**The Master’s College 2015-2016 Catalog**

**128**

**UNDERGRADUATE PROGRAMS**

**MA412 Integrated Review (1)**

A comprehensive review of the undergraduate

mathematics curriculum for the purpose of

preparing students for standardized examinations,

such as the CSET (for prospective teachers), the

GRE (for prospective graduate students), actuarial

examinations (for prospective actuaries), and the

senior subject examination in mathematics. This

course is a capstone integrative course.

*Prerequisite:*

*Senior standing in Mathematics.*

**MA425 Mathematical Modeling (3)**

This course covers the application of mathematical

tools to enlighten and solve selected problems in

the “real world.” Areas may include economics,

finance, life sciences, computer science and physics.

*Prerequisite: MA282.*

**MA445 Real Analysis I (3)**

The first semester of a unified course, this class

covers topology in real space, the axioms of the real

numbers, sequences, limits, continuity, convergence,

and differentiation.

*Prerequisite: MA302.*

**MA448 Real Analysis II (3)**

The optional second semester of a unified course,

this class covers the Riemann integral, the inverse

and implicit function theorems, integration and

other advanced topics of calculus. This course is

recommended for those students who are interested

in pursuing graduate studies in mathematics.

*Prerequisite: MA445.*

**MA453 Abstract Algebra I (3)**

The first semester of a unified course, this class

covers groups, homomorphisms, factor groups,

isomorphisms and free groups.

*Prerequisite: MA302.*

**MA458 Abstract Algebra II (3)**

The optional second semester of a unified course,

this class will cover rings, factor rings, fields, ideals,

factorization, extension fields, automorphisms

and elementary Galois Theory. This course is

recommended for those students who are interested

in pursuing graduate studies in mathematics.

*Prerequisite: MA453.*

**MA463 Introduction to AppliedMathematics (3)**

This course is a broad and systematic introduction to

Applied Mathematics, providing a general framework

Euclidean geometry, constructions, non-Euclidean

geometries and other topics in geometry.

*Prerequisite:*

*MA302.*

**MA355 Number Theory & the History of**

**Mathematics (3)**

This course is designed to acquaint the student with

the widely known theorems, conjectures, unsolved

problems and proofs of number theory. In addition,

the history of mathematics, from the beginning of

recorded civilization to the present, will be covered.

Topics may include divisibility, primes, congruences,

Diophantine equations and arithmetic functions.

*Prerequisite: MA302.*

**MA366 Probability (3)**

A general course in elementary probability theory.

Topics to be covered may include the normal

distribution, random variables, uni- and multi-variate

probability distributions, and the Central Limit

Theorem.

*Prerequisite: MA221.*

**MA368 Mathematical Statistics (3)**

This class covers the mathematical foundations and

some applications of statistical methods. Statistics

make possible data-based decision making based on

the collection, tabulation, analysis, and interpretation

of quantitative and qualitative data. Topics covered

will include sampling and estimation techniques:

consistency, unbiasedness, maximum likelihood,

confidence intervals, hypothesis-testing; type I and

II errors, likelihood ratio tests, test for means and

variances; regression and correlation, Chi-square

tests, decision theory, nonparametric statistics. This

class assumes some prior knowledge of probability

theory.

*Prerequisite: MA366.*

**MA383 Complex Analysis (3)**

This course is an introduction to complex analysis.

Topics to be covered may include complex numbers,

analytic functions, elementary functions, integrals,

Laurent series, residues, poles and applications of

residues.

*Prerequisite: MA302.*

**MA400 Mathematics Seminar (1)**

A lecture/discussion course reviewing recent articles

appearing in mathematical journals accessible to

undergraduate mathematics majors. May be repeated

once for credit. This course is a capstone integrative

course.

*Prerequisite: MA302.*