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Course Descriptions
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All Whatcom Community College math courses are 5 credits with the following exceptions.
 MATH 207 Taylor Series (1 credit)
 MATH 208  Sequences and Series (3 credits)
 MATH 295  Honors Seminar (2 credits)
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(coordinator: Crystal Holtzheimer)
Textbook: Math Lit, A Pathway to College Mathematics, 2nd Ed., by Kathleen Almy and Heather Foes
Course Description:
First course in a twocourse sequence preparing nonSTEM students for collegelevel math coursework (either MATH& 107 or MATH& 146). Topics include creating and interpreting charts and graphs, order of operations, linear versus exponential growth, basic probability and statistics, dimensional analysis, rates of change, and critical reasoning. Graphing calculator required.Prerequisite: MATH 94 or ABE 50 or equivalent with a grade of "C" or better.
Course outcomes: Upon successful completion of this course, each student should be able to...
1.
Organize data and information using graphical displays.
2.
Make predictions by recognizing patterns.
3.
Model change using linear and exponential functions.
4.
Convert from one unit system to another.
5.
Solve equations by using the order of operation to simplify expressions.
6.
Calculate and interpret measures of average (mean, median, mode).
7.
Calculate perimeters, areas, and volumes of geometric figures.
Course Content:
 Cycle One: Where do we start?
 1.1  Focus Problem
 1.2  Reviewing Prealgebra
 1.3  Graphing Points
 1.4  Ratios and Proportions
 1.5  Probability Basics
 1.6  Understanding Integers
 1.7  Integer Operations
 1.8  Means
 1.9  Making and Interpreting Graphs
 1.10  Scatterplots
 1.11  Converting Units
 1.12  Percent Change
 1.13  Algebraic Terminology
 1.14  Recognizing Patterns
 1.15  Linear and Exponential Change
 1.16  Perimeter and Area
 Cycle Two: How does that work?
 2.1  Focus Problem
 2.2  Weighted Means
 2.3  Basic Exponent Rules
 2.4  Adding Polynomials
 2.5  Applying Order of Operations
 2.6  Rewriting Expressions
 2.7  Distributive Property
 2.8  Equivalent Expressions
 2.9  Using Operations Correctly
 2.10  Verifying Solutions
 2.11  Solving Simple Equations
 2.12  More Equation Solving
 2.13  Writing and Solving Equations
 2.14  Using Proportions
 2.15  Pythagorean Theorem
 2.16  Theoretical Probability
 2.17  Volume and Surface Area
 Cycle One: Where do we start?
(coordinator: Crystal Holtzheimer)
Textbook: Math Lit, A Pathway to College Mathematics, 2nd Ed., by Kathleen Almy and Heather Foes
Course Description:
Second course in a twocourse sequence preparing nonSTEM students for collegelevel math coursework (either Math& 107 or Math& 146). Topics include linear relationships and problemsolving, standard deviation, nonlinear equations, variation, scientific notation, function notation, the quadratic formula, and right triangle trigonometry. Graphing calculator required.Prerequisite: MATH 87 with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Express relationships between two variables using equations, tables, and graphs.
2. Use direct and inverse variation equations.
3. Create and graph lines of best fit using data.
4. Solve problems using linear equations and systems.
5. Compute standard deviation.
6. Determine when a graph represents a function, and define its domain and range.
7. Write the six trigonometric ratios for an acute angle of a right triangle.
8. Utilize the vertex form of a quadratic function.
Course Content: Cycle Three: When is it worth it?
 3.1  Focus Problem
 3.2  Correlation
 3.3  Slope
 3.4  Distance Formula
 3.5  Linear Relationships
 3.6  SlopeIntercept Form
 3.7  Writing Linear Equations
 3.8  Exponential Functions
 3.9  Solving Nonlinear Equations
 3.10  Rewriting Formulas
 3.11  Greatest Common Factors
 3.12  Factoring Quadratic Expressions
 3.13  The Quadratic Formula
 3.14  Graphing and Substitution
 3.15  Elimination
 3.16  Quadratic Functions
 Cycle Four: What else can we do?
 4.1  Focus Problem
 4.2  Dimensional Analysis
 4.3  Scientific and Engineering Notation
 4.4  Negative Exponents
 4.5  Standard Deviation
 4.6  Understanding Logarithmic Scales
 4.7  Direct Variation
 4.8  Inverse Variation
 4.9  Function Notation
 4.10  Vertical Line Test, Domain, and Range
 4.11  Vertex Form of a Quadratic Function
 4.12  Trigonometric Functions
 Cycle Three: When is it worth it?
(coordinator: Yumi Clark)
Textbook: Elementary Algebra, OpenStax
Course Description:
The first in a two course elementary algebra sequence. The course will include solving one variable linear equations and applications, graphing linear equations, properties of exponents, systems of linear equations and applications, and polynomial operations. A graphing calculator is required.
Prerequisite: MATH 94 or ABE 50 or equivalent with a grade of "C" or better.
Course Outcomes: Students will be able to…
1.
Solve linear equations and inequalities of one variable.
2.
Analyze relationships between linear equations and their graphs.
3.
Use a variety of methods to solve systems of linear equations, including substitution, elimination, and graphical methods.
4.
Solve application problems involving linear equations and linear systems.
5.
Add, subtract, and multiply polynomial expressions.
Course Content:
 Numerical Operations and Expressions (Foundations)
* Optional reviews of prealgebra concepts throughout chapter 1.
