Mathematics
J. Alan Alewine, Ph.D., Assistant Professor of Mathematics;
Linda Lawton, Ph.D., Assistant Professor of Mathematics;
lblawton@mckendree.edu; (618) 537-6932; Voigt Science Hall 120
Dennis Ryan, Ph.D., Professor of Mathematics; Associate Dean of the College;
dryan@mckendree.edu; (618) 537-6926, Wildy Hall 3rd Floor;
(618) 537-6937, Voigt Science Hall 119
Within the Division of Science and Mathematics, we seek to provide a broad-based education that prepares graduates to be scientifically and mathematically literate, socially responsible, and professionally successful.
Within the program in mathematics, we have established the following goals for
our graduates:
• -Content: Graduates should have a broad-based understanding of core mathematical concepts as well as an understanding of concepts and techniques specific to their
specialization.
• -Practice: Graduates should be able to formulate and solve problems relevant to their area of specialization.
• -Communication: Graduates should be able to access existing mathematical knowledge and effectively communicate their own work to a broader community.
• -Professional Awareness: Graduates should develop personal and professional goals, the tools to achieve these goals, and an understanding of professional
responsibilities.
An undergraduate degree in mathematics prepares a student for a wide variety of career opportunities. Besides pursuing graduate degrees or teaching, graduates may be employed by government agencies and private industries. Moreover, an increasing number of employers are hiring mathematics majors for careers not usually considered mathematical because the problem solving skills developed by the mathematics student can be applied to other areas.
The mathematics major may seek a Bachelor of Arts or a Bachelor of Science degree in the general or secondary education track, or a Bachelor of Science degree with a finance/actuary concentration. For the Bachelor of Arts degree, the student must complete the mathematics, computer and/or economics courses listed below. For the Bachelor of Science degree, the student must satisfy these same requirements and must, in addition, complete either four science courses from two science areas, or a sequence of business courses. The student must complete all major requirement courses with a minimum cumulative grade point average of 2.25 and with no grade lower than C-. No course, including support courses, taken to satisfy a major requirement or number of hours requirements may be taken using the Pass/C-/D/Fail grading option.
The general concentration is designed for students interested in mathematics for graduate school or computing (with computer science as a second major).
Students seeking secondary school certification should pursue the secondary education track and, in addition, complete the general and professional education components. These are listed in the section entitled “Initial Secondary Certificate” in the Courses of Study section of this catalog under Education. If student teaching conflicts with one of the required mathematics courses, another course may be substituted with approval of the student’s advisor and the Provost. The education track is specifically designed to meet both the requirements of the State of Illinois and the standards set by the National Council of Accreditation of Teacher Education (NCATE), in conjunction with the National Council of Teachers of Mathematics (NCTM).
Students interested in mathematical finance, or in taking actuarial exams, should pursue the finance/actuary track. Students have the option of either a senior seminar or an internship as a capstone experience. Upon finishing the track, a graduate should be prepared to immediately seek employment with a variety of companies and/or to take the first three actuarial exams.
To obtain a minor in mathematics, the student must complete MTH 210, 211, 213, and an additional six credits in mathematics from courses numbered 300 or higher, excluding MTH 310. The same requirement regarding minimum cumulative grade point average and the Pass/C-/D/Fail grading option which applies to the major applies to the minor. Students majoring in Accounting or Economics and Finance may obtain a minor in actuarial sciences by taking mathematics courses 210 Calculus I, 211 Calculus II, 320 Financial Mathematics, 340 Introduction to Probability, 341 Applied Statistics, and 342 and by satisfying the Actuarial Track Supplementary requirements. The same requirement regarding minimum cumulative grade point average and the Pass/C/D/Fail grading option which applies to the major applies to the actuarial sciences minor.
