Use an appropriate rational equation to model an application problem to solve and interpret the results.
• SLO #7: Solve systems of linear equations and systems of linear inequalities as well as their applications and effectively organize, present, and summarize the quantitative information using algebraic, numerical and graphical methods.
• ~ Calculate the solution to a 2x2 system of linear equations using the methods of graphing, substitution, and elimination and identify the types of 2x2 systems.
• ~ Construct a system of linear equations for applications and solve the applications by solving the system and appropriately interpret the solution.
• ~ Compute the solution to a system of linear inequalities using a graph and describe the meaning of this solution.
• SLO#8: Demonstrate with proficiency how to use arithmetic operations on radicals and simplify radical expressions.
• ~ Simplify different types of radicals, rationalize denominators and combine radicals when it is appropriate.
• ~ Solve radical equations and evaluate radical expressions.
• ~ Solve applied problems using radical equations and using the Pythagorean Theorem to solve triangles and applications.
• ~ Verify how to extend the definition of an exponent to a rational exponent and interpret a rational exponent as a radical.
• ~ Use radicals to solve quadratic equations by taking roots, completing the square, and using the quadratic formula, and employ quadratic equations in various applications.

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

• SLO#1: Use increased computational skills and number sense, recognize the order of operations and properties of real numbers; include evaluating various mathematical formulas and extending operations to variable expressions and combining like terms
• ~Simplify expressions using the order of operations and basic properties of real numbers.
• ~ Compute with accuracy problems involving the basic operations of arithmetic (addition, subtraction, multiplication, division, exponents, order of operations) on signed numbers.
• ~ Multiply and divide numbers expressed in scientific notation.
• SLO#2: Solve first-degree equations, inequalities, and applications.
• ~Identify the types of equations including conditional equations, contradiction, and identity and techniques for their solution.
• ~Solve linear inequalities and write the solution in both set-builder and interval notation.
• ~ Apply problem-solving skills to construct equations and inequalities for application problems and solve the applications by solving the equations or inequalities and appropriately interpreting the results.
• SLO#3: Identify and analyze linear equations, and graphs of linear equations and linear inequalities.
• ~ Interpret the slope of a line as a rate of change and graph a line.
• ~ Generate an algebraic model for data that follows linear behavior and interpret the result of this model. Applications of linear models include linear growth, linear depreciation, and rates.
• SLO#4: Apply mathematical terminology, symbols and operations to develop and extend arithmetic operations on polynomials and to evaluate polynomial expressions.
• ~ Evaluate and expand polynomial expressions and expressions written in scientific notation.
• ~ Apply rules of exponents (including negative exponents) to simplify algebraic expressions.
• ~ Demonstrate proficiency in all arithmetic operations on polynomials, particularly multiplying using FOIL.
• ~ Use operations on polynomials to solve certain polynomial equations and applications.
• SLO #5: Solve systems of linear equations and systems of linear inequalities as well as their applications and effectively organize, present, and summarize the quantitative information using algebraic, numerical and graphical methods.
• ~ Calculate the solution to a 2x2 system of linear equations using the methods of graphing, substitution, and elimination and identify the types of 2x2 systems.
• ~ Construct a system of linear equations for applications and solve the applications by solving the system and appropriately interpret the solution.
• ~ Compute the solution to a system of linear inequalities using a graph and describe the meaning of this solution.

