In brief terms, mathematics is not something a student takes, but rather something which he or she creates. Whether a student wants to teach math, plans graduate study, plans to apply mathematics in a career in industry or desires the ability to reason logically and analytically, the study of mathematics adds up to an intellectual experience which, from the abacus to the rocket, has been essential to civilization.
The Mathematics Department offers an undergraduate program in
Mathematics. Students may prepare for graduate study or for careers in
secondary education or industry. Students may also prepare to teach
elementary grades and select a Mathematics minor.
Chair: Guanshen Ren, Ph.D.
Majors Core courses required for all Mathematics majors: MTH 2221, 2222, 3321, 3322, 3401, 4332 and 4411. In addition students select one option below:
Preparation for middle/secondary teaching: MTH 3302, 3533, 3535, 4421 and two credits of upper division electives of math; CIS 2085 or demonstrated mastery of a high level computer language approved by the department. Students should also see the Secondary Education Licensure Program requirements published by the Education Department.
Preparation for graduate school or general job opportunities: MTH 4421 and 10 credits of upper division electives of math; CIS 2085. Additional electives are encouraged.
Other options for a major may be designed by the individual student in consultation with the department. Programs must be approved by the Mathematics Department and contain at least 10 credits of upper level math electives and a CIS course.
All Mathematics majors are required to take MTH 4500-Senior Seminar to do independent reading or research and present their papers in their junior or senior year. Mathematics majors are encouraged to take more computer courses than the minimum required. Consult with the Mathematics Department for appropriate courses.
Minor Courses required for Mathematics minors: MTH 2221, 2222, 3322, 3401 and six credits of electives of upper level math courses approved by the Mathematics Department.
This specialty is designed to give a breadth of study in mathematics suitable for teaching math in grades 5-8. Students must apply for admission to this concentration and obtain approval of the elective courses from the Mathematics Department to insure an appropriate balance of courses.
The requirements are a minimum total of 20 credits in Mathematics courses numbered above 1111 approved by the Mathematics Department, including:
Admission and Retention
Students admitted to the major must have an overall 2.0 GPA and a
minimum grade of C in all required Math courses. Students must keep a
minimum of C in all courses required for the major and remain in good
academic standing with the College to maintain status as a Mathematics
major.
Program Outcomes
Mathematics major graduates will be able to:
MTH 1110 Liberal Arts Mathematics (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, and mathematics 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 1113 Mathematical 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 school mathematics or
instructor's permission.
MTH 1114 Mathematics 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 school math or instructor's
permission.
MTH 1116 Mathematics for Elementary School Teachers 4 cr.
A mathematics course for elementary school teachers. Topics include
patterns and functions; number sense; geometric shape and measurement;
basic statistics and probability. Prerequisite: permission from the
Education Department. For EDU majors only.
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 score.
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 score.
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
score.
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 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
3401 or instructor's permission.
MTH 3321 Multivariable Calculus 4 cr.
Topics include functions of several variables, gradients, partial
derivatives and multiple 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 3401 Discrete Mathematics I 4 cr.
Elementary graph theory including matrix 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 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 of math related to high
school teaching revisit some important concepts in core math courses.
Prerequisites: completion of at least five mathematics courses in the
major program including Cal. II and Discrete Math I. Pre or
corequisites: EDU 3800 and 3535.
MTH 3535 Math Methods Field Experience 1 cr.
Introduces students to the culture of a high school environment. They
observe and assist a math 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 homomorphism and basic properties of fields.
Prerequisite: MTH 3322 or instructor's permission.
MTH 4341 Topics for Mathematics Teachers 1-4 cr.
Study of mathematics topics of particular interest to teachers of
mathematics.
MTH 4402 Discrete Mathematics II 2 cr.
Extensions of elementary investigations included in MATH 3401. 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 3401
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 in Math 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.
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