# Mathematics

The mathematics department embraces the Bluffton University institutional goal of emphasizing individual inquiry, critical thinking and lifelong learning.

For mathematics majors, we maintain a program that guarantees both depth and breadth. Each student is required to study several areas of mathematics to a depth reasonable for an undergraduate. A program goal is that majors can choose from a wide variety of vocations and professions that value analytical reasoning, mathematical knowledge and problem-solving skills. Our program endeavors to prepare students for graduate school or for positions in business, industry, actuarial mathematics or teaching. We anticipate that some of our graduates will find careers in other professional positions as diverse as law, music and the pastorate.

A related goal of the mathematics program is to provide service to other departments
by offering courses in mathematics appropriate for students in business, social sciences,
physical and life sciences and early childhood and intervention specialist majors.

More about mathematics at Bluffton...

#### Major

(43 hours)

Bluffton University placement tests and advanced placement tests taken in high school
will be considered to assist appropriate placement and potential credit or waivers.
The following courses are required:

MAT 135 Calculus 1 (5)

MAT 136 Calculus 2 (5)

MAT 220 Discrete Mathematics (3)

MAT 225 Multivariate Calculus (3)

MAT 230 Linear Algebra (3)

MAT 211 Introductory Geometry (3)

MAT 312 Advanced Geometry (alternate year) (3)

MAT 332 Abstract Algebra (alternate year) (3)

MAT 340 Probability and Statistics (3)

MAT 350 Differential Equations and Modeling (alternate year) (3)

MAT 360 Operations Research (alternate year) (3)

MAT 401 Analysis I (alternate year) (3)

CPS 108 Computer Programming (3)

CPS 320 and PHY 211 are strongly recommended for all mathematics majors.

*Restrictions and alternatives*

MAT 390 may be considered as an elective in mathematics and is repeatable as distinct investigations.
At least one upper level mathematics course shall be taken during the senior year.
Departmental honors may be sought by a student majoring in mathematics by way of an
approved plan of independent studies.

#### License to teach mathematics

Students interested in teaching mathematics in middle school must complete a middle childhood education major with mathematics as one of the two areas of concentration.

#### Adolescent/young adult licensure in integrated mathematics

Students who wish to teach mathematics in secondary school should complete a mathematics major along with the following professional education courses for an adolescent/young adult license in integrated mathematics.

**Required professional education courses:** (34 hours)

EDU 200 Introduction to Teaching in a Diverse Society (3)

EDU 205 Field Experience (1)

EDU 220 Curriculum and Assessment (2)

EDU 305 Content Area Literacy/General Methods (3)

EDU 332 Social and Philosophical Issues in Education(3)

EDU 353 Educational Psychology & Instructional Practices(3)

MAT 380 Mathematics and Methods Seminar (2)

SED 220 The Adolescent: Development and Diversity (2)

SED 389 Issues in Special Education (1)

EDU 404 Adolescent/Young Adult Special Methods: Mathematics (2)

*All of the previously listed professional education courses, plus the completion of all licensure
area course work, are prerequisites for clinical practice:*

EDU 425 Leadership Seminar (2)

EDU 451 Clinical Practice (Adolescent/Young Adult) (10)

In a consortium with Ohio Northern University, AYA mathematics licensure candidates
will complete EDU 404 in a semester prior to clinical practice, as well as completing the clinical practice
experience at ONU. Students will also complete a leadership seminar during the clinical
practice experience, under the leadership of ONU faculty.

#### Minor

(19 hours)

**Required:**

MAT 135 Calculus 1 (5)

MAT 136 Calculus 2 (5)

Electives:

*Select at least three of the following mathematics courses, with at least one numbered
above 300, for a minimum total of 9 semester hours. Substitutions with other upper
level mathematics courses will be considered in special cases.*

MAT 220 Discrete Mathematics (3)

MAT 225 Multivariate Calculus (3)

MAT 230 Linear Algebra (3)

MAT 340 Probability and Statistics (3)

MAT 350 Differential Equations and Modeling (3)

MAT 360 Operations Research (3)

CPS 320 Numerical Analysis (3)

#### Computer Science minor

(18-19 hours)

The computer science minor allows students desiring a computer background within another
major to obtain a solid foundation in the field.

Required computer science courses: (12 hours)

CPS 108 Computer Programming (3)

CPS 112 Object Oriented Programming with Applied Data Structures (3)

CPS 322 Database Systems (3)

CPS 343 Network and Systems Administration (3)

Two additional courses must be taken from the following list: (6-7 hours)** **CPS 320 Numerical Analysis (3)

CPS 333 Systems Programming (3)

CPS 352 Digital Electronics and Computers (4)

If the student's major requires any of the above courses, those courses can count for both the major and the computer science minor.