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

• SLO#1: Apply mathematical terminology, symbols, and operations to develop and extend arithmetic operations on polynomials and to evaluate polynomial expressions.
• ~ Apply rules of exponents (including negative exponents) to simplify algebraic expressions.
• ~ Demonstrate proficiency in all arithmetic operations on polynomials, particularly multiplying using FOIL.
• ~ Use operations on polynomials to solve certain polynomial equations and applications.
• SLO#2: Identify prime polynomials and factor polynomials into primes using various techniques.
• ~ Factor out common factors and factor by grouping.
• ~ Factor the difference of two squares and factor trinomials including perfect square trinomials.
• ~ Solve polynomial equations by factoring and using the zero factor property.
• ~ Think critically and abstractly by modeling an application problem using a polynomial equation to solve and interpret the result.
• SLO#3: Simplify, combine and evaluate rational expressions using the operations of arithmetic.
• ~ Multiply and divide rational expressions and incorporate factoring to simplify to lowest terms.
• ~ Add and subtract rational expressions using the algebraic method and least common denominator.
• ~ Solve rational equations by multiplying by the least common denominator.
• ~ Use an appropriate rational equation to model an application problem to solve and interpret the results.
• SLO#4: Demonstrate with proficiency how to use arithmetic operations on radicals and simplify radical expressions.
• ~ Simplify different types of radicals, rationalize denominators and combine radicals when it is appropriate.
• ~ Solve radical equations and evaluate radical expressions.
• ~ Solve applied problems using radical equations and using the Pythagorean Theorem to solve triangles and applications.
• ~ Verify how to extend the definition of an exponent to a rational exponent and interpret a rational exponent as a radical.
• ~ Use radicals to solve quadratic equations by taking roots, completing the square, and using the quadratic formula, and employ quadratic equations in various applications.

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

• solve linear, quadratic, absolute value, square root, exponential, logarithmic equations.
• solve systems of linear equations in two variables and linear and absolute value inequalities.
• graph linear, quadratic, absolute value, exponential, and logarithmic functions.
• apply elementary operations on functions.
• use mathematical modeling to solve applications.

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

• clearly state and correctly use definitions, postulates, and theorems of Euclidean geometry.
• compute segment lengths and angle measures of geometric objects using definitions, postulates, and theorems of Euclidean geometry.
• apply appropriate formulas when finding areas of planar figures, surface area and volume of solids, and when analyzing diagrams in the Cartesian coordinate system.
• perform geometric constructions using a straightedge and compass.
• write direct proofs and analytic proofs using the definitions, postulates, and theorems of Euclidean geometry.

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

• simplify expressions and solve equations involving absolute values, polynomials, rational expressions, radicals, exponentials, and logarithms.
• solve systems of equations and solve linear, polynomial, rational, and absolute value inequalities.
• use the definition of a function to determine if a relation is a function and use function notation, including the algebra of functions, composite functions, and inverse functions.
• sketch the graphs of basic functions, quadratic functions, transformations of these functions, and conic sections.
• apply algebraic methods when solving word problems.

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

• simplify expressions and solve equations involving absolute values, polynomials, rational expressions, and radicals.
• solve linear and absolute value inequalities.
• define functions, use function notation, and perform the four arithmetic operations on functions.
• sketch the graphs of basic functions and transformations of the functions.
• apply algebraic methods when solving word problems.

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

• solve quadratic equations using a variety of methods, solve exponential and logarithmic equations, and solve equations quadratic in form.
• solve linear and nonlinear systems of equations and solve polynomial and rational inequalities.
• find composite and inverse functions.
• graph quadratic functions, conic sections, exponential functions, and logarithmic functions, including transformations.
• apply algebraic methods when solving word problems.

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

• choose appropriate mathematical models for analyzing democratic and social phenomenon.
• compare and choose among financial options such as loans and annuities or make other relevant financial decisions.
• compute and compare risk factors in various situations.
• create visual and graphical representations of data relevant to topics.
• compute unit conversions in various contexts.
• explain positions on topics using valid arguments.
• demonstrate the use of mathematics and critical thinking in contemporary vocational and technical fields.

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

• demonstrate preparedness for subsequent UC Davis mathematics courses such as precalculus or calculus. The students will place into the next mathematics course based on scores from the UCD Mathematics Placement Exam, which they will take upon completion of MATH 170.
• solve mathematical problems involving polynomials, rational expressions, equations and inequalities, exponents, radical, and logarithms and demonstrate conceptual rather than strictly procedural knowledge of these topics.
• demonstrate increased competence in problem solving, including application problems, and a higher level of mathematical maturity.
• model substantive interpretation of algebraic problems.

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

• demonstrate understanding of the mathematical concepts studied in the course.
• demonstrate competence in the mathematical skills studied in the course.

