# Mathematics Course Descriptions

## MATH 004: Algebra Support

**Credits:**5.0

Students learn to read, write and interpret a wide variety of complex mathematical information. Orientation and advising are required before taking this course. S/U only.

**Course Level Objectives**

- Demonstrate solutions to mathematical problems.
- Develop and apply a more precise and sophisticated mathematical vocabulary.
- Demonstrate increased ability to participate in group assignments and discussions.
- Read, summarize and take notes on college level material for developing mastery of key concepts.
- Develop and apply study skills necessary for comprehending and retaining college level material and concepts.

## MATH 010: Support for Business Precalculus

**Credits:**3.0

Corequisite support course for MATH 140. Concurrent enrollment in MATH 140 is required. Intermediate algebra topics include algebraic operations on and applications with linear, quadratic, exponential, and logarithmic functions. College success skills are addressed. This course allows students who are close to college readiness to take MATH 140. **Prerequisite(s):** MATH77 with a 3.0 or higher; or satisfactory completion of MATH11; or placement into MATH87.

**Course Level Objectives**

- Construct linear models and graphs and use them to answer questions in the context of an applied problem.
- Develop and apply functional relationships presented in applications, words, tables, graphs, and symbols.
- Simplify mathematical expressions and solve linear equations, quadratic equations, polynomials and formulas.
- Solve systems of two linear equations in two variables (including systems generated from an application) by graphing, elimination, and substitution.
- Apply rules of exponents to simplify expressions involving integer and rational exponents, and radicals.
- Graph exponential functions and use properties of logarithms (or technology) to solve exponential equations and applied problems.
- Interpret the mathematical meaning of expressions and results in the context of an applied problem.
- Demonstrate the use of learning strategies to comprehend, retain, and apply class content.
- Identify individual math strengths, skills, and characteristics within the growth mindset framework.
- Apply effective study and communication skills when engaging with peers, instructors, and the college community.

## MATH 011: Support for Precalculus

**Credits:**3.0

Corequisite support course for MATH& 141. Concurrent enrollment in MATH& 141 is required. Intermediate algebra topics include algebraic operations on and applications with polynomial, exponential, rational, radical, and logarithmic functions. College success skills are addressed. This course allows students who are close to college readiness to take MATH&141. **Prerequisite(s):** MATH87 with a 3.0 or higher or placement into MATH97.

**Course Level Objectives**

- Construct graphs with and without technology and interpret important graphical features.
- Use graphs to model and solve linear, quadratic, polynomial, radical, rational, exponential and logarithmic equations.
- Use multiple representations of functions to represent relationships and the related concepts of domain, range, symmetry, difference quotient, average rate of change, composition, and inverses.
- Solve polynomial equations and related applied problems by graphing, factoring and quadratic formula.
- Perform algebraic operations to simplify and solve linear, absolute value, quadratic, polynomial, radical, rational, exponential and logarithmic expressions and equations, inequalities and formulas.
- Construct mathematical models to evaluate and interpret applied problems.
- Demonstrate the use of learning strategies to comprehend, retain, and apply class content.
- Identify individual math strengths, skills, and characteristics within the growth mindset framework.
- Apply effective study and communication skills when engaging with peers, instructors, and the college community.
- Identify, access, and navigate college math resources.

## MATH 016: Support for Statistics

**Credits:**2.0

Corequisite support course for MATH& 146. Concurrent enrollment in MATH& 146 is required. Intermediate algebra topics include linear and exponential functions, graphing, inequalities and operations on formulas. College success skills are addressed. This course allows students who are close to college readiness to take MATH& 146. **Prerequisite(s):** Completion of MATH77 with a 3.0 or higher;or satisfactory completion of MATH10 or MATH11; or placement into MATH87.

**Course Level Objectives**

- Simplify expressions and solve linear equations, inequalities, and formulas, including applications involving ratios, percentages,proportions and decimals.
- Construct linear models using point-slope and slope-intercept methods, and use technology to find a linear regression equation.
- Construct and interpret graphical representations of data.
- Interpret mathematical expressions used in statistics such as sets and subsets indices, sigma notation, factorials and Venn diagrams.
- Interpret the mathematical meaning of expressions and results in the context of an applied problem.
- Demonstrate the use of learning strategies to comprehend, retain, and apply class content.
- Identify individual math strengths, skills, and characteristics within the growth mindset framework.
- Apply effective study and communication skills when engaging with peers, instructors, and the college community.
- Identify, access, and navigate college math resources.

## MATH 017: Support for Math in Society

**Credits:**2.0

Corequisite support course for MATH& 107. Concurrent enrollment in MATH& 107 is required. Intermediate algebra topics include linear and exponential functions, graphing, inequalities and operations on formulas. College success skills are addressed. This course allows students who are close to college readiness to take MATH& 107. **Prerequisite(s):** Completion of MATH77 with a 3.0;placement into MATH87; or satisfactory completion of MATH10, MATH11 or MATH16.

