# Mathematics

##### Mathematics

**(School of Sciences)**

**MTH 1110 Liberal ArtsMathematics (V)**

4 cr.

This course covers mathematical topics of use and/or interest to students who do not need a technical course in algebra to succeed in sciences or pre-calculus. Topics cover a broad range such as the interpretation of graphical data, basic properties of exponential functions,an introduction to the basics of probability and statistics,game theory,and voting theory, the real number system, geometry and fractals, andmathematics in nature.Prerequisite: three years of high school math or instructor's permission.

**MTH 1111 Elementary Functions I (V)**

4 cr.

Topics include a brief review of elementary algebra, introduction to polynomial, exponential, logarithmic and trigonometric functions using both symbolic and graphic approaches. Emphasis is on applications in a variety of disciplines and solutions of real-world problems. Students planning to continue mathematics receive appropriate preparation. Prerequisite: three years of high school math or instructor's permission.

**MTH 1113Mathematical Ideas I (V)**

4 cr.

Topics selected to give a broad view of mathematics needed for a liberal education. Investigations emphasize mathematics needed by prospective teachers of elementary grades to address the strands:patterns and functions; number sense from whole numbers to real numbers.Prerequisite: three years of high schoolmathematics or instructor's permission.

**MTH 1114Mathematics Ideas II (V)**

4 cr.

Continuation of MTH 1113 for students intending to teach math in elementary grades and for liberal arts education.Topics include basic statistics and probability, measurement, space and shape in geometry. Prerequisite: three years of high schoolmath or instructor's permission.

**MTH 1116 Mathematics for Elementary School Teachers (V)**

4 cr.

Amathematics course for elementary school teachers. Topics include patterns and functions; number sense; geometric shape and measurement; basic statistics and probability. Prerequisite: permission fromthe Education Department.

**MTH 1122 Elementary Functions II**

4 cr.

Precalculus mathematics, further properties of polynomial functions, exponential and logarithmic functions, trigonometric functions and their graphs, trigonometric identities and equations, inverse trigonometric functions, introduction of analytic geometry. Prerequisite: MTH 1111 or placement exam.

**MTH 2211 Short Calculus**

4 cr.

Introduction to limits, continuity, differentiation and integration, applications to other disciplines and solutions of real world problems. This course is designed for students needing basic calculus concepts but not majoring in math. Prerequisite: MTH1111 or placement exam.

**MTH 2221 Calculus I**

4 cr.

Limits, continuity and fundamental theory of differentiation, symbolic and numerical calculations of derivatives, applications of derivatives; definite integrals and Riemann sums. Prerequisite: MTH1122 or placement exam.

**MTH 2222 Calculus II**

4 cr.

Study of numerical integration,applications of definite integrals, improper integrals, sequences and infinite series, basic idea and methods for solving differential equations, and calculus in polar coordinates. Prerequisite: MTH 2221.

**MTH 2401 DiscreteMathematics I**

4 cr.

Elementary graph theory includingmatrix representation; coding and sorting applications; combinations and permutations; voting and apportionment; introduction to logic; elementary algorithm analysis and design; mathematical induction. Prerequisites: MTH 1122 or C++ language or instructor's permission.

**MTH 2777 Topics in Math**

2 cr.

**MTH 3302 Contemporary Geometry**

4 cr.

Foundations of Euclidean geometry, solid geometry; introductions to non-Euclidean geometry; spherical geometry.Course includes dynamic geometry investigations using appropriate software. Prerequisite: MTH 2401 or instructor's permission.

**MTH 3321 Multivariable Calculus**

4 cr.

Topics include functions of several variables,gradients, partial derivatives andmultiple integrals, vector fields, Green's and Stoke's theorems, and applications. Prerequisite: MTH 2222.

**MTH 3322 Linear Algebra**

4 cr.

Further study of systems of linear equations,matrices and determinants,vector spaces and subspaces, linear transformations, eigenvalues and eigenvectors, diagonalization. Prerequisite: MTH 2222 or instructor's permission.

