Here are some of the CMU Math Department’s Student Learning Outcomes (SLOs)
that faculty are required include on their course syllabi proceeded by the phrase
Upon satisfactory completion of [The Course], students should be able to:
- Math110 Investigations
- Describe how mathematics can contribute to the solution of problems in the natural world or human society.
- Solve problems that involve multi-step solutions using algorithms or formulas.
- Apply appropriate technologies such as calculators and spreadsheets to perform computations and analyze mathematical concepts.
- Express mathematical analysis symbolically, graphically, and in written language that clarifies/ justifies/ summarizes reasoning.
- Use accurate mathematical language and notation in describing and explaining quantitative problems.
- Apply problem solving and critical thinking skills in the context of quantitative problems.
- Employ mathematical logic and reasoning to analyze claims and determine their validity.
- Communicate methods of solutions and solutions to problems for the clarity of the receiver.
- Investigate real-world scenarios using quantitative methods and technologies.
- Recognize patterns discovered through individual or group investigations and formulate generalizations based on such patterns.
- Implement informed decision-making in the areas of social and financial responsibility using logic and mathematical thinking.
- Employ critical thinking skills, drawing upon prior knowledge when possible, to analyze and confidently explore new and unfamiliar problems.
- Math113 College Algebra
- Identify and describe behavior and properties of functions.
- Choose the type of function (linear, polynomial, rational, exponential, or logarithmic) that best applies in a given scenario.
- Use an appropriate method (algebraic, graphical, or computational) to solve problems involving linear, polynomial, rational, exponential, logarithmic, and inverse functions.
- Solve equations, inequalities, and systems of equations, and interpret solutions in context of applications.
- Sketch graphs of linear, polynomial, rational, exponential, logarithmic, and inverse functions and interpret graphs in context of applications.
- Apply appropriate technologies such as calculators and spreadsheets to perform computations and analyze mathematical concepts.
- Translate between geometric concepts and their algebraic representations.
- Communicate mathematical ideas and solutions to problems using correct mathematical notation and terminology.
- Communicate mathematical analysis symbolically, graphically, and in written language that clarifies/justifies/summarizes reasoning.
- Math119a Algebra for Calculus
- Solve equations and inequalities and interpret solutions in context of applications.
- Sketch and interpret graphs of linear, polynomial, rational, exponential, logarithmic, and inverse functions.
- Use function notation to evaluate expressions and perform operations on functions.
- Identify and describe behavior and properties of functions.
- Apply properties of exponentials and logarithms to simplify and evaluate expressions.
- Translate between geometric concepts and their algebraic representations.
- Communicate mathematical ideas and solutions to problems using correct mathematical notation and terminology.
- Communicate mathematical analysis symbolically, graphically, and in written language that clarifies/justifies/summarizes reasoning.
- Math119b Trigonometry for Calculus
- Apply unit circle and triangle definitions to evaluate trigonometric expressions and functions.
- Identify and describe behavior and properties of trigonometric functions.
- Sketch and interpret graphs of trigonometric functions.
- Solve equations and inequalities and interpret solutions in context of applications.
- Use function notation to evaluate expressions and perform operations on functions.
- Translate between geometric concepts and their algebraic representations.
- Communicate mathematical ideas and solutions to problems using correct mathematical notation and terminology.
- Communicate mathematical analysis symbolically, graphically, and in written language that clarifies/justifies/summarizes reasoning.
- Math130 Trigonometry
- Describe points in the plane using the Cartesian and polar coordinate systems.
- Evaluate trigonometric expressions and functions.
- Sketch and interpret graphs of trigonometric functions.
- Use trigonometric functions to solve problems involving angles.
- Perform basic computations with vectors in two and three dimensions.
- Give analytic descriptions of points, lines, circles and planes.
- Compute distances between points, lines and planes.
- Communicate mathematical ideas and solutions to problems using correct mathematical notation and terminology.
- Math135 Engineering Calculus I
- Determine limits of functions graphically, numerically, and algebraically
- Calculate derivatives by a variety of techniques
- Use basic techniques of integration to find antiderivatives
- Apply the Fundamental Theorem of Calculus to evaluate definite integrals
- Describe properties and behavior of functions using limits, derivatives, and integrals
- Interpret concepts of calculus including limits, derivatives, and integrals
- Use differentiation and integration to solve application problems
- Communicate mathematical ideas and solutions to problems using correct mathematical notation and terminology
- Communicate mathematical analysis symbolically, graphically, and in written language that clarifies/justifies/summarizes reasoning
- Math136 Engineering Calculus II
- Perform the calculus of exponential, logarithmic, and inverse trigonometric functions.
- Compute integrals, including improper integrals, by a variety of techniques, such as integration by parts, trigonometric substitution, partial fractions, and using technology.
- Compute limits of sequences and sums of series.
- Determine convergence or divergence of series using a variety of tests, such as the divergence test, integral test, ratio/root tests, and the alternating series test.
- Represent functions by power series, and vice versa.
- Apply numerical methods to approximate integrals and sums of series.
- Solve application problems using differentiation and integration.
- Communicate mathematical ideas and solutions to problems using correct mathematical notation and terminology.
- Communicate mathematical analysis symbolically, graphically, and in written language that clarifies/justifies/summarizes reasoning.
- Math253 College Algebra
- Describe lines, planes, and space curves analytically in the three-dimensional coordinate system.
- Evaluate and interpret the geometric meaning behind partial derivatives, directional derivatives, and gradients of functions of several variables.
- Determine maxima and minima of scalar-valued functions.
- Set up and evaluate multiple integrals of scalar-valued functions in 2 and 3 dimensions, in rectangular, polar, cylindrical, and spherical coordinates.
- Integrate functions of several variables by a variety of methods, including change of variable and changing the order of integration.
- Set up and evaluate line integrals and surface integrals, and interpret them in terms of applications, such as work or flux.
- Evaluate integrals using Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem.
- Communicate mathematical ideas and solutions to problems using correct mathematical notation and terminology.
- Communicate mathematical analysis symbolically, graphically, and in written language that clarifies/justifies/summarizes reasoning.