# Department of Mathematics

25 University Avenue, Room 101

610-436-2440

Kathleen Jackson, *Chairperson *

Clifford Johnston, *Assistant Chairperson *

PROFESSORS: Gallitano, Gallop, Glidden, Nitica, Rieger, Szymanski, Tan, Wolfson

ASSOCIATE PROFESSORS: Gupta, Jackson,

Johnston, Marano, McClintock, McLaughlin, Moser, Parsell

ASSISTANT PROFESSORS: Bowen, Crossett, Fisher, George, Ilaria, Kolpas,

Sullivan, Zimmer

INSTRUCTORS: Gysling, Matus

The Department of Mathematics offers a program leading to the bachelor of arts degree in mathematics, a program leading to a bachelor of science degree in education, and a program leading to a bachelor of science in mathematics.

1. The B.A. in MATHEMATICS enables each student to receive the basic preparation for the career of his/her choice, such as college teaching, research, and service in industry and government. In all cases, the student receives a sound preparation for graduate study in the field of mathematics.

2. The B.S. in EDUCATION - MATHEMATICS focuses on a heavy concentration in mathematics while the student earns certification to teach mathematics on the middle, junior high, or senior high school levels.

3. The B. S. in MATHEMATICS provides students with a wide choice of career-oriented programs by allowing the declaration of a concentration in various branches of applied mathematics. The program is designed to position its graduates for a career in applied mathematics.

Students enrolled in this program are required to declare a concentration. Current concentrations include actuarial science, statistics, mathematics of finance, industrial mathematics, and computational mathematics. Students generally spend most of the first two years taking core requirements common to all concentrations or certain prerequisites. Mathematics and cognates (courses in fields closely related to mathematics) required for a specific concentration are normally taken during the final two years of the program. The mathematics courses are aimed at linking the course content to applications in the real world. Cognates are aimed at demonstrating the pervasiveness and importance of mathematics in other applied-oriented disciplines.

The Student Handbook for Mathematics Majors should be consulted for current requirements in mathematics degree programs.

## BACHELOR OF ARTS — MATHEMATICS

120 semester hours

- General ed. requirements, see pages 38-44 (48 semester hours)
- Language requirement (6 semester hours)

At the 200 level - Related requirements (11 semester hours)

CSC 141* and PHY 170*

- Major requirements (27 semester hours)

MAT 161, 162, 200, 261, 311*, 411, 421, and 441

*Satisfies general education requirement. - Electives in mathematics (21 semester hours)

Selected from upper-division (300 level or higher) mathematics courses, one in each of the areas of algebra, analysis, and applied mathematics

## Requirement of a Minor

Students in the B.A. degree program are required to complete either a minor or, with the approval of the student's adviser and the Department of Mathematics chairperson, an additional nine credit hours of upper-division mathematics. The discipline chosen for the minor will reflect a student's post-baccalaureate goals. The department recommends completing a minor in the natural sciences (astronomy, biology, chemistry, earth sciences, geology, and physics), computer science, economics, or finance, but other minors may be selected with the approval of the student's adviser and the mathematics chairperson.

All math major courses must be pased with a C- or better.

## BACHELOR OF SCIENCE IN EDUCATION — MATHEMATICS

125 semester hours

Students should be advised that some required courses count in more than one of the categories listed below. Further information can be found in the current Department of Mathematics Student Handbook.

- General ed. requirements, see pages 38-44 (48 semester hours)
- Mathematics requirements (42 semester hours)

MAT 161*, 162, 200, 261, 311, 331, 350 (credited to professional education), 354, 401, 411, 414, 421, and 441

*Satisfies general education requirement. - Professional education requirements (35 semester hours)

EDA 103 and 304; EDR 347; EDP 250; EDS 306 and 411-412; HIS 444*; LANG/ENG 382* - Related requirements (11 semester hours)

CSC 141* and PHY 170*-180

*Satisfies general education requirement. - Electives in mathematics (9 semester hours)

Selected from upper-division (300 level or higher mathematics courses; at least one course in both applied mathematics and analysis

All math major courses must be passed with C or better.

