# MATHEMATICS

**MA 049. ARITHMETIC SKILLS IMPROVEMENT 2 HRS.**

This course is for students whose Gateway, a required departmental

examination for MA307, scores indicate a need for improving

arithmetic skills prior to reenrolling in MA307 or enrolling in MA308.

Course content includes arithmetic skills, including addition,

subtraction, multiplication, and division of fractions and decimals;

percentages and their applications; and geometric concepts such as area

and perimeter.

**MA 095. BEGINNING ALGEBRA 3 HRS.**

(Prerequisite, for students whose ACT scores and/or departmental

screening examination indicate basic need for computational and

algebraic skills prior to enrollment in the proper general education

course.) Review of computational skills in the arithmetic of whole

numbers, fractions, and decimals. Review of proportion and percent

concepts. Review of basic algebra skills including signed numbers,

algebraic expressions and simplification, laws of algebra, factoring,

equation solving, graphing, and formula usage. Computer aided

instruction will enhance skills development.

**MA 096. GEOMETRY CONCEPTS AND SKILLS DEVELOPMENT 2 HRS.**

(Successful completion of the course MA 095 or successful completion

of a departmental screening exam designed to exempt a student from the

necessity of taking MA 095.) (Prerequisite for students whose results in

the departmental screening exam indicate a need for basic geometric

skills and knowledge.) Basic concepts in geometry including names and

properties of geometric figures, concepts of parallelism and

perpendicularity, congruence and similitude. Measurements associated

with geometric figures. Use of basic geometry concepts as they relate to

applications of a geometric nature. Coordinate Geometry. Computer

aided instruction used to enhance concepts.

**MA 098. INTERMEDIATE ALGEBRA 3 HRS.**

(Prerequisite, MA 095 or appropriate ACT score or appropriate score on

the math placement exam.) A thorough review of the fundamentals of

elementary algebra, linear and quadratic equations, exponents and

radicals.

**MA 103. ALGEBRA ENHANCEMENT 3 HRS.**

(Corequisite, concurrent enrollment in MA 098 and consent of

instructor.) This course is designed to enrich the mathematical

experiences of students who are enrolled in MA 098, Intermediate

Algebra. Students work in collaborative groups to solve open-ended

and non-routine problems. The use of current technology, which

includes computers and graphing calculators, is used in solving

application problems involving linear and quadratic models.

**MA 107. TECHNICAL MATHEMATICS 3 HRS.**

(For Flint Hills Technical College students only.) Technical

Mathematics is designed to provide many of the math skills needed in

the general and technical courses that follow as students progress

through the Power Plant Technology Program.

**MA 110. COLLEGE ALGEBRA 3 HRS.**

(Prerequisite, MA 095 and MA 098, or appropriate ACT score or

appropriate score on the math placement exam.) Basic operations,

products and factoring, linear and quadratic equations, graphs, ratio and

proportion, inequalities, logarithms, mathematical induction,

permutations, combinations, determinants.

**MA 112. TRIGONOMETRY 2 HRS.**

(Prerequisite, MA 110 or equivalent.) Trigonometric functions,

identities, graphs, trigonometric equations, radian measure, complex

numbers, polar coordinates, solving triangles, applications.

**MA 120. ELEMENTARY STATISTICS 3 HRS.**

(Prerequisite, High school Algebra or MA 095 is highly recommended.)

This course is designed to introduce students to basic statistics,

summarizing univariate data, correlation and regression for bivariate

data, concepts of probability, probability distributions, simulation,

sampling distributions, estimation, and hypothesis testing. Some uses of

statistical software will be incorporated into this course.

**MA 125. INTRODUCTION TO MATHEMATICS 1 HR.**

(Prerequisite, course will be required for all students with Math or Math

Ed. Majors, who are new to the program, whether freshman or transfer

students.) This course introduces incoming majors to the math

department, the world of mathematics and the college environment. It

addresses goals, expectations, responsibilities, math classes, decision

making, study skills, problem solving and the joy of doing mathematics,

as well as career choices in mathematics.