Variables, Expressions, Like Terms (Language of Algebra) [1.2]
Order of Operations, Evaluating Expressions [1.4]
Properties of Real Numbers [1.9]  Solving Linear Equations and Inequalities
Addition Property of Equality [2.1]
Multiplication Property of Equality [2.2]
Solve Linear Equations in One Variable [2.3, 2.4, 2.5]
Solving Linear Inequalities [2.7]  Applications (Math Models)
Intro to word problems [3.1]
Various applications [3.3 – 3.5]
 Graphing Linear Equations
The Cartesian Coordinate System [4.1]
Graphing Linear Equations [4.2]
Graph with Intercepts [4.3]
Slope and the SlopeIntercept Form [4.4, 4.5]
Find the Equation of a Line [4.6]
 Systems of Linear Equations
Solve Systems by Graphing [5.1]
Solve Systems by Substitution [5.2]
Solve Systems by Elimination [5.3]
Applications [5.4, 5.5]
 Polynomials
Add and Subtract Polynomials [6.1]
Use Multiplication Properties of Exponents [6.2]
Multiply polynomials, Special Products [6.3,6.4]
 Numerical Operations and Expressions (Foundations)
(coordinator: Mei Luu)
Textbook: Elementary Algebra, OpenStax.
Course Description:
Second in a two course elementary algebra sequence. Students are expected to be proficient in the first half of an Elementary Algebra course sequence (Math 97 or equivalent). Topics include dimensional analysis, exponent rules (including negative and rational exponents), simplifying radical expressions and solving radical equations, solving and graphic quadratic equations.
Prerequisite: MATH 97 or equivalent with a grade of "C" or better.
Course Outcomes: Students will be able to…
1.
Factor polynomials
2.
Simplify expressions using exponent rules including negative and rational exponents.
3.
Simplify radical expressions.
4.
Solve radical equations.
5.
Solve quadratic equations.
6.
Analyze relationships between quadratic equations and their graphs.
Course Content:
 Polynomials
Review of multiplication properties of exponents [6.2]
Divide Monomials (Quotient Property of Exponents) [6.5]
Divide Polynomials [6.6] *** Division by monomial only
Integer Exponents and Scientific Notation [6.7]
 Factoring
Factoring (GCF, Grouping) [7.1]
Factoring Quadratics (a=1, a not equal to 1) [7.2,7.3]
Special Factoring (difference of squares, perfect square trinomials) [7.4]
General Strategy for Factoring Polynomials [7.5]
Solve Equations by Factoring [7.6]
 Ratios/Proportions [8.7]
 Dimensional Analysis [1.10]
 Roots and Radicals (No graphing of basic radical equation)
Simplify and Use Square Roots [9.1]
Simplify Square Roots [9.2]
Operations (add, subtract, multiply, and divide) with Square Roots [9.3,9.4.9.5]
Solving Equations with Square Roots [9.6]
Higher Roots [9.7]
Rational Exponents [9.8]
 Quadratics Equations
Solving Quadratic Equations [10.1,10.2,10.3] (with real solutions only)
Applications [10.4]
Graphing Quadratic Equations [10.5]
 Polynomials
(coordinator: Carrie Muir)
Textbook: Elementary Algebra, OpenStax. Algebra & Trig, OpenStax.
Course Description:
A course in functions and fundamentals of algebra intended to prepare students planning to take additional courses in science, technology, engineering, and mathematics. Topics include quadratic equations, rational expressions and equations, functions and graphs, systems of equations (3variable and nonlinear), exponential and logarithmic functions. Graphing calculator required.
Prerequisite: MATH 98 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1.
Solve quadratic equations with real or complex solutions.
2.
Simplify rational expressions and solve rational equations.
3.
Determine the domain and range of a function represented either graphically, numerically, or symbolically.
4.
Evaluate functions and their sums, differences, products, quotients, and compositions.
5.
Analyze the effects of parameter changes on the graphs of functions.
6.
Graph and solve simple exponential and logarithmic equations.
7.
Solve systems of equations with up to 3 variables (includes linear and nonlinear systems using graphs, substitution, and elimination)
Course Content:
 Quadratic Equations and Equations in Quad Form
Complex Numbers [AT 2.4]
Quadratic Equations Including Complex Solutions [AT 2.5]
Equations in Quadratic Form Including Complex Solutions [AT 2.6]
(optional) Other Equations Including Complex Solutions [AT 2.6]
 Rational Expressions and Equations
Simplify Rational Expressions [EA 8.1]
Multiply/Divide Rational Expressions [EA 8.2]
Add/Subtract Rational Expressions [EA 8.3, 8.4]
Complex Fractions [EA 8.5]
Solve Rational Equations [EA 8.6]
Applications [EA 8.8, 8.9]
 Functions
Function and Function Notation [AT 3.1]
Basic Function Graphs [AT 3.1]
Domain and Range [AT 3.2]
Function Algebra and Composition [AT 3.4]
Transformations [AT 3.5]
Inverse Functions [AT 3.7]
 Exponential and Logarithmic Functions
Exponential Functions, Graphs, and Applications [AT 6.1, 6.2]
Logarithmic Functions, Graphs, and Application [AT 6.3, 6.4]
Common and Natural Logs [AT 6.3]
Change of Base Formula and Power Rule [AT 6.5]
(optional) Other Logarithmic Properties [AT 6.5]
Solve Simple Exponential Equations [AT 6.5, 6.6]
Applications [embedded throughout AT chapter 6]
 Larger Systems
Two variable system review [AT 11.1]
Larger linear systems [AT 11.2]
Intro to nonlinear systems [AT 11.3]
Applications [Embedded throughout AT chapter 11]
(optional) Solving Systems with Matrix Operations [AT 11.6, 11.6]
 (optional) Trigonometry
(optional) Right Triangle Trigonometry [AT 7.2 or supplement]
(optional) Sine, Cosine, and Tangent [AT 7.2 or supplement]
(optional) Applications of Right Triangle Trigonometry [AT 7.2 or supplement]
(optional) Inverse Trigonometric Fucntions [AT 8.1 or supplement]
(Please note: The Math 99 coursepack includes sections from both OpenStax Elementary Algebra and OpenStax Algebra & Trig. EA and AT refer to these two texts respectively.