**Course Level Objectives**

- Simplify expressions and solve linear equations, inequalities, and formulas, including applications involving ratios, percentages, proportions and decimals.
- Construct linear and exponential models and graphs and use them to answer questions in the context of an applied problem.
- Develop and apply functional relationships presented in applications, words, tables, graphs, and symbols.
- Simplify mathematical expressions and solve linear equations, quadratic equations, polynomials and formulas.
- Interpret the mathematical meaning of expressions and results in the context of an applied problem.
- Demonstrate the use of learning strategies to comprehend, retain, and apply class content.
- Identify individual math strengths, skills, and characteristics within the growth mindset framework.
- Identify, access, and navigate college math resources.

## MATH 041: Pre-Algebra 1

**Credits:**2

This course is the first two credits of a five-credit sequence of courses that comprises Pre-Algebra.Review of operations with integers, order of operations, exponents, fractions, decimals and percentages, and applications. Introduction to the concepts of algebra, including simplifying and evaluating expressions and solving linear equations; focus on problem solving and math success skills. Intended for students who have had little or no algebra.MATH041/042/043/044 must all be completed with a 2.0 within a 12-month period.

**Course Level Objectives**

- Apply the concepts and procedures of arithmetic, including whole number operations, fraction and decimal operations, proportions, percents, and signed number operations.
- Evaluate a numerical expression by applying the order of operations.
- Set up, solve, and assess the results of applications.
- Use common financial and geometric formulas to write andsolve equations.
- Demonstrate solutions to problems and interpret results.

## MATH 042: Pre-Algebra 2

**Credits:**1

This course is the third creditof a five-credit sequence of courses that comprises Pre-Algebra. Review of operations with integers, order of operations, exponents, fractions, decimals and percentages, and applications. Introduction to the concepts of algebra, including simplifying and evaluating expressions and solving linear equations; focus on problem solving and math success skills. Intended for students who have had little or no algebra.MATH 041/042/043/044 must all be completed with a 2.0 within a 12-month period. **Prerequisite(s):** MATH 041 with a minimum grade of 2.0 OR concurrent enrollment in MATH 041.

**Course Level Objectives**

- Apply the concepts and procedures of arithmetic, including whole number operations, fraction and decimal operations, proportions, percents, and signed number operations.
- Convert numbers from one form to another, among percentage, decimal, and fraction forms.
- Evaluate a numerical expression by applying the order of operations.
- Set up, solve, and assess the results of applications.
- Use common financial and geometric formulas to write and solve equations.
- Demonstrate solutions to problems and interpret results.

## MATH 043: Pre-Algebra 3

**Credits:**1

This course is the fourth creditof a five-credit sequence of courses that comprises Pre-Algebra.Review of operations with integers, order of operations, exponents, fractions, decimals and percentages, and applications. Introduction to the concepts of algebra, including simplifying and evaluating expressions and solving linear equations; focus on problem solving and math success skills. Intended for students who have had little or no algebra.MATH041/042/043/044 must all be completed with a 2.0 within a 12-month period. **Prerequisite(s):** MATH 042with a minimum grade of 2.0 OR concurrent enrollment in MATH 042.

**Course Level Objectives**

- Apply the concepts and procedures of arithmetic, including whole number operations, fraction and decimal operations, proportions, percents, and signed number operations.
- Convert numbers from one form to another, among percentage, decimal, and fraction forms.
- Evaluate a numerical expression by applying the order of operations.
- Set up, solve, and assess the results of applications.
- Use common financial and geometric formulas to write and solve equations.
- Demonstrate solutions to problems and interpret results.

## MATH 044: Pre-Algebra 4

**Credits:**1

This course is the fifth creditof a five-credit sequence of courses that comprises Pre-Algebra. Review of operations with integers, order of operations, exponents, fractions, decimals and percentages, and applications. Introduction to the concepts of algebra, including simplifying and evaluating expressions and solving linear equations; focus on problem solving and math success skills. Intended for students who have had little or no algebra. MATH041/042/043/044 must all be completed with a 2.0 within a 12-month period. **Prerequisite(s):** MATH 043 with a minimum grade of 2.0 OR concurrent enrollment in MATH 043.

**Course Level Objectives**

- Convert numbers from one form to another, among percentage, decimal, and fraction forms.
- Evaluate a numerical expression by applying the order of operations.
- Solve linear equations of one variable.
- Set up, solve, and assess the results of applications.
- Use common financial and geometric formulas to write and solve equations.
- Demonstrate solutions to problems and interpret results.