All students seeking a B.S.Ed. must formally apply for admission to teacher education. (See Educator Preparation Programs in this catalog, see pages 91-93.) Only those students formally admitted to teacher education will be eligible to enroll in MAT 354.

## BACHELOR OF SCIENCE — MATHEMATICS

120 semester hours

- General ed. requirements, pages 38-44 (48 semester hours)
- Mathematics requirements (21 semester hours)

MAT 161, 162, 200, 261, 311*, 343

**Satisfies general education requirement* - Related cognates (3 semester hours)

ENG 368 or 371 or 375 - Concentration requirements
- Actuarial science concentration
- Required mathematics courses (21 semester hours)

MAT 319, 345, 403, 406, 421, 422; STA 311 - Related cognates (15 semester hours)

ACC 201; ECO 111*, 112, 340; FIN 325, 330

*Satisfies general education requirement - Free electives or internship (15 semester hours)

Chosen under advisement - Computational mathematics concentration
- Required mathematics courses (21 semester hours)

MAT 151, 319, 325, 413, 425, 443, 427 or 493 - Related cognates (15 semester hours)

CSC 141*, 142, 240, 241, 242 or 405

*Satisfies general education requirement - Free electives and/or internship (20 semester hours)

Chosen under advisement - Industrial mathematics concentration
- Required mathematics courses (21 semester hours)

MAT 319, 325, 413, 425, 443, 445, and 427 or 493 - Related cognates (20 semester hours)

CSC 141*; PHY 170*, 180, 240, 300, 350

*Satisfies general education requirement - Free electives and/or internship (16 semester hours)

Chosen under advisement - Mathematical finance concentration
- Required mathematics courses (18 semester hours)

MAT 319, 406, 409, 421, 443, 345 or 422 - Related cognates (22 semester hours)

ACC 201; CSC 141*; ECO 111*, 112; FIN 325; and one of FIN 337 or 344; PHY 170*

*Satisfies general education requirement - Free electives and/or internship (20 semester hours)

Chosen under advisement - Statistics concentration
- Required mathematics courses (21 semester hours)

MAT 121, 122, 319, 345, 421, 422; STA 311 - Related cognates (9 semester hours)

Three electives chosen from either pharmaceutical design, finance, economics, marketing, or computer science and approved by department chair - Free electives and/or internship (21 semester hours)

Chosen under advisement - Mathematics concentration
- Required mathematics courses (12 semester hours)

MAT 411, 421, 441, 445 - Mathematics electives (18 semester hours)

At least one course in analysis, applied mathematics, and algebra, selected from upper-division (300 level or higher) mathematics courses - Related cognates (5 semester hours)

CSC 141*, ENG 371*, PHY 170*, PHY 180, SPK 230* - Independent study and free elective (16 semester hours)

Chosen under advisement
All math major courses must be passed with a C or better. - Required courses (12 semester hours)

MAT 161, 162, 261, and 311 - Approved electives (6 semester hours)

Any two courses in mathematics with course numbers above 311 with the exception of those courses with a primary focus on teacher training or those courses restricted to students majoring in elementary education.

*Indicates course satisfies a general education requirement.

## Minor in Mathematics (18 semester hours)

Baccalaureate students may receive transcript recognition for a minor area of study in mathematics by completing four required courses and two electives selected from the approved list.