 Quadratic Equations and Equations in Quad Form
(coordinator: Carrie Muir)
Textbook: OER Materials
Course Description:
Exploration of mathematical concepts with emphasis on observing closely, developing critical thinking, analyzing and synthesizing techniques, improving problem solving skills, and applying concepts to new situations. Core topics are probability and statistics. Additional topics may be chosen from a variety of math areas useful in our society. Graphing calculator required.Prerequisite: MATH 88 or MATH 99 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1.
Solve contextbased problems by identifying, comparing and using proportional relationship from various scenarios (e.g., verbal, graphical, symbolic, numeric).
2.
Solve application problems using growth/decay models, including linear and exponential models.
3.
Solve contextbased scenarios using formulas and relevant calculations pertaining to personal finance (e.g., the study of future value, present value, compound interest, annuities, financial loans).
4.
Calculate and interpret probabilities given contextual information, including: theoretical, experimental, conditional, and compound probabilities.
5.
Calculate, interpret, analyze, and critique numerical summaries of data.
6.
Create, interpret, analyze, and critique graphical displays of data.
Course Content:
 Describing Data
 Growth Models
 Financial Mathematics
 Probability
Time permitting additional topics can be chosen from topics at the discretion of the instructor.
 Describing Data
(coordinator: Crystal Holtzheimer)
Textbook: Quantitative Reasoning and the Environment: Mathematical Modeling in Context, 1st edition by Langkamp and Hull
Course Description:
Exploration of linear, power, exponential, logistic, logarithmic, and difference equations using data analysis. Students will create mathematical models from environmentally themed data sets to better understand different types of relationships between variables. Quantitative reasoning will be heavily emphasized. A graphing calculator is required.Prerequisite: MATH 99 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Create mathematical models for environmental data sets. These include linear, exponential, power, difference equation, and logistic models.
2. Determine the most appropriate model to use for a specific set of data.
3. Use mathematical models to analyze the behavior of environmental data.
4. Solve linear, exponential, power, and difference equations.
Course Content:
 Linear Functions and Regression [Ch. 4]
 Modeling with Linear Functions
 Units of Measure in Linear Equations
 Dependent versus Independent Variables
 Graphing Linear Functions
 Approximating AlmostLinear Data Sets
 The straightedge method
 Least Squares Regression
 The Correlation Coefficient
 Correlation Fallacies
 Exponential Functions and Regression [Ch. 5]
 Exponential Rates and Multipliers
 The General Exponential Model
 Finding Exponential FunctionsThe More General Case
 Solving Exponential Equations
 Doubling Times and HalfLives
 Approximating AlmostExponential Data Sets
 Power Functions [Ch. 6]
 Basic Power Functions
 Solving Power Equations
 Approximating PowerLike Data
 Power Law Distributions and Fractals
 Introduction to Difference Equations [Ch. 7]
 Sequences and Notation
 Modeling with Difference Equations
 Linear Difference Equations
 Exponential Difference Equations
 Why Use Difference Equations?
 Affine Difference Equations
 Affine Solution Equations and Equilibrium Values [Ch. 8]
 The Solution Equation to the Affine Model
 Equilibrium Values
 Classification of Equilibrium Values
 Logistic Growth, harvesting and Chaos [Ch. 9]
 Modeling Logistic Growth with Difference Equations
 Logistic Equilibrium Values
 Harvest Models
 Periodic Behavior
 Chaotic Behavior
 Optional
 Systems of Difference Equationsa
 Exponential Change and Stable Age Distributions
 Linear Functions and Regression [Ch. 4]
(coordinator: Nathan Hall)
Textbook: Precalculus: Mathematics for Calculus, 7th Edition by Stewart, Redlin, and Watson
Course Description:
The basic properties and graphs of functions and inverses of functions, operations on functions, compositions; various specific functions and their properties including polynomial, absolute value, rational, exponential and logarithmic functions; applications of various functions; conics. A graphing calculator is required.Prerequisite: MATH 99 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1.
Analyze the graphs of polynomial, rational, exponential, logarithmic, and piecewise functions.
2.
Analyze relationships between real and complex zeros, linear factors, and xintercepts of a polynomial function.
3.
Solve polynomial, exponential, and logarithmic equations.
4.
Perform function composition.
5.
Analyze the relationships between graphs of conic sections and their standard equations.
Course Content:
 Complex numbers and operations (should be review) [1.6]
 Polynomials
 Polynomial models to motivate topic (suggested, not required) [3.1]
 Graphs of Polynomials (End behavior, turns, zeros) [3.2]
 Finding zeros of Polynomials (real and complex) [3.3, 3.4] (dividing polynomials and real zeros)
 Theorems: Fundamental Theorem of Algebra, Complex Zeros Theorem [3.5]
 Rational Graphs
 Vertical Asymptotes, Horizontal Asymptotes, Holes, Zeros [3.6]
 Oblique Asymptotes [3.6]
 Piecewise Functions
 Graphing Piecewise Functions [S.1]
 Absolute Value as a Piecewise Function (include piecewise supplement) [S.1]
*topics appear in 2.2, but use Supplement 1 for content and exercises*
 Function Composition
 Algebra of Compositions [2.7]
 Graphing Compositions [2.7]
 Inverse functions [2.8]
 Exponentials and Logs
 Graphs of Exponentials and Logs [4.1, 4.2, 4.3]
 Properties of Logs [4.4]
 Change of base [4.4]
 Solve Exponential and Logarithmic Equations [4.5]
 Applications/Models of Exponentials and Logs [4.6]
 Logarithmic Scales [4.7]
 Conics
 Circles [1.9]
 Parabolas [11.1]
 Ellipses [11.2]
 Hyperbolas [11.3]
 Shifted Conics [11.4]
 Complex numbers and operations (should be review) [1.6]
(coordinator: Lee Singleton)
Textbook: Precalculus: Mathematics for Calculus, 7th Edition by Stewart, Redlin, and Watson
Course Description:
Second in a two course sequence designed to prepare students for the study of Calculus. Intended for students planning to major in math and/or science. Course to include right triangle trigonometry; trigonometric functions and their graphs; trigonometric identities and formulae; applications of trigonometry; parametric equations; polar coordinates. A graphing calculator is required.Prerequisite: MATH& 141 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1.