#### Mathematics courses

** MAT 050 Basic Mathematics** (3) (only 2 count toward graduation)

Students review and apply basic computational and algebraic concepts and skills. Problem solving is a major focus of the course, including basic applications to geometry. Graphing calculators are provided and used throughout the course whenever appropriate.

**MAT 100 College Algebra** (3)

This course presents concepts and skills typically found in a college algebra course
including development of real number systems, simplifying algebraic expressions, solving
equations and inequalities, and solving mathematical problems that model real world
situations. Numerical, algebraic and graphical representations are used throughout
the course. Graphing calculators are required and are used to accommodate numerical
and graphical solution techniques in addition to traditional paper and pencil methods.
Prerequisites: MAT 050 or two years of high school mathematics and qualification for placement.

* MAT 105 Understanding Numerical Data (*2)

Designed to help students understand, interpret and think critically about numerical information. The main focus of the course is concept development rather than mathematical manipulation. Use of graphing calculators and spreadsheets give students experience in handling numerical data. Prerequisites: MAT 050 or placement into MAT 100 or above.

**MAT 114 Precalculus** (4)

A study of families of elementary functions and their important properties power
functions, polynomials, logarithmic and trigonometric functions and their inverses.
Numerical, algebraic and graphical representations of each family are included. Polya
s problem-solving methods are used to solve mathematical problems that model real-world
situations. Graphing calculators are required and are used extensively. Prerequisites:
three years high school math and qualification for placement.

**MAT 115 Business Calculus** (3)

A study of functions and applied differential calculus for economics, business and
other social sciences. Emphasis is on spreadsheet analysis of common elementary situations.
Other topics covered include systems of linear equations and an introduction to linear
programming. Prerequisite MAT 100 or placement into MAT 114 or above.

**MAT 135 Calculus 1** (5)

A study of fundamental concepts and applications of the differential calculus of
one variable, as well as introductory integral calculus. Polya s problem-solving methods
are used to solve mathematical problems that model real-world situations and which
require methods of differential calculus for their solution. The historical roles
of Newton and Leibniz are discussed. Graphing calculators are required and are used
extensively. Projects that require use of computer algebra systems such as *Mathematica* or *Maple* are included. Prerequisites: MAT 114 or four years of high school math and qualification for placement.

**MAT 136 Calculus 2** (5)

The fundamental concept and applications of the definite integral of one variable,
infinite series and introductory differential equations including series solutions
are included. Polya's problem-solving methods are applied to solve mathematical problems
that model real-world situations and which require methods of integral calculus for
their solution. The historical roles of Newton and Leibniz are discussed. Graphing
calculators are required and are used extensively. Projects that require use of computer
algebra systems such as *Mathematica* or *Maple* are included. Prerequisites: MAT 135 or its equivalent.

**MAT 185 Fundamental Mathematics Concepts for Early Childhood** (3)

This course includes pre-number ideas, early number concepts, numeration systems,
place value foundations and applications, understanding the basic algorithms of arithmetic,
techniques of estimation, problem solving methods, basic concepts of geometry and
measurement. Calculators and their role in mathematical problem solving are included
from the perspective of learning to judge the most effective approach to a problem
estimation, mental calculation, paper and pencil or calculator. Prerequisites: MAT 050 or readiness for college algebra (or higher) on mathematics placement, EDU 200, EDU 205, PSY 110.

**MAT 186 Fundamental Mathematics Concepts for Middle Childhood** (3)

This course includes the content of integers and fractions, rational and irrational
numbers, decimal notation, ratio and percent, equations and inequalities, probability
and motions in geometry. Calculators and their role in mathematical problem solving
are included from the perspective of learning to judge the most effective approach
to a problem estimation, mental calculation, paper and pencil or calculator. Prerequisite:
MAT 185.

* MAT 211 Introductory Geometry *(3)

A study of classical theorems from plane Euclidean geometry. Discovery methods and inductive reasoning are used with a computer geometry program as a tool to discover relationships. Four proof methods vector, analytical, synthetic and transformation are compared and contrasted as discovered relationships are proven. The historical contributions of Greek, Indian, Arab and European mathematicians are discussed, particularly those of Euclid, Pythagoras, Desargues, Pappus, Archimedes, Ptolemy, Heron, Brahmagupta, Bhaskara, Fermat, Poincare, Ceva, Minkowski, Steiner and Feuerbach. Prerequisite: MAT 136.

