Upon successful completion of Math 080, the student should be able to:

1. Multiply and divide whole numbers.
2. Add, subtract, reduce, multiply and divide positive fractions.
3. Add, subtract, multiply, and divide positive decimal numbers.
4. Solve proportions and set up and solve application problems using ratios and proportions.
5. Set up and solve application problems using percentages.
6. Calculate perimeters, areas, and volumes of basic geometric shapes.
7. Add, subtract, multiply, and divide integers.
8. Solve basic linear equations in one unknown.
9. Increase their confidence in their ability to learn math.

This course is an individualized course based on the student’s current math skills. Students will complete a selected number of outcomes based on their individual goals and needs. The outcomes for each student will be chosen from those listed for Math 070, Math 080 and/or Math 085.

Upon successful completion of Math 080, the student should be able to:

1. Perform the operations of addition, subtraction, multiplication and division with real numbers.
2. Evaluate numerical and algebraic expressions using the Order of Operations.
3. Solve linear equations.
4. Set-up and solve linear application problems.
5. Identify the exponents and the bases in algebraic expressions that involve exponents.
6. Graph a linear equation.
7. Find the slope of a line given two points, the equation, or the graph.
8. Solve a system of equations by graphing.
9. Solve systems of two linear equations by utilizing the methods of substitution and elimination.
10. Set-up and solve application problems involving two linear equations.

Upon successful completion of Math 085, the student should be able to:

1. Identify polynomials and classify them by degree.
2. Simplify algebraic expressions using the laws of exponents.
3. Perform the operations of addition, subtraction, multiplication and division of polynomials.
4. Identify the greatest common factor of a polynomial and factor the greatest common factor out of the polynomial.
5. Identify common group factors of a polynomial and utilize the method of group factoring to factor the polynomial.
6. Identify trinomials in quadratic form and factor them using a variety of methods, including special formulas.
7. Identify rational expressions, identify restrictions on the variables contained in rational expressions, and reduce rational expressions.
8. Perform the operations of addition, subtraction, multiplication and division of rational expressions.
9. Solve equations involving rational expressions.  Solve application problems by representing the given information as a rational equation then solving the rational equation.
10. Identify radical expressions involving square roots, identify restrictions on the variables contained in radical expressions involving square roots, and simplify radical expressions involving square roots.
11. Perform the operations of addition, subtraction, multiplication, and division of radical expressions involving square roots.
12. Identify quadratic equations and write them in standard form.
13. Solve quadratic equations by factoring, extraction of roots, and the quadratic formula.
14. Solve application problems by representing the given information as a quadratic equation, then solving the quadratic equation.

Upon successful completion of Math 097, the student should be able to:

1. Add, subtract, multiply and divide fractions and decimals.
2. Convert a decimal to a fraction and a fraction to a decimal.
3. Convert a percent to a decimal and a decimal to a percent.
4. Compute a percentage from a given problem.
5. Calculate the missing side of a right triangle using the Pythagorean Theorem.
6. Calculate numerical square roots.
7. Add, subtract, multiply and divide real numbers (signed numbers).
8. Simplify a numerical expression using the order of operations.
9. Simplify algebraic expressions by removing parentheses and combining like terms.
10. Solve linear equations and graph a line from an equation, set up and solve application problems using linear equations.
11. Compare mathematical quantities using inequality notation.
12. Plot ordered pairs on a rectangular coordinate system and Interpret data from a table.
13. Compute the slope of a line, given two ordered pairs and interpret the meaning of slope in applied contexts.
14. Identify the solution(s) to a system of equations from graphed lines.
15. Solve a system of linear equations graphically.
16. Simplify exponential expressions (with integer exponents) using the laws of exponents.
17. Convert scientific notation to numerical form and numerical form to scientific notation.
18. Add, subtract and multiply polynomials; divide polynomials by monomials.
19. Identify common factors and factor quadratic trinomials of the form
    • x² + bx + c.
20. Solve quadratic equations by factoring and extract information from symbolic quadratic models.