Analyze the relationships between right triangles, circles, and trigonometric functions using radian or degree measurements.
2.
Solve geometric problems using triangle relationships. These include right triangle identities, the Law of Sines, and the Law of Cosines.
3.
Relate trigonometric functions to their corresponding graphs, including vertical and horizontal shifts and stretches.
4.
Transform trigonometric expressions using identities. (These include, but are not limited to: quotient, reciprocal, sum and difference, double angle, even/odd, or Pythagorean relationships.)
5.
Solve trigonometric equations symbolically or in reference to an application.
6.
Examine relationships between polar coordinates, Cartesian coordinates, polar equations, and polar graphs. 7.
Analyze relationships between standard equations, parametric equations, and their graphs.
Course Content:

Trigonometric Functions
 Radian and Degree Measure [6.1]
 Right Triangle Trigonometry [6.2]
 The Unit Circle [5.1]
 Trigonometric Functions of Any Angle [5.2, 6.3]
 Graphs of sine and cosine Functions [5.3]
 Graphs of other Trigonometric Functions [5.4]
 Inverse Trigonometric Functions [5.5, 6.4]
 Applications and Models [5.6]
 Laws of Sines [6.5]
 Law of Cosines [6.6]
(This ordering is based on the previous text, but chapters 5 and 6 can be taught in any order. Another combined approach suggested by the text is: 5.1, 5.2, 6.1, 6.2, 6.3, 5.3, 5.4, 5.5, 5.6, 6.4, 6.5, 6.6. Another option is to teach these two chapters sequentially.)
 Analytic Trigonometry
 Fundamental Trigonometric Identities [7.1]
 Verifying Trigonometric Identities [7.1]
 Sum and Difference Formulas [7.2]
 MultipleAngle Formulas (i.e. double angle and half angle) [7.3]
 ProductSum Formulas (optional) [7.3]
 Solving Trigonometric Equations (single and multiple angle)[7.4, 7.5]
 Parametric and Polar Equations
 Polar Coordinates [8.1]
 Graphs of Polar Equations [8.2], (11.6 optional)
 Parametric Equations [8.4]
 Limits
 Introduction to Limits (optional) [13.1]
 Methods of Evaluating Limits (optional) [13.2]

Trigonometric Functions
(coordinator: TBA)
Textbook: Mathematics with Applications, 12th edition by Lial, Hungerford, and Holcomb
Course Description:
Applications of linear, quadratic, exponential, and logarithmic equations; functions and graphs; mathematics of finance; solution of linear systems using matrices; linear programming using the simplex method. A graphing calculator is required.Prerequisite: MATH 99 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Construct regression models (linear, quadratic, cubic, or quartic) representing data, and use them to solve application problems, calculate residuals; state a correlation coefficient and defend the quality of fit.
2. Evaluate a linear, quadratic, absolute value, rational, polynomial, exponential, logarithmic, piecewise, or greatest integer function. Determine the domain of at least one of these functions.
3. Solve inequalities involving linear, quadratic, absolute value, or rational functions.
4. Graph linear inequalities in two variables.
5. Solve linear programming problems graphically and apply them to business applications.
6. Set up and solve a system of three equations with three unknowns.
7. Calculate business application function values. These include simple interest and discount, compound interest, a breakeven point, an equilibrium point, an annual percentage yield APY, or amortization values.
8. Employ technology to determine the maximum value of the objective function and state where it occurs as an ordered pair.
Course Content:
 Graphs, Lines, and Inequalities
 Graphs [2.1]
 Equations of a Line (slopeintercept, pointslope, general, vertical, horizontal) [2.2]
 Linear Models (Applications) [2.3]
 Linear Inequalities [2.4]
 Polynomial and Rational Inequalities (using graphing calculator) [2.5]
 Functions
 Functions [3.1]
 Graphs of Functions [3.2]
 Applications of Linear Functions [3.3]
 Quadratic Functions [3.4]
 Application of Quadratic Functions [3.5]
 Polynomial Functions [3.6]
 Rational Functions [3.7]
 Exponential and Logarithmic Functions
 Exponential Functions [4.1]
 Applications of Exponential Functions [4.2]
 Logarithmic Functions (solving log equations) [4.3]
 Logarithmic and Exponential Functions (Applications) [4.4]
 Mathematics of Finance
 Simple Interest and Discount [5.1]
 Compound Interest [5.2]
 Annuities, Future Values, Sinking Funds [5.3]
 Present Value of an Annuity: Amortization [5.4]
 Systems of Linear Equations
 Systems of Two Linear Equations in Two Variables [6.1]
 Larger Systems (The GaussJordan Method) [6.2]

Linear Programming
 Systems of Linear Inequalities [7.1]
 Linear Programming (graphical approach) [7.2]
 Application of Linear Programming [7.3]
 The Simplex Method: Maximization [7.4]
 Application of Maximization [7.5]
 Graphs, Lines, and Inequalities
(coordinator: Crystal Holtzheimer)
Textbook: Introductory Statistics, OpenStax
Course Description:
Rigorous introduction to statistical methods and hypothesis testing. Includes descriptive and inferential statistics. Tabular and pictorial methods for describing data; central tendencies; mean; modes; medians; variance; standard deviation; quartiles; regression; normal distribution; confidence intervals; hypothesis testing, one and twotailed tests. Applications to business, social sciences, and sciences.Prerequisite: MATH 88 or MATH 99 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Interpret values and draw conclusions from data using appropriate statistical terminology.
2. Organize data using tabular and graphical methods.3. Summarize data using numerical measures of center and spread that are appropriate for the data set.