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BACHELOR OF ARTS MAJOR REQUIREMENTS:
General track
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42-44 crs. |
MTH 210
MTH 211
MTH 213
MTH 300
MTH 360
MTH 391
MTH 392
MTH 393
MTH 490
CSI 130
CSI 230 |
CALCULUS I
CALCULUS II
VECTOR FUNCTIONS AND MATRICES
SET THEORY
LINEAR ALGEBRA
MULTIVARIATE CALCULUS
INTRODUCTION TO ANALYSIS
MODERN ALGEBRA I
SEMINAR IN MATHEMATICS
INTRODUCTION TO COMPUTING I
INTRODUCTION TO COMPUTING II
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(3)
(3)
(3)
(3)
(1-3)
(4)
(4)
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Two additional courses selected from:
MTH 301
MTH 330
MTH 340
MTH 341
MTH 350
MTH 366
MTH 370
MTH 375
MTH 376
MTH 394 |
COLLEGE GEOMETRY
COMPLEX ANALYSIS
PROBABILITY AND MATHEMATICAL STATISTICS I
PROBABILITY AND MATHEMATICAL STATISTICS II
INTRODUCTION TO ACTUARIAL MODELS
NUMERICAL ANALYSIS
DIFFERENTIAL EQUATIONS
DISCRETE STRUCTURES
GRAPH THEORY
MODERN ALGEBRA II
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(3)
(3)
(3)
(3)
(3)
(3)
(3)
(3)
(3)
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BACHELOR OF ARTS MAJOR REQUIREMENTS:
Secondary Education Track
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41-43 crs. |
MTH 210
MTH 211
MTH 213
MTH 300
MTH 301
MTH 340
MTH 370
MTH 375
MTH 391
MTH 393
MTH 490
CSI 130 |
CALCULUS I
CALCULUS II
VECTOR FUNCTIONS AND MATRICES
SET THEORY
COLLEGE GEOMETRY
PROBABILITY AND MATHEMATICAL STATISTICS I
DIFFERENTIAL EQUATIONS AND MODELING
DISCRETE STRUCTURES
MULTIVARIATE CALCULUS
MODERN ALGEBRA I
SEMINAR IN MATHEMATICS
INTRODUCTION TO COMPUTING I
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(4)
(4)
(4)
(3)
(3)
(3)
(3)
(3)
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(3)
(1-3)
(4) |
Two additional courses selected from:
MTH 330
MTH 341
MTH 350
MTH 360
MTH 366
MTH 376
MTH 392
MTH 394 |
COMPLEX ANALYSIS
PROBABILITY AND MATHEMATICAL STATISTICS II
INTRODUCTION TO ACTUARIAL MODELS
LINEAR ALGEBRA
NUMERICAL ANALYSIS
GRAPH THEORY
INTRODUCTION TO ANALYSIS
MODERN ALGEBRA II
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(3)
(3)
(3)
(3)
(3)
(3)
(3)
(3) |
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BACHELOR OF SCIENCE MAJOR REQUIREMENTS:
Finance/Actuary Track
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56-60 crs. |
MTH 210
MTH 211
MTH 213
MTH 300
MTH 320
MTH 340
MTH 341
MTH 342
MTH 391
MTH 440
MTH 470
or
MTH 490
CSI 130 |
CALCULUS I
CALCULUS II
VECTOR FUNCTIONS AND MATRICES
SET THEORY
FINANCIAL MATHEMATICS
PROBABILITY AND MATHEMATICAL STATISTICS I
PROBABILITY AND MATHEMATICAL STATISTICS I I
SEMINAR FOR EXAM P/1
MULTIVARIATE CALCULUS
ACTUARIAL MODELS I
INTERNSHIP IN MATHEMATICS
SEMINAR IN MATHEMATICS
INTRODUCTION TO COMPUTING I
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| Supplementary requirements |
20 crs. |
ACC 261
ACC 262
ECO 211
ECO 21
FIN 308
FIN 355 |
PRINCIPLES OF ACCOUNTING I
PRINCIPLES OF ACCOUNTING II
PRINCIPLES OF MICROECONOMICS
PRINCIPLES OF MACROECONOMICS
PRINCIPLES OF BUSINESS FINANCE
INVESTMENTS
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Recommended Elective
| CSI 230 |
INTRODUCTION TO COMPUTING II |
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| BACHELOR OF SCIENCE MAJOR REQUIREMENTS |
52-60 crs.
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Same as above for Bachelor of Arts with one of the following two options
in addition;
1. -Four science courses from at least two of the following sciences: biology, chemistry (except CHE 100 and CHE 101) and physics (except PHY 101).
2. -Four business courses including ACC 261, ECO 211,
but not including BUS 310.
