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Student Learning Outcomes

Discipline: Degree: AS-T - Mathematics - S0333

Course Name	Course Number	Objectives
C++ Language and Object Development	CSCI 140	Students will be able to analyze problems and design algorithms in pseudocode. For a given algorithm students will be able to write modular C++ code using classes in an OOP approach. Students will be able to use given classes and virtual functions in a class hierarchy to create new derived classes and the code that uses them. Students will be able to read, understand and trace the execution of programs written in C++ language.
Calculus and Analytic Geometry	Math 180	Students can evaluate integrals of elementary functions using the method of substitution.
Calculus and Analytic Geometry	Math 280	Students can evaluate multiple integrals to compute volumes, surface areas, moments and centers of mass, flux, and work.
Calculus and Analytic Geometry	Math 180	Students can compute instantaneous rates of change in applications.
Calculus and Analytic Geometry	Math 181	Students can integrate algebraic and transcendental function using a variety of techniques. Students can apply the definite integral to applications.
Calculus and Analytic Geometry	Math 280	Students can compute partial and directional derivatives for functions of several variables.
Calculus and Analytic Geometry	Math 180	Students can evaluate integrals of elementary functions using the method of substitution.
Calculus and Analytic Geometry	Math 181	Students can integrate algebraic and transcendental function using a variety of techniques Students can apply the definite integral to applications. Students can determine convergence of infinite series of various forms using various techniques.
Calculus and Analytic Geometry	Math 180	Students can solve optimization problems. Students can compute instantaneous rates of change in applications Students can differentiate algebraic and transcendental functions
Calculus and Analytic Geometry	Math 280	Students can apply partial derivatives to optimization problems. Students can evaluate multiple integrals to compute volumes, surface areas, moments and centers of mass, flux, and work. Students can analytically describe the physical states of objects with mass traveling in three dimensions. Students can compute partial and directional derivatives for functions of several variables
Calculus and Analytic Geometry	Math 181	Students can describe objects algebraically and geometrically in various 2- or 3-dimensional coordinate systems.
Elementary Statistics	Math 110	Describe and apply probability concepts and distributions. Identify appropriate statistical techniques and use technology-based statistical analysis to describe, interpret, and communicate results. Evaluate ethical issues in statistical practice. Assess how data were collected and recognize how data collection affects what conclusions can be drawn from the data. Identify appropriate graphs and summary statistics for variables and relationships between them and correctly interpret information from graphs and summary statistics. Demonstrate an understanding of, and ability to use, basic ideas of statistical processes, including hypothesis tests and confidence interval estimation.
Elementary Statistics -Honors	Math 110H	Students will be able to use sample statistics to develop a confidence interval for population parameters. Using sample statistics from one or more samples, students will be able to test a claim made about a population parameter. Assess how data were collected and recognize how data collection affects what conclusions can be drawn from the data. Identify appropriate graphs and summary statistics for variables and relationships between them and correctly interpret information from graphs and summary statistics. Describe and apply probability concepts and distributions. Identify appropriate statistical techniques and use technology-based statistical analysis to describe, interpret, and communicate results. Evaluate ethical issues in statistical practice.
Engineering Physics	PHYS 4A	Students will be able to correctly analyze non-constant forces that vary with time or position. Students will be able to propagate uncertainty. Students will be able to experimentally and analytically find the period of a physical pendulum. Students will be able to draw free body diagrams appropriate to the situation presented. Students will be able to integrate with respect to mass over objects and apply that knowledge to be able to solve problems related to center of mass, moment of inertia and gravitational field of objects. Students will be able to write up lab findings scientifically.
Finite Mathematics	Math 120	Students will be able to solve a binomial probability distribution problem. Students will be able to solve a linear programming problem using the geometric approach
Linear Algebra and Differential Equations	Math 285	Identify and solve the following ordinary differential equations (ODEs): separable, 1st order linear. Set up and solve differential equations for the following applications: simple and logistic population growth model, simple electric circuits, mixing, orthogonal trajectories. Plot slope fields and numerically solve 1st order differential equations using Euler's and Runga Kutta methods. Demonstrate the operations of matrix algebra, row operations for linear systems, and the methods of Gaussian Elimination and matrix inversion for solving linear systems. Evaluate determinants using cofactors and row operations. Demonstrate the properties of determinants and matrix inversion using cofactors. Math students feel they have the resources necessary for their success. Students will feel that mathematics is a beneficial part of their education Students can prove and apply facts regarding vector spaces, subspaces, linear independence, bases, and orthogonality. Solve problems pertaining to the definitions of vector space, subspace, span, linear dependence and independence, basis and dimension, row and column space and inner product space. Demonstrate the use of the Gram-Schmidt process for orthogonalization. Solve problems pertaining to the definitions of linear transformation, kernel and range. Compute eigenvalues and eigenvectors. Diagonalize a square matrix, with the special case of orthogonal diagonalization of symmetric matrices. Demonstrate matrix representation of a linear transformation, change of bases. 6. Solve linear differential equations of order n with constant coefficients (homogeneous or non-homogeneous,) the methods of undetermined coefficients and variation of parameters with applications to RLC circuits or mass spring systems. Express a linear system of differential equations in vector form, and then solve the system using eigenvalues and eigenvectors. Analyze non-linear systems numerically, including phase-plane analysis, using a computer algebra system. Apply the Laplace Transform and its inverse, using the rules of the Laplace Transform, along with the 1st Shifting Theorem. Solve linear differential equations with constant coefficients using the Laplace Transform. Solve ODEs using power series.

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