|
|
Programs of Study
People with
backgrounds in mathematics are in great demand for jobs that
require the ability to think analytically. In particular,
mathematics is essential to the fields of engineering and
natural science, business and finance, medicine, economics and
social sciences.
Mathematics majors at Austin Peay choose from three
concentration areas:
mathematics,
mathematics education,
and
statistics. All three
concentrations require a major core of thirty one semester
hours consisting of
CSCI 1010:
Introduction to Programming I
(3)
Description:
History of computing, computer organization, computer
applications, algorithm design, stepwise refinement of
algorithms, structured programming using C++, array
representation of data, processing of character data, text file
processing, subprograms, and parameter passing.
MATH 1910: Calculus and Analytic
Geometry (5)
Prerequisite:
Four years of high school mathematics including trigonometry
Description:
Elements of plane analytic geometry, functions, limits,
derivatives of algebraic and trigonometric functions,
integration, and applications.
MATH 1920: Calculus and Analytic
Geometry (5)
Prerequisite:
Math 1910
Description:
Polar coordinates, numerical
integration, infinite series, techniques of integration,
improper integral, conic sections, and transcendental functions.
MATH 2110: Calculus (3)
Prerequisite:
Math 1920
Description:
Three dimensional vectors, partial
derivatives, multiple integration, and vector calculus.
MATH 3010: Introduction to Math Reasoning (3)
Prerequisite: MATH 1920
Description: Topics include inductive and deductive
reasoning, symbolic logic, truth tables, set theory, and
functions, with emphasis on various techniques in proving
mathematical theorems. Applications to geometry, number theory,
algebra, analysis, and topology.
MATH 3450: Linear Algebra
Prerequisite:
Math 1920
Description: Systems of
linear equations, determinants, vector spaces with emphasis on
finite-dimensional spaces, linear transformations, similarity,
eigenvalues and eigenvectors, diagonalization, quadratic forms,
numerical methods, and applications.
MATH 4240: Probability
(3)
Prerequisite: MATH 1920
Description:
A mathematical introduction to probability: sample spaces; probability
functions, counting techniques; conditional probability; independence,
total probability and Bayes's rule; discrete and continuous random
variables, expectation, median, variance; joint and conditional
distributions; moment generating functions; laws of large numbers and
the central limit theorem.
MATH 4450: Mathematical Models
MATH 4810: Senior Seminar
Please
refer to the four-year
course schedule for planning purposes. In
addition to the major core, each student selects an area
of concentration. Each concentration requires additional
coursework.
|
Concentration in Mathematics
Mathematics provides elegant and effective
tools for solving problems in virtually every area of human endeavor,
from the sciences to business and economics to the social sciences and
is especially appealing to students who like to solve problems. The
purpose of the Mathematics concentration is to give students an
understanding of the structure of mathematics, to stimulate their
interest in research, and to prepare them for later work. Students can
use their background in mathematics as an entry to other fields such as
physics, computer science, software engineering, economics, business,
finance, medicine or law. We invite you to join us in exploring the
fascinating world of mathematics and its applications.
The following courses
are required for the concentration in mathematics:
MATH 3120: Differential Equations I
(3)
Prerequisite: MATH 2110
Description: First order differential equations and
applications, linear equations of higher order and applications, series
solutions of differential equations, Bessel functions and other
classical functions obtained by series solutions.
MATH 3130: Differential Equations II
(3)
Prerequisite: MATH 3120
Description: The Laplace transform and its application to
differential equations, systems of linear differential equations,
numerical methods. Fourier series and the solution of boundary value
problems involving partial differential equations such as the heat
equation and the wave equation.
MATH
4250: Mathematical Statistics
(3)
Prerequisite: MATH 4240
Description: A mathematical treatment of
statistics including;: properties of estimators; maximum likelihood
estimation; confidence intervals; hypothesis testing; analysis of
categorical data; non-parametric statistics.
MATH
4500: Modern Algebra
(3)
Prerequisite: MATH 1920
Description: Relations, maps, abstract algebras, groups, rings,
integral domains, order, morphisms, fields, and factorization.
Also required: one 3-hour
approved math elective at the 3000 level and one
3-hour approved math
elective at the 4000 level. |
|
Concentration in Mathematics Education
The Mathematics
Education concentration leads to a secondary certification in
mathematics. The secondary certification licensure is designed for
individuals desiring to teach mathematics in grades 7-12 in both middle
and high school settings. Additional coursework in education is also
required.