*In this minor, a student must earn a minimum grade of C- in each course and have an average of at least 2.0 over all the courses taken in the minor.*

## Minor in Middle Grade Mathematics (4–8) (21 semester hours)

Required courses:

MAT 101, 102, 121, 312, 313, 351, and 352

*In this minor, a student must earn a minimum grade of C- in each course and have an average of at least 2.0 over all the courses taken in the minor.*

## Advanced Placement Policy

Course credit for success on AP exams in mathematics is awarded as follows:

AP Test | Score on AP Test | ||

3 | 4 | 5 | |

Calculus AB | MAT 108 | MAT 161 | MAT 161 |

Calculus BC | MAT 161 | MAT 162 | MAT 162 |

Statistics | MAT 121 | MAT 121 | MAT 121 |

## COURSE DESCRIPTIONS

### MATHEMATICS

Symbol: MAT

Q00 Fundamentals of Algebra (3) This course aims at strengthening basic algebraic skills. A student (other than an early childhood, elementary, and special education major) with a math SAT score greater than or equal to 440 and less than 480 must successfully complete this course with a grade of at least C- before enrolling in a 100-level mathematics course. Credits earned in Q00-level courses do not count toward the 120 hours of credit needed for graduation.

Q01 Fundamental Skills in Arithmetic (3) A course designed to strengthen basic arithmetic skills and to introduce the elements of algebra. Students, in general, are placed in MAT Q01 if their math SAT is less than 440. A student (other than an early childhood, elementary, or special education major) must complete this course and the subsequent course MAT Q00 with a grade of C- before enrolling in a 100-level mathematics course. An early childhood, elementary, or special education major with a math SAT score less than 480 must complete this course with a grade of at least C- before enrolling in MAT 101.

101 Mathematics for Teachers of Children I (3) Sets; functions; logic; development of whole numbers, integers, and rationals (including ratios, proportions, and percents); number theory; problem solving. For students seeking certification in grades PreK–4 or 4–8 only.

102 Mathematics for Teachers of Children II (3) Development of real numbers; geometry; measurement; probability and statistics; problem solving. For students seeking certification in grades PreK–4 or 4–8 only.

103 Introduction to Mathematics (3) This course is a liberal arts introduction to the nature of mathematics. Topics are chosen from among logic, graph theory, number theory, symmetry (group theory), probability, statistics, infinite sets, geometry, game theory, and linear programming. These topics are independent of each other and have as prerequisite the ability to read, reason, and follow a logical argument.

104 Introduction to Applied Mathematics (3) The course is designed to help prepare students to understand almost any quantitative issues they will encounter in contemporary society. Topics are selected from the following: principles of reasoning, problem-solving tools, financial management, exponential growth and decay, probability, putting statistics to work, mathematics and the arts, discrete mathematics in business and society, and the power of numbers.

105 College Algebra and Trigonometry (3) A unified course in algebra and trigonometry. PREREQ: High school algebra.

107 College Algebra (3) A thorough treatment of college algebra. Topics covered include the study of polynomial, exponential, and logarithmic functions, plus systems of linear equations. PREREQ: SAT score of 480 or above, or passing a placement exam, or obtaining at least a C- in MAT Q00.

108 Brief Calculus (3) An intuitive approach to the calculus of one and several variables with emphasis on conceptual understanding and practical application. PREREQ: C or better in MAT 105 or 107 or 110.

110 Precalculus (3) A preparation for MAT 161, Calculus I. Topics include polynomial and rational functions, algebra of functions, graphs of functions, transcendental functions, trigonometry, series, induction, and complex numbers.

121 Statistics I (3) Basic concepts of statistics. Frequency distributions, measures of central tendency and variability, probability and theoretical distribution, significance of differences, and hypothesis testing.

122 Statistics II (3) Continuation of MAT 121. Inference about the means, standard deviations and proportions, goodness of fit, analysis of variance, regression analysis, correlation, and nonparametric tests. PREREQ: MAT 121.

151 Introduction to Discrete Mathematics (3) Set theory, Boolean logic, elementary combinatorics, proofs, simple graph theory, and simple probability.

161 Calculus I (4) Differential and integral calculus of real-valued functions of a single real variable, with applications. PREREQ: C or better in MAT 110 or math SAT score of 590 or better and successfully pass challenge exam.

