### Mathematics and Statistics Course SLOs

Math101AMath​​101BMath​​111; Stat1

Math 1A – At the conclusion of the course, students will be able to:

• Evaluate limits and use them to find derivatives.
• Evaluate derivatives and interpret derivatives as rates of change and/or slopes of tangent lines.
• Solve applications that require differentiation such as applied optimization and related rates.
• Determine the behavior of a function from its derivatives.
• Evaluate integrals and interpret integrals as total changes and/or bounded areas.
• Compose simple proofs.

Math 1B – At the conclusion of the course, students will be able to:

• Calculate derivatives and integrals of algebraic and transcendental functions.
• Determine the convergence or divergence of sequences and series.
• Demonstrate the ability to apply the appropriate technique to integration and to the determination of convergence of sequences and series.

Math 1C – At the conclusion of the course, students will be able to:

• Compute partial derivatives, the gradient and extrema of functions.
• Evaluate double and triple integrals.

Math 2 – At the conclusion of the course, students will be able to:

• Classify DEs as linear, separable, homogeneous, exact, &c.
• Solve nth-order linear differential equations.
• Solve ordinary differential equations by applying an appropriate technique.

Math 3 – At the conclusion of the course, students will be able to:

• Solve a system of linear equations using matrix methods; Calculate eigenvalues and eigenvectors for a 3×3 matrix.
• Formulate transformations between n-dimensional vector spaces.

Math 9 – At the conclusion of the course, students will be able to:

• Graph a function using the first and second derivatives.
• Solve an application problem that involves the marginal cost, marginal profit, or marginal revenue.
• Solve an application problem that involves optimization.
• Find an equation of the tangent line to the graph of a function.
• Find the area bounded by the graphs of two functions.  One of the functions may be  f(x) = 0.
• Solve an application problem that involves integration.

Math 10 – At the conclusion of the course, students will be able to:

• Demonstrate an understanding of a variety of mathematical ideas and systems.

Math 15 – At the conclusion of the course, students will be able to:

• Demonstrate a depth of understanding of number systems.
• Demonstrate a depth of understanding of Polya’s method for problem solving.

Math 16 – At the conclusion of the course, students will be able to:

• Students will demonstrate an understanding of geometric ideas, basic probability and statistics, and methods of problem solving.

Math 20 – At the conclusion of the course, students will be able to:

• Solve an equation by applying a combination of methods
• Simplify a difference quotient
• Analyze a rational function
• Find the domain of a function
• Find the zeros of a polynomial

Math 21 – At the conclusion of the course, students will be able to:

• Graph and analyze the graph of a trigonometric function
• Solve a trigonometric equation
• Solve an application problem involving right triangles
• Prove an identity
• Find the value of a trigonometric function of an unknown angle given the value of a different trigonometric function of that angle.

Math 25 – At the conclusion of the course, students will be able to:

• Translate word problems into linear programming problems and solve those using the Simplex algorithm.
• Calculate present and future values of account balances, loans and annuities.
• Translate word problems into systems of equations and solve those using matrix methods.
• Solve enumeration problems by applying basic combinatorial principles.

Math 51 – At the conclusion of the course, students will be able to:

• Identify the appropriate definition, postulate, or theorem that justifies a statement in a proof.

Math 52 – At the conclusion of the course, students will be able to:

• Demonstrate understanding of logarithmic properties
• Perform operations on rational expressions
• Analyze and graph a quadratic function
• Solve a problem involving exponential equations
• Solve a problem involving quadratic equations
• Perform operations on radical expressions

Math 52A – At the conclusion of the course, students will be able to:

• Perform operations on rational expressions
• Perform operations on radical expressions
• Solve a quadratic equation by factoring

Math 52B – At the conclusion of the course, students will be able to:

• Demonstrate understanding of logarithmic properties
• Analyze and graph a quadratic function
• Solve a problem involving exponential equations
• Solve a problem involving quadratic equations

Math 58 – At the conclusion of the course, students will be able to:

• Differentiate fallacious and valid arguments.
• Solve problems that use percentages, ratios, indices, tables or graphs and identify abuses.

Math 101 – At the conclusion of the course, students will be able to:

• Derive the equation of a line.
• Solve linear inequalities in one variable.
• Graph and analyze linear equations.
• Translate an application problem into a linear equation or a system of linear equations.
• Perform arithmetic operations on polynomial expressions.
• Apply the properties of integer exponents.
• Solve systems of linear equations.

Math 101A – At the conclusion of the course, students will be able to:

• Derive the equation of a line.
• Solve linear inequalities in one variable.
• Graph and analyze linear equations.
• Translate an application problem into a linear equation.
• Simplify an expression involving rational numbers using order of operations.

Math 101B – At the conclusion of the course, students will be able to:

• Perform arithmetic operations on polynomial expressions.
• Solve linear inequalities in one variable.
• Apply the properties of integer exponents.
• Solve systems of linear equations.
• Translate an application problem into a system of linear equations.

Math 111 – At the conclusion of the course, students will be able to:

• Perform arithmetic operations on signed real numbers.
• Convert between fractions, decimals and percents.
• Identify applications of the field axioms.
• Solve linear equations in one variable.
• Solve applied problems involving percents and proportions.
• Add, subtract, multiply and simplify polynomials.

Stat 1 – At the conclusion of the course, students will be able to:

• Calculate and interpret measures of center and measures of dispersion for given data.
• Find probabilities for applications involving normal random variables.
• Construct and interpret a confidence interval for a population mean or proportion.
• Formulate decisions about rejection or failures to reject hypotheses based on data/information provided.

### Mathematics and Statistics Program SLOs

Computation 1: Solve equations and inequalities

Computation 2: Perform operations on mathematical objects (e.g. numbers, expressions, functions, matrices).

Computation 3: Graph equations, functions, and inequalities

Critical Thinking 1: Solve applied problems using mathematical or statistical methods

Critical Thinking 2: Prove identities and theorems

Critical Thinking 3: Apply definitions, notation and properties of mathematical concepts