The following courses
are required for the concentration in mathematics education:
MATH 3000: Discrete Mathematics
(3)
Prerequisites: MATH 1820 or 1920, or permission of instructor
Description: The study of algorithms, counting methods and
combinatorics, graph theory, trees, Boolean algebras and combinatorial
circuits.
MATH 3630: College Geometry (3)
Prerequisites: MATH 1910 and one year of high school geometry
Description: An introduction to modern elementary geometry,
transformational geometry, projective geometry, non-Euclidean geometry,
and foundations of geometry.
MATH
4010: History of Mathematics (3)
Prerequisite:
Permission of instructor
Description: Development of elementary mathematics and a study
of the individuals who contributed to it.
MATH 4110: Number Theory (3)
Prerequisite: MATH 1920
Description: Divisibility, properties of primes, analysis of
congruence, quadratic residues, and Diophantine analysis.
MATH 4400: The Teaching of Secondary School
Mathematics
(3)
Prerequisites: Provisional admission to teacher education; 22 hours
of mathematics courses in the major.
Corequisite: MATH 3630
Description: Basic strategies for teaching mathematics
and for evaluating mathematics teaching. Particular emphasis will be
placed upon the current literature pertaining to these strategies. Field
experience required.
MATH 4200: Mathematics Content and Pedagogy for Middle School
Prerequisites: Provisional admission
to Teacher Education and MATH 3630 or MATH 1410, 1420
Description: Using appropriate technology, students will
investigate and apply concepts of algebra, geometry, trigonometry,
probability, and calculus. The course will also address pedagogy in the
middle school mathematics classroom. Field experience required.
MATH 3250: Statistical Methods I (3)
Prerequisite: MATH 1910
Description:
An introduction to sampling and design methods, descriptive statistics,
basic probability and probability distributions, parametric and
non-parametric estimation and hypothesis tests, tests for
goodness-of-fit and independence, utilization of Minitab and SAS.
|
Concentration in Statistics
Statistics is the the
science of gathering and analyzing data. Statisticians are
employed all over the world in many capacities: to determine
effectiveness and safety of new medicines for pharmaceutical companies;
to control quality in manufacturing processes; to determine policy
premiums and estimate probable payoffs for insurance companies; to
analyze consumer demand; to plan and develop services for various
segments of society by government agencies.
For more
information on careers in statistics, please visit the website for the
American Statistical Association:
http://www.amstat.org/careers
Although there are
jobs for statisticians with undergraduate degrees, a number of employers
require an advanced degree. The statistics concentration at Austin
Peay provides
excellent preparation for work at the Master's level; our graduates have
gone to graduate school in statistics or taken actuary exams.
In addition to the
mathematics core courses, the following courses
are required for the concentration in statistics:
MATH 3250: Statistical Methods I (3)
Prerequisite: MATH 1910
Description:
An introduction to sampling and design methods, descriptive statistics,
basic probability and probability distributions, parametric and
non-parametric estimation and hypothesis tests, tests for
goodness-of-fit and independence, utilization of Minitab and SAS.
MATH 3260:
Statistical Methods II
(3)
Prerequisite: MATH 3250
Description: Analysis of variance and multiple comparisons,
elementary regression models, multiple regression and the general linear
model, logistic regression.
MATH 3270: Experimental
Design
(3)
Prerequisite: MATH 3260
Description:
Design concepts for experiments and studies: ANOVA for standard designs;
analysis of covariance and other experimental designs.
MATH 4250: Mathematical
Statistics
(3)
Prerequisite: MATH 4240
Description: A mathematical treatment of
statistics including;: properties of estimators; maximum likelihood
estimation; confidence intervals; hypothesis testing; analysis of
categorical data; non-parametric statistics.
Also required:
six hours of
approved upper division electives, preferably including
MATH 4260: Stochastic
Processes
(3)
Prerequisite:
MATH
4240
Description:
An introduction to stochastic processes and their applications: Poisson
and compound Poisson processes; discrete and continuous time Markov
chains; renewal theory; random walks and Brownian motion.
MATH 4270: Nonparametric
Statistics
(3)
Prerequisite: MATH 4240
Description: Distribution free techniques for estimation of
parameters and comparison of populations. |
