Mathematics

Professor John Nichols, Chair, Division of Mathematics and Computer Science

The Major in Mathematics consists of 56/55 hours in mathematics and related fields. Required courses in mathematics are 125, 225, 232, 235, 236, 299, 302, 315, 321, 326, 351, 352, 399, and two courses selected from 303, 316, 322, or 349. Three related courses are chosen from Physics 201, Physics 202, Computer Science 111 and Computer Science 112. Any student who expects to attend graduate school is advised to acquire intermediate-level proficiency in French or German. Students desiring more depth in the related fields of Computer Science, Physics, or Statistics are encouraged to complete a minor in one or more of these areas.

The Major in Mathematics for Teacher Licensure consists of 50 hours in mathematics and related fields and 6 additional hours in liberal studies. Required courses in mathematics are 125, 225, 232, 235, 299, 301, 302, 315, 321, 326, 351, 352, and 399. Related courses are Physics 201 and 202 and Computer Science 111. Liberal studies courses are Psychology 101 and Sociology 271. Students pursuing this track must complete 29 credit hours of professional courses in teacher education. These courses are listed under Education in this catalog.

The Minor in Mathematics requires a minimum of 16 credit hours, including Mathematics 125, 225, 232 and five additional credit hours in mathematics above Mathematics 225 excluding Mathematics 307, 308 and 399.

The Minor in Statistics consists of 16 semester hours, including Mathematics 125, 221, 222, 321, and 322 or 343 (3 hours).