**MA 156. PRINCIPLES OF MATHEMATICS 3 HRS.**

(Prerequisite, MA 098 or appropriate ACT score or appropriate score on

the Mathematics Placement examination.) A course in mathematics for

the nontechnically oriented student. Problem solving skills and critical

thinking skills are developed through a selection of interesting and

unique mathematical content and topics. Previously learned skills in

algebra and geometry are enhanced and improved as students develop a

greater awareness of and appreciation for mathematics.

**MA 160. PRECALCULUS 3 HRS.**

(Prerequisites, MA098 or ACT math score of 22 or higher.) This course

provides the background in algebra and trigonometry that is necessary

for calculus. It focuses on functions as mappings, associations, and

ordered pairs; graphs of algebraic, absolute value, greatest integer,

logarithmic, trigonometric, and exponential functions; and operations

on and inverses of functions.

**MA 161. CALCULUS I 5 HRS.**

(Prerequisite, MA 110 and MA 112 or equivalent, or appropriate ACT

score.) Calculus is the mathematics of change. This course focuses on

the differential calculus of one variable. It includes the study of limits,

differentiation, implicit differentiation, the Mean Value Theorem,

optimization, related rates; it illustrates applications from other fields.

**MA 165. BASIC CALCULUS 5 HRS.**

(Prerequisite, MA 110 or equivalent.) A course designed for non-math

majors which emphasizes the application of calculus procedures to

Economics, Business, Social Sciences, Life Sciences, and other areas.

Topics include limits, derivatives, and integrals.

**MA 180. PROBABILITY 2 HRS.**

(Prerequisite, two years of high school algebra or equivalent.) An

introduction to the theory of probability, probability models, random

sampling, frequency distributions, binomial, normal and uniform

distributions.

**MA 210. HONORS SEMINAR 1 HR.**

(Prerequisite, Honors Program.) An in-depth study of problem solving

techniques dealing with material from the student’s previous and/or

current mathematics courses.

**MA 225. MATHEMATICS AS A DECISION MAKING TOOL 3 HRS.**

(Prerequisite, MA 110.) This course is designed for non-mathematics

majors. The focus of this course is to develop quantitative skills, and

reasoning ability necessary to help students read critically and make

decisions in our technical information society. A project tying this

course to the student's own interests is a course requirement. Major

topics include: collecting and describing data, inferential statistics and

probability; geometric similarity, geometric growth, symmetry and

patterns.

**MA 240. DISCRETE MATHEMATICS 3 HRS.**

(Prerequisites, MA 161, MA 165, or permission of the instructor.)

Discrete mathematics is the study of relationships between finite and

countable sets as well as the analysis of processes involving a finite

number of steps. This course will introduce and emphasize the concept

and methods of proof, while studying topics such as sets, logic,

functions and relations, mathematical induction, and recursion.

**MA 262. CALCULUS II 5 HRS.**

(Prerequisite, MA 161 or equivalent.) As a continuation of Calculus I,

this course emphasizes integration. Topics include techniques of

integration, improper integrals, numerical integration, basic differential

equations, sequences, infinite series; applications to other fields are

illustrated throughout the course.

**MA 291. MATHEMATICAL MODELING 3 HRS.**

(Prerequisite, MA 161 or MA 165.) Mathematical modeling is the "art"

of using math to help understand, describe, and forecast real-world

phenomena. Topics include the modeling process, model fitting,

optimization, experimental modeling, simulation, and modeling using

the derivative.

**MA 307. MATHEMATICS FOR THE ELEMENTARY TEACHER 3 HRS.**

(Prerequisites, a score of 80% on a departmental arithmetic proficiency

exam or the successful completion of MA 049:Arithmetic Skills

Improvement, and have a grade of “C” or higher in MA 110.) This

course will prepare prospective elementary and middle school teachers

to know, understand, and use the basic principles and concepts of

mathematics involving sets, whole numbers, integers, rational numbers,

and real numbers.

**MA 308. MATHEMATICS FOR ELEMENTARY/MIDDLE SCHOOL TEACHER II 3HRS.**

(Prerequisite, must have a “C” or higher in MA 307.) This course will

prepare prospective elementary and middle school teachers to know,

understand, and use the basic principles and concepts of mathematics

involving probability, statistics, measurement, and geometric concepts,

such as properties of two and three-dimensional shapes, congruency,

similarity, and transformations.