4. Compute probabilities, including binomial and Normal probabilities.
5. Create confidence intervals for population parameters.
6. Conduct hypothesis tests for population parameters.
7. Compute the least squares regression line for bivariate linear data.
Course Content:Section 1.1: Definitions of Statistics, Probability, and Key Terms
Section 1.2: Data, Sampling, and Variation in Data and Sampling
Section 1.3: Frequency, Frequency Tables, and Levels of Measurement
Section 1.4: Experimental Design and Ethics
Section 2.1: StemandLeaf Graphs, Line Graphs, and Bar Graphs
Section 2.2: Histograms, Frequency Polygons, and Time Series Graphs
Section 2.3: Measures of the Location of the Data
Section 2.4: Box Plots
Section 2.5: Measures of Center of the Data
Section 2.6: Skewness and the Mean, Median, and Mode
Section 2.7: Measures of the Spread of the Data
Section 3.1: Probability Terminology
Section 3.2: Independent and Mutually Exclusive Events
Section 3.3: Two Basic Rules of Probability
Section 3.4: Contingency Tables
Section 3.5: Tree and Venn Diagrams
Section 4.1: Probability Distribution Function for a Discrete Random Variable
Section 4.2: Mean or Expected Value and Standard Deviation
Section 4.3: Binomial Distribution
Section 5.1: Continuous Probability Functions
Section 6.1: The Standard Normal Distribution
Section 6.2: Using the Normal Distribution
Section 7.1: The Central Limit Theorem for Sample Means (Averages)
Section 8.1: Confidence Intervals for a Single Population Mean using the Normal Distribution
Section 8.2: Confidence Intervals for a Single Population Mean using the Student t Distribution
Section 8.3: Confidence Intervals for a Population Proportion
Section 9.1: Null and Alternative Hypotheses
Section 9.2: Outcomes and the Type I and Type II Errors
Section 9.3: Distribution Needed for Hypothesis Testing
Section 9.4: Rare Events, the Sample, Decision and Conclusion
Section 9.5: Additional Information and Full Hypothesis Test Example s
Section 9.6: Hypothesis Testing of a Single Mean and Single Proportion
Section 10.1: Testing Hypotheses About Two Population Means with Unknown Standard Deviations
Section 10.2: Testing Hypotheses About Two Population Means with Known Standard Deviations
Section 10.3: Testing Hypotheses Comparing Two Independent Population Proportions
Section 10.4: Testing Hypotheses About Matched or Paired Samples
Section 12.1: Linear Equations
Section 12.2: Scatter Plots
Section 12.3: The Regression Equation
Section 12.4: Testing the Significance of the Correlation Coefficient
Section 12.5: Prediction
Section 12.6: Outliers
(coordinator: TBA)
Textbook: Mathematics with Applications, 12th edition by Lial, Hungerford, and Holcomb
Course Description:
Limits, derivatives, marginal analysis, optimization, antiderivatives, and definite integrals. Examples taken from management, life and social sciences. A graphing calculator is required.Prerequisite: MATH& 141 or MATH 145 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Apply limit laws algebraically, graphically, or numerically to evaluate real valued limits and limits involving infinity.
2. Determine the first and second derivative of polynomial, exponential, or logarithmic functions. These include the product, quotient, or composition of these functions.
3. Evaluate the first and second derivative of polynomial, exponential, or logarithmic functions including the product, quotient, or composition of these functions.
4. Apply the concept of a limit, derivative, or continuity to business, management, natural, or social science.
5. Determine the antiderivative of a function.
6. Using the Fundamental Theorem of Calculus, calculate the value of a definite integral.
7. Apply definite and indefinite integrals to applications involving business, management, natural, or social science.
Course Content:
 Differential Calculus
 Limit Laws [11.1]
 Onesided limits, limits at infinity [11.2]
 Rates of Change; Instantaneous velocity [11.3]
 The Derivative; Slope of Tangent [11.4]
 Derivative Laws; Marginal Analysis [11.5]
 Derivative laws; Product Rule; Quotient Rule [11.6]
 The Chain Rule and Function Composition f(g(x)) [11.7]
 Derivative of exponential e^{x} and logarithmic ln(x) [11.8]
 Continuity and Differentiability [11.9]
 Applications of the Derivative
 Derivatives and increasing/decreasing functions, critical points, max & min, first derivative test [12.1]
 Second Derivative: concavity and inflection. Second Derivative Test [12.2]
 Applications. Average Cost, Elasticity (optional) [12.3]
 Graphing: xint, yint; vert. & horiz. asym; inc & dec; concavity, inflection [12.4]
 Integral Calculus
 Antiderivatives. Integral laws [13.1]
 Substitution Method of Integral [13.2]
 Definite Integral. Net Area between xaxis and f(x) [13.3]
 Fundamental Theorem of Calculus (Definite Integral) [13.4]
 Area Between Curves and other Applications [13.5]
 Table of Integrals (optional) [13.6]
 Differentiable Equations, find the function that makes the equation true. (optional) [13.7]
 Differential Calculus
(coordinator: Nathan Hall)
Textbook: Calculus Volume I, OpenStax
Course Description:
A traditional first course in differential calculus intended for math and science majors. Some proofs of derivative laws. Study of functions, limits, continuity, limits at infinity, differentiation of algebraic, exponential, logarithmic, and trigonometric functions and their inverses. Applications. A graphing calculator is required.Prerequisite: MATH& 142 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Compute limits using graphical, tabular, algebraic, and L’Hopital’s Rule methods.
2. Apply the definitions of limit, continuity, and derivative appropriately.
3. Determine derivatives of polynomial, exponential, trigonometric, and logarithmic functions, and combinations thereof.
4. Demonstrate the relationship between the derivative as a slope and as a rate of change (ex: velocity and acceleration).
5. Apply the Chain Rule to differentiate and implicitly differentiate functions.
6. Develop and analyze math models for related rate and optimization problems.
7. Calculate extrema and inflection points using derivative analysis.
8. Analyze the behavior of a function using graphical, tabular, or algebraic representations of the derivative of the function.
