Learning Outcomes

The intended learning outcomes for students pursuing a Bachelor of Science degree in mathematics
are indicated in the following sections: 

1)   Students will know and be able to interrelate a core of basic mathematical concepts.

    1.  Students understand the function concept, and they can apply it in a variety of contexts.
    2.  Students understand the calculus concepts of limit, derivative, and definite integral, and
            they can explain how the three are related.
    3.  Students are able to investigate and describe the behavior of functions defined by
            infinite series.  
    4.  Students know properties of vectors and vector operations in the plane and in space.
    5.  Students know properties of matrix algebra, and they are able to use matrices in a variety
           of contexts.
    6.  Students are familiar with some discrete mathematical concepts and related results.
    7.  Students know basic properties of probability and probability distributions and how these
            are applied to problems involving uncertainty.
    8.  Students know fundamental principles and procedures of data analysis.
    9.  Students are familiar with the fundamental algebraic structures of group, ring, and field
            as well as related results.
 
2)  Students will be able to use a variety of problem solving strategies.

    1.  Students are able to use algebraic techniques to solve problems involving equations,
            systems of equations, and inequalities.
    2.  Students are able to use functions as mathematical models and to investigate their
            behavior analytically, numerically, and graphically.
    3.  Students are able to solve problems using tools of differential and integral calculus.
    4.  Students are able to use vectors and matrix algebra to solve problems involving
            geometric concepts, physical systems, and data analysis.
    5.  Students are able to solve problems using tools of discrete mathematics including
            modular arithmetic, mathematical induction, counting principles, algorithms, and
            graph theory.
    6.  Students are able to use probabilistic reasoning and procedures of statistical analysis
            to solve problems involving data.

3)  Students will be able to construct and communicate valid mathematical arguments.

    1.  Students are able to distinguish between inductive and deductive reasoning.
    2.  Students are able to recognize and follow valid mathematical arguments.
    3.  Students are able to use different methods of proving conjectures, including direct
            argument, contradiction, contrapositive, and mathematical induction.
    4.  Students are able to verify falsity of conjectures by supplying counterexamples.
    5.  Students are able to effectively communicate mathematical reasoning, both orally
            and in writing.
 
4)  Students will be able to apply mathematical skills to problems in other disciplines.

    1.  Students are able to apply methods of calculus to problems in the physical, social, and
            life sciences.
    2.  Students are able to use vectors and matrix algebra to solve problems in the physical
            and social sciences.
    3.  Students are able to use discrete mathematical concepts in the contexts of algorithm
            development and computer programming.
    4.  Students are able to apply procedures of statistical analysis to problems in the physical 
           and social sciences.

 5)  Students will be able to make use of technology as a problem solving tool.

    1.  Students are proficient in the use of a graphing calculator.
    2.  Students are proficient in the use of a computer algebra system.
    3.  Students are experienced in the use of an electronic spreadsheet and statistical
            software.
    4.  Students are able to program computers in a high-level language.