Formulate Taylor Series to approximate functions, errors, and their upper bounds.
Devise algorithms to locate approximated roots of equations and numerically solve linear systems of equations.
Analyze engineering data using the least squares method.
Use polynomials to interpolate collected precise engineering data or approximate function.
Program algorithms to compute the derivative and the integral of a given function, estimate the approximation error involved and upper bound, and interpret engineering ordinary and partial differential equations.
Identify relationships among methods, algorithms, and computer errors.
Apply numerical and computer programming tools to solve common engineering problems.
Define basic concepts of topology such as set theory, open, closed, closure, interior and boundary of a set.
Distinguish between a metric topology a nonmetrizable topology.
Decide whether a given function is continuous.
Define and apply connectedness, compactness and Tychonoff theorem.
Distinguish between countability and separation axioms including countable basis, countable dense subsets, normal spaces, Urysohn lemma and Tietze extension theorem.
Explain the metrization problem and Urysohn Metrization theorem.
Recognize some properties and applications of complete metric spaces.
Define and describe basic concepts and graph theory terminology: induced subgraphs, cliques, matchings, covers in graphs, graph coloring.
Recognize different families of graphs and their properties such as Hamiltonian, Eulerian and planar Graphs.
Describe automorphism groups and different types of graph matrices and their use.
Solve problems involving vertex and edge connectivity, planarity and crossing numbers.
Construct spanning trees, matching, and different matrices.
Apply different proof techniques in theorems and exercises.
Apply Graph Theory to solve and model real world problems and Networks.
Distinguish between a sample and a population and between a statistic and a parameter and classify business data into the most appropriate type and measurement levels.
Organize, manage, and present data.
Analyze statistical data graphically and analyze statistical data using measures of central tendency, dispersion, and location manually and by MINITAB.
Demonstrate an understanding of the basic concepts of probability and random variables. and explain the basic probability rules, including additive and multiplicative laws, using the terms, independent and mutually exclusive events and calculate expected values for continuous and discrete probability distribution models.
Recognize and use the correct probability distribution model for a particular business application manually and by MINITAB.
Understand the concept of the sampling distribution of a statistic, and in particular describe the behavior of the sample mean.
Understand the foundations for classical inference involving confidence intervals manually and by MINITAB.