Upon successful completion of Math 098, the student should be able to:

1. Simply algebraic expressions.
2. Write the equation of a line from data.
3. Calculate the length of a line segment.
4. Solve linear systems in two variables using graphing and algebraic methods.
5. Set up and solve application problems using linear systems.
6. Interpret and solve linear inequalities.
7. Add, subtract, multiply and divide polynomials.
8. Factor trinomials including expressions with more than one factoring step.
9. Solve quadratic equations by appropriate methods.
10. Graph quadratic equations.
11. Extract information from quadratic models.
12. Add, subtract, multiply and divide basic rational expressions (algebraic fractions).
13. Solve basic rational equations.
14. Set up and solve application problems using inverse variation, direct variation and proportions.
15. Simplify exponent expressions using the laws of exponents.
16. Convert from radical notation to rational exponent notation and from  exponent notation to radical notation.
17. Solve basic exponential equations and simplify square root expressions.
18. Add, subtract and multiply radical expressions.
19. Solve basic radical equations.
20. Identify independent and dependent variables.
21. Identify domains of linear and quadratic functions.
22. Analyze geometric relationships and solve geometric application problems.

Upon successful completion of Math 099, the student should be able to:

1. Evaluate expressions using function notation.
2. Represent functions using formulas, tables and graphs.
3. Write the equation of a line from data.
4. Identify the domain of functions.
5. Identify parallel and perpendicular lines.
6. Solve linear systems in two variables using graphing and algebraic methods.
7. Set up and solve application problems using linear systems.
8. Solve quadratic equations by factoring, completing the square and the quadratic formula.
9. Determine the number of solutions to a quadratic equation using the discriminant.
10. Graph a quadratic function and determine it’s vertex and intercepts.
11. Set up and solve quadratic application problems.
12. Add, subtract, multiply, divide and factor polynomials.
13. Add, subtract, multiply and divide rational expressions (algebraic fractions).
14. Solve rational equations.
15. Set up and solve application problems using inverse variation, direct  variation and proportions.
16. Simplify radical expressions and solve radical equations.
17. Convert from radical notation to rational exponent notation and from exponent notation to radical notation.
18. Convert from logarithmic form to exponential form; and from exponential form to logarithmic form.
19. Solve exponential and logarithmic equations.
20. Graph exponential and logarithmic functions.
21. Solve exponential and logarithmic application problems.

Upon successful completion of Math& 107, the student should be able to:

1. Construct graphs (vertices connected by edges), Euler circuits, Hamilton circuits and minimal spanning trees to model a variety of applied situations.
2. Use algorithms to find "optimal solutions" to a variety of routing problems involving Euler circuits, Hamilton circuits and minimal spanning trees.
3. Construct project di-graphs from precedence data for various jobs.  Use project di-graphs and critical path analysis to determine optimal job-completion times.
4. Use heuristic algorithms to construct "optimal" schedules for completing a variety of jobs.
5. Use voters' preference ballots to determine the results of elections conducted by several voting methods, such as plurality, Borda count, pairwise comparison and approval.
6. Describe imperfections inherent in all voting methods.
7. Use two or three appropriate algorithms to distribute items among competing parties, so that each party is satisfied with the share received.  (e.g., inheritance, divorce, dissolution of business partnerships, etc.)
8. Understand and describe the role of randomization in statistical investigations.
9. Understand and describe the difference between surveys and statistical experiments.  Evaluate the "validity" of results obtained from surveys and statistical experiments.
10. Interpret the results of statistical studies given in terms of measures of center and spread and statistical diagrams.  Use measures of center and spread, along with appropriate visual displays, to summarize numerical data sets.
11. Analyze data sets.  Use the normal distribution, percentiles and standard scores to extract information from appropriate collections of data.