## MATH 047I: Pre-Algebra

**Credits:**5.0

Review of operations with integers, order of operations, exponents, fractions, decimals and percentages, and applications. Introduction to the concepts of algebra, including simplifying and evaluating expressions and solving linear equations; focus on problem solving and math success skills. Intended for students who have had little or no algebra. **Prerequisite(s):** Appropriate score on Math Placement Test.

**Course Level Objectives**

- Convert numbers from one form to another, among percentage, decimal, and fraction forms.
- Evaluate a numerical expression by applying the order of operations.
- Solve linear equations of one variable.
- Set up, solve and assess the results of applications.
- Use common financial and geometric formulas to write and solve equations.
- Demonstrate solutions to problems and interpret results.

## MATH 047J: College Prep Math

**Credits:**5.0

Review of operations with integers, order of operations, exponents, fractions, decimals and percentages, and applications. Introduction to the concepts of algebra, including simplifying and evaluating expressions and solving linear equations; focus on problem solving and math success skills. Intended for students who have had little or no algebra. S/U grade option.

**Course Level Objectives**

- Convert numbers from one form to another, among percentage, decimal, and fraction forms.
- Evaluate a numerical expression by applying the order of operations.
- Solve linear equations of one variable.
- Set up, solve and assess the results of applications.
- Use common financial and geometric formulas to write and solve equations.
- Demonstrate solutions to problems and interpret results.

## MATH 077: Introductory Algebra

**Credits:**5.0

Introduction to the concepts of algebra. Operations on signed numbers, solution of linear equations, exponents and algebraic fractions, and basic operations on polynomials. Includes a review of some properties and operations of arithmetic. Intended for students who have had little or no algebra recently. **Prerequisite(s):** MATH 44, MATH 47 or PREP 47with a minimum grade of 2.0, or appropriate score on the math placement test.

**Course Level Objectives**

- Perform operations with fractions, decimals, percents, and signed numbers, and use these operations to solve applied problems.
- Apply the order of operations to evaluate and simplify mathematical expressions with and without variables.
- Solve formulas and linear equations in one variable and use them to solve applied problems.
- Convert units including those from the metric system.
- Graph linear equations in two variables using intercepts and use those graphs to solve equations and applied problems.
- Apply rules of exponents to simplify expressions and solve problems involving integer exponents.
- Perform operations on monomials and polynomials to simplify algebraic expressions and solve applied problems.
- Present solutions to problems and interpret results.

## MATH 081: Essentials of Intermediate Algebra 1

**Credits:**2

This course is the first two credits of a five-credit sequence of courses that comprises Essentials of Intermediate Algebra. Introduction to the concepts of linear, exponential, and logarithmic functions. Operations on polynomials, solutions to linear and polynomial equations, and rules of exponents. Registration permitted first seven weeks (six in summer) as space is available.MATH081/082/083/084 must all be completed with a 2.0 within a 12-month period. **Prerequisite(s):** MATH 074, MATH 77, or PREP 077 with a minimum grade of 2.0 ORPREP 87, ABE 087, or HSC 087 with a minimum grade of 3.0 ORappropriate score on math placement test.

**Course Level Objectives**

- Graph linear equations in two variables using point-plotting, slope and a point, intercepts, and technology, and interpret the slope as a rate of change in the context of an applied problem.
- Simplify expressions and solve linear equations, inequalities, and formulas, including applications
- Construct linear models using point-slope and slope-intercept methods, and use technology to find a linear regression equation.
- Solve systems of two linear equations in two variables (including systems generated from an application) by graphing, elimination, and substitution.
- Perform operations with polynomial expressions.
- Apply rules of exponents to simplify expressions involving integer exponents.
- Demonstrate solutions to problems and interpret results.

## MATH 082: Essentials of Intermediate Algebra 2

**Credits:**1

This course is the third credit of a five-credit sequence of courses that comprises Essentials of Intermediate Algebra.Introduction to the concepts of linear, exponential, and logarithmic functions. Operations on polynomials, solutions to linear and polynomial equations, and rules of exponents. Registration permitted first seven weeks (six weeks in summer) as space is available.MATH081/082/083/084 must all be completed with a 2.0 within a 12-month period. **Prerequisite(s):** MATH 081 with a minimum grade of 2.0 OR concurrent enrollment in MATH 081.

**Course Level Objectives**

- Apply rules of exponents to simplify expressions involving integer exponents, and simplify basic radical expressions.
- Simplify expressions and solve linear equations and formulas, including applications involving ratios, percentages, and proportions.
- Solve quadratic equations using basic factoring techniques and the quadratic formula, and find approximate solutions to polynomial equations using technology.
- Demonstrate solutions to problems and interpret results.

