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Mathematics Major Learning Outcomes

  1. Learning Goal 1: Be able to write clear and correct mathematical proofs. (Communication, critical thinking, ethical reasoning)
    1. Learning Outcome: Understand (and reproduce) rigorous proofs of theorems in the setting of mathematical analysis of one real variable.
    2. Learning Outcome: Develop independently and write solutions to problems and proofs of theorems (in the same setting as Outcome 1) that meet rigorous standards based on content, organization and coherence, argument and support, and style and mechanics.
  2. Learning Goal 2: Be able to utilize technology, such as graphing calculators and symbolic manipulation software, as an aid for solving mathematical problems. (Quantitative literacy, ethical reasoning)
    1. Learning Outcome: Use a graphing calculator to enter a function, display a graph of the function using an appropriate graphing window, find the derivative and definite integral of the function, and solve equations.
    2. Learning Outcome: Use statistical software for exploratory data analysis of a single variable, determine the nature of the relationship between two or more variables by using correlation and regression analyses, and carry out tests of statistical significance.
    3. Learning Outcome: Use geometric software to draw geometric figures, and use the tools of geometric software (including measurement tools) to determine the properties of, and to formulate conjectures about the properties of, geometric figures.
  3. Learning Goal 3: Be able to convert from symbolic to graphical or pictorial representations, and be able to utilize these representations to solve mathematical problems. (Communication, critical thinking)
    1. Learning Outcome: Given a symbolic representation of a mathematical equation or function, be able to convert the symbolic representation into an appropriate graphical or pictorial representation.
    2. Learning Outcome: Given a graphical or pictorial representation of a mathematical equation or function, be able to convert into an appropriate symbolic representation.
    3. Learning Outcome: Given a mathematical function, choose an appropriate representation to determine the properties of the mathematical function.
    4. Learning Outcome: Given a mathematical equation, choose an appropriate representation to solve the equation.
  4. Learning Goal 4: Be proficient in computational and symbolic manipulation. (Critical thinking, quantitative literacy)
    1. Learning Outcome: Be able to determine if two algebraic expressions are algebraically equivalent.
    2. Learning Outcome: Be able to determine a simpler, equivalent form of a symbolic representation of a mathematical expression.
  5. Learning Goal 5: Be able to formulate models corresponding to “real-world” problems, including “ill-posed” problems, and be able to solve the mathematical problems arising from such models. (Communication, critical thinking, quantitative literacy)
    1. Learning Outcome: Translate problems formulated verbally into mathematical functions and equations that capture the essential properties of the verbal problem.
    2. Learning Outcome: Consider the reasonableness of the solution of mathematical problems in light of a given “real-world” problem.
  6. Learning Goal 6: Given a problem related to the mathematics of change, be able to outline a method of solution and carry out detailed correct calculations to arrive at a solution. (Communication, critical thinking, quantitative literacy)
    1. Learning Outcome: Mathematically formulate problems involving the mathematics of change.
    2. Learning Outcome: Differentiate and integrate functions in order to solve problems involving the mathematics of change.
    3. Learning Outcome: Solve multistep algebraic problems (often encountered in problems related to the mathematics of change).