After successfully completing Math 130, a student will be able to:

1. Use the main statistical functions on a TI-83.
2. Construct and interpret appropriate displays of data, including time plots, scatterplots, histograms and pie charts.
3. Recognize the difference between continuous and discrete variables.
4. Identify the population and recognize bias in sampling and select a simple random sample and recognize sources of error.
5. Distinguish between observational studies and experiments.
6. Outline the design of a completely random experiment and recognize the placebo effect.
7. Recognize when a double blind experiment is appropriate.
8. Find the mean, median, mode and mid-range of a set of data and compute variance and standard deviation.
9. Explain what the standard deviation tells us about a set of data.
10. Use the standard deviation to compute z-scores and percentiles.
11. Explain the concept of (mathematical) randomness and list the sample space of simple probability experiments.
12. Explain what the Law of Large Numbers does NOT say and how it relates to classical probability.
13. Apply the rules of probability in context and compute expected values.
14. Apply the definition of dependence and independence to determine if events are independent or dependent.
15. Recognize when the Normal Distribution is appropriate and when it's not.
16. Solve problems involving the Standard Normal Distribution.
17. Use the Central Limit Theorem to find probabilities of sampling means.
18. Interpret and find confidence intervals.
19. Test hypotheses dealing with means and proportions.
20. Use Regression Analysis to test correlation of data and find an equation relating data.

Upon successful completion of Math 138, the student should be able to:

1. Understand the concept of a function; recognize linear functions; compute the slope and the equation of a line; set up and solve application problems using linear functions.
2. Recognize and apply quadratic functions, polynomial functions, and rational functions.
3. Recognize and apply exponential functions; solve applications using exponential functions and logarithmic functions; solve applications using logarithmic functions.
4. Understand and apply the echelon method and Gauss-Jordan method ; perform matrix operations including matrix multiplication; find an inverse matrix; apply matrix methods to solve applications problems.
5. Graph linear inequalities in two variables; solve linear programming problems graphically; solve applications of linear programming; understand and compute solutions using the simplex method (optional).
6. Understand and use sets, Venn diagrams, tree diagrams and tables to calculate probabilities and interpret them in applied context and conditional probability.
7. Optional topics:  Compute simple interest and discount, compound interest;  optional:  annuities, present value of an annuity,  and amortization.

Upon successful completion of Math& 141, the student should be able to:

1. Simplify algebraic, exponential and radical expressions.
2. Solve linear equations and inequalities.
3. Graph linear equations.
4. Solve absolute value, non-linear and rational inequalities.
5. Simplify complex fractions.
6. Factor expressions and solve equations containing negative and fractional exponents.
7. Identify functions from algebraic, graphical, tabular and verbal representations. Use function notation when evaluating functions and sketching graphs of functions.
8. Identify domain and range of functions.
9. Graph a piece-wise defined function.
10. Identify properties of graphs such as relative and global maximum and minimum, symmetry, increasing, decreasing, even, and odd.
11. Translate the graph of a function.
12. Translate the graph of a circle in standard or general form.
13. Solve application problems and interpret, and draw inferences from, the results.
14. Analyze and graph quadratic functions by hand and using a graphing calculator.
15. Find the equations of quadratic functions from given data.
16. Set up and solve quadratic applications, including maximum/minimum problems.
17. Perform operations on functions, including composition of functions.
18. Identify one-to-one functions.
19. Identify, analyze and graph the inverse of a function. Find the inverse of a given function.
20. Analyze and graph polynomials functions of degree greater than 2.
21. Divide two polynomial functions.
22. Apply the Remainder Theorem and Factor Theorem.
23. Perform basic operations on complex numbers.
24. Find real and complex zeros of polynomials.
25. Use a calculator to assist in finding real zeros of polynomials.
26. Graph rational functions.
27. Analyze and graph exponential and logarithmic functions
28. Solve exponential and logarithmic equations.
29. Set up and solve exponential and logarithmic application problems.
30. Solve a non-linear system of equations.
31. Solve a system of linear equations using matrices and a graphing calculator.
32. Set up and solve application problems using a system of equations

