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Student Learning Outcomes

Discipline: Degree: AA - Liberal Arts Emphasis Math - A8989
Course Name Course Number Objectives
C++ Language and Object Development CSCI 140
• 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.
• Students will be able to analyze problems and design algorithms in pseudocode.
• Students will feel that computer science is a beneficial part of their education
• CS students feel they have the resources necessary for their success.
Calculus and Analytic Geometry Math 280
• Students can evaluate multiple integrals to compute volumes, surface areas, moments and centers of mass, flux, and work.
• Students can apply partial derivatives to optimization problems.
• Students can compute partial and directional derivatives for functions of several variables
• Students can analytically describe the physical states of objects with mass traveling in three dimensions.
• Identify and classify extrema and saddle points of functions of several variables, using the second partials test.
• Compute domain of functions of several variables, plot surfaces, level curves and level surfaces for functions of several variables.
• Plot and parameterize space curves, compute velocity and acceleration vectors, decompose acceleration vector into normal and tangential components, compute arc length and curvature.
• Perform vector operation, including linear combinations, dot and cross products and projections.
• Plot points, graph cylinders and quadric surfaces, computer distances and give equations of lines and planes in three dimensional rectangular, cylindrical and spherical coordinate systems.
• Students will feel that mathematics is a beneficial part of their education
• Compute the equations for tangent planes and normal lines to surfaces.
• Compute directional derivatives and the gradient vector, solve application problems using their properties.
• Compute the total differential for a function of several variables, and apply this to error estimation.
• Determine differentiability and evaluate partial derivatives, including the use of Chain Rule.
• Evaluate limits for functions of several variables and test for continuity.
• Math students feel they have the resources necessary for their success.
Calculus and Analytic Geometry Math 181
• Students can describe objects algebraically and geometrically in various 2- or 3-dimensional coordinate systems.
• Students can determine convergence of infinite series of various forms using various techniques.
• Students can apply the definite integral to applications.
• Students can integrate algebraic and transcendental function using a variety of techniques
• Use power series in applications.
• Determine representations of functions as power series including Taylor and Maclaurin series.
• Test for convergence for sequences and series using the integral, comparison, alternating series, ratio, and root tests.
• Plot curves parametrically and in polar coordinates, using calculus to compute associated areas, arc-lengths, and slopes.
• Solve separable differential equations with applications.
• Evaluate indefinite and definite integrals (proper and improper) using integration by parts, trigonometric identities and substitutions, partial fractions, tables, computer algebra systems, and numerical techniques.
• Differentiate hyperbolic functions and integrate functions that result in hyperbolic forms.
• Use definite integrals to calculate areas between curves, volumes - including solids of revolution, work, the mean value of functions, arc lengths, areas of surfaces of revolution, moments, centers of mass, and other physics applications.
• Students will feel that mathematics is a beneficial part of their education
• Math students feel they have the resources necessary for their success.
Calculus and Analytic Geometry Math 180
• Math students feel they have the resources necessary for their success.
• Represent functions verbally, algebraically, numerically and graphically. Construct mathematical models of physical phenomena. Graph functions with transformations. Use logarithmic and exponential functions in applications. Solve calculus problems using a computer algebra system.
• Students will feel that mathematics is a beneficial part of their education
• Students can evaluate integrals of elementary functions using the method of substitution.
• Students can compute instantaneous rates of change in applications
• Students can solve optimization problems.
• Students can differentiate algebraic and transcendental functions
• Evaluate indefinite integrals and definite integrals using the Fundamental Theorem of Calculus. Evaluate integrals using the substitution rule and integration by parts.
• Apply derivatives to rates of change and related rates problems, linear approximations and differentials, increasing and decreasing functions, maximum and minimum values, inflections and concavity, graphing, optimization problems, and Newton's Method. Apply the Mean Value Theorem in example problems. Use L'Hospital's Rule to evaluate limits of indeterminate forms. Use a Computer Algebra Systems in applications of calculus.
• Compute first and higher order derivatives of polynomial, exponential, logarithmic, trigonometric, and inverse trigonometric functions. Evaluate derivatives using the product, quotient and chain rules and implicit differentiation.
• Prove limits using properties of limits and solve problems involving the formal definition of the limits. Solve problems involving continuity of functions. Evaluate limits at infinity and represent these graphically. Use limits to find slopes of tangent lines, velocities, other rates of change and derivatives.
• Students will understand the use of the integral and will be able to accurately integrate a given function as suggested by the notation and/or the wording of the problem.
• Students will understand the use of the derivative and be able to accurately differentiate a given function as suggested by the notation and/or the wording of the problem.
• Solve separable differential equations.
• Analyze a variety of applied problems using calculus.
• Apply calculus techniques to analyze functions of several variables.
• Select and use the appropriate integration technique suitable to given problems.
• Solve real-life problems using the Fundamental Theorem of Calculus.
• Apply the derivative to curve sketching, related rates, and optimization problems.
• Determine the first and higher-order derivatives for functions (algebraic, exponential, logarithmic and combinations of these), explicitly and implicitly.
• Apply the definition of continuity.
• Evaluate the limit of a function.
• Students will feel that mathematics is a beneficial part of their education
• Math students feel they have the resources necessary for their success.
