# Mathematics SAMPLE Student Learning Outcomes

These learning outcomes are meant only as sample and are not representative of Santa Ana College's learning outcomes.

## MATH 1 – Pre-Calculus | |

1. | Apply concepts of functions to help solve application problems. |

2. | Solve algebraic equations or simplify expressions that contain compositions of
functions. |

3. | Express graphically the behavior of rational functions near asymptotes and at infinity using the concept of the limit. |

## MATH 2 – Pre-Calculus with Analytic Geometry | |

1. | Apply concepts of analytic geometry to help solve application problems. |

2. | Evaluate functions at numerical values and simplify algebraic expressions with
functions evaluated at symbolic values and analyze and simplify compositions of
functions. |

3. | Establish the behavior of rational functions graphically near asymptotes and at
infinity using the concept of the limit. |

## MATH 3A – Calculus I | |

1. | Applications: Construct and solve mathematical models using the derivative. |

2. | Algebra: Evaluate derivatives of many functions and antiderivatives of simple
functions. |

3. | Graphs: Generate solutions to quantitative problems using numerical, graphical,
and algebraic methods. |

## MATH 3B – Calculus II | |

1. | Applications: Construct antiderivatives of many different types of functions and
solve mathematical models using the integral. |

2. | Algebra: Reframe functions as power series and test these series for
convergence. |

3. | Graphs: Generate solutions to problems using parametric and polar
representations of functions. |

## MATH 3C – Calculus III | |

1. | Applications: Construct and interpret models of circulation and force using vector
valued functions. |

2. | Algebra: Evaluate derivatives and integrals of multivariable functions including
the use of Green’s Theorem, Stokes’s Theorem and Gauss’s Theorem. |

3. | Graphs: Create graphs for multivariable and vector valued functions. |

## MATH 3E – Linear Algebra | |

1. | Applications: Diagnose application problems by applying systems of equations to
the problems of curve fitting, electrical circuits, economic models, and
communication technology. |

2. | Algebra: Modify and solve a system of equations using a variation of Gaussian
Elimination and other methods, including the use of matrices. |

3. | Graphs: Construct a basis for a vector space, such as the kernel for a given
transformation or the image of a given matrix. |

## MATH 3F – Differential Equations | |

1. | Applications: Formulate models for various real-world phenomena using first
order, second order and systems of differential equations. |

2. | Algebra: Generate solutions to first order, second order and systems of
differential equations using a variety of different techniques Develop approximate
solutions to first order ordinary differential equations numerically and evaluate the
accuracy of these approximations. |

## MATH 11 – Discrete Mathematics | |

1. | Design algorithms and compute their efficiency. |

2. | Defend conclusions by proving mathematical statements inductively and defining
mathematical concepts recursively. |

3. | Create circuits representing Boolean functions and minimize them using
Karnaugh maps and the Quine-McCluskey method. |

## MATH 13 – Introduction to Statistics | |

1. | Create inferences about populations based on data obtained from samples. |

2. | Decide whether or not a particular analytical methodology is appropriate given a
particular statistical or probabilistic context and justify your response. |

3. | Formulate analyses of graphical relationships between variables in a sample or a
population. |

## MATH 15 – Mathematics for Liberal Arts | |

1. | Applications: Compute, with sophisticated formulas, such quantities as interest
payments for amortized loans. |

2. | Algebra: Solve, using algebraic methods, various types of measurement
problems, for example: perimeter, surface area and/or volume. |

3. | Graphs: Analyze, using a graph of an Euler and/or Hamiltonian Circuit, to decide
on the solvability of such types of circuits. |

## MATH 16A – Calculus for Business and Life/Social Sciences | |

1. | Applications: Construct and solve mathematical applications related to business
using the derivative. |

2. | Algebra: Integrate multiple rules of differentiation to compute derivatives of many
functions. |

3. | Graphs: Analyze the graph of a linear function to identify such quantities as
marginal cost or marginal profit. |

## MATH 16B – Calculus for Business and Life/Social Sciences | |

1. | Applications: Determine solutions to optimization problems, for example find
maximum profit from a combination of labor and capital, by applying the method
of Lagrange multipliers. |

2. | Algebra: Compute derivatives and anti-derivatives of trigonometric functions, and
solve linear differential equations. |