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

• analyze inferences and conjectures present in a variety of mathematical ideas and systems.
• construct well written solutions to mathematical exercises.
• apply critical thinking skills developed in studying a mathematical topic to issues that transcend mathematics.
• research and demonstrate an understanding of and explain mathematical ideas that are at an appropriate skill level.

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

• create a personal budget and determine if home buying is the right choice from one's personal and cultural perspective.
• compute the appropriate unit conversions in context of a task at hand, and confirm that the resulting value is realistic.
• explain features of data such as measures of center, measures of spread, and the shape of the distribution.
• critique graphical and tabular representations for bias.
• examine analytical test results to determine whether a claim is rejected.
• solve linear equations and solve formulas for a variable in the context of chemistry and various technical careers.
• graph linear functions through point-plotting, and determine the slope and equation of the line from a given graph.
• compute phase angles using right triangles as applied in various technical careers.
• graph exponential functions and use laws of exponents to solve exponential equations in the context of chemistry and other technical career fields.

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

• explain mathematical relationships inherent in problems and situations.
• make conjectures about mathematical relationships and content.
• prove or disprove conjectures about mathematical relationships and content.
• develop an appreciation of mathematical relevance to every day life.
• analyze documents directing the study of mathematics in American schools, as well as the strategies, procedures, and emphases advocated in those documents.

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 rational, linear, absolute value, polynomial, exponential, and logarithmic equations.
• solve linear and nonlinear systems of equations and inequalities.
• use functions and other algebraic techniques to model real world applications.
• demonstrate 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:

• find the derivatives of polynomial, rational, exponential, and logarithmic functions.
• find the derivatives of functions involving constants, sums, differences, products, quotients, and the chain rule.
• sketch the graphs of functions using horizontal and vertical asymptotes, intercepts, first and second derivatives to determine intervals where the function is increasing and decreasing, maximum and minimum values, intervals of concavity, and points of inflection.
• analyze the marginal cost, profit, and revenue when given the appropriate function.
• determine maxima and minima in optimization problems using the derivative.
• use derivatives to find rates of change and tangent lines.
• use calculus to analyze revenue, cost, and profit.
• find definite and indefinite integrals by using the general integral formulas, integration by substitution, and other integration techniques.
• use integration in 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.
• calculate both present and future values involving compound interest and annuities.
• analyze applications of annuities involving loan amortization and sinking funds, applying necessary formulas.
• identify and graph linear, quadratic, power, polynomial, exponential, and logarithmic functions.
• formulate and apply exponential growth or decay functions pertaining to business applications.
• 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 using a graphical approach.

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

• simplify algebraic and trigonometric expressions as they appear in calculus computations.
• compute limits and discuss the continuity of a given function.
• apply differentiation and integration techniques to algebraic, exponential, logarithmic, and trigonometric functions.
• apply differentiation techniques to curve sketching and optimization problems.
• solve problems in biology and medicine involving exponential, logarithmic, and trigonometric functions through the application of calculus techniques.
• apply the Fundamental Theorem of Calculus to the evaluation of definite integrals.
• solve separable and first-order linear differential equations.
• interpret results of the analysis of mathematical modeling in applications of population growth or decay, manufacturer and consumer perspectives, chemical mixtures and reactions, and other course topics.

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

• calculate double integrals.
• calculate partial derivatives of functions of several variables and calculate and explain the significance of extrema of these functions in applied settings.
• analyze surfaces and graph functions of two variables in the three-dimensional coordinate system.
• devise models and solve linear systems of ordinary differential equations.
• evaluate and apply the chain rule, directional derivatives, and gradient vectors for functions of several variables.
• analyze results of computing eigenvalues and eigenvectors.
• compute counts and probabilities in a variety of experimental events.
• compute and apply Bayes' Formula.

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

• solve equations and inequalities and manipulate expressions.
• solve systems of equations and inequalities.
• demonstrate a deep understanding of functions and their properties.
• demonstrate a deep understanding of inverse functions and their algebraic and graphical relationship to their parent functions.
• graph a variety of curves (showing intercepts, asymptotes, vertices, etc.).
• solve application problems by creating and using mathematical models that involve synthesis of course concepts.