Upon successful completion of Math& 142 the student should be able to:

1. Measure angles in degrees and radians and convert from one system to the other.
2. State the definitions of sine and cosine on the unit circle and for right triangles and give the values of sine and cosine at the “special” angles on the unit circle.
3. Define tangent, cotangent, secant, and cosecant in terms of sine and cosine.
4. State and use the fundamental identities relating the trigonometric functions.
5. Solve right triangle application problems.
6. Graph sine and cosine functions using amplitude, period, vertical shift and phase shifts  (graph tangent, cotangent, secant and cosecant).
7. Use a graphing calculator to create graphs of trigonometric functions and combinations of trigonometric functions.
8. Use sine and cosine functions to model simple harmonic motion.
9. Define and graph inverse trigonometric functions.
10. Solve trigonometric equations by hand and using calculators (and extend calculator results to additional solutions).
11. Verify trigonometric identities and find counterexamples to false “identities.”
12. Use a variety of trigonometric identities (sum, difference, double angle, half angle, etc.)
13. Use the laws of sines and cosines to solve non-right triangles and applications.
14. Define and graph vectors in 2-D and 3-D and use the properties of vectors to add, subtract and stretch vectors and solve applications.
15. Calculate the dot product of two vectors and use it to find the angle between them.
16. Calculate and sketch the projection of a vector onto a vector.
17. Plot points and graph functions given by  parametric equations by hand and using a calculator.
18. Plot points and graph functions in polar coordinates by hand and using a calculator.
19. Define and graph and list some reflection properties of parabolas, ellipses and hyperbolas.
20. Use the listed tools to solve multi-step problems and applications.

Upon successful completion of Math& 148, the student should be able to:

1. Use the product, quotient and chain rules to differentiate simple algebraic, exponential and logarithmic functions.
2. Construct equations for tangent lines and find average and instantaneous rates of change from symbolic, graphical and numerical information.
3. Apply the concepts, techniques and vocabulary of limits, continuity and first and second derivatives to solve problems in contexts such as marginal analysis, product elasticity, related rates, exponential growth/decay and optimization.
4. Use simple substitutions and tables to determine anti-derivatives of simple algebraic and exponential functions.
5. Determine the values (exact or approximate, as appropriate) of definite integrals using the Fundamental Theorem of Calculus and areas.
6. Apply the ideas of definite and indefinite integrals to solve problems in contexts such as total change/accumulation, consumer and producer surplus, exponential growth and decay, etc.
7. Determine appropriate units for definite integrals and derivatives.
8. Calculate partial derivatives of simple functions of two variables, and apply them to solve optimization problems, compute marginal productivity, and interpret three-dimensional graphics.

Upon successful completion of Math& 151, the student should be able to:

1. Calculate or estimate limits of functions given by formulas, graphs, or tables; also using properties of limits and L’hopital’s Rule.
2. Determine whether a function given by a graph or formula is continuous or differentiable at a given point or on a given interval.
3. Distinguish between average and instantaneous rate of change, and interpret the definition of the derivative graphically.
4. Calculate derivatives of polynomial, rational, common transcendental functions, combinations of these functions, and implicitly defined functions.
5. Apply the ideas and techniques of derivatives to
   • related rate problems,
   • parametric equation models (optional).
6. finding extreme values of modeling functions given by formulas or graphs:
   •  predict, construct and interpret the shapes of graphs,
   •  solving equations (i.e. Newton’s Method),
   •  find linear approximations of functions (differentials).
7. Estimate a slope, a rate of change and the reasonableness of a result.
8. Interpret solutions to applied problems, attaching the appropriate units to an answer.
9. Distinguish assumptions and conclusions in mathematical statements.