## MATH 083: Essentials of Intermediate Algebra 3

**Credits:**1

This course is the fourthcreditof a five-credit sequence of courses that comprises Essentials of Intermediate Algebra. Introduction to the concepts of linear, exponential, and logarithmic functions. Operations on polynomials, solutions to linear and polynomial equations, and rules of exponents. Registration permitted first seven weeks (six in summer) as space is available.MATH 081/082/083/084 must all be completed with a 2.0 within a 12-month period. **Prerequisite(s):** MATH 082with a minimum grade of 2.0 OR concurrent enrollment in MATH 082.

**Course Level Objectives**

- Develop functional relationships presented in applications, words, tables, graphs, and symbols using function notation, and express domains and ranges using inequalities or intervals.
- Apply rules of exponents to simplify expressions involving integer exponents, and simplify basic radical expressions.
- Simplify expressions and solve linear equations and formulas, including applications involving ratios, percentages, and proportions.
- Solve quadratic equations using basic factoring techniques and the quadratic formula, and find approximate solutions to polynomial equations using technology.
- Demonstrate solutions to problems and interpret results.

## MATH 084: Essentials of Intermediate Algebra 4

**Credits:**1

This course is the fifth credit of a five-credit sequence of courses that comprises Essentials of Intermediate Algebra.Introduction to the concepts of linear, exponential, and logarithmic functions. Operations on polynomials, solutions to linear and polynomial equations, and rules of exponents. Registration permitted first seven weeks (six weeks in summer) as space is available. MATH081/082/083/084 must all be completed with a 2.0 within a 12-month period. **Prerequisite(s):** MATH 083with a minimum grade of 2.0 OR concurrent enrollment in MATH 083.

**Course Level Objectives**

- Develop functional relationships presented in applications, words, tables, graphs, and symbols using function notation, and express domains and ranges using inequalities or intervals.
- Graph linear equations in two variables using point-plotting, slope and a point, intercepts, and technology, and interpret the slope as a rate of change in the context of an applied problem.
- Simplify expressions and solve linear equations, inequalities, and formulas, including applications involving ratios, percentages, and proportions.
- Construct linear models using point-slope and slope-intercept methods, and use technology to find a linear regression equation.
- Solve systems of two linear equations in two variables (including systems generated from an application) by graphing, elimination, and substitution.
- Perform operations with polynomial expressions, solve quadratic equations using basic factoring techniques and the quadratic formula, and find approximate solutions to polynomial equations using technology.
- Apply rules of exponents to simplify expressions involving integer and rational exponents, and simplify basic radical expressions.
- Graph exponential functions and use properties of logarithms (or technology) to solve exponential equations and applied problems.
- Demonstrate solutions to problems and interpret results.

## MATH 087: Essentials of Intermediate Algebra

**Credits:**5.0

Introduction to the concepts of linear, exponential, and logarithmic functions. Operations on polynomials, solutions to linear and polynomial equations, and rules of exponents. **Prerequisite(s):** PREP 87 orHSC 87 with a minimum grade of 3.0;MATH 77 or MATH 74 with a minimum grade of 2.0; or appropriate score on the math placement test.

**Course Level Objectives**

- Develop functional relationships presented in applications, words, tables, graphs, and symbols using function notation, and express domains and ranges using inequalities or intervals.
- Graph linear equations in two variables using point-plotting, slope and a point, intercepts, and technology, and interpret the slope as a rate of change in the context of an applied problem.
- Simplify expressions and solve linear equations, inequalities, and formulas, including applications involving ratios, percentages, and proportions.
- Perform operations with polynomial expressions, solve quadratic equations using basic factoring techniques and the quadratic formula, and find approximate solutions to polynomial equations using technology.
- Apply rules of exponents to simplify expressions involving integer and rational exponents, and simplify basic radical expressions.
- Graph exponential functions and use properties of logarithms (or technology) to solve exponential equations and applied problems.
- Demonstrate solutions to problems and interpret results.

## MATH 093: Algebra for Precalculus I

**Credits:**2.0

This course is the first two credits of a five-credit sequence of courses that comprises Algebra for Precalculus. Covers many topics of MATH 87 in greater depth. Operations on polynomials, algebra functions, symbolic approaches for solving equations, and geometric formulas. Exponential, logarithmic, and quadratic functions. Intended to prepare students for MATH 141. Registration permitted first seven weeks (six in summer) as space is available. MATH 93 and MATH 94 must be completed with a 2.0 within two consecutive quarters (excluding summer). **Prerequisite(s):** MATH 84 or MATH 87 or equivalent with a minimum grade of 2.0; or satisfactory completion of MATH 10, MATH 11, MATH 16, or MATH 17; or appropriate placement.