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

• apply trigonometric functions to the angles of a right triangle and arcs on the unit circle.
• evaluate trigonometric functions of common angles (using both radian and degree measure) and inverse trigonometric functions.
• recognize, apply, and prove trigonometric identities and solve trigonometric equations.
• create and analyze graphs of trigonometric functions, inverse trigonometric functions, curves in parametric form, and curves in polar form. (Trigonometric function graphing will include changes in period, phase, and amplitude.)
• convert between polar and rectangular coordinates and equations, compute and solve equations involving complex numbers in standard and trigonometric form, and use DeMoivre's Theorem to evaluate powers and roots of complex numbers.
• apply trigonometric and algebraic concepts as problem-solving tools by modeling problems with appropriate equations, including use of the Laws of Sines and Cosines and vector applications with vectors represented in both (a, b) and ai+bj form.
• prove simple mathematical facts.

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 a 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:

• determine limits of algebraic and transcendental functions using algebraic, graphical, and/or numerical methods
• determine derivatives of algebraic and transcendental functions.
• evaluate integrals of algebraic and transcendental functions.
• apply derivatives and integrals to solve physics, economic, geometric, and/or other application problems.
• write proofs related to limits, continuity, and differentiability, including delta-epsilon proofs.

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

• evaluate integrals using a variety of integration techniques including integration by parts, partial fraction decomposition, trigonometric substitution and others.
• devise and evaluate integrals to find the volume and surface area of a solid of revolution, total work, the length of a curve, the center of mass of a solid, and other applications of integration.
• estimate integrals using numerical techniques.
• evaluate improper integrals.
• evaluate the calculus components of parametric and polar relations including finding tangent lines, areas, and arc lengths.
• prove convergence or divergence of sequences and series using Test for Divergence, Integral Test, p-Series Test, Comparison Tests, Alternating Series Test, Maclaurin and Taylor series, and power series.
• construct power series representations of functions, derivatives, and integrals and determine radius and intervals of convergence of power series.
• estimate and determine maximum errors in finding function values using infinite and finite power series.
• solve separable differential equations.

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

• find the distance between a point and a line, a point and a plane, two parallel planes, or two parallel and/or skew lines; find the equations of lines and planes.
• calculate the arc length and curvature at any point in the domain of the function for a space curve.
• compute a number of vector based function values on plane curves and space curves. These include velocity vectors, acceleration vectors, speed, curvature, arc-length, binormal vectors, unit tangent and unit normal vectors.
• find the limit of a multivariate function at a point or show that the limit does not exist.
• evaluate partial derivatives and directional derivatives. Find the extrema for functions of two variables; find the absolute maximum and absolute minimum values of a function defined on a closed boundary.
• evaluate double and triple integrals using rectangular, polar, cylindrical, and spherical coordinate systems as well as evaluating a double integral by employing a change of variables; calculate volumes, surface area, and other physical phenomena by applying double and triple integrals
• find the gradient of a scalar field and the divergence and curl of a vector field.
• evaluate line and surface integrals using Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem.

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

• prove basic results of linear algebra, using appropriate proof-writing techniques.
• solve linear systems using matrices and matrix operations.
• utilize abstract concepts such as Euclidian n-space, multidimensional vector spaces, subspaces of vector spaces, and the relationship between matrices and n-tuples.
• analyze relationships between systems of equations, matrices, determinants, inverse matrices, vectors, linear transformations, row space, column space, null space, kernel, eigenvalues, and eigenvectors in linear algebra problems.
• analyze properties of inner product spaces and orthogonality and use them in applications

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

• solve a variety of ordinary differential equations using techniques such as reduction of order, method of undetermined coefficients, variation of parameters, power series, and Laplace transforms.
• perform qualitative analysis on first-order equations using directions fields and phase portraits
• analyze, model, and solve elementary applied science problems such as Newton's Law of Cooling, mixing, falling bodies, spring/mass systems, and Newton's Second Law of Motion with ordinary differential equations.
• identify differential equations such as linear, separable, exact, and Cauchy-Euler.
• solve systems of linear differential equations.
• apply numerical techniques (Euler's method, modified Euler's, RK4) to approximate solutions to first order equations

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

• demonstrate understanding of the mathematical concepts studied in the course.
• demonstrate competence in the mathematical skills studied in the course.