College Algebra Math 130
• Students will be able to graph a function (or relation) that is either polynomial, rational, exponential or logarithmic.
• Students will be able to solve an equations that is either polynomial, rational, radical, exponential, logarithmic, or literal.
• Students will be able to simplify an expression that is either polynomial, rational, radical, exponential or logarithmic.
• Demonstrate properties of matrices.
• Recognize patterns in sequences and series (arithmetic and geometric) to determine terms and find sums, using sigma notation as appropriate.
• Prove statements using mathematical induction.
• Expand powers of binomials using the Binomial Theorem.
• Analyze a variety of applied problems (including variation problems) and work with the resulting equation or function to respond to the problem, using complete sentence responses.
• Solve systems of equations (linear and non-linear) by methods of substitution, elimination, graphing and matrices.
• Math students feel they have the resources necessary for their success.
• Perform operations with functions including composition and determine the domain, range and inverse of a function.
• Students will feel that mathematics is a beneficial part of their education
Fundamentals of Computer Science CSCI 110
• For a given algorithm students will be able to write the C++ code using a modular approach.
• Students will be able to read, understand and trace the execution of programs written in C++ language.
• Students will be able to use data representation for the fundamental data types and perform conversions between binary-hexadecimal-decimal representations.
• Students will be able to use and differentiate between basic concepts of computer hardware and software.
• Create correct code, and debug simple errors in one of the higher level languages (C, C++ or Java.)
• Write, organize and assemble program documentation.
• Demonstrate number system conversion to and from binary, decimal and hexadecimal.
• Describe various data representations.
• Define computer terminology.
• Students will feel that computer science is a beneficial part of their education
• CS students feel they have the resources necessary for their success.
• Utilize appropriate data types and structures.
• Utilize text editors, compilers and IDEs.
• Analyze and design efficient algorithms for problem solving.
• Describe instruction set, computer organization and operating system features.
• Discuss fundamental units of digital computers.
Java Language and Object Oriented Programming CSCI 145
• Students will be able to analyze problems and design appropriate algorithms.
• Demonstrate debugging techniques.
• Develop standards for comparing the efficiency of various algorithms.
• Write, organize and assemble program documentation.
• Students will be able to provide code for a Java class given objects’ attributes and behaviors.
• Students will be able to code provided algorithms using Java language.
• Students will be able to use existing Java classes to perform required tasks.
• Demonstrate the paradigm of object oriented programming.
• Utilize recursion, iteration and arrays.
• Recognize and produce proper Java syntax.
• Code algorithms into the Java language.
• Students will feel that computer science is a beneficial part of their education
• CS students feel they have the resources necessary for their success.
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.
• Students can solve linear differential equations using power series
• Students can diagonalize square matrices and apply these results to the solutions of linear systems of differential equations.
• Solve ODEs using power series.
• 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.
• 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.
• 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.
• 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.
• Students can prove and apply facts regarding vector spaces, subspaces, linear independence, bases, and orthogonality.
• Students can formulate and solve differential equations which model real-world phenomena
• Students can solve non-homogeneous linear differential equations of any order using a variety of methods
• Students will feel that mathematics is a beneficial part of their education
• Math students feel they have the resources necessary for their success.
• Evaluate determinants using cofactors and row operations. Demonstrate the properties of determinants and matrix inversion using cofactors.
• Demonstrate the operations of matrix algebra, row operations for linear systems, and the methods of Gaussian Elimination and matrix inversion for solving linear systems.
Precalculus Mathematics Math 160
• Use the binomial theorem.
• Analyze arithmetic and geometric sequences.
• Solve and graph systems of nonlinear equations.
• Graph conic sections; recognize or derive their properties, and write their equations.
• Find the partial fraction decomposition of rational expressions.
• Math students feel they have the resources necessary for their success.
• Operate with functions.
• Determine the domains of functions.
• Graph functions using translations and reflections.
• Students will feel that mathematics is a beneficial part of their education
• Students will be able to solve different types of trigonometric equations.
• Students will be able to analyze a variety of functions.
• Operate with vectors, including the dot product; use vectors to solve application problems.
• Solve polynomial, rational, exponential, logarithmic, and trigonometric equations.
• Analyze polynomial, rational, exponential, logarithmic, and trigonometric equations.
• Solve for the complex roots of polynomial functions.
• Use linear and quadratic functions to solve application problems.
• Find the inverse of functions
Trigonometry Math 150
• The student will be able to accurately solve trigonometric equations over a given interval, including equations that use multiple angles, identities, and quadratic forms.
• Without the use of a calculator, students will be able to graph the six trigonometric functions in a precise manner, stating the period, amplitude, phase shift, and translation as appropriate.
• Solve problems using vectors and vector operations.
• Apply the principles of trigonometry to problem solving.
• Apply DeMoivre's Theorem to powers and roots of complex numbers.
• Prove and use trigonometric identities.
• Solve trigonometric equations.
• Graph trigonometric and inverse trigonometric functions.
• Apply inverse trigonometric functions.
• Solve right and oblique triangles.
• Evaluate trigonometric functions of angles measured in degrees and radians.
• Students will feel that mathematics is a beneficial part of their education
• Math students feel they have the resources necessary for their success.