Course Descriptions

105. Fundamentals of Mathematics
0 credit hours
A review of basic algebraic skills, signed numbers, fractions, exponents, linear and quadratic equations, inequalities, absolute value, and scientific notation. This course may be included as a three-credit entry in the determination of full-time status, but it does not count toward the minimum hours needed for graduation, and it is not used in the calculation of grade point average. Required of all students who lack an entrance credit in algebra or who perform below minimum standards on the mathematics assessment.
115. Precalculus Mathematics
4 credit hours
Prerequisite: Satisfactory performance on the mathematics assessment or Mathematics 105
A foundational course in college algebra and trigonometry. Topics include functions, polynomial and rational functions, exponential and logarithmic functions, trigonometric functions, analytic trigonometry, and complex numbers.
125. Calculus I
4 credit hours
Prerequisite: Mathematics 115 or the equivalent
An introduction to calculus using computer technology. Topics include functions, limits, the derivative and its applications, and the definite integral. All topics are presented geometrically, numerically, and algebraically.
221. Inferential Statistics
3 credit hours
Prerequisite: Statistics 120
Topics include interval estimation, hypothesis testing, analysis of variance, basic experimental design, nonparametric statistics, and chi-square tests.
222. Regression Analysis
3 credit hours
Prerequisite: Statistics 120
Topics include linear regression, multiple regression, nonlinear regression, and regression diagnostics.
225. Calculus II
4 credit hours
Prerequisite: Mathematics 125
A continuation of Mathematics 125. Topics include the definite integral and its applications, sequences and series, and approximations using Taylor series.
232. Linear Algebra
3 credit hours
Prerequisite: Mathematics 125
Topics include linear equations, vector spaces, linear transformations, determinants, matrices, and applications.
235. Calculus III
4 credit hours
Prerequisite: Mathematics 225
A course in multivariable calculus using computer technology. Topics include functions of several variables, vectors, partial differentiation, multiple integration, parametric equations, vector fields, and line integrals.
236. Ordinary Differential Equations
3 credit hours
Prerequisite: Mathematics 225
An introduction to linear and non-linear differential equations. Topics include methods of undetermined coefficients, variation of parameters, differential operators, Laplace transforms, and qualitative methods. Applications are taken from the natural and social sciences.
299. Foundations of Higher Mathematics
2 credit hours
Prerequisite: Mathematics 232 or the permission of the Mathematics/Computer Science Division Chair
A seminar designed to help students make the transition from freshman/sophomore level mathematics to the more theoretical junior/senior level mathematics. Topics include proof techniques, set theory, and logic. The course emphasizes reading, writing, and presentation of mathematical proofs.
301. Principles of Geometry
3 credit hours
Pre- or co-requisite: Mathematics 299
Topics from Euclidean and Non-Euclidean Geometry both from the synthetic and the analytical points of view. This course is designed specifically for secondary teachers of mathematics.
302. Modern Algebra
3 credit hours
Prerequisite: Mathematics 299
An introduction to abstract algebra. Topics include groups, rings, integral domains, and fields.
303. Advanced Algebra
3 credit hours
Prerequisite: Mathematics 302 or the permission of the instructor
Topics will be selected from the areas of groups, rings, fields, vector spaces, and transformations.
307. Mathematics and Instructional Strategies for K-6 and 4-8 Teachers I
3 credit hours
Prerequisites: Level I Screening, Junior Standing, and Statistics 120 | Co-Requisite: Education 303
Students develop an understanding of essential mathematical knowledge that integrates content and instructional strategies appropriate for elementary grades K-6 and middle grades 4-8. Content areas include mathematical processes, number/operations, and algebra. Peer teaching, micro-teaching, and field observations are integral components.
308. Mathematics and Instructional Strategies for K-6 and 4-8 Teachers II
3 credit hours
Prerequisites: Mathematics 307 and Education 303 or permission of the division chairs of Mathematics/Computer Science and Behavioral Sciences
A continuation of Mathematics 307. Content areas include geometry, measurement, and data analysis and probability. Peer teaching, microteaching, and field observations are integral components.
315. Advanced Calculus
3 credit hours
Prerequisites: Mathematics 235 and 299
An introduction to Real Analysis. Topics include sequences, the theory of limits, continuity, differentiation and integration.
316. Advanced Calculus II
3 credit hours
Prerequisite: Mathematics 315 or permission of the instructor
A continuation of Mathematics 315. Topics include the theory of Riemann integration, infinite series, sequences and series of functions, and power series.
321. Probability and Statistics I
3 credit hours
Prerequisites: Statistics 120 and Mathematics 299 and junior standing; or Mathematics 125 and permission of the instructor
An introduction to probability, including counting methods, discrete and continuous probability distributions and their properties, and sampling distributions.
322. Probability and Statistics II
3 credit hours
Prerequisite: Mathematics 321 or permission of instructor
A continuation of Mathematics 321. Topics include point estimation, including maximum likelihood estimation and methods of moments, confidence intervals, tests of hypotheses, and regression.
326. Numerical Analysis
3 credit hours
Prerequisites: Mathematics 225; and Mathematics 299 or permission of the instructor.
An introduction to the techniques of obtaining numerical solutions on a computer. Topics include roots of equations, numerical integration, least squares, simultaneous equations, and curve fitting.
337. Internship in Mathematics
7 to 15 credit hours
Practical off-campus experience in a field setting. One credit hour is associated with each week of full-time employment.
343. Practicum in Mathematics
2 to 6 credit hours
Prerequisite: Junior standing
Practical experience enabling students to apply classroom knowledge in an organizational setting. One credit hour is associated with each three hours of work every week for a 14-week semester.
349. Selected Topics in Mathematics
3 credit hours
Prerequisites: Junior standing and permission of instructor
Topics selected from such areas as Real Anaylsis, Complex Analysis, History of Mathematics, Number Theory, or Partial Differential Equations, depending on current faculty and student interest.
351-352. Senior Study
6 credit hours
Prerequisites: FRS 140, English Proficiency Exam, junior standing; and at least 21 hours in mathematics courses, including 6 hours at the 300-level, that satisfy requirements for the Major in Mathematics
The Senior Study requirement is fulfilled with this two-course sequence. The study may take one of several forms: activity directed toward the creation or discovery of new mathematics, works of scholarship about mathematics, independent study or a mathematical topic outside of the curriculum, or an individual or collaborative project involving experimentation, data collection, and statistical analysis. All involve individual study and research under the guidance of a faculty supervisor and culminate in a formal paper that follows a division-specific format.
399. Research Seminar
1 credit hour
Prerequisite: Junior standing
A seminar focusing on development of research skills and methods in mathematics to prepare students for the Senior Study experience. Topics include literature search strategies, mathematical writing, poster and report preparation, and techniques for oral presentations. Students will be introduced to discipline-specific software used in Senior Study, as well as to professional organizations and trends in professional issues.