# Course Descriptions

## 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**

- 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.
- 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**

- 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.
- 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 060J: Introduction to Algebra

**Credits:**Maximum of 5.0 possible

Class covers basic operations on signed numbers, solution of linear equations, exponents and fractions. Includes review of some properties and operations of arithmetic. Intended for students who have had little or no algebra. **Prerequisite(s):** Ability to do basic arithmetic, or appropriate score on Math Placement Test, or instructor permission.

**Course Level Objectives**

- Evaluate a numerical expression by applying the order of operations.
- Add, subtract, multiply and divide positive and negative numbers.
- Simplify algebraic expressions by applying the commutative, associative and distributive properties.
- Factor algebraic expressions using prime factorization and the distributive property.
- Identify terms in an algebraic expression.
- Simplify rational expressions by factoring out common factors.
- Multiply and divide algebraic fractions with monomial denominators.
- Add and subtract algebraic fractions with monomial denominators.
- Solve linear equations of one variable.
- Solve simple literal equations for a given variable.
- Translate English sentences into equations and solve for the unknown.
- Add, subtract, multiply and divide decimals.
- Round numbers.
- Convert numbers from one form to another, among percentage form, decimal form and fraction form.
- Solve percentage word problems.
- Evaluate expressions with exponents.
- Simplify algebraic expressions with exponents.

## 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. Registration permitted first seven weeks (six in summer) as space is available. **Prerequisite(s):** MATH 047 or PREP 047 with 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 087: Essentials of Intermediate Algebra

**Credits:**5.0

**Prerequisite(s):** PREP 087, ABE 087, or HSC 087 with a minimum grade of 3.0; MATH 077 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.
- 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 097: Algebra for Precalculus

**Credits:**5.0

Covers many topics of MATH 087 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 as space is available. **Prerequisite(s):** MATH 087 or equivalent with a minimum grade of 2.0 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):** MATH 087 or MATH 097 with a minimum grade of 2.0; or PREP 087, ABE 087, or HSC 087 with a minimum grade of 3.0.

**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):** MATH 087 with a minimum grade of 2.5, MATH 097 with a minimum grade of 2.0, or appropriate placement.

**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):** MATH 097 with a minimum grade of 2.0 or appropriate placement.

**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):** MATH& 141 or equivalent 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& 144: Precalculus I and II

**Credits:**5.0

An intensive refresher course in precalculus topics intended for students who plan to take the calculus sequence beginning with MATH& 151. Combines all topics of MATH& 141 and MATH& 142. Graphing calculator required. **Prerequisite(s):** Appropriate score on the Math Placement Test and high school precalculus.

**Course Level Objectives**

- Solve problems involving an understanding of the concept of a function and the related concepts of domain, range, composition of functions and inverse functions; and demonstrate understanding of these concepts using functions given in graphical, symbolic, or numerical form.
- Correctly use mathematical notation and language related to the above concepts.
- Graph a variety of functions and be able to interpret their graphs.
- Formulate and apply properties, graphs, and some appropriate applications of linear, polynomial, rational, exponential, logarithmic, trigonometric, and inverse trigonometric functions.
- Solve equations and inequalities involving the aforementioned functions, both graphically and algebraically.
- Demonstrate how and when to use technology as a tool in solving equations and investigating the behavior of functions and graphs.
- Construct equations and functions involving the aforementioned functions that model situations described in words.
- Solve problems involving right triangle trigonometry, the law of sines and the law of cosines.
- Distinguish identities from conditional equations, apply trigonometric identities to solve equations, and prove identities algebraically.
- Solve problems involving the main graphical features of conic sections and the relationships between their graphs and equations.
- Solve problems involving unit circle trigonometry.
- 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 the above abilities to solve word problems and to 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):** MATH 087 with a minimum grade of 2.5; MATH 097 with a minimum grade of 2.0; or PREP 087, ABE 087, or HSC 087 with a minimum grade of 3.0; and placement in ENGL& 101.

**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; and d. two means.
- When appropriate, use chi-square methods to perform: a. goodness-of-fit tests; b. tests of homogeneity; and 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):** MATH 140 or MATH& 141 with a minimum grade of 2.0.

**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):** 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.
- Demonstrate an understanding of the precise definition of a limit.
- 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& 151 with 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

**Prerequisite(s):** 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: 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 199: Special Projects in 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):** 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: 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 Projects in 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.