**Course Level Objectives**

- Use multiple representations of functions; graph functions; find domains of functions; use and interpret function notation, difference quotients, and average rate of change; and create mathematical models using functions.
- Perform algebraic operations on polynomials; factor polynomials (using grouping, special products, and greatest common factor); and solve polynomial equations and related applied problems.
- Perform algebraic operations and simplify rational functions, and simplify complex rational expressions.
- Demonstrate solutions to problems and interpret results.

## MATH 094: Algebra for Precalculus II

**Credits:**3

This course is the last three credits of a five-credit sequence of courses that comprises Algebra for Precalculus.Operations on polynomials, algebra functions, symbolic approaches for solving equations, and geometric formulas. Exponential, logarithmic, and quadratic functions. Intended to prepare students for MATH 141.Registration permitted first seven weeks (six in summer) as space is available. MATH93/94 must bothbe completed with a 2.0 within two consecutive quarters (excluding Summer). **Prerequisite(s):** MATH 93 with a minimum grade of 2.0or concurrent enrollment.

**Course Level Objectives**

- Use multiple representations of functions; graph functions; find domains of functions; use and interpret function notation, difference quotients, and average rate of change; and create mathematical models using functions.
- Perform algebraic operations on polynomials; factor polynomials (using grouping, special products, and greatest common factor); and solve polynomial equations and related applied problems.
- Graph quadratic functions, model real-world situations using quadratic equations, and solve quadratic equations and related applied problems using: square roots, completing the square, the quadratic formula, and technology.
- Perform algebraic operations and simplify radical and rational functions, rationalize denominators of radical functions, simplify complex rational expressions, and solve radical and rational equations and related applied problems involving proportions and similar triangles.
- Use the Pythagorean Theorem, distance formula, midpoint formula, and absolute value function (including its algebraic definition) to solve equations, absolute-value inequalities, and related applied problems, with and without use of technology.
- Use exponential and logarithmic functions, properties of exponents, and properties of logarithms to solve equations and applied problems, with and without use of technology.
- Demonstrate mathematical solutions to problems and interpret results.

## MATH 097: Algebra for Precalculus

**Credits:**5.0

Covers many topics of MATH 87 in greater depth. Operations on polynomials, algebraic functions, symbolic approaches for solving equations, and geometric formulas. Exponential, logarithmic, and quadratic functions. Intended to prepare students for MATH& 141. **Prerequisite(s):** MATH 84 or MATH 87 or equivalent with a minimum grade of 2.0; or satisfactory completion of MATH 10, MATH 11, MATH 16or MATH 17; or appropriate placement.

**Course Level Objectives**

- Use multiple representations of functions; graph functions; find domains of functions; use and interpret function notation, difference quotients and average rate of change; and create mathematical models using functions.
- Perform algebraic operations on polynomials; factor polynomials (using grouping, special products and greatest common factor); and solve polynomial equations and related applied problems.
- Graph quadratic functions, model real-world situations using quadratic equations, and solve quadratic equations and related applied problems using: square roots, completing the square, the quadratic formula, and technology.
- Perform algebraic operations and simplify radical and rational functions, rationalize denominators of radical functions, simplify complex rational expressions, and solve radical and rational equations and related applied problems involving proportions and similar triangles.
- Use the Pythagorean Theorem, distance formula, midpoint formula, and absolute value function (including its algebraic definition) to solve equations, absolute-value inequalities, and related applied problems, with and without use of technology.
- Use exponential and logarithmic functions, properties of exponents, and properties of logarithms to solve equations and applied problems, with and without use of technology.
- Demonstrate solutions to problems and interpret results.

## MATH& 107: Mathematics In Society

**Credits:**5.0

A math course for students not planning to take additional math courses. Introduces math topics used in a variety of liberal arts disciplines, such as mathematical modeling, representational statistics, probability, and finance math. **Prerequisite(s):** Completion ofMATH84,MATH87, PREP 78, PREP 84, MATH94,MATH97, PREP 94, orPREP 97with minimum grade of 2.0; or satisfactory completion ofMATH10,MATH11,MATH16, orMATH17; or appropriate placement. Students with completion ofMATH77 with a 3.0 or higher or placement intoMATH87 are eligible for MATH& 107 with concurrent enrollment inMATH17.

**Course Level Objectives**

- Construct mathematical models for a variety of situations, using linear, quadratic, exponential, or logarithmic relationships.
- Solve financial applications, using the appropriate formula or mathematical model.
- Read, interpret, and verbalize information when it is presented in tables, graphs, or by numerical measurements.
- Summarize and tabulate data by tables, graphs, or by numerical measurements.
- Calculate probabilities using basic probability rules.
- Compute basic statistics, including the mean, standard deviation, and normal distribution.
- Solve application problems and express solutions clearly.