Upon successful completion of Math& 152, the student should be able to:

1. Calculate the Riemann sum for a given function, partition and collection of evaluation points
2. Describe a definite integral as:
•  the limit of a Riemann sum,
• the area under a curve,
• the distance traveled by a moving object,
• a total accumulation.
3. Determine the appropriate units for a definite integral.
4. Describe the meaning of the antiderivative of a function.
5. Determine the antiderivatives of polynomial, trigonometric, exponential and logarithmic functions.
6. Determine the values of definite integrals using antiderivatives and areas.
7. Approximate the numerical values of definite integrals.
8. State and paraphrase the Fundamental Theorem of Calculus.
9. Apply the ideas of definite integrals to solve problems of:
   •  Areas,
   • Volumes,
   • Work,
   • centers of mass,
   • other assorted applications.
10. Recognize separable differential equations and to use integration to solve separable initial value problems.
11. Solve problems of exponential growth and decay and to understand the meanings and limitations of those solutions.
12. Differentiate the inverse trigonometric functions and to use them with integrals.
13. To describe the meaning of an improper integral and to evaluate some classes of improper integrals.
14. To apply the techniques of integration by parts, substitution, partial fractions and tables of anti-derivatives to evaluate integrals.

Upon successful completion of Math& 153, the student should be able to:

1. Describe conic sections as loci of points, and apply reflection properties of conics in physical and geometric contexts.
2. Sketch graphs of polar equations, convert rectangular equations to polar equations, and convert polar equations to rectangular equations.
3. Use derivatives and integrals to calculate slopes, rates of change and areas in polar coordinates.
4. Classify conic sections by their eccentricity and describe conics in terms of polar coordinates.
5. Sketch graphs of parametric equations in two-dimensions, and extract information from parametric equations and their graphs.
6. Use parametric equations to model linear, rotational and other motion.
7. Use derivatives and integrals to calculate direction (slope, angle), speed and distance measured along a curve.
8. Illustrate convergence and divergence of sequences graphically.
9. Given a bound for the difference between the terms of a convergent sequence and its limit, determine the minimal index that achieves that bound.
10. Carefully define the meaning of convergence/sum of an infinite series of numbers in terms of its partial sums.  Use this definition to discuss the behavior of some selected series.
11. Determine the sum of any geometric series.
12. Determine whether a series converges or diverges by selecting an appropriate convergence test  (nth-term, comparison, integral, p-test, alternating, ratio, absolute convergence) and applying it.
13. Use partial sums to estimate the sum of a convergent series, and find error bounds where appropriate (e.g., using integrals, the alternating series test and Taylor's remainder).
14. Use power series to represent functions.  Use the ratio test to determine the intervals on which they converge.  Do algebra and calculus with power series.
15. Create Maclaurin series and Taylor series for familiar transcendental functions.
16. Use Maclaurin series and Taylor series to approximate values of transcendental functions and definite integrals.
17. Give "physical" examples to illustrate the distinction between vector and scalar quantities.
18. Represent vectors in two/three dimensions as ordered pairs/triples, as arrows, and by specifying magnitude and direction.
19. Perform vector addition and scalar multiplication both geometrically and symbolically.  Apply these operations to motion problems.
20. Calculate the dot product of vectors, and apply it in geometric and "physical" contexts (angles, projection, work, etc.).

Upon finishing Math 171, the student will be able to…

1. After completing this course, students should be able to:
2. Use problem-solving models and will be able to apply them to concepts introduced throughout the course.
3. Explain the structure of the Real Number system and how this structure relates to learning mathematics.
4. Use various algorithms, mental computations, and electronic computing techniques and will utilize them to solve problems dealing with whole numbers, fractions and decimals.
5. Demonstrate a knowledge of the changing role of technology as it relates to learning and teaching mathematics and will be able to demonstrate concepts using calculators.
6. Implement strategies for helping K-8 students learn the concepts of mathematics.
7. Demonstrate a knowledge of the National Council Teachers of Mathematics Standards document and the Washington’s Essential Academic Learning Requirements in mathematics and explore ways to relate them to mathematical concepts.
8. Use basic geometry and will apply it to solve real world applications.
9. Implement strategies (including language, writing, art, literature, music, etc.) for K-8 students to learn mathematics concepts.

