**Learning Outcomes for Mathematics Courses**

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Math 1111 College Algebra

Upon completing this course students should be able to:

1. Produce solutions to various algebraic equations.

2. Demonstrate the use of elementary graphing techniques.

3. Use theorems of algebra to analyze the zeros of polynomials.

4. Describe exponential and logarithmic functions.

Math 1113 Precalculus

Upon completing this course students should be able to:

1. Apply the principles of trigonometry to the solution of equations and verification of identities.

2. Sketch the graphs of the trigonometric functions.

3. Identify the basic properties of vectors.

4. Use matrix properties to solve systems of linear equations.

Math 2240 Survey of Calculus

Upon completing this course students should be able to:

1. Find limits of functions and determine continuity of functions.

2. Find derivatives of algebraic, logarithmic, and exponential functions, and use derivatives to solve applied problems.

3. Find integrals of some algebraic and exponential functions, and use integrals to solve applied problems.

Math 2253 Calculus I

Upon completing this course students should be able to:

1. Find limits of functions and determine continuity of functions.

2. Find derivatives of algebraic and some trigonometric functions, and use derivatives to solve applied problems.

3. Find integrals of some algebraic and trigonometric functions, and use integrals to solve applied problems.

Honors Math 2253 Honors Calculus I

Upon completing this course students should be able to:

1. Find limits of functions and determine continuity of functions.

2. Find derivatives of algebraic and some trigonometric functions, and use derivatives to solve applied problems.

3. Find integrals of some algebraic and trigonometric functions, and use integrals to solve applied problems.

4. Find integrals of some logarithmic and exponential functions, and use integrals to solve applied problems.

5. Demonstrate clear and effective oral and written communication skills as they pertain to course concepts.

Math 2254 Calculus II

Upon completing this course students should be able to:1. Find derivatives and integrals of transcendental functions

2. Apply techniques to evaluate integrals

3. Use tests to determine series convergence

4. Determine Taylor series for common functions

5. Describe curves in parametric form and polar coordinates

Honors Math 2254 Honors Calculus II

Upon completing this course students should be able to:

1. Find indefinite and improper integrals using different integration techniques, apply L'Hopital's rule for indeterminate forms.

2. Use various tests to determine series convergence, perform standard operations with convergent power series, find Taylor and Maclaurin representations.

3. Write parametric equations of conic sections, sketch their graphs in polar and Cartesian coordinates, use conic sections to solve applied problems.

4. Demonstrate clear and effective oral and written communication skills as they pertain to course concepts.

Math 2255 Calculus III

Upon completing this course students should be able to:

1. Define and use vector operations in two and three dimensions.

2. Define and use vector methods to analyze plane and space curves, and curvilinear motion.

3. Define and use the standard techniques of multivariable calculus, both differential and integral, and utilize them to solve selected applied problems.

Math 2260 Probability and Statistics

Upon completing this course students should be able to:

1. Calculate elementary probabilities.

2. Compute probabilities related to normal random variables.

3. Construct confidence intervals.

4. Construct and evaluate hypothesis tests.

Math 2306 Ordinary Differential Equations

Upon completing this course students should be able to:

1. Solve first-order separable and linear differential equations, and use these methods to solve applied problems.

2. Solve higher-order constant-coefficient linear differential equations and systems of differential equations, and use these methods to solve applied problems.

3. Find Laplace transforms and inverse transforms, and apply these to solve differential equations.

4. Find the Fourier series of a function.

Math 2335 Numerical Methods I

Upon completing this course students should be able to:

1. Understand errors in Taylor polynomials, loss of significance errors, and propagation of errors; know how to estimate the errors.

2. Approximate roots of equations using bisection, Newton's method, and method of fixed point iteration; perform error analysis.

3. Have the knowledge of interpolation, extrapolation, numerical integration, and numerical differentiation; know how to approximate definite integrals and derivatives.

Math 2345 Discrete Mathematics

Upon completing this course students should be able to:

1. Write a correct formal proof.

2. Write the converse, contrapositive, and negation of a statement.

3. Determine whether a relation is reflexive, symmetric, or transitive.

4. Identify isomorphism invariants of graphs.

5. Construct minimal spanning trees for weighted graphs using Kruskal's and Prim's algorithms.

Math 3261 Statistical Methods

Upon completing this course students should be able to:

1. Understand Central Limit Theorem and its application to confidence intervals of mean and proportion; conduct hypothesis testing for mean, deviation, and proportion.

2. Understand correlation and regression; know how to perform linear regression analysis.

3. Test hypotheses involving one or two variances by using Chi-square and F distributions; perform one-way and two-way analysis of variance.

Math 3268 Probability Theory

Upon completing this course students should be able to:

1. Understand Axioms of probability, conditional probability, and Bayes rule; know how to compute classical probability using counting techniques.