## MATH 140: Business Precalculus

**Credits:**5.0

Linear, quadratic, exponential, and logarithmic functions; solving equations; matrices; and financial applications. Intended for business transfer students. **Prerequisite(s):** Completion ofMATH84,MATH87,PREP 78, or PREP 84 with a minimum grade of 2.5; completion ofMATH94,MATH97, PREP 94, or PREP 97 with a minimum grade of 2.0; satisfactory completion ofMATH10 orMATH11; or appropriate placement. Students with completion ofMATH77 with a 3.0 or higher or placement intoMATH87are eligible for MATH& 140 with concurrent enrollment in MATH10.

**Course Level Objectives**

- Develop and evaluate mathematical models for business using linear, quadratic, exponential, simple rational, and logistic functions in symbolic, graphical, written, and numerical representations.
- Perform basic function operations.
- Solve equations arising from the mathematical models using multiple symbolic and graphical techniques.
- Develop and evaluate mathematical models for business relationships involving simple and compound interest (i.e., savings, loans, annuities, and mortgages).
- Develop and evaluate matrix models of business situations involving linear systems of equations and input-output matrices.
- Perform basic matrix operations.
- Solve a system of equations using multiple symbolic and graphical techniques.

## MATH& 141: Precalculus I

**Credits:**5.0

General nature of functions. Linear, quadratic, polynomial, rational, exponential, and logarithmic functions. Applications. **Prerequisite(s):** Completion ofMATH94,MATH97, PREP 94,or PREP 97 with a minimum grade of 2.0; satisfactory completion ofMATH11; or appropriate placement. Students with completion ofMATH87 with a 3.0 or higher or placement intoMATH97 are eligible forMATH& 141with concurrent enrollment in MATH11.

**Course Level Objectives**

- Solve problems involving the concept of a function and the related concepts of domain, range, symmetry, composition, and inverses using functions given in graphical, symbolic, or numerical form.
- Graph (with and without the aid of technology) linear, quadratic, polynomial, rational, exponential, and logarithmic functions and interpret these graphs, identifying, locating, and communicating important graphical features.
- Use algebra to determine the real and complex zeros of polynomial and rational functions and be able to relate this information to their graphs.
- Solve equations and inequalities involving involving linear, quadratic, polynomial, rational, exponential, and logarithmic functions using both graphical and algebraic methods, as well as technology.
- Use the aforementioned functions to model situations described in words and solve applied problems.
- Correctly use mathematical notation and language related to the concepts mentioned above.

## MATH& 142: Precalculus II

**Credits:**5.0

Continuation of MATH& 141. Trigonometric and inverse-trigonometric functions, conic sections, parametric equations, polar coordinates, vectors, and applications. **Prerequisite(s):** Completion of MATH& 141 with a minimum grade of 2.0 or appropriate placement.

**Course Level Objectives**

- Evaluate trigonometric functions at values given in radians or degrees, using both right-angle and unit-circle approaches.
- Identify and communicate important features of trigonometric and inverse trigonometric functions (including domains, ranges, symmetry, periods and graphs) and important graphical features of conic sections.
- Solve trigonometric equations using trigonometric identities, inverse trigonometric functions, algebra and technology.
- Prove trigonometric identities.
- Translate between graphical and algebraic representations, between the Cartesian and parametric representations of equations and graphs, and between polar and rectangular coordinates.
- Recognize and sketch graphs of equations given in polar coordinates.
- Perform vector operations, including vector algebra and dot product.
- Use parametric representation, trigonometric functions, right-triangle trigonometry, the Law of Sines, the Law of Cosines, and vectors to model situations given in words and to solve applied problems.
- Express solutions clearly with correct use of mathematical notation and terminology.

## MATH& 146: Introduction to Statistics

**Credits:**5.0

Introduction to statistical methods and applications: organization of data, sampling, testing hypotheses, confidence intervals, regression, and correlations. **Prerequisite(s):** Completion of MATH 84, MATH 87, PREP 84, or PREP 78 with minimum grade of 2.5; completion of MATH 94, MATH 97, PREP 94, or PREP 97 with minimum grade of 2.0; satisfactory completion of MATH 10, MATH 11 or MATH 16; or appropriate placement; and placement into ENGL& 101. Students with completion of MATH 77 with a 3.0 or higher or placement into MATH 87 are eligible for MATH& 146 with concurrent enrollment in MATH 16

**Course Level Objectives**

- Distinguish between quantitative and categorical data.
- Display categorical data using frequency tables and two-way tables.
- Construct appropriate graphical displays of quantitative and categorical data by hand and using technology.
- Compute appropriate summary statistics for quantitative variables.
- Perform computations using the Normal model.
- Construct and interpret scatterplots of bivariate quantitative data.
- When appropriate, compute the correlation of two quantitative variables.
- When appropriate, construct and interpret a linear regression model on two quantitative variables.
- Interpret a residual plot.
- Use random numbers to perform a simulation.
- Appropriately use terms related to sample surveys, experiments and observational studies.
- Perform basic probability computations.
- Compute the expected value and standard deviation of a random variable.
- Perform computations with probability models, including the binomial model.
- When appropriate, construct and interpret a confidence interval and perform a hypothesis test in situations involving: a. one proportion; b. two proportions; c. one mean; d. two means.
- When appropriate, use chi-square methods to perform: a. goodness-of-fit tests; b. tests of homogeneity; c. tests of independence.