162 Calculus II (4) Continuation of MAT 161 including the study of series, methods of integration, transcendental functions, and applications to the sciences. PREREQ: C or better in MAT 161.

200 The Nature of Mathematics (3) Topics include the role of mathematics in contemporary society, career opportunities, mathematical notation and argument, structure of proofs, basic facts about logic, mathematical proofs, problem-solving techniques, and introductions to mathematical software packages. PREREQ: C or better in MAT 161. Course should be taken by end of sophomore year.

202 Elementary Functions and Essential Calculus I (3) Elementary functions from an advanced viewpoint with detailed discussion of formal manipulations. Special emphasis on applications and the use of technology. Open only to prospective grade 4-8 certification students. PREREQ: MAT 102.

203 Elementary Functions and Essential Calculus II (3) Continued discussion of elementary functions. Introduction to the intuitive ideas of derivative and integral with applications. PREREQ: MAT 202.

261 Calculus III (4) The calculus of several variables. Topics include polar coordinates, vectors and three-dimensional analytic geometry, differentiation of functions of several variables, multiple integrals, and line and surface integrals. PREREQ: C or better in MAT 162.

301 The Scientific Revolution (3) This course addresses how modern science began in the 17th century by examining its origins and including introductions to the heroes of science - Copernicus, Kepler, Galileo, and Newton. This course counts toward the writing emphasis requirement.

Approved interdisciplinary course. *Writing emphasis course.*

309 Topics in Mathematics for the Elementary Teacher (3) Introduction to programming in BASIC; computer uses for the classroom teacher; descriptive statistics with applications for teaching; and measurements of length, area, volume, and temperature that focus on the SI metric system with practice in the classroom. Additional topics in applied mathematics will be considered. PREREQ: MAT 102.

311 Linear Algebra (3) An introduction to linear algebra. Topics covered include matrices, systems of linear equations, vector spaces, linear transformation, determinants, eigenvalues, spectral theorem, and triangulation. COREQ or PREREQ: MAT 162.

312 Algebra for Teachers in Grades 4-8 (3) Formal structure of groups, rings, and fields with examples from the elementary curriculum. Topics from linear algebra including matrices, determinants, and linear programming. PREREQ: MAT 102.

313 Geometry for Teachers in Grades 4-8 (3) Modern informal approach to two- and three-dimensional geometric figures, measurement, similarity, congruence, coordinate geometry, and the postulational method. PREREQ: MAT 102.

319 Applied Statistics (3) This course will cover simple and multiple linear regression methods and linear time series analysis with an emphasis on fitting suitable models to data and testing, and evaluating models against data.

321 Combinatorics and Graph Theory (3) Introduction to set theory, graph theory, and combinatorial analysis. Includes relations, cardinality, elementary combinatorics, principles of inclusion and exclusion, recurrence relations, zero-one matrices, partitions, and Polya's Theorem. PREREQ: C or better in MAT 162.

325 Computational Mathematics (3) This course is designed to introduce the computer as an investigative tool in mathematics with emphasis on experimental techniques involving graphical and numerical displays, application of techniques from numerical analysis to data-driven problems, and the use of computers in solution techniques. PREREQ: C or better in MAT 162.

330 Using Technology in Teaching Elementary School Mathematics (3) Using computer software, calculators, and the Internet as aids in teaching elementary school mathematics. PREREQ: MAT 101 and 102.

331 Foundations of Geometry (3) Geometric foundations from an advanced viewpoint. Topics are chosen from euclidean and noneuclidean geometrics. PREREQ: C or better in MAT 162.

332 Differential Geometry (3) Classical differential geometry from a modern viewpoint. Curves and surfaces and shape operators. Introduction to Riemann geometry. PREREQ: C or better in MAT 200, 261, and 311.

343 Differential Equations (3) The general theory of nth order, and linear differential equations including existence and uniqueness criteria and linearity of the solution space. General solution techniques for variable coefficient equations, series solutions for variable coefficient equations, and study of systems of linear equations. PREREQ or COREQ: MAT 311; C or better in MAT 162.