**MA 312. ALGEBRA FOR THE ELEMENTARY/MIDDLE SCHOOL TEACHER 3 HRS.**

(Prerequisite, MA 225 or equivalent.) Algebraic concepts needed for

today’s elementary/middle schools including properties of the field of

real numbers, algebraic and graphic solutions of equations and of

inequalities. Concrete models, such as algebra tiles, will be examined in

the teaching and learning of algebra.

**MA 313. GEOMETRY FOR THE ELEMENTARY/MIDDLE SCHOOL TEACHER 3 HRS.**

(Prerequisite, MA 308.) Geometric concepts needed for today’s

elementary/middle schools including geometric constructions,

experimental geometry, and a study of congruences, similarity, and

measurement.

**MA 315. TECHNICAL CALCULUS I 3 HRS.**

(Prerequisite, K.G.E. employees only.) A new course in differential

calculus designed solely for the Kansas Gas & Electric (KGE) education

program at the Wolf Creek Nuclear Power Plant offered by the

continuing education program at ESU.

**MA 316. TECHNICAL CALCULUS II 3 HRS.**

(Prerequisite, KGE employees only.) A new course in calculus designed

solely for the Kansas Gas & Electric (KGE) education program at the

Wolf Creek Nuclear Power Plant offered by the continuing education

program at ESU. This is the sequence to Technical Calculus I.

**MA 317. APPLIED DIFFERENTIAL EQUATIONS 3 HRS.**

(Prerequisite, KGE employees only.) A new course in differential

equations covering methods of solution of elementary and linear

differential equations, including Laplace transforms, with applications

to geometry and the physical sciences; designed to meet the needs of

KGE and offered by the continuing education program at ESU.

**MA 322. INTRODUCTION TO LINEAR ALGEBRA 3 HRS.**

(Prerequisites, MA 240 or permission of instructor.) This course

provides additional experience with proof while introducing the

methods and applications of solving systems of linear equations. Topics

include: elementary vector arithmetic and matrix arithmetic, Gaussian

Elimination and the Reduced Echelon Form, linear transformations,

linear independence, basis, dimension, range, null space, rank, and

determinants.

**MA 331. THE MATHEMATICS OF FINANCE 3 HRS.**

(Prerequisite, two years high school algebra or equivalent.) Simple and

compound interest and discount, present value and accumulated value

of annuities, bonds, amortizations, sinking funds, depreciation, life

annuities and life insurance. Introduction to linear programming for

solution of problems of business and industry.

**MA 335. DIFFERENTIAL EQUATIONS 3 HRS.**

(Prerequisite, MA 262.) Differential equations are essential in modeling

various phenomena in the world since the rates at which quantities

change are of great interest when trying to understand or forecast future

results. The course involves the basic qualitative and quantitative

analysis of the solutions of ordinary differential equations. Topics

covered include: direction fields, first order differential equations,

higher order linear differential equations, basic numerical

approximation techniques, and series solutions. Several applications are

demonstrated throughout the course.

**MA 341. INTRODUCTION TO PROBABILITY AND STATISTICS 3 HRS.**

(Prerequisites, MA 110 or equivalent.) An introductory study of

probability and statistics for students who wish to apply statistics to

their field of study. The course includes methods of presenting and

interpreting data. Topics include frequency distributions, measures of

central tendency, measures of dispersion, probability, probability

distributions, normal distributions, sampling distributions, confidence

intervals for large and small samples, and hypothesis testing of means

for large and small samples.

**MA 363. CALCULUS III 3 HRS.**

(Prerequisite, MA 262 or equivalent.) Multivariable calculus, double

integral, triple integral and partial derivatives. Vectors, polar

coordinates, parametric equations, and vector valued functions.

**MA 380. PROBABLITIY AND STATISTICS 3 HRS.**

(Prerequisite, MA 262 or consent of instructor.) The study of

probability and statistics provides methods to analyze data. This course

is an introduction to basic probability and counting techniques as well

as statistical methods using distribution theory, confidence intervals,

significance tests, and sampling.