9. Apply the Mean Value Theorem.
10. Use Newton’s Methods to approximate the solution of an equation.
Course Content:
 Limits
 Tangent & Velocity [2.1.12.1.4]
 Limit of a Function [2.2]
 Limit Laws, Squeeze Theorem [2.3]
 Delta Epsilon Limits [2.5]
 Continuity [2.4]
 Limits at Infinity [4.6] (may want to cover with other Ch. 4 content)
 Derivatives: Rates of Change [3.1]
 Derivative of a Function [3.2]
 Derivatives
 Derivatives: Polynomial and Exponential f(x) [3.3.1]
 Product & Quotient Rules [3.3.33.3.6]
 Trig Function Derivatives [3.5]
 Chain Rule [3.6]
 Implicit Differentiation, Inverse Trig Derivatives [3.8, 3.7]
 Log Function Derivatives [3.9]
 Rates of Change: Natural/Social Science [3.4]
 Related Rates [4.1]
 Differentials and Linear Approximations [4.2]
 Hyperbolic Functions (focus on derivatives) [6.9]
 Applications of the Derivative
 Maximum and Minimum Values [4.3]
 Mean Value & Rolle's Theorem [4.4]
 Derivatives and Graphing [4.5]
 Indeterminate Form, L'Hospital's Rule [4.8]
 Applications: Optimization [4.7]
 Newton's Method [4.9]
 Limits
(coordinator: Nathan Hall)
Textbook: Calculus Volume II, Openstax
Course Description:
The Study of Riemann Sums, Methods of Integration, Numerical Methods, Fundamental Theorem of Calculus, Areas of Regions, Volumes of Solids, Centroids, Length of Curves, Surface Area. Course includes an Introduction to Differential Equations. A graphing calculator is required.Prerequisite: MATH& 151 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. State fundamental antiderivatives and their integral representations.
2. Utilize a Riemann sum in determining a definite integral.
3. Use finite sums to approximate the value of definite integrals.
4. Calculate integrals using substitution, parts, partial fractions, and trigonometric methods.
5. Set up definite integrals to calculate areas, volumes and other applications.
6. Use the Fundamental Theorem of Calculus to evaluate definite integrals.
7. Solve separable differential equations.
Course Content:
 Integrals
 Antiderivatives [Volume 1, 4.10] (remaining sections from Volume 2)
 Indefinite Integrals [Volume 1, 4.10]
 Area under a curve, sigma notation [1.1]
 Definite Integral [1.2] (may be included with "applications" instead)
 Average Value [1.2]
 Fundamental Theorem of Calculus [1.3]
 Integration Formulas and the Net Change Theorem [1.4]
 Integrals Involving Exponential and Logarithmic Functions [1.6] (also 2.7, but requires usubstitution)
 Integrals Resulting in Inverse Trigonometric Functions [1.7] (also 2.9, but requires usubstitution)
 Substitution Rule [1.5]
Appendix A has a table of integrals
 Applications of Integration
 Area between Curves [2.1]
 Volumes (cross sections, disc method) [2.2]
 Volumes (shell method) [2.3]
 Work [2.5] 
Techniques of Integration
 Integration by Parts [3.1]
 Powers of Trigonometric Functions [3.2]
 Trigonometric Substitution [3.3]
 Method of Partial Fractions [3.4]
 Approximate Integration [3.6]
 Improper Integrals [3.7] 
Further Applications of Integration (may be included with the rest of Chapter 2)
 Arc Length [2.4]
 Surface Area of Solid of Revolution [2.4]
 Centroids [2.6] 
Introduction to Differential Equations
 Ordinary Differential Equations [4.1]
 Separable Equations [4.3]
 Integrals
(coordinator: Yumi Clark)
Textbook: Openstax Calculus Volume 3
Course Description:
Multivariate integral and differential calculus. Geometry in R3 and in the plane. The study of vectors, acceleration, curvature; functions of several variables, partial derivatives; directional derivatives and gradients; extreme values; double and triple integrals; applications.Prerequisite: MATH& 152 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Perform vector arithmetic. These include dot and cross products, in geometric and component form.
2. Use vectors to compute projections, equations of lines, and equations of planes.
3. Using the concepts of derivatives and integrals to vectorvalued functions, compute and describe arclength, curvature, and motion in space.
4. Use partial derivatives and the gradient in a variety of applied problems. These include directional derivatives, optimization, linear approximations, and tangent planes.
5. Apply the many forms of the chain rule for partial derivatives as appropriate.
6. Set up and evaluate double and triple integrals.
Course Content:
 Vectors and the Geometry of Space
ThreeDimensional Coordinate Systems [2.2]
Vectors [2.1, 2.2]
Dot Product [2.3]
Cross Product [2.4]
Equations of Lines and Planes. Distance. [2.5]
Cylinders & Quadric Surfaces [2.6, 2.7] Vector Functions
Vector Functions [3.1]
Derivatives & Integrals of Vector Functions [3.2]
Arc Length & Curvature [3.3]
Velocity & Acceleration in Space [3.4] Partial Derivatives
Functions of Several Variables [4.1]
Limits; Continuity [4.2]
Partial Derivatives [4.3]
Tangent Planes; Linear Approximations [4.4]
Chain Rule [4.5]
Directional Derivatives; Gradient Vector [4.6]
Maximum/Minimum Values [4.7]
Lagrange Multipliers [4.8] Multiple Integrals
Double Integrals (Rectangular) [5.1]
Iterated Integrals [5.1]
Double Integrals (General Regions) [5.2]
Applications of Double Integrals [5.6]
Triple Integrals [5.4](coordinator: Will Webber)
Textbook: Elementary Linear Algebra: Applications Edition, 11th edition by Anton and Rorres
Course Description:
Elementary study of the fundamentals of linear algebra. Course to include the study of systems of linear equations, matrices, ndimensional vector space, linear independence, bases, subspaces and dimension. Introduction to determinants and the eigenvalue problem, applications. A graphing calculator is required.Prerequisite: MATH& 151 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Use matrices to solve systems of linear equations.