MTH 105 INTERMEDIATE ALGEBRA (3)
This course is for students who have had no more than one year of high school algebra or who have not had mathematics for some time. The course consists of a review of elementary algebra and additional work in linear and quadratic equations, factoring, exponents, polynomials, graphing and linear systems. Students may not apply credit for both MTH 105 and MTH 111 toward fulfillment of the core curriculum requirements. Each semester.
MTH 111 MATHEMATICS FOR EDUCATORS (3)
Elementary topics and fundamental concepts studied from a modern point of view. Real number system developed carefully. This course is designed to be a review for the Illinois Basic Skills Test required for admission to the Teacher Education Program. Each semester.
MTH 131 COLLEGE ALGEBRA (3)
A course beginning with the fundamentals of the real numbers and sets which are used to develop a logical system of algebra including the study of linear equations, radicals, quadratic equations, inequalities, permutations and probability. Prerequisites: One and one-half units of entrance algebra and one unit of geometry or MTH 105 or consent of instructor. Each semester.
MTH 132 TRIGONOMETRY (3)
Study of trigonometric functions, identities, addition formulas, solution of triangles, inverse functions, logarithms. May be taken the same term as MTH 131. Prerequisite: MTH 131 or consent of instructor. Each semester.
MTH 142 FINITE MATHEMATICS (3)
Introduction to elementary combinatorial mathematics. Topics to be discussed include logic, sets, relations and functions, number systems, matrices, finite probability, mathematics of computer computation, and linear programming. Prerequisites: One and one half units of algebra and one unit of geometry or MTH 105 or consent of the instructor. Each semester.
MTH 210 CALCULUS I (4)
The calculus of single variable algebraic, exponential, logarithmic, and trigonometric functions culminating in the Fundamental Theorem of Calculus. Prerequisite: MTH 132 or consent of the instructor. Each semester.
MTH 211 CALCULUS II (4)
Techniques of integration, applications of integration, parametric equations, polar coordinates, and infinite sequences and series. Prerequisite: MTH 210. Each semester.
MTH 213 VECTOR FUNCTIONS AND MATRICES (4)
A study of the calculus of vector functions and elementary matrix algebra. Prerequisite: MTH 211. Annually, Fall.
MTH 220 SURVEY OF CALCULUS (3)
An introductory survey of the essential ideas of calculus. Topics are drawn from the differential, integral, and multivariate calculus. Historical considerations are discussed as appropriate. This course is appropriate for elementary education majors concentrating in mathematics, but does not fulfill the calculus requirement for mathematics majors in any track. Prerequisite: College algebra or consent of the instructor. May not be taken for major credit. Annually, Fall, or as needed.
MTH 280-289 SPECIAL TOPICS IN MATHEMATICS (1-3)
As needed.
MTH 300 SET THEORY (3)
Introduction to the methods of proof through the study of sets, logic, relations, mappings, cardinality, and elementary structures. Prerequisite: MTH 210 or consent of the instructor. Annually, Fall.
MTH 301 COLLEGE GEOMETRY (3)
The study of geometry including a review of elementary geometry, Euclidean, non-Euclidean, and transformational geometries. Prerequisite: MTH 210 or MTH 220. Annually, Fall.
MTH 310 STATISTICS (4)
This is an introductory course in descriptive and inferential statistics, approached through intuition, algebra, and problem solving. Understanding of central concepts and methods is stressed. Practical applications in the fields of social and physical sciences are studied. Real-world problems are solved through use of statistical computer packages such as SPSS, SAS, or MINITAB. Prerequisites: MTH 105 and computer literacy. Each semester.
MTH 320 Financial Mathematics (3)
Interest rate measurement, annuities, loan repayment, bond valuation, measuring rate of return of investment, term structure of interest rates, cashflow duration and immunization, and other topics as found on Actuarial Exam FM/2. Prerequisite: MTH 211. Alternate years, Fall ‘07
MTH 330 COMPLEX ANALYSIS (3)
Introduction to the study of holomorphic functions of one complex variable. Cauchy-Riemann equations, elementary functions, Laurent series, integral theorems, mappings, applications. Prerequisite: MTH 213. As needed.