345 Applied Probability (3) This course covers the standard concepts and methods of stochastic modeling as well as the applications of stochastic processes to other disciplines, including biology, management, social sciences, and statistics. PREREQ: C or better in MAT 261.

350 Foundations of Mathematics Education (3) Historical overview of mathematics education with emphasis on influential curricular programs, programs for exceptional students, implications of learning theory, significance of research, identification of current issues, organizational alternatives for the classroom, and evaluation resources. PREREQ: MAT 261.

351 Methods for Teaching Children Mathematics I (3) Concepts, learning aids, syllabi, texts, and methods in elementary school mathematics. PREREQ: MAT 101-102.

352 Methods for Teaching Children Mathematics II (3) Techniques for teaching children concepts such as geometry in two and three dimensions, number sentences, graphing, ratios and percentages, quantifiers, etc. Use of laboratory materials will be emphasized. PREREQ: MAT 351, field clearances, formal admission to teacher education.

354 Techniques of Teaching Secondary School Mathematics (3) Techniques used in the presentation of specific mathematical concepts, associated materials, including methods for exceptional students; levels of questioning, and motivational devices. Scope and sequence of secondary mathematics topics. Criteria for text evaluation. Preview of student teaching. PREREQ: MAT 350, formal admission to teacher education required.* Writing emphasis course.*

357 Teaching Mathematics to Diverse Populations (3) Methods and materials associated with the presentation of mathematics to the handicapped. Emphasis on individualization and involving thinking skills at the concrete level. Evaluative and interpretive techniques are included. PREREQ: MAT 101-102.

362 Calculus IV (3) The calculus of vector-valued functions of a vector variable. Derivatives and properties of the derivative including the chain rule, fields and conservative fields, integration, and Green's, Stokes's, and Gauss' theorems. PREREQ: C or better in both MAT 261 and 311.

381 Discrete Mathematics (4) This course is designed to provide a foundation for the mathematics used in the theory and application of computer science. Topics include mathematical reasoning, the notion of proof, logic, sets, relations and functions, counting techniques, algorithmic analysis, modelling, cardinality, recursions and induction, graphs, and algebra. PREREQ: C or better in MAT 162.

390 Seminar in Mathematics Education (3) This course is the capstone course for grades 4–8 certification students completing the 30-credit mathematics certification option. Topics selected from mathematics, statistics, the history of mathematics, and mathematics education for their significance and interest. Field experience may be required. PREREQ: Formal admission to teacher education.

*This course may be taken again for credit.*

400 History of Mathematics for Elementary Teachers (3) History and development of elementary mathematics from primitive times to the discovery of calculus. Problems of the period are considered. PREREQ: MAT 212 and 233.

401 History of Mathematics (3) Development of mathematics from the Babylonian era to the 18th century. Some modern topics included. PREREQ: C or better in MAT 261.

*Writing emphasis course.*

403 Fundamentals of Actuarial Science (3) Students completing this course will have a better understanding of actuarial models of life contingencies. More specifically, students will understand that payments such as life insurance, life annuity, and pension are determined by financial random variables dependent on human life. PREREQ: C or better in MAT 261.

405 Special Topics in Mathematics (3) Topics announced at the time of offering. PREREQ: Written permission of instructor required.

*This course may be taken again for credit.*

406 Mathematics of Finance (3) This course covers the mathematical theory of interest in a deterministic setting. Students will become familiar with compound interest and time value of money and learn how the two are used to compute the present and accumulated annuities values and bond prices, yield rates on investments, and the time required to accumulate a given amount or repay a loan. In addition, students should be able to apply interest theory to amortization of lump sums, fixed income securities, depreciation, and mortgages to name a few. PREREQ: C or better in MAT 261.