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

• design and discuss a proposal of study with a supervising mathematics instructor.
• demonstrate the ability to independently pursue a course of study or project in mathematics.
• demonstrate understanding of the mathematical concepts studied in the course.
• demonstrate competence in the mathematical skills studied in the course.

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

• utilize mathematical terminology and articulate mathematical concepts appropriate to the relevant area of study.
• employ mathematical skills appropriate to the relevant level and area of study.
• analyze a mathematical problem and apply an appropriate set of problem-solving skills.

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

• use support mathematics skills to simplify expressions and solve equations involving absolute values, polynomials, rational expressions, radicals, exponentials, and logarithms.
• use support mathematics skills to solve systems of equations and solve linear, polynomial, rational, and absolute value inequalities.
• use support mathematics skills to use the definition of a function to determine if a relation is a function and use function notation, including the algebra of functions, composite functions, and inverse functions.
• use support mathematics skills to sketch the graphs of basic functions, quadratic functions, transformations of these functions, and conic sections.
• use support mathematics skills to apply algebraic methods when solving word problems.

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

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

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

• use support mathematics skills to find the derivatives of polynomial, rational, exponential, and logarithmic functions.
• use support mathematics skills to find the derivatives of functions involving constants, sums, differences, products, quotients, and the chain rule.
• use support mathematics skills to sketch the graphs of functions using horizontal and vertical asymptotes, intercepts, first and second derivatives to determine intervals where the function is increasing and decreasing, maximum and minimum values, intervals of concavity, and points of inflection.
• use support mathematics skills to analyze the marginal cost, profit, and revenue when given the appropriate function.
• use support mathematics skills to determine maxima and minima in optimization problems using the derivative.
• use support mathematics skills to find rates of change and tangent lines.
• use support mathematics skills to analyze revenue, cost, and profit.
• use support mathematics skills to find definite and indefinite integrals when applying the general integral formulas, integration by substitution, and other integration techniques.
• use support mathematics skills in business and economics applications.

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

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

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

• use mathematical support skills to determine the limits of algebraic and transcendental functions using algebraic, graphical, and/or numerical methods.
• use mathematical support skills to determine derivatives of algebraic and transcendental functions.
• use mathematical support skills to evaluate integrals of algebraic and transcendental functions.
• use mathematical support skills to apply derivatives and integrals to solve physics, economic, geometric, and/or other application problems.
• use mathematical support skills to write proofs related to limits, continuity, and differentiability, including delta-epsilon proofs.

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

• use mathematical support skills to simplify algebraic and trigonometric expressions as they appear in calculus computations.
• use mathematical support skills to compute limits and discuss the continuity of a given function.
• use mathematical support skills to apply differentiation and integration techniques to algebraic, exponential, logarithmic, and trigonometric functions.
• use mathematical support skills to apply differentiation techniques to curve sketching and optimization problems.
• use mathematical support skills to solve problems in biology and medicine involving exponential, logarithmic, and trigonometric functions through the application of calculus techniques.
• use mathematical support skills to apply the Fundamental Theorem of Calculus to the evaluation of definite integrals.
• use mathematical support skills to solve separable and first-order linear differential equations.
• use mathematical support skills to interpret results of the analysis of mathematical modeling in applications of population growth or decay, manufacturer and consumer perspectives, chemical mixtures and reactions, and other course topics.

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.
• use mathematics support skills to demonstrate a deep understanding of inverse functions and their algebraic and graphical relationships to their parent functions.
• use mathematics support skills to graph a variety of curves (showing intercepts, asymptotes, vertices, etc.).
• use mathematics support skills to solve application problems by creating and using mathematical models that involve synthesis of course concepts.