**MA 386. INTERNSHIP: MATHEMATICS 1-3 HRS.**

(Prerequisite, 20 hours in mathematics courses.) An academic course to

provide students with an opportunity to gain field experience in

mathematics through professional experience. The academic experience

is developed jointly by the student and the faculty advisor. No more

than 3 hours in MA 386 may be counted toward the mathematics major.

**MA 410. SEMINAR IN MATHEMATICS 0-4 HRS.**

(Prerequisite, permission of mathematics department.) A seminar

involving various topics in mathematics.

**MA 421. COLLEGE GEOMETRY 5 HRS.**

(Prerequisites, MA 240.) This course is designed to help students learn

the axiomatic development of Euclidean Geometry using conjectures,

models, constructions and proofs. Transformations, coordinate

geometry, and technology (dynamic geometric systems) are explored.

Included is an introduction to Non-Euclidean geometries such as:

Finite, Hyperbolic, Elliptical and Projective.

**MA 425. ABSTRACT ALGEBRA 3 HRS.**

(Prerequisite, MA 322 or permission of instructor.) Foundations of

deductive mathematical reasoning and proof. Basic concepts of abstract

algebra including symbolic logic, proof strategies, sets, relations

mapping and binary operations. A study of some algebraic structures

including groups, rings, integral domains and fields.

**MA 450. INTERDISCIPLINARY SCIENCES: MATHEMATICS 3 HRS.**

(Prerequisite, permission of instructor.) In this interdisciplinary course

students and faculty will collaborate to conduct quantitative research on

biological systems. Weekly meetings will entail group discussions in

which we will identify potential questions, design experiments to

investigate those questions, and interpret the results of the experiments.

With the use of sophisticated computer technologies we will analyze

phenomena that were previously too fast, slow, small or large to be

investigated with quantitative precision. Digital video and image

processing techniques will be used to measure properties of biological

systems. A variety of mathematical and statistical software will be used

to analyze and model the observation. Students will develop written

reports of their investigations; students will make public presentations

of their findings at university seminars and possibly at professional

meetings.

**MA 460. HISTORY OF MATHEMATICS 1 HR.**

(Prerequisites, MA 161 or MA 165 or permission of instructor.) This

course explores the historical development of mathematics from Ancient

times through Calculus. Contributions of different cultures and

individuals as well as problems of historical significance are

investigated.

**MA 470. TEACHING MATHEMATICS IN THE MIDDLE/HIGH SCHOOL 2-3 HRS.**

(Prerequisite, at least junior standing or permission of instructor.)

Students enrolled in this course examine multiple approaches to helping

middle and high school students learn mathematics. Attention is given

to current research, state and national standards, ELL and IEP'ed

students, assessment, and technology. Experiences are provided in a

mathematics classroom.

**MA 480. INDEPENDENT STUDY (MATHEMATICS) 1-4 HRS.**

(Open only to qualified juniors and seniors.) Topics of special interest

in some area of mathematical study not included in regularly listed

courses.

**MA 510. TECHNOLOGY IN MATHEMATICS 3 HRS.**

(Prerequisite MA 262 or graduate standing.) Provides an introduction

to the latest technologies that are used for the teaching, learning, and

presenting of mathematics.

**MA 532. MATHEMATICAL STATISTICS I 3 HRS.**

(Prerequisite, MA 262 and MA 380.) Fundamental principles of a

random variable and its distribution; the binomial, normal, the F, the

Student-t, and Chi-Square; testing hypotheses, estimation, and

applications.

**MA 561. TEACHING PERSPECTIVES IN CALCULUS 3 HRS.**

(Prerequisite, MA 262 or graduate standing.) Provides a survey of the

topics of single variable calculus from the perspective of someone who

will teach calculus or pre-calculus. It will emphasize the underlying

concepts of calculus and present the most effective ways of conveying

those concepts to students.

**MA 570. TEACHING COLLEGE MATHEMATICS 1 HR.**

(Prerequisite, graduate standing.) This course provides an introduction

to the current techniques, methods and technologies that are used in the

teaching of undergraduate college mathematics through both classroom

observation and supervised teaching. This course is intended for

graduate students only.