2. Compute vector arithmetic in Rn, including calculations of the dot and the cross products.
3. Prove whether a given set is or is not a vector space.
4. Prove whether a given subset of a vector space is or is not a subspace.
5. For a given set of vectors determine if it spans the vector space, is linearly independent,
and is a basis for the vector space.6. Describe transformations of R2 and R3 using matrices.
7. Solve eigenvalue and eigenvector problems.
Course Content:
 Systems of Linear Equations and Matrices
 Introduction to Systems of Linear Equations [1.1]
 Gaussian Elimination [1.2]
 Matrices and Matrix Operations [1.3]
 Inverses, Algebraic Properties of Matrices [1.4]
 Elementary Matrices and Finding the Inverse Matrix [1.5]
 More on Linear Systems and Invertible Matrices [1.6]
 Diagonal, Triangular, and Symmetric Matrices [1.7]
 Determinants
 Determinants by Cofactor Expansion [2.1]
 Evaluating Determinants by Row Reduction [2.2]
 Properties of Determinants, Cramer's Rule [2.3]
 Euclidean Vector Spaces
 Vectors in 2, 3, and nspace [3.1]
 Norm, Dot Product, and Distance in Rn [3.2]
 Orthogonality [3.3]
 The Geometry of Linear Systems [3.4]
 Cross Product [3.5]
 General Vector Spaces
 Real Vector Spaces [4.1]
 Subspaces [4.2]
 Linear Independence [4.3]
 Coordinates and Basis [4.4]
 Dimension [4.5]
 Change of Basis [4.6]
 Row Space, Column Space, and Null Space [4.7]
 Rank, Nullity, and the Fundamental Matrix Spaces [4.8]
 Matrix Transformations from Rn to Rm [4.9]
 Properties of Matrix Transformations [4.10]
 Geometry of Matrix Operators on R2 [4.11]
 Eigenvalues and Eigenvectors
 Eigenvalues and Eigenvectors [5.1]
 Systems of Linear Equations and Matrices
(coordinator: Johnny Hu)
Textbook: Taylor Polynomials and Taylor Series for MATH 126 (Handout), University of Washington Math Department
Course Description:
Introduction to the derivation and uses of Taylor Series, intended for math and science majors. The course includes a discussion of error bounds in approximating curves with polynomials, Taylor polynomials, Taylor series expansion, and intervals of convergence.Prerequisite: MATH& 152 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Create a Taylor polynomial of finite length for a given function
2. Determine an error bound for a Taylor polynomial approximation to a curve
3. Create a Taylor Series for a given function
Course Content:
 Tangent Line Approximation and Error Bound
 Quadratic Approximation and Error Bound
 Taylor Polynomials
 Higher Order Approximation and Taylor's Inequality
 Taylor Series
 Operations with Taylor Series
 Interval of Convergence
 Tangent Line Approximation and Error Bound
(coordinator: Johnny Hu)
Textbook: Calculus: Early Transcendentals, 7th edition by James Stewart
Course Description:
A course in the techniques of working with infinite sequences and series. It is intended for math and science majors. The course includes Limits of sequences, series, alternating series, absolute and conditional convergence, power series, Taylor and Maclaurin series, applications.Prerequisite: MATH& 152 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Evaluate the limit of a sequence
2. Evaluate the limit of an infinite series
3. Test the convergence of an infinite series
4. Represent a function as a power series
5. Represent a function as a Taylor series
6. Determine the error bound for a Taylor polynomial approximation to a function
7. Use series in application problems
Course Content:
 Infinite Sequences and Series
 Sequences [11.1]
 Series [11.2]
 The Integral Test [11.3]
 The Comparison Tests [11.4]
 Alternating Series [11.5]
 Absolute Convergence and the Ratio and Root Tests [11.6]
 Strategy for Testing Series [11.7]
 Power Series [11.8]
 Representations of Functions as Power Series [11.9]
 Taylor and Maclaurin Series [11.10]
 Applications of Taylor Polynomials [11.11]
 Infinite Sequences and Series
(coordinator: Will Webber)
Textbook: Elementary Differential Equations, 11th edition by Boyce
Course Description:
Introductory course in differential equations. Topics include first and higher order linear equations, power series solutions, systems of first order equations, numerical methods, LaPlace transforms, applications. A graphing calculator is required.Prerequisite: MATH& 152 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Solve first order differential equations using the techniques of separable, linear, autonomous and exact equations.
2. Use approximation techniques to estimate solutions to differential equations.
3. Solve second order homogeneous and linear differential equations.
4. Use differential equations to solve a variety of application problems.
5. Solve nth order linear differential equation.
6. Use power series to solve differential equations.
7. Apply LaPlace transforms to solve differential equations.
Course Content:
 First Order Differential Equations
 Linear Equations, Integrating Factors [2.1]
 Separable Equations [2.2]
 Modeling with First Order Equations [2.3]
 Linear and Nonlinear Equations [2.4]
 Autonomous Equations [2.5]
 Exact Equations [2.6]
 Euler's Method [2.7]
 The Existence and Uniqueness Theorem [2.8]
 Second Order Linear Equations
 Homogeneous Equations with Constant Coefficients [3.1]
 Solutions of Linear Homogeneous Equations, Wronskian [3.2]
 Complex Roots of the Characteristic Equations [3.3]
 Repeated Roots, Reduction of Order [3.4]
 Nonhomogeneous Equations, Method of Undetermined Coefficients [3.5]
 Variation of Parameters [3.6]
 Mechanical and Electrical Vibrations [3.7]
 Forced Vibrations [3.8]
 Higher Order Linear Equations
 nth order Linear Equations [4.1]
 Homogeneous Equations with Constant Coefficients [4.2]
 Method of Undetermined Coefficients [4.3]
 Series Solutions of Second Order Linear Equations
 Power Series [5.1]
 Series Solutions, part I [5.2]
 Series Solutions, part II [5.3]
 Euler Equations [5.4]
 The Laplace Transform
 Definition of the Laplace Transform [6.1]
 Initial Value Problems [6.2]
 Step Functions [6.3]
 First Order Differential Equations
(coordinator: Crystal Holtzheimer)
Textbook: Applied Statistics and Probability for Engineers, 7th ed, Montgomery, D.C. & Runger, G.C.