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

• use mathematics support skills to apply trigonometric functions to the angles of a right triangle and arcs on the unit circle.
• use mathematics support skills to evaluate trigonometric functions of common angles (using both radian and degree measure) and inverse trigonometric functions.
• use mathematics support skills to recognize, apply, and prove trigonometric identities and solve trigonometric equations.
• use mathematics support skills to create and analyze graphs of trigonometric functions, inverse trigonometric functions, curves in parametric form, and curves in polar form. (Trigonometric function graphing will include changes in period, phase, and amplitude.)
• use mathematics support skills to convert between polar and rectangular coordinates and equations, compute and solve equations involving complex numbers in standard and trigonometric form, and use DeMoivre's Theorem to evaluate powers and roots of complex numbers.
• use mathematics support skills to apply trigonometric and algebraic concepts as problem-solving tools by modeling problems with appropriate equations, including use of the Laws of Sines and Cosines and vector applications with vectors represented in both (a, b) and ai+bj form.
• use mathematics support skills to prove simple mathematical facts.

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

• apply learning strategies to achieve success in Pre-Calculus.
• use the methods from arithmetic necessary to be successful in Pre-Calculus.
• use the methods from algebra necessary to be successful in Pre-Calculus.
• use methods from geometry necessary to be successful in Pre-Calculus.

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

• use support mathematics skills to analyze inferences and conjectures present in a variety of mathematical ideas and systems.
• use support mathematics skills to construct well written solutions to mathematical exercises.
• use support mathematics skills to apply critical thinking skills developed in studying a mathematical topic to issues that transcend mathematics.
• use support mathematics skills to research and demonstrate an understanding of and explain mathematical ideas that are at an appropriate skill level.

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

• use support mathematics skills to explain mathematical relationships inherent in problems and situations.
• use support mathematics skills to make conjectures about mathematical relationships and content.
• use support mathematics skills to prove or disprove conjectures about mathematical relationships and content.
• use support mathematics skills in developing an appreciation of mathematical relevance to every day life.
• use support mathematics skills to analyze documents directing the study of mathematics in American schools, as well as the strategies, procedures, and emphases advocated in those documents.

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

• use support mathematics skills to select, produce, and interpret appropriate graphical and numerical summaries of data.
• use support mathematics skills to distinguish between probability models appropriate to different chance events and calculate probabilities according to these methods.
• use support mathematics skills to construct and interpret confidence intervals for various characteristics of a population.
• use support mathematics skills to utilize the basic components of hypothesis testing by conducting various hypothesis tests and interpreting their results.
• use support mathematics skills to use correlation and regression to analyze relationships between two numerical variables (bivariate data).
• use support mathematics skills when utilizing technology to perform statistical tasks.
• use support mathematics skills when using appropriate statistical techniques to analyze and interpret applications of data from the real world.

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

• modify and simplify linear expressions, solve linear equations and inequalities, and evaluate statistical formulas using the order of operations agreement.
• sketch the graphs of linear and exponential functions, and find equations of linear and exponential functions given two points on the line or curve, to represent relationships in quantitative data.
• construct, evaluate, and analyze algebraic and statistical models when solving everyday problems.

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

• select, produce, and interpret appropriate graphical and numerical summaries of data.
• distinguish between probability models appropriate to different chance events and calculate probabilities according to these methods.
• interpret and solve probability applications that relate to everyday life.
• construct and interpret confidence intervals for various characteristics of a population.
• utilize the basic components of hypothesis testing by conducting various hypothesis tests and interpreting their results.
• use correlation and regression to analyze relationships between two numerical variables (bivariate data).
• utilize technology to perform statistical tasks.
• use appropriate statistical techniques to analyze and interpret applications of data from the real world.

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

• select, produce, and interpret appropriate graphical and numerical summaries of data.
• distinguish between probability models appropriate to different chance events and calculate probabilities according to these methods.
• construct and interpret confidence intervals for various characteristics of a population.
• utilize the basic components of hypothesis testing by conducting various hypothesis tests and interpreting their results.
• use correlation and regression to analyze relationships between two numerical variables (bivariate data).
• utilize technology to perform statistical tasks.
• use appropriate statistical techniques to analyze and interpret applications of data from the real world.

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

• design and discuss a proposal of study with a supervising instructor.
• demonstrate the ability to independently pursue a course of study or project in statistics.
• prepare a final report or project incorporating results of study or activities.