## MATH& 148: Business Calculus

**Credits:**5.0

Introduction to differential and integral calculus. For students in business or other programs requiring a brief course in calculus; not for math or science majors. **Prerequisite(s):** Completion of MATH 140 or MATH& 141 with minimum grade of 2.0 or appropriate placement.

**Course Level Objectives**

- Find slope, average rate of change, and instantaneous rate of change from a graph, equation, or data.
- Estimate and calculate slopes of secant and tangent lines.
- Estimate and interpret rates of change.
- Find the derivative from a numerical, graphical, and algebraic viewpoint.
- Apply derivative rules to find rate-of-change formulas.
- Find and graph derivative functions.
- Apply derivative formulas to solve business application problems.
- Find extreme points and solve optimization problems.
- Find and interpret inflection points.
- Approximate area and accumulated change by using sums of rectangles.
- Find and interpret general and specific antiderivatives.
- Use numerical and graphical approaches to estimate definite integrals.
- Use the Fundamental Theorem of Calculus to compute definite integrals.
- Solve business application problems using integration.

## MATH& 151: Calculus I

**Credits:**5.0

Limits, continuity, derivatives and applications. Differentiation of algebraic, exponential, logarithmic, trigonometric and inverse-trigonometric functions. **Prerequisite(s):** Completion of MATH& 142 with a minimum grade of 2.0 or appropriate placement.

**Course Level Objectives**

- Solve problems involving the concept of a limit using symbolic, graphical and numerical techniques.
- Solve problems involving the concept of the derivative using symbolic, graphical and numerical techniques.
- Interpret the meaning of the derivative in various contexts.
- Use differentiation techniques (including the product rule, quotient rule, chain rule and implicit differentiation) to compute derivatives.
- Solve problems involving applications of the derivative by constructing functions and computing derivatives to model situations described by words.
- Solve problems involving the relationship between the graph of a function and its derivatives.
- Express solutions to problems clearly with correct usage of mathematical notation and terminology.

## MATH& 152: Calculus II

**Credits:**5.0

The integral and its applications. Integration involving algebraic, exponential, logarithmic, trigonometric, and inverse-trigonometric functions. **Prerequisite(s):** MATH& 151with a minimum grade of 2.0.

**Course Level Objectives**

- Compute definite and indefinite integrals of the standard algebraic and transcendental functions.
- Use integration techniques (including substitution, partial fractions, integration by parts, trigonometric substitution and tables) to compute definite and indefinite integrals.
- Evaluate improper integrals.
- Compute approximations for definite integrals (using left-hand sum, right-hand sum, midpoint rule, trapezoid rule or Simpson's rule) given data in graphical or table form.
- Compute approximations for definite integrals (using left-hand sum, right-hand sum, midpoint rule, trapezoid rule or Simpson's rule) of functions.
- Apply the Fundamental Theorem of Calculus.
- Use integrals to compute the average value of a function.
- Use integrals to compute change in velocity given acceleration.
- Use integrals to compute displacement and total distance traveled given velocity.
- Use integrals to compute areas and volumes.
- Use integrals to determine the length of a curve.
- Use integrals to determine the work done on an object.
- Use slope fields to analyze solutions of a differential equation.
- Solve separable differential equations.
- Model exponential growth and decay using differential equations.

## MATH& 153: Calculus III

**Credits:**5.0

Sequences, series, power series, vectors, vector-valued functions, lines and planes in 3D, calculus with parametric equations and polar coordinates, and partial derivatives. **Prerequisite(s):** Completion of MATH& 152 with a minimum grade of 2.0.