Course Description:
Rigorous introduction to probability, discrete and continuous probability distributions, descriptive and inferential statistics, and regression and correlation with an emphasis on engineering applications. Statistical inference will include one and two sample methods for hypothesis tests and confidence intervals. The use of computer statistical packages is introduced.Prerequisite: MATH& 152 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Compute probabilities using probability rules and axioms
2. Compute probabilities using probability distribution functions, including the binomial distribution, poisson distribution, normal distribution, and exponential distribution
3. Calculate summary statistics for a given set of data
4. Create data displays
5. Interpret the significance of values computed from a given data set
6. Calculate confidence intervals using single sample methods
7. Test hypotheses using single sample and two sample methods
8. Analyze bivariate linear data using regression and correlation
Course Content:
Chapter 1
 11: The Engineering Method and Statistical Thinking
 12: Collecting Engineering Data
Chapter 2
 21: Sample Spaces and Events
 22: Interpretations and Axioms of Probability
 23: Addition Rules
 24: Conditional Probability
 25: Multiplication and Total Probability Rules
 26: Independence
 27: Bayes’ Theorem
 28: Random Variables
Chapter 3
 31: Discrete Random Variables
 32: Probability Distributions and Probability Mass Functions
 33: Cumulative Distribution Functions
 34: Mean and Variance of a Discrete Random Variable
 36: Binomial Distribution
 39: Poisson Distribution
Chapter 4
 41: Continuous Random Variables
 42: Probability Distributions and Probability Density Functions
 43: Cumulative Distribution Functions
 44: Mean and Variance of a Continuous Random Variable
 45: Continuous Uniform Distribution
 46: Normal Distribution
 47: Normal Approximation to the Binomial and Poisson Distributions
 48: Exponential Distribution
Chapter 6
 61: Numerical Summaries of Data
 63: Frequency Distributions and Histograms
 64: Box Plots
 67: Probability Plots
Chapter 7
 72: Sampling Distributions and the Central Limit Theorem
 74: Methods of Point Estimation
Chapter 8
 81: Confidence Interval on the Mean of a Normal Distribution, Variance Known
 82: Confidence Interval on the Mean of a Normal Distribution, Variance Unknown
 84: LargeSample Confidence Interval for a Population Proportion
Chapter 9
 91: Hypothesis Testing
 92: Tests on the Mean of a Normal Distribution, Variance Known
 93: Tests on the Mean of a Normal Distribution, Variance Unknown
 95: Tests on a Population Proportion
 97: Testing for Goodness of Fit
Chapter 10
 101: Inference on the Difference in Means of Two Normal Distributions, Variances Known
 102: Inference on the Difference in Means of Two Normal Distributions, Variances Unknown
 104: Paired tTest
 106: Inference on Two Population Proportions
Chapter 11
 111: Empirical Models
 112: Simple Linear Regression
 113: Properties of the LeastSquares Estimators
 114: Hypothesis Tests in Simple Linear Regression
 115: Confidence Intervals
 116: Prediction of New Observations
 117: Adequacy of the Regression Model
 118: Correlation
(coordinator: Will Webber)
Textbook: Openstax Calculus Volume 3
Course Description:
This is the second quarter of multivariable calculus. Topics include multiple integration in different coordinate systems, the gradient, the divergence, and the curl of a vector field. Also covered are line and surface integrals, Green’s Theorem, Stoke’s Theorem and Gauss’ Theorem.Prerequisite: MATH& 163 or equivalent with a grade of "C" or better.
Course outcomes: Students will be able to…
1. Compute integrals of two or three variables in the plane or in space.
2. Compute the change in the volume element when coordinate systems are changed.
3. Describe surfaces parametrically.
4. Describe vector fields and their flows.
5. Apply the fundamental theorem for line integrals and Green's theorem in the plane.
6. Compute flux integrals for parametrized surfaces.
7. Apply the divergence theorem to compute flux integrals.
8. Apply the concept of the curl to a vector field.
9. Apply Stoke's theorem to compute flux integrals (and line integrals).
Course Content:
 Multiple Integrals
 Double Integrals over Rectangles [5.1]
 Iterated Integrals [5.1]
 Double Integrals over General regions [5.2]
 Polar Coordinates Intro (graphing optional) [1.3]
 Double Integrals in Polar coordinates [5.3]
 Applications of Double Integrals [5.6A]
 Change of Variables in Double Integrals (the Jacobian) [5.7A]
 Triple Integrals [5.4]
 Cylindrical/Spherical Intro [2.7]
 Triple Integrals in Cylindrical and Spherical Coordinates [5.5]
 Applications of Triple Integrals [5.6B]
 Change of Variables in Triple Integrals (the Jacobian) [5.7B] Vector Calculus
 Vector Fields [6.1]
 Line Integrals [6.2]
 The Fundamental Theorem for Line Integrals [6.3]
 Green’s Theorem [6.4]
 Curl and Divergence [6.5]
 Parametric Surfaces and Their Areas [6.6]
 Surface Integrals [6.6]
 Stokes’ Theorem [6.7]
 The Divergence Theorem [6.8]Textbook: Varies, contact the instructor
Course Description:
Courses offered in conjunction with the Whatcom Community College Honors Program. Open only to Whatcom Community College Honors Program students. Limited enrollment of 10 students.
Prerequisite: Varies by course
Course Content:
Contact instructor for a syllabus for a specific quarter and year in which the course is offered.