409 Financial Calculus (3) This course provides an introduction to the mathematics behind derivative pricing and portfolio management. Pricing theory is first developed through the typical binomial model and then is extended to continuous time via the Black-Scholes model. In addition, students will learn how to use arbitrage in pricing more complicated derivatives, such as call options on dividend-paying securities and exotic options. PREREQ: C or better in MAT 261.

411 Algebra I (3) Abstract algebra. Algebraic systems, groups, rings, integral domains, and fields. PREREQ: C or better in MAT 200, 261, and 311.

412 Algebra II (3) Abstract algebra. Algebraic systems, groups, rings, integral domains, and fields. PREREQ: C or better in MAT 411. MAT 411 must precede 412.

413 Computer Algebra (3) The focus of this course will be to introduce students to computer algebra packages and review important topics in algebra, calculus, and linear algebra. PREREQ: C or better in MAT 162 and 311.

414 Theory of Numbers (3) Properties of integers; primes, factorization, congruences, and quadratic reciprocity. PREREQ: C or better in MAT 200 and 261.

421-422 Probability theory, discrete and continuous random variables, distributions, and moment generating functions. Statistical sampling theory, joint and interval estimation, test of hypothesis, regression, and correlation. PREREQ: C or better in MAT 261, MAT 421 must precede 422, and must have a C or better in 441 to take 442.

425 Numerical Analysis (3) Numerical methods for the approximate solution of applied problems. Interpolation theory, curve fitting, approximate integration, and numerical solution of differential equations. PREREQ: C or better in CSC 141, and MAT 261, 325, and 343.

427 Introduction to Optimization Techniques (3) Nature of optimization problems: deterministic and stochastic, and discrete and continuous. Computer methods of solution, systematic and random search, linear quadratic, dynamic programming, and others. PREREQ: C or better in MAT 261 and 311.

432 Topology (3) Elements of point set topology. Separation axioms. Connectedness, compactness, and metrizability. PREREQ: C or better in MAT 200 and 261.

441 Real Analysis I (3) A rigorous treatment of the calculus of a single real variable. Topics in several real variables and an introduction to Lebesque integration. PREREQ: C or better in MAT 200 and 261.

442 Real Analysis II (3) A rigorous treatment of the calculus of a single real variable. Topics in several real variables and an introduction to Lebesque integration. PREREQ: C or better in MAT 441.

443 Applied Analysis I (3)The techniques of analysis applied to problems in the physical sciences. Topics include partial differential equations, orthogonal functions, complex integration, and conformal mapping. PREREQ: C or better in MAT 261, 311, and 343.

444 Applied Analysis II (3) The techniques of analysis applied to problems in the physical sciences. Topics include partial differential equations, orthogonal functions, complex integration, and conformal mapping. PREREQ: C or better in MAT 261 and 311, MAT 443 must precede 444, and must have a C or better in MAT 443 to take 444.

445 Complex Variables (3) Introduction to functions of a complex variable. Analytic functions, mappings, differentiation and integration, power series, and conformal mappings. PREREQ: C or better in MAT 261.

491 Internship in Applied Mathematics (2-4) In cooperation with regional businesses and industrial companies, students will perform an internship in applied mathematics. PREREQ: 3.0 GPA in major and related cognate courses.

*This course may be taken again for credit.*

493 Mathematical Modeling (3) The idea of a mathematical model of a real situation. Techniques and rationales of model building. Examples from the life, physical, and social sciences. PREREQ: C or better in MAT 261 and 343.

499 Independent Study in Mathematics (1-3) Independent investigation of an area of mathematics not covered in the department's course offerings. PREREQ: Written permission of the instructor.

This course may be taken again for credit.

### Symbol: STA

311 Introduction to Statistical Computing and Data Management (3) Course will give students the ability to manage and manipulate data effectively, conduct basic statistical analysis, and generate reports and graphics primarily using the SAS Statistical Software Program. PREREQ: C or better in MAT 121 or 421.