**MA 581. MATHEMATICAL MODELING 3 HRS.**

(Prerequisite, MA262.) Mathematical modeling is the study of the use

of mathematics to describe and forecast real-world phenomena. A

variety of modeling techniques are introduced. The course includes a

review of relevant topics from algebra, trigonometry, calculus, statistics,

and differential equations. The prerequisite can be overridden by the

consent of the department.

**MA 591. TOPICS IN MATHEMATICS 1-3 HRS.**

(Prerequisites will vary with topic.) An in-depth study of selected

topics in mathematics not currently found in other mathematics courses.

May be repeated with different topics for a maximum of six credits.

See Schedule of Classes for specific topic and prerequisites when

offered.

**MA 592. TOPICS IN ELEMENTARY/MIDDLE SCHOOL MATHEMATICS 1-3 HRS.**

(Prerequisites will vary with topic, possibly including but not limited to

MA 312 or MA 313.) A course designed to enrich and supplement the

teaching of elementary/middle school mathematics. May be repeated

with different topics for credit. See Schedule of Classes for specific

topic (and prerequisites) when offered.

**MA 715. TOPOLOGY 3 HRS.**

(Prerequisite, consent of mathematics department.) Theory of point sets

with applications to analysis. Topological, metric, and function spaces,

sequences, continuity, connectedness, compactness, separation,

completions.

**MA 721. PROJECTIVE GEOMETRY 3 HRS.**

(Prerequisite, MA 421 or consent of department.) Projective geometry

of one and two dimensions, its axiomatic foundation, and the

fundamental ideas of the projective plane. Duality, harmonic forms,

coordinates, conics, polarities, and a brief introduction to geometry of

higher dimensions.

**MA 722. NON-EUCLIDEAN GEOMETRY 3 HRS.**

(Prerequisite, MA 421 or consent of department.) A comparison of

non-Euclidean geometries with Euclidean geometry. Hilbert's axioms,

history of the parallel postulate, elementary theorems of hyperbolic

plane geometry and a brief introduction to elliptic geometry.

**MA 727. GROUPS, RINGS, AND FIELDS 3 HRS.**

(Prerequisites, MA 322 and MA 425 or consent of the mathematics

department.) The properties of groups, rings and fields with emphasis

on the algebraic structure and morphisms. Algebraic and transcendental

field extensions.

**MA 728. VECTOR SPACES 3 HRS.**

(Prerequisite, MA 322 and MA 425 or consent of department.) The

structure of vector spaces, algebras and fields. Transformations, linear

independence, bases and other topics are studied.

**MA 731. STATISTICS USING SAS 3 HRS.**

This course provides an overview of a wide array of concepts and

methods of statistical analysis, and how these methods can be

implemented using SAS to perform data analysis. Concepts typically

covered are graphical summaries of data, populations and samples,

measures of central tendency, measures of dispersion and variability,

probability, the normal distribution, an introduction to hypothesis

testing, assessing normality, simple t-tests, two-sample hypotheses,

analysis of variance and multiple comparisons, and modern regression

analysis. Programming assignments in SAS are an important component

of the course. The course should be of interest to mathematics majors

and to graduate students in other disciplines with an interest in

statistical analysis of data. It is recommended that students who enroll in

this course have already taken at least one course in statistics.

**MA 733. MATHEMATICAL STATISTICS II 3 HRS.**

(Prerequisite, MA 532.) Probability, distributions, expected values,

moments, sampling distribution and point estimation. Multivariate

normal distribution, maximum likelihood estimation, interval

estimation, test of hypotheses, linear regression, experimental design

and analysis of variance.

**MA 734. COMPLEX VARIABLES 3 HRS.**

(Prerequisite, MA 263.) A study of the complex plane, holomorphic

functions, the elementary functions, complex integration. Taylor’s series

and the Laurent expansion, the calculus of residues and conformal

mapping.

**MA 735. ADVANCED CALCULUS I 3 HRS.**

(Prerequisite, MA 262 and MA 425 or permission of instructor.) This

course rigorously proves the results of Calculus I and II. Topics include

an axiomatic characterization of the real numbers, sequences, functions,

limits, continuity, differentiation, Riemann integration, and infinite

series.

**MA 736. ADVANCED CALCULUS II 3 HRS.**

(Prerequisite, MA 735.) As a continuation of Advanced Calculus I, this

course provides a rigorous treatment of multi-variable calculus. Topics

include topology, convergence, differentiability, and integration on Rn.