Upon finishing Math 172, the student will be able to…

1. Use problem-solving models and will apply them to concepts introduced throughout the course.
2. Demonstrate a knowledge of the structure of the Real Number system and how this structure relates to learning mathematics
3. Use various algorithms, mental computations, and electronic computing techniques and will be apply them to solve problems dealing with decimals, ratios, proportions, and percents.
4. Apply problem-solving techniques to basic concepts involving probability and statistics.
5. Apply concepts of statistics to gather appropriate data, organize information in charts or graphs, and interpret information from displays of data.
6. Apply probability techniques of experimentation and simulation to make hypotheses, test conjectures and refine theories.
7. Apply standard and non-standard measurement skills to geometric concepts.
8. use basic geometry to solve real world applications.
9. implements strategies (including language, writing, art, literature, music, etc.) for K-8 students to learn mathematics concepts.

Upon successful completion of Math 208, the student should be able to:

1. Solve systems of linear equations -- small ones manually by row reduction techniques and larger ones using technology.
2. Use linear systems to model and analyze applied situations.
3. Perform matrix operations, including matrix inversion.
4. Translate linear systems into matrix equations, and use matrix inverses to solve, where appropriate.
5. Perform vector operations in Rn and interpret them geometrically in R2 and R3.
6. Use vectors to solve "physical" problems.
7. Verify and/or refute the validity of vector space axioms in specific examples.
8. Use the vocabulary of vector spaces (linear combination, span, subspace, linear independence and linear dependence, basis, dimension, and orthogonal) appropriately in R2 and R3.
9. Apply the vocabulary of vector spaces (linear combination, span, subspace, linear independence and linear dependence, basis, dimension, and orthogonal) to specific examples in Rn.
10. Identify and construct examples of linear combinations, spans, subspaces, linear independence and linear dependence, bases, dimension, and orthogonality in spaces of matrices and function spaces.
11. Exemplify linear transformations in R2, R3 and more general settings, and distinguish linear transformation from non-linear mappings.
12. Construct and analyze matrix representations of linear transformations, and relate them to matrix operations.
13. Describe the effect (including null space and image) of linear transformations on sets of vectors, especially in R2 and R3.
14. Compute determinants of 2x2 and 3x3 matrices, and relate them to the geometry of linear transformations and to the solution of linear systems.

Upon successful completion of Math& 238, the student should be able to:

1. Use symbolic methods to find general and particular solutions to first order differential equations using the techniques of separation of variable, integrating factors, power series and Laplace transforms.
2. Use Euler's method to approximate solutions for first order differential equations.
3. Use symbolic methods to find general and particular solutions of second order linear differential equations using the techniques of undetermined coefficients, variation of parameters, power series and Laplace transforms.
4. Use symbolic methods to solve homogeneous first order linear systems.
5. Use direction fields, phase lines and phase portraits to qualitatively analyze the solutions to differential equations.

Upon successful completion of Math& 254, the student should be able to:

1. Visualize, plot and interpret points, lines, vectors, curves, and surfaces in 2-D and 3-D.
2. Translate among rectangular, cylindrical and spherical coordinate systems and state some advantages and disadvantages of each system.
3. Perform basic vector operations and apply these operations.
4. Write equations for and solve problems involving lines and planes and their intersections.
5. Interpret the fundamental ideas of rates of change and accumulation for curves in higher dimensions:
   •  tangent vectors,
   •  arc length,
   •  curvature,
   •  simple line integrals.
6. Interpret the fundamental ideas of rates of change and accumulation for surfaces in higher dimensions:
   •  partial derivatives,
   •  directional derivatives,
   •  tangent planes,
   •  gradient vectors,
   •  max/min applications,
   •  volumes & surface areas.
7. Use CAS and the listed tools to solve multi-step problems and applications.