MLO 1 Mathematical Content

  1. 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. 
  2. 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.
  3. Computer Programming. Students design, develop and document computer programs to solve problems.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.

  9. Area of Concentration Competency. Students demonstrate depth in a chosen area of mathematics by completing an appropriate sequence of learning experiences.

Required Courses