**MAT 220 Discrete Mathematics** (3)

This course introduces the student to general methods of discrete mathematics on
topics selected from sets, relations and functions, graphs, trees, matching problems,
counting techniques and recurrence. An algorithmic approach to problem solving is
a common thread that ties these various topics together. Historical contributions
of mathematics to graph theory and discrete mathematics are discussed, particularly
those of Cantor, Euler, Fibonacci, Hamilton, Gauss, Boole and Russell. Prerequisite:
qualification for placement at the calculus level.

**MAT 225 Multivariate Calculus** (3)

A development of vector calculus, partial derivatives and multiple integrals, properties
of vectors and transformations on coordinate systems, line and surface integrals,
and projects that make use of systems such as *Mathematica* or *Maple* for three-dimensional display is included throughout the course. Prerequisite: MAT 136.

**MAT 230 Linear Algebra** (3)

A study of vector spaces and subspaces, linear transformations, matrices and determinants,
eigenvalues and eigenvectors of matrices. Real world problems are modeled and solved
using whatever methods are appropriate paper and pencil, graphing calculator or computer
algebra systems. Prerequisite: MAT 136.

**MAT 277 Algebra: Functions and Modeling** (3)

This course includes topics related to the NCTM K-8 curriculum in algebra, number
theory, data analysis and problem solving. Mathematics is presented using a variety
of pedagogical methods including discussion in groups, cooperative learning groups
and individual and group investigation of mathematical content. One goal of the course
is to make students secure in their ability to be independent learners of mathematical
content. Prerequisite: MAT 185 or consent of the instructor. Offered alternate years.

**MAT 312 Advanced Geometry** (3)

This course uses a formal axiomatic development to study both Euclidean and non-Euclidean
geometries. The course includes a significant amount of mathematical history particularly
as the discovery of non-Euclidean geometry relates to the development of modern mathematics
of the past century. Formal proof is a major focus of this course. Prerequisite: MAT 211. Offered alternate years.

**MAT 332 Abstract Algebra** (3)

A study of groups and rings using properties of sets, equivalence relations and number
theory. Historical contributions of mathematicians to number theory and algebra are
discussed, particularly those of Diophantus, Fermat, Euler, Lagrange, Abel, Cayley,
Cauchy, Galois, Jordan, Noether, Germain, Artin, Dedekind and Sylow. Prerequisite:
MAT 230. Offered alternate years.

* MAT 340 Probability and Statistics *(3)

A study of the theory of probability and inferential statistics, including both discrete and continuous probability distributions. The distributions studied include the binomial, geometric, Poisson, normal, gamma, exponential, chi-square,

*t*and

*F*distributions. Includes random sampling, estimation theory, unbiased estimators and some study of tests of hypotheses, linear regression and correlation. Historical contributions of mathematicians to probability and statistics are discussed, particularly those of Bayes, Bernoulli, Chebyshev, Gauss and Poisson. Prerequisite: MAT 136; MAT 225 recommended.

**MAT 350 Differential Equations and Modeling** (3)

A study of differential equations generated from modeling nature and the physical
world using analytic, numeric and graphical techniques. The course begins with the
study of elementary differential equations and introductory models in classroom and
computer laboratory settings, then more complex general mathematical models are introduced.
Calculator and computer technology are used extensively. Group and individual projects are
required. Prerequisite: MAT 136. Offered alternate years.

**MAT 360 Operations Research** (3)

A study of introductory topics in operations research: linear programming, integer
programming, network models and applications to the transportation problem and the
Program Evaluation and Review Technique, Markov chains, queuing theory and simulation.
Computer technology is used extensively. Group and individual projects are required.
Prerequisite: MAT 230. Offered alternate years.

* MAT 380 Mathematics and Methods Seminar* (2)

This course includes both contents and methods. Content topics discussed are ones that can be adapted to either elementary or secondary levels and relate to "mathematics enrichment." The course also includes discussion of professional behavior topics and students study the K-12 reform curriculum of the NCTM standards, the integrated mathematics curriculum vs. the traditional mathematics curriculum, other current trends in mathematics education, and the future of mathematics education. In addition the course includes selected topics from the history of mathematics.

**MAT 390 Independent Study in Mathematics** (2-5) (By arrangement)

Two courses of independent study in mathematics are required for graduation with
honors in mathematics; also available by proposal from any student majoring in mathematics.

* MAT 401 Analysis I* (3)

This course is intended as a first course in analysis following multivariate calculus. The study of sets, sequences and mappings becomes a foundation for more theoretical study of real and complex analysis. Topics included are countable, connected, open and closed sets, convergence of sequences, continuity and uniform continuity, and a first investigation of metric spaces, separability and compactness. Prerequisite: MAT 225. Offered alternate years.