**MTH 3323 Differential Equations**

4 cr.

Introduction to the theory of differential equations, varied methods to solve linear, nonlinear equations, quantitative analysis of solutions of equations. Prerequisites: MTH 2222,MTH 3321.

**MTH 3533 Mathematics Teaching Methods**

4 cr.

This course consists of two portions. Secondary planning for mathematics instruction includes classroom observations and the study of mathematics curriculum, assessment, teaching methods and resources for teaching and learning aids. Highlights ofmath related to high school teaching revisit some important concepts in core math courses. Prerequisites: completion of at least five mathematics courses in the major programincluding Cal. II and DiscreteMath I. Co-requisite: EDU 3800.

**MTH 3535MathMethods Field Experience**

1 cr.

Introduces students to the culture of a high school environment. They observe and assist amath teacher, interview school personnel, talk with students, and teach technology-integrated math lessons and content area reading strategies. Assessment practices are observed and practiced.Co-requisite:MTH 3533.

**MTH 4332 Abstract Algebra I**

4 cr.

Introduction to groups, ring and field theory; group homomorphism and isomorphism, Caley's theorem, and quotient groups,LaGrange's theorem; rings, ideals, ring homomorphismand basic properties of fields.Prerequisite: MTH 3322 or instructor's permission.

**MTH 4341 Topics forMathematics Teachers**

1-4 cr.

Study of mathematics topics of particular interest to teachers of mathematics.

**MTH 4402 DiscreteMathematics II**

2 cr.

Extensions of elementary investigations included in MATH 2401. Students study set theory including principle of inclusion-exclusion; advanced counting techniques and combinatorics; recurrence relations including solving homogeneous linear difference equations; Boolean algebra; graph theory including investigation of isomorphic and homomorphic graphs. Prerequisite: MTH 2401.

**MTH 4405 Numerical Analysis**

4 cr.

Theory for error analysis, numerical methods for solving algebraic equations, differentiation and integration, interpolation and approximation to functions, and solving initial value problems of differential equations. Prerequisites: MTH 2222 and MTH 3322. Students are encouraged to take MTH 3323 before taking MTH 4405.

**MTH 4411 Probability and Statistics I**

4 cr.

A survey course in mathematical probability and statistics. It includes probability distributions and densities, mathematical expectations, functions of random variables, introduction to estimation theory and hypothesis testing and applications. Prerequisite: MTH 2222.

**MTH 4412 Probability and Statistics II**

2 cr.

Study of multivariate distributions, theory of estimation, hypotheses testing, and statistical inference and their applications. Prerequisites: MTH 4411 and MTH 3321.

**MTH 4421 Principles of Analysis I**

4 cr.

Introduction to real analysis. It includes completeness of the real number system, topology of the real line, sequences, convergence, limits, continuity,differentiability and the Riemann integral, the Fundamental Theorem of Calculus. Prerequisites: MTH 3321,MTH 3322.

**MTH 4422 Principles of Analysis II**

2 cr.

Sequences of functions, uniform convergence, the Bounded Convergence Theorem, infinite series, topology of the set of real numbers, Heine-Birel Theorem and metric spaces. Prerequisite: MTH 4421.

**MTH 4432 Abstract Algebra II**

2 cr.

More topics of rings and fields,maximal and principal ideals, complete ordered fields, polynomial rings, factorization in F[x], fields extension. Prerequisite: MTH 4332.

**MTH 4500 Senior Seminar**

2 cr.

This course is required for all Mathematics majors. Under the direction of Mathematics faculty, students pick topics in any area of math, do research/independent reading and write papers for presentation. Prerequisite: instructor's permission.

**MTH 4777 Topics inMath**

2-4 cr.

Concentrated study of various subject areas. Prerequisite: permission of instructor.

**MTH 4999 Independent Study**

1-4 cr.

Research projects for upper-division students. Prerequisite: permission of instructor.