## Learning Outcomes

### MLO: Mathematical Content

**Calculus and Differential Equations.** Students explain and apply the basic concepts of single and multivariate calculus including the various forms of derivatives and integrals, differential equations, their interconnections and their uses in analyzing and solving real-world problems.
**Discrete Mathematics.** Students perform operations on sets and use basic mathematical logic. Students represent and solve both theoretical and applied problems using such techniques as graph theory, matrices, sequences, linear programming, difference equations and combinatorics.
**Computer Programming.** Students design, develop and document computer programs to solve problems.
**Foundations of Modern Mathematics.** Students explain the nature and purpose of axiomatic systems, utilize various methods of mathematical proof and prove fundamental theorems utilizing various axiomatic systems.
**Statistics and Probability.** Students use a variety of methods and techniques to determine the probability of an event or events, including the use of density functions and associated probabilities of both discrete and continuous probability distributions. Students work with applications of probability to mathematical statistics such as point estimation and hypothesis testing.
**Linear Algebra.** Students set up and solve systems of linear equations using various methods. Students work with vector spaces and linear transformations. Students apply matrix techniques to applied problems from various disciplines.
**Abstract Algebra.** Students use a variety of algebraic representations to model problem situations. Students explain the theory of and operations with groups, rings and fields. Students work with advanced algebraic structures and explain how these manifest themselves within the algebra studied in introductory and pre-college mathematics courses.
**Real and Complex Analysis.** Students explain the underlying set, operations and fundamental axioms that yield the structure of the real and complex number system. Students apply analytic techniques to real-world problems. Students give a rigorous mathematical explanation of the development of calculus from first axioms.
**Area of Concentration Competency.** Students demonstrate depth in a chosen area of mathematics by completing an appropriate sequence of learning experiences.

### MLO 2: Service to the Community

Students demonstrate the ability to combine disciplinary knowledge and community experiences to share the relevance and importance of mathematics with culturally, linguistically, technologically and economically diverse populations in the context of issues of social responsibility, justice, diversity and compassion.

### MLO 3: Problem Solving

Students demonstrate the ability to: (a) place mathematical problems in context and explore their relationship with other problems; (b) solve problems using multiple methods and analyze and evaluate the efficiency of the different methods; (c) generalize solutions where appropriate and justify conclusions; and (d) use appropriate technologies to conduct investigations, make conjectures and solve problems.

### MLO 4: Mathematics as Communication

Students demonstrate the ability to: (a) articulate mathematical ideas verbally and in writing, using appropriate terminology; (b) present mathematical explanations suitable to a variety of audiences with differing levels of mathematical knowledge; (c) analyze and evaluate the mathematical thinking and strategies of others; (d) use clarifying and extending questions to learn and communicate mathematical ideas; and (e) use models, charts, graphs, tables, figures, equations and appropriate technologies to present mathematical ideas and concepts.

### MLO 5: Mathematical Reasoning

Students demonstrate the ability to: (a) reason both deductively and inductively; (b) formulate and test conjectures, construct counter-examples, make valid arguments and judge the validity of mathematical arguments; and (c) present informal and formal proofs in oral and written formats.

### MLO 6: Mathematical Connections

Students demonstrate the ability to: (a) investigate ways mathematical topics are interrelated; (b) apply mathematical thinking and modeling to solve problems that arise in other disciplines; (c) illustrate, when possible, abstract mathematical concepts using applications; (d) recognize how a given mathematical model can represent a variety of situations; (e) create a variety of models to represent a single situation; and (f) understand the interconnectedness of topics in mathematics from a historical perspective.

### MLO 7: Technology

Students demonstrate the ability to: (a) analyze, compare and evaluate the appropriateness of technological tools and their uses in mathematics; (b) use technological tools such as computers, calculators, graphing utilities, video and other interactive programs to learn concepts, explore new theories, conduct investigations, make conjectures and solve problems; and (c) model problem situations and solutions, and develop algorithms (including computer programming).