2. Demonstrate an understanding of the binomial, hypergeometric, geometric, Poisson, normal, student's t, Chi-Square, and F distributions.

3. Understand moment generating function and its application to the proof of the Central Limit Theorem.

Math 3310 Introduction to Advanced Mathematics

Upon completing this course students should be able to:

1. Evaluate logical expressions and perform the basic operations on sets.

2. Use the direct method, the contrapositive method, the contradiction method, and the mathematical induction to write a rigorous mathematical proof.

3. Verify a relation as an equivalence relation and prove properties related to the images and inverse images of sets under a function.

Math 3312 Linear Algebra

Upon completing this course students should be able to:

1. Perform elementary matrix and vector operations in Euclidean n-space and use them in applications.

2. Identify and construct examples of elementary vector space ideas in Euclidean n-space as well as in general vector spaces.

3. Find eigenvalues and eigenvectors and use them in diagonalization problems and other applications.

Math 3320 Introductory Real Analysis I

Upon completing this course students should be able to:

1. Understand the axiomatic description of the field of real numbers and prove theorems from the given set of axioms.

2. Apply the topological structure of the real line in constructing mathematically rigorous proofs.

3. Use a rigorous approach in applying limits to problems on limits of sequences and functions.

Math 3321 Introductory Real Analysis II

Upon completing this course students should be able to:

1. Prove the Mean Value Theorem and the Taylor’s Theorem and apply them in approximating functions.

2. Know the definition of the Riemann integral, prove elementary properties of the Riemann integral and the Fundamental Theorem of Calculus.

3. Describe the pointwise and uniform convergence of series of functions.

Math 3336 Numerical Methods II

Upon completing this course students should be able to:

1. Find approximate solutions of systems of equations utilizing iterative methods.

2. Define and perform near-minimax approximation of functions.

3. State, perform, and understand the theory of, standard numerical solution methods for ordinary differential equations, including the derivation of, and limitations of, error bounds for some of these methods.

Math 3396 Combinatorics

Upon completing this course students should be able to:

1. Use ordinary generating functions to count unordered selections with restrictions.

2. Prove identities combinatorially.

3. Apply theorems on graph coloring and planarity to existence problems.

Math 3496 Number Theory

Upon completing this course students should be able to:

1. Demonstrate their knowledge of divisibility, prime numbers and the Euclidean Algorithm.

2. Solve linear Diophantine equations and congruences of various types, and use the theory of congruences in applications.

3. Prove and apply properties of multiplicative functions such as the Euler phi-function and of quadratic residues.

Math 3596 Topology

Upon completing this course students should be able to:

1. Prove elementary theorems involving sets and functions.

2. Determine whether a topological space has any of various topological properties.

3. Prove elementary theorems involving the concepts of topological space, continuous function, compactness, and connectedness.

Math 3696 Geometry

Upon completing this course students should be able to:

- State Euclid’s Postulates.
- Explain the role of the Parallel Postulate in the development of geometry from classical to modern times.
- Define a projective plane.
- Prove theorems up to modern standards of rigor.

Math 4406 Differential Equations II

Upon completing this course students should be able to:

1. Recognize exact and nearly exact differential forms and solve certain related differential equations.

2. Obtain power series solutions for certain classes of linear ordinary differential equations.

3. Recognize Sturm-Liouville equations, be aware of the existence and uniqueness properties of boundary value problems, and demonstrate the orthogonality property of solutions of Sturm-Liouville equations.

4. Classify second order linear partial differential equations as parabolic, elliptic, or hyperbolic, and obtain solutions to certain equations by the method of separation or Laplace transforms.

Math 4407 Vector Analysis

Upon completing this course students should be able to:

1. Define, and understand the geometry of, vector differential operators and line and surface integrals.

2. State and use the major theorems of vector analysis.

3. Utilize vector analysis techniques to solve selected applied problems.

Math 4417 Functions of a Complex Variable

Upon completing this course students should be able to:

1. Differentiate elementary functions of a complex variable.

2. Perform elementary calculations involving Laurent series for functions of a complex variable.

3. Evaluate elementary contour integrals.

Math 4440 Abstract Algebra

Upon completing this course students should be able to:

1. Classify groups, rings, integral domains, and fields.

2. Apply Lagrange's Theorem to analyze the structure of groups.

3. Relate normal subgroups, homomorphisms, and factor groups.

Math 4451 Capstone Mathematics Project

Upon completing this course students should be able to:

1. Explain a topic, at or above the level of a mathematics course numbered 4000 or above, to their peers in a classroom setting.

2. Apply what they have learned about their topic to articulate solutions to problems that require the use of known mathematics.

3. Summarize their studies in a written paper.