MTH 340 Introduction to Probability and Statistics (3)
Probability axioms, basic statistical measures including mean, variance, and standard deviation, commonly used discrete and continuous distribution, transformations, moment generating functions, and multivariate distributions as well as the multivariate calculus necessary to work with the multivariate
distributions. Alternate years, Spring ‘06 or as needed. Alternate years, Fall ‘06 or as needed.
MTH 341 Applied Statistics (3)
Regression analysis (least square estimates of parameters, single and multiples linear regression, hypothesis testing) and time series (linear time series models, moving average, autoregressive and/or ARIMA models, estimation, data analysis and forecasting with time series models, forecast errors and confidence intervals). Prerequisite: MTH 213 or consent of the instructor. Alternate years, Spring ‘07 or as needed.
MTH 342 Seminar for Exam P/1 (3)
Probability, commonly used discrete and continuous distributions, and multivariate distributions with emphasis on applications to insurance and the actuarial sciences phrased in the language of those fields. Prerequisite: MTH 340 or consent of instructor. Alternate years, Spring ‘08
MTH 360 LINEAR ALGEBRA (3)
An introduction to the techniques of linear algebra. Topics include vector spaces, linear independence, basis, dimension, linear transformations, eigenvalues, and eigenvectors. Prerequisite: MTH 213 and MTH 300 or permission of the instructor. Alternate years, Spring ‘08 or as needed.
MTH 366 NUMERICAL ANALYSIS (3)
An introductory course in numerical methods, including computational techniques for locating roots of equations, interpolation, differentiation, integration, approximation, and systems of linear equations; to include detection, prediction, and control of computational errors. Problem solving using mathematical computer programs and computer programming of algorithms is stressed. Prerequisite: MTH 213 and CSI 230; same as CSI 366. As needed.
MTH 370 DIFFERENTIAL EQUATIONS AND MODELING (3)
An introductory course in the solution of elementary differential equations and of their applications in a variety of real world contexts. A general study of mathematical modeling is included . Prerequisite: MTH 211 or consent of instructor. Annually, Spring.
MTH 375 DISCRETE STRUCTURES (3)
An introduction to the methods of discrete mathematics. Topics may include logic, sets and mappings, recurrence relations, graphs, techniques and applications of group theory and linear algebra, finite automata, algorithms, and computational complexity. Prerequisite: MTH 210 or consent of the instructor. Annually, Spring.
MTH 376 Graph Theory (3)
Introductory concepts and definitions, trees, planar graphs, chromatic numbers, matchings, and Ramsey theory. Prerequisite: MTH 211. Annually, Fall, or as needed.
MTH 380-389 SPECIAL TOPICS IN MATHEMATICS (1-3)
As needed.
MTH 391 MULTIVARIATE CALCULUS (3)
Limits, derivatives, and integrals of functions of several variables. Vector fields, line and surface integrals; the theorems of Green, Gauss, and Stokes. Prerequisite: MTH 213. Annually, Spring.
MTH 392 INTRODUCTION TO ANALYSIS (3)
Introduction to analysis on the real line with emphasis on careful development of limits, continuity, and differentiation. Prerequisite: MTH 212 and MTH 300. Alternate years or as needed. Spring ‘07.
MTH 393 MODERN ALGEBRA I (3)
Prerequisite: MTH 300. Alternate years, or as needed. Fall ‘06, with MTH 394 an introduction to the basic notions of modern algebra. Topics covered include: the integers, groups, rings, fields, homomorphiems and related notions.
MTH 394 MODERN ALGEBRA II (3)
A continuation of MTH 393. Prerequisite: MTH 393. Spring ‘07.
MTH 440 Actuarial Models I (3)
Survival and severity models, frequency models, compound (aggregate) models, and life contingencies. Prerequisite: MTH 340 & MTH 342, or consent of instructor. Alternate years, Fall ‘06.
MTH 441 Actuarial Models II (3)
Construction of empirical models, construction and selection of parametric mo0dels, credibility, interpolation and smoothing, and simulation Prerequisite: MTH 441 or consent of instructor. Alternate years, Spring ‘07.
MTH 470 INTERNSHIP IN MATHEMATICS (3-8)
MTH 480 INDEPENDENT STUDY IN MATHEMATICS (1-4)
MTH 490 SEMINAR IN MATHEMATICS (3)
Topics drawn from a variety of advanced topics in mathematics. Prerequisite: Permission of the instructor. Annually, Fall.