**Course Level Objectives**

- Identify the different types of sequences and series.
- Determine when a sequence or series is convergent or divergent.
- Perform basic convergence tests (including the ratio test, comparison test and integral test).
- Compute the radius and interval of convergence for a power series.
- Compute the Taylor Series expansion of a function.
- Perform vector arithmetic computations.
- Compute using vector components.
- Perform vector operations (including dot product, cross product and projections).
- Find an equation of a line and plane using vector notation.
- Differentiate and integrate vector-valued functions.
- Find tangent and unit tangent vectors to a smooth curve at a point.
- Compute curvature.
- Find the unit normal and binormal vectors of a smooth curve defined by a vector-valued function.
- Determine the tangential and normal components of the acceleration vector.
- Convert points and equations between rectangular coordinates and polar coordinates.
- Recognize and sketch graphs of equations in polar coordinates.
- Construct graphs, find domains and ranges, and analyze continuity and differentiability of functions with two or more independent variables.
- Write expressions for partial derivatives using limits.
- Calculate partial derivatives using formulas.

## MATH 155: Special Topics in Math

**Credits:**Maximum of 5.0 possible

Seminars of current interest in mathematics.

**Course Level Objectives**

- Demonstrate learning objectives as determined by the supervising instructor.

## MATH 199: Special Project: Mathematics

**Credits:**5.0

Note: Credit available with approval. For information contact the division secretary in Alderwood Hall 218 or phone 425.640.1679.

**Course Level Objectives**

- Demonstrate learning objectives as determined by the supervising instructor.

## MATH& 254: Calculus IV

**Credits:**5.0

Partial differentiation, multiple integration, vector fields, line and surface integrals, Green's Theorem, Stokes' Theorem, Divergence Theorem and applications. **Prerequisite(s):** Completion of MATH& 153 with a minimum grade of 2.0.

**Course Level Objectives**

- Apply the chain rule for multivariable functions.
- Compute the gradient and apply it to find equations of tangent lines and planes and to compute directional derivatives for multivariable functions.
- Find extreme values of multivariable functions, with or without constraints.
- Compute and apply double and triple integrals.
- Change variables in multiple integrals, including changing from rectangular coordinates to polar, cylindrical, or spherical coordinates.
- Use vector and scalar fields appropriately, particularly when computing a gradient, curl, or divergence.
- Use and compute line and surface integrals.
- Apply Green's Theorem, Stokes' Theorem and the Divergence Theorem.

## MATH 255: Special Topics in Mathematics

**Credits:**Maximum of 5.0 possible

Seminars of current interest in mathematics.

**Course Level Objectives**

- Demonstrate learning objectives as determined by the supervising instructor.

## MATH 271: Differential Equations

**Credits:**5.0

First- and second-order differential equations and their applications, Laplace transforms, and series solutions of ordinary differential equations. **Prerequisite(s):** MATH& 153 with a minimum grade of 2.0.

**Course Level Objectives**

- Classify ordinary differential equations (ODEs) and initial value problems (IVPs).
- Use existence and uniqueness theorems and direction fields to describe the number and behavior of solutions to IVPs.
- Solve first-order linear, separable and exact ODEs and IVPs.
- Model physical situations using first-order IVPs.
- Solve second-order linear, homogeneous and nonhomogenous equations by means of undetermined coefficients and variation of parameters.
- Model physical situations using second-order IVPs.
- Use Laplace transforms to solve IVPs.
- Use power series to compute series solutions to second-order linear ODEs and IVPs.

## MATH 272: Linear Algebra

**Credits:**5.0

Matrices, systems of equations, vector spaces, linear transformations, and eigenvalues. **Prerequisite(s):** MATH& 153 with a minimum grade of 2.0.

**Course Level Objectives**

- Perform elementary row operations on a matrix to put it in row-echelon or reduced row-echelon form.
- Apply the row reduction of an augmented matrix to solve systems of linear equations, as well as the equivalent vector and matrix forms for those systems.
- Express the solution set of a nonhomogeneous system of linear equations in terms of a particular solution and the solution set of the corresponding homogeneous system.
- Find the standard matrix of a linear transformation.
- Perform the matrix operations of addition, scalar multiplication, and matrix multiplication.
- Determine whether a given matrix is invertible.
- Compute the inverse of a given nonsingular matrix.
- Determine the dimension of and find a basis for a subspace of n-dimensional real space, given a spanning set.
- Compute the determinant of a square matrix using row or column expansion.
- Compute the determinant of a square matrix using properties of the determinant.
- Apply Cramer's rule to solve a system of linear equations.
- Find bases for the null space and column space of a matrix, and for the kernel and range of a linear transformation.
- Find coordinates of a vector with respect to a given basis.
- Change the basis for a linear transformation.
- Compute eigenvalues and eigenvectors for a matrix or linear transformation.
- Diagonalize a transformation with distinct eigenvalues.
- Use definitions and theorems to justify statements regarding any of the above concepts.

## MATH 299: Special Project: Mathematics

**Credits:**5.0

Note: Credit available with approval. For information contact the division secretary in Alderwood Hall 218 or phone 425.640.1679. S/U grade.

**Course Level Objectives**

- Demonstrate learning objectives as determined by the supervising instructor.