Programs

Students will be guided by the outline of baccalaureate Degrees, the University Core Curriculum, and the concentration areas listed below.

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COURSES:

MATHEMATICAL SCIENCES (MATHS)

108 Intermediate Algebra. (3)
Reviews factoring, quadratic equations and inequalities, relations and functions, rational exponents, systems of linear equations, and exponential and logarithmic functions.  Offered credit/no credit only.
Recommended background: two years of college preparatory mathematics in high school or the equivalent.  
Not open to students who have credit in MATHS courses numbered higher than 108 except MATHS 125.

111 Pre-Calculus Algebra.  (3) 
Such topics as polynomial functions and equations, exponential and logarithmic functions, determinants, systems of equations and inequalities, mathematical induction, the binomial theorem, permutations and combinations, and progressions.  
Prerequisite: MATHS 108, or appropriate score on the SAT/ACT or mathematics placement test, or permission of the department chairperson.  
Not open to students who have credit in MATHS 161 or higher.

112 Precalculus-Trigonometry. (3)
Trigonometric functions, identities, and equations; graphs of the trigonometric and inverse trigonometric functions; solution of right and general triangles; polar coordinates; and complex numbers. Students will be required to use scientific calculators.
Prerequisite: MATHS 108 or 111 or permission of the department chairperson.
Not open to students who have credit in MATHS 161 or higher.

125 Mathematics and Its Applications. (3)
University Core Curriculum course including such topics as mathematical modeling, problem solving, geometrical concepts, growth patterns, and applications to the physical sciences, social sciences, and economics.
Recommended background: three years of college preparatory mathematics in high school.

150 Introduction to Secondary Mathematics Education. (3) 
An introduction to secondary mathematics teaching. Content includes constructing an informed vision of mathematics and mathematics teaching, developing basic skills for teaching mathematics, and beginning preparation for teacher licensure.  Prerequisite or parallel: MATHS 165 or permission of the department chairperson.

161 Applied Calculus 1. (3)
Discussion of limits, derivatives, differentials, and definite and indefinite integrals. Focuses on the application of these topics in the applied sciences.
Prerequisite: MATHS 112 or permission of the department chairperson.
Not open to students who have credit in MATHS 165.

162 Applied Calculus 2. (3)
Derivatives and integrals of transcendental functions with additional applications, techniques of integration, improper integrals, calculus in higher dimensions and series.
Prerequisite: MATHS 161 or 165.
Not open to students who have credit in MATHS 166.

165 Calculus 1. (4)
Differential calculus of algebraic and transcendental functions and applications, antidifferentiation and the Riemann integral.  Includes the use of graphing calculators and computer software.  Prerequisite: MATHS 111, 112; or sufficient background in algebra and trigonometry as evidenced by the student’s high school record, SAT/ACT scores, and/or score on the mathematics placement test.

166 Calculus 2. (4)
Standard techniques of integration, applications of the integral, sequences and series, indeterminate forms, and numerical methods. Includes the use of graphing calculators and computer software.
Prerequisite: MATHS 165.

181 Elementary Probability and Statistics. (3)
Algebra-based introduction to statistical applications through descriptive methods, probability, normal distributions, confidence intervals, hypotheses tests, regression, and correlation.  Misuses of statistics and common probability misconceptions are discussed. Statistical experiments and simulations are conducted. Technology use is integrated throughout. 
Prerequisite: qualifying ACT or SAT score, or appropriate score on the mathematics placement test, or MATHS 108, or permission of the department chairperson.

201 Number, Algebra, and Probability for the Elementary Teacher. (4) 
In-depth treatment of concepts underlying common topics in the elementary mathematics curriculum including concepts in number and operation, algebra, and probability. Use of selected concrete manipulatives and technology is included.
Prerequisite: qualifying score on Gateway Examination and any of the following: qualifying ACT or SAT score, or appropriate score on the mathematics placement test, or MATHS 108, or permission of the department chairperson.
Open only to majors in elementary, special, or early childhood education.

202 Data Analysis, Geometry, and Measurement for the Elementary Teacher. (3)
In-depth treatment of concepts underlying common topics in the elementary mathematics curriculum including concepts in data analysis, geometry, and measurement. Use of selected concrete manipulatives and technology is included. May be substituted for MATHS 203.
Prerequisite: qualifying score on Gateway Examination and MATHS 201 with a C- or better grade.
Not open to students who have credit in MATHS 203.

203 Data Analysis, Geometry and Measurement for the Primary Grades Teacher. (2)
In-depth treatment of concepts underlying common topics in the elementary mathematics curriculum including selected concepts in data analysis, geometry, and measurement. Use of selected concrete manipulatives and technology is included.
Prerequisite: qualifying score on Gateway Examination and MATHS 201 with a C- or better grade.
Not open to students who have credit in MATHS 202.

207 Mathematics for the Teacher of the Exceptional
Learner. (4)
Development of concepts in number and operation, algebra, geometry, measurement, data analysis, and probability needed by teachers of exceptional learners. Use of selected concrete manipulatives and technology is included.
Prerequisite: qualifying score on Gateway Examination and any of the following: qualifying ACT or SAT score, or appropriate score on the mathematics placement test, or