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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 pseudo code.
• 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.
• For a given algorithm students will be able to write modular C++ code using classes in an OOP approach.
• Students will be able to read, understand and trace the execution of programs written in C++ language.
• CS students feel they have the resources necessary for their success.
• Students will feel that computer science is a beneficial part of their education
Calculus and Analytic Geometry Math 180
• Students can compute instantaneous rates of change in applications
• Students can evaluate integrals of elementary functions using the method of substitution.
• Students can differentiate algebraic and transcendental functions
• Students can solve optimization problems.
• Math students feel they have the resources necessary for their success.
• Students will feel that mathematics is a beneficial part of their education
• 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.
• 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.
• 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.
• 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.
• Evaluate indefinite integrals and definite integrals using the Fundamental Theorem of Calculus. Evaluate integrals using the substitution rule and integration by parts.
Calculus and Analytic Geometry Math 181
• Students can determine convergence of infinite series of various forms using various techniques.
• Students can describe objects algebraically and geometrically in various 2- or 3-dimensional coordinate systems.
• Students can integrate algebraic and transcendental function using a variety of techniques
• Students can apply the definite integral to applications.
• Math students feel they have the resources necessary for their success.
• Students will feel that mathematics is a beneficial part of their education
• 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.
• Differentiate hyperbolic functions and integrate functions that result in hyperbolic forms.
• 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.
• Solve separable differential equations with applications.
• Plot curves parametrically and in polar coordinates, using calculus to compute associated areas, arc-lengths, and slopes.
• Test for convergence for sequences and series using the integral, comparison, alternating series, ratio, and root tests.
• Determine representations of functions as power series including Taylor and Maclaurin series.
• Use power series in applications.
Calculus and Analytic Geometry Math 280
• 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
• 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.
• Math students feel they have the resources necessary for their success.
• Students will feel that mathematics is a beneficial part of their education
• 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.
• Perform vector operation, including linear combinations, dot and cross products and projections.
• Plot and parameterize space curves, compute velocity and acceleration vectors, decompose acceleration vector into normal and tangential components, compute arc length and curvature.?
• Compute domain of functions of several variables, plot surfaces, level curves and level surfaces for functions of several variables. ?
• Evaluate limits for functions of several variables and test for continuity.?
• Determine differentiability and evaluate partial derivatives, including the use of Chain Rule.
• Compute the total differential for a function of several variables, and apply this to error estimation.
• Compute directional derivatives and the gradient vector, solve application problems using their properties. ?
• Compute the equations for tangent planes and normal lines to surfaces.?
• Identify and classify extrema and saddle points of functions of several variables, using the second partials test.
Elementary Statistics Math 110
• Determine the appropriate statistical methods by data type and number of populations or treatments.
• Utilize statistical techniques with a variety of applications that pertain to business, the social, natural and physical sciences.
• Students will be able to determine descriptive statistics from a sample
• 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.
• Using bivariate data, students will be able to determine whether a significant linear correlation exists between two variables and determine the equation of the regression line.
• Math 110 students will feel comfortable in their math class.
• Math 110 students will demonstrate the thinking skill of accurate self-assessment.
• Math 110 students will feel that mathematics is a beneficial part of their education.
• Math 110 students will feel they have the resources necessary for their success.
• Math 110 students will demonstrate the ability and willingness to take the steps necessary to succeed in their math class.
• Define basic statistical terms and notation.
• Describe the proper methods of sampling.
• Describe the distributions of quantitative data in terms of center, shape, and spread.
• Infer from observational and experimental studies.
• Explain the basic concepts of probability theory and calculate probabilities.
• Employ the principles of inferential statistics in estimation and hypothesis testing.
• Utilize computer technology in statistical analyses.
Elementary Statistics -Honors Math 110H
• Students will be able to determine descriptive statistics from a sample.
• 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
• Using bivariate data, students will be able to determine whether a significant linear correlation exists between two variables and determine the equation of the regression line.
• Math 110H students will feel comfortable in their math class.
• Math 110H students will demonstrate the thinking skill of accurate self-assessment.
• Math 110H students will feel that mathematics is a beneficial part of their education.
• Math 110H students will feel they have the resources necessary for their success.
• Math 110H students will demonstrate the ability and willingness to take the steps necessary to succeed in their math class.
• Define basic statistical terms and notation.
• Describe the proper methods of sampling.
• Describe the distributions of quantitative data in terms of center, shape, and spread.
• Infer from observational and experimental studies.
• Explain the basic concepts of probability theory and calculate probabilities.
• Determine the appropriate statistical methods by data type and number of populations or treatments.
• Employ the principles of inferential statistics in estimation and hypothesis testing.
• Utilize statistical techniques with a variety of applications that pertain to business, the social, natural and physical sciences.
• Utilize computer technology in statistical analyses.
• Demonstrate ability to combine appropriate data gathering techniques and ability to express statistical conclusions in formal writing to complete a large, semester-long project.
Engineering Physics PHYS 4A
• Physics 4A students will be able to calculate the moment of inertia of a typical continuous body.
• Students will be able to apply the material from the course to real life situations.
• Students will be able to design an experiment to find the rotational inertia of an object.
• Students will be able to propagate uncertainty.
• Students will analytically predict the period of a physical pendulum, then design an experiment to measure the period.
Finite Mathematics Math 120
• Students will be able to solve a linear programming problem using the geometric approach
• Students will be able to solve a binomial probability distribution problem.
• Math students feel they have the resources necessary for their success.
• Students will feel that mathematics is a beneficial part of their education
• Apply techniques of mathematical modeling to problems from business, economics and social sciences using formulas, graphs, and systems of equations.
• Apply linear programming techniques for maximizing and minimizing linear functions.
• Apply formulas for calculating interest, present value, annuities, and sinking funds, as well as determine payments and lump sum deposits.
• Translate large amounts of real life data into mathematical models involving matrices, and use matrix theory to manipulate data.
• Propose appropriate counting models involving sets, permutations, and combinations for situations where straightforward counting is impractical.
• Formulate probabilistic models and calculate the probability of various events.
• Develop models that use Markov chains to study patterns for the future and to make predictions.
• Analyze, organize, and interpret numerical data.
• Students will be able to solve a linear programming problem using the simplex approach.
Linear Algebra and Differential Equations Math 285
• Students can solve non-homogeneous linear differential equations of any order using a variety of methods
• Students can formulate and solve differential equations which model real-world phenomena
• Students can diagonalize square matrices and apply these results to the solutions of linear systems of differential equations.
• Students can solve linear differential equations using power series
• Students can prove and apply facts regarding vector spaces, subspaces, linear independence, bases, and orthogonality.
• Math students feel they have the resources necessary for their success.
• Students will feel that mathematics is a beneficial part of their education
• 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.
• 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.