**MA 740. NUMBER THEORY 3 HRS.**

(Prerequisite, MA 425 or consent of department.) Properties of

numbers, prime and composite, Euclid’s algorithm, indeterminate

problems. Diophantine problems, congruences and residues, Buler’s

Theorem, Fermat’s Theorem, classical problems.

**MA 744. INTRODUCTION TO MATHEMATICAL LOGIC 3 HRS.**

(Prerequisites, MA 240, MA 161.) Deductive logic as applied in

secondary school mathematics. Symbolic Aristotelian logic, truth tables,

rules of inference, methods of deductive proof, and the restricted

predicate calculus.

**MA 745. VECTOR ANALYSIS 3 HRS.**

(Prerequisite, MA 263.) Fundamental principles of vector analysis,

algebra and calculus of vectors, applications of vectors to geometry and

physics.

**MA 764. REGRESSION ANALYSIS 3 HRS.**

(Prerequisite, MA 380 or equivalent.) Computer oriented statistics

methods course. Topics include estimating parameters, testing

hypotheses, analysis of variance, and multiple linear and nonlinear

regression methods.

**MA 791. TOPICS IN MATHEMATICS 1-3 HRS.**

(Prerequisites will vary with topic.) An in-depth study of selected

topics in mathematics not currently found in other mathematics courses.

May be repeated with different topics for a maximum of six credits.

See Schedule of Classes for specific topic and prerequisites

when offered.

**MA 792. TOPICS IN ELEMENTARY/MIDDLE SCHOOL MATHEMATICS 1-3 HRS.**

(Prerequisite, in-service teacher or consent of department.) A course

designed to enrich and supplement the teaching of elementary/middle

school mathematics. May be repeated with different topics for credit.

See Schedule of Classes for specific topic (and prerequisites) when

offered.

**MA 793. TOPICS IN SECONDARY SCHOOL MATHEMATICS 1-3 HRS.**

(Prerequisite, in-service teacher or consent of department.) A course

designed to enrich and supplement the teaching of secondary school

mathematics. May be repeated with different topics for credit. See

Schedule of Classes for specific topic (and prerequisites) when offered.

**MA 810. SEMINAR IN MATHEMATICS 0-4 HRS.**

Directed reading and research in a selected field.

**MA 820. DIFFERENTIAL GEOMETRY 3 HRS.**

(Prerequisite, MA 263.) A study of curves and surfaces in Euclidean

space. Frenet formulas, curvature, geodesics, and fundamental forms.

**MA 825. GROUP THEORY 3 HRS.**

(Prerequisite, MA 727.) An introduction to the theory of groups. Topics

included are classifications of groups, such as cyclic, Abelian, solvable,

nilpotent, etc., homomorphisms and isomorphisms, types of subgroups

and factor groups, and the Sylow theorems.

**MA 832. DIFFERENTIAL EQUATIONS II 3 HRS.**

(Prerequisite, MA 335.) Extension of MA 335 and an introduction to

systems of differential equations and partial differential equations;

applications.

**MA 835. FUNCTIONS OF A REAL VARIABLE 3 HRS.**

(Prerequisite, MA 736.) The study of linear sets of points, sequences of

functions, upper and lower semi-continuity, equi-continuity, Lebesgue

measure, Lebesgue integration, Borel sets, Baire functions and

measurable functions.

**MA 847. RESEARCH PROJECTS IN MATHEMATICS 1-5 HRS.**

Independent study and research in mathematics. Allowed on master's

degree program with consent of mathematics department.

**MA 850. THESIS, MA, or MS 1-6 HRS.**

Required for the Master of Arts degree with a major in Mathematics.

Independent study and research in an approved field. Frequent

conferences with the instructor.

**MA 955. CURRENT LITERATURE IN**

**MATHEMATICS 0-3 HRS.**

(Prerequisite, Master’s degree.) Directed reading of current literature

and research in mathematics with individual reports and group

discussions.

**MA 957. THESIS, ED.S. 1-5 HRS.**

Required for the Specialist in Education with a major in mathematics.

Independent study and research in mathematics