Below are the descriptions of each class typically included
in the Masters of Science of Mathematics. As always, the official descriptions are in the Hardin-Simmons
University Graduate Catalog.
the first summer, the program builds the graduate level foundation of
Introduction of Topology and Advanced Topics in Calculus I. In these courses, students review and build on
their abilities to write mathematical proofs and their knowledge of calculus.
the fall, we will continue our study with Advanced Topics of Calculus II. Then in the spring, we turn our attention to
Linear Algebra. After this first year
foundation, we will be ready to study the three major foci of the program
Real Analysis I and II:
Analysis is the typical foundation of advanced mathematics found in most
graduate programs across the United States.
Mathematical Modeling with
Differential Equations I and II: Much of mathematics was developed to solve a specific
problem, which is the focus of applied
mathematics. To apply mathematics
correctly, one must understand and develop the necessary theory. The goal
is not the development of mathematics, but the correct and appropriate
applications of mathematics.
Mathematical Statistics I
To teach or use statistics, a strong understanding of the
theory of statistics is required. Mathematical
Statistics focuses on the mathematical foundations of statistics typically
taught at the undergraduate level.
MATH 5301 Introduction to Topology: Topological
spaces, continuous functions, metric spaces, connectedness, compactness, separation
axioms, fundamental group, covering spaces, metrication theorems. The focus of the course is on proving theorems.
Introduction to Topology covers the
mathematical background for Real Analysis I and II. By first focusing on a review of set theory
and the structure of the real number line, the course provides the student with
a mathematical foundation for understanding the proofs of Real Analysis. The course then extends this foundation in
additional topics of topology.
The course is focused on proofs,
refreshing the student’s ability to read, understand, create and write proofs
using a correct structure and mathematical language.
MATH 5302 Topics Advanced Topics in
Calculus I: Sequences and series of functions, multiple integrals, improper
multiple integrals, functions of several variables, extreme value problems, and
implicit function theorems. The focus of
this course will be the proofs of calculus and advanced computational skills.
MATH 5103: The historical development
of mathematics in a cultural context.
Emphasis will be on the developments of algebra and analytical geometry up
to the discovery of calculus.
MATH 5104: The historical development
of mathematics in a cultural context. Emphasis will be on the developments of differential and integral
Knowing the history of mathematics,
doing problems in their original context and notation, leads to deeper
appreciation of the beauty, power, and effectiveness of today’s mathematics. This course is primarily a one unit reading
course with evaluation based on discussion and assignments.
6305: Linear Algebra: Matrix algebra, eigenvalues and eigenvectors, canonical
forms, orthogonal and unitary transformations, and quadratic forms. Proofs and
applications of these concepts
The theory and power of matrices and
the theory of linear functionals have all the structure found in algebra. A strong understanding of Linear Algebra will
increase the teacher’s abilities in multiple dimension calculus, Mathematical
Statistics, Real Analysis, and Mathematical Modeling.
MATH 6310: Mathematical
Statistics I: Random Variables, Probability, Sampling Distributions, Limiting
Distributions, Point Estimation, Interval Estimation.
MATH 6312: Mathematical Statistics II:
A continuation of MATH 6310. Hypothesis Testing, General Linear Models,
Analysis of Variance, Empirical Methods
Statistics is increasingly important in
today’s society. An instructor should
know the theoretical background of statistics, and know the importance of satisfying
the hypothesis before applying a statistical method.
MATH 6320: The course emphasizes
applications of modeling and analysis for deterministic and stochastic
biological systems. Analysis includes equilibria, stability, phase-plane
methods, limit-cycles, bifurcations, separation of variables. Applications
include but are not limited to continuous and discrete-time models for
population growth, epidemiology, predator-prey, age-structure, Markov chains,
MATH 6321: A continuation of
Mathematical Modeling with Differential Equations I.
mathematics requires understanding, developing a strong understanding of the
relevant theory and then using this mathematical knowledge to solve significant
problems.This course uses theory of
MATH 6340: Borel sets, measure and
measurable sets, measurable functions, and the Lebesgue integral.
MATH 6341: Real Analysis II is a
continuation of Real Analysis I. Function spaces, abstract measure, and differentiation.
Real Analysis is considered an
extension of continuous mathematics beyond Calculus I, II and II and beyond
Differential Equations (undergraduate level).Real Analysis is, in some sense, what comes after calculus and the
related theory. One specific example:
Real Analysis extends the Riemann integral found in Calculus I to the more general
MATH 6150: Summary review of topics
from MATH 6310, 6312, 6320, 6321, 6340, and 6341 with a comprehensive exam.
Description is in the Graduate Catalog for the year you are admitted into the
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