3. | Graphs: Analyze the graphs of multivariable functions for maximum/minimum
problems – be able to report the max/min of the function as well as the
combination of inputs that correspond to the max/min. |

## MATH 50 – Trigonometry | |

1. | Applications: Construct equations involving trigonometric functions to solve
applications. |

2. | Algebra: Assemble solutions to trigonometric equations. |

3. | Graphs: Create graphs of trigonometric functions. |

## MATH 201 – Elementary Algebra | |

1. | Applications: Formulate a linear model of a real world application and use it to
interpolate/extrapolate. Interpret the slope and y-intercept in the context of the
application. |

2. | Algebra: Solve a linear equation involving at least two of the following: fractions,
decimals, parentheses, and like terms for a variable. |

3. | Graphs: Create a linear graph based on given attributes of a line (e.g., two
points, slope and point, slope and y-intercept, etc). Identify key characteristics of
a given linear graph (e.g. slope, y-intercept, x-intercept, etc). (NOTE: include
scaling, table, define variables, etc). |

## MATH 202 – Geometry | |

1. | Apply the properties of parallel lines to solve problems. |

2. | Identify and solve special and similar triangles. |

3. | Apply the properties of circles and special polygons. |

## MATH 203 – Intermediate Algebra | |

1. | Applications: Formulate a nonlinear model (either quadratic or exponential) of a
real world application. Interpret the key characteristics of the graph (vertex,
intercepts, maximum value, minimum value, asymptotes, growth rate, decay rate,
etc.) in the context of the application. |

2. | Algebra: Solve a nonlinear equation (e.g. quadratic, exponential, logarithmic,
absolute value, radical, rational, etc). |

3. | Graphs: Create a graph based on a given nonlinear (e.g. quadratic, exponential,
logarithmic, etc) function and identify key characteristics of the graph (e.g.,
vertex, intercepts, maximum value, minimum value, asymptotes, etc). |

## MATH 208 – Mathematics for Laboratory Sciences | |

1. | Applications: Estimate dosages, concentrations and dilutions. |

2. | Algebra: Interpret scientific notation in the context of solving a proportion problem
algebraically. |

3. | Graphs: Prepare data to be analyzed using a spreadsheet program, in particular,
by use of spreadsheet-generated graphs. |

## MATH 213 – Support for Statistics | |

1. | Create inferences about populations based on data obtained from samples |

2. | For given sampling methods, decide whether or not a particular method of
inference (Hypothesis Test or Confidence Interval) is appropriate and justify the
response. |

3. | Analyze the relationship between 2 variables, using the tools of linear regression. |

## MATH 215 - Support for Pre-Calculus | |

1. | Develop problem solving abilities: Translate words into math language, and
construct an abstract model that describes the problem. (Proof and Deductive
Reasoning skills. |

2. | Create, write and manipulate complex algebraic expressions and general
functions, and solve algebraic and transcendental equations. (Compute, simplify
and solve.) |

3. | Analyze information, and create a graph that is correctly titled and labeled,
appropriately designed, and accurately emphasizes the most
important/interesting characteristics of the graph. |

## MATH 216 - Support for Trigonometry | |

1. | Using reference triangles in the plane, students will be able to find exact values
of all six trigonometric ratios (of any angle measure). |

2. | Analyze information, and create a graph that is correctly titled and labeled,
appropriately designed, and accurately emphasizes the most important aspects.
(Graphing skills). |

3. | Develop problem solving abilities: Translate words into math language, and
construct an abstract model that describes the problem. (Proof and Deductive
Reasoning skills). |

## MATH 221 – Technical Mathematics (Lecture) | |

1. | Applications: Solve application word problems related the career technical fields. |

2. | Algebra: Solve equations in one variable and/or two variables in the context of
real world applications. |

3. | Calculate the lengths of sides, perimeter, area and volume of a geometric figure. |

## MATH 253 – Pre-Algebra | |

1. | Applications: Solve simple real-world application problems involving percentages. |

2. | Algebra: Solve basic linear equations. |

3. | Simplify expressions using order of operations. |

## MATH 261 – Pre-Algebra Foundations | |

1. | Applications: Solve application problems that deal with percentages or
proportions. |

2. | Algebra: Simplify expressions and solve linear equations. |

3. | Graphs: Read and interpret graphs. |

Source: Laney College