#### Computer Science courses

** CPS 108 Computer Programming** (3)

This course is an introduction to computer programming which emphasizes the application of fundamental principles to problem solving and programming techniques. Structured programming concepts using a C-type programming language are stressed. Some familiarity with computers is assumed

*.** CPS 112 Object Oriented Programming with Applied Data Structures* (3)

This course is a study of the design of data structures and the analysis of the algorithms used to manipulate them. The fundamental concepts studied in this course serve as a foundation for the advanced computer science concepts studied in later courses. Topics include data types, records, recursion, queues, stacks, linked lists, trees, graphs, searching, sorting, algorithm complexity and classes of algorithms. Software engineering principles are introduced. Prerequisite: CPS 108.

** CPS 220 Introduction to Object-oriented Programming** (3)

This course is an introduction to the object-oriented programming paradigm. Emphasis is placed on methods, objects, graphics, graphical user interfaces and components, applets and applications, and program development tools. Prerequisite: CPS 112.

** CPS 221 Applications in Object-oriented Programming** (2)

This course focuses on the application of the object-oriented programming paradigm using Java. Areas covered include multithreaded applications, internationalization and security issues, graphics and animation, and simulation. Students work on a term project in their area of interest. Prerequisite: CPS 220.

** CPS 320 Numerical Analysis** (3)

This course focuses on the applications of the computer in science and mathematics. Topics include calculation of functions, roots of equations, integration, Fourier analysis, differential equations, Monte-Carlo methods, and curve fitting. Lectures present the concepts of the numerical analysis topics covered and their corresponding algorithms; students are expected to be familiar with the underlying mathematical concepts and the programming methodology necessary for algorithm implementation. Prerequisites: CPS 108 and MAT 136. Offered alternate years.

** CPS 322 Database Systems** (3)

This course has its primary focus on the relational model for database organization. Topics include the relational data structure, relational algebra, normalization, integrity, recovery, concurrency and distributed databases. Assignments include team projects involved in the various stages of information systems development: definition, design, implementation, testing, and documentation. Prerequisite: CPS 112. Offered alternate years.

** CPS 331 Programming Languages and Compilers** (3)

This course studies the design and implementation of modern programming languages, compilers, and interpreters. Concepts of data representation, storage allocation, scope, code generation, lexical analysis, and parsing of context-free grammars are examined. Students design and implement a simple compiler. Prerequisite: CPS 221. Offered alternate years.

* CPS 333 Systems Programming* (3)

This course focuses on the writing of programs that utilize web, network, and operating system services in order to perform a task. Topics include Internet protocols, CGI, RPC, XML, DOM, SOAP, and AJAX. Operating shell programming is also introduced. Prerequisite: CPS 221. Offered alternate years.

** CPS 341 Operating Systems** (3)

Students are provided with an examination of the characteristics of modern operating systems and its related software. Topics include process and memory management, scheduling issues, performance metrics, and concurrent programming. Case studies of various operating systems are conducted. Prerequisite: CPS 220 or junior standing. Offered alternate years.

** CPS 343 Network and Systems Administration** (3)

This course deals with issues involving both network configuration and systems administration. The OSI layered reference model serves as an outline to the course. Topics include the physical architecture of computer networks, networking protocols and services, resource management, directory services, system and network security/privacy, and network and system monitoring. A special emphasis is placed on understanding TCP/IP and various related services (DNS, DHCP, SMTP, HTTP, LDAP). In addition, Windows NT Server is frequently used as a case study. Prerequisite: CPS 341. Offered alternate years

*.*** CPS 350 Computer Organization and Assembly Language** (3)

Students are provided with an introduction to computer hardware organization, the instruction execution cycle, and the relationship between machine/assembly languages and high-level programming languages. The Intel 8086 family of microprocessors is used to provide opportunities for machine and assembly language programming. Architectural and organizational issues are also addressed. Prerequisite: CPS 220 or junior standing. Offered alternate years.

** CPS 352 Digital Electronics and Computers** (4)

This course presents a study of digital electronics and an overview of its use in computers. Topics include logic, logic integrated circuits, processors, memory, processor-peripheral communication, and instrument interfacing. Prerequisites: CPS 350 and PHY 212. Offered alternate years.

** CPS 390 Independent Study in Computer Science** (credit varies)

By arrangement.

** CPS 399 Special Topics in Computer Science** (credit varies)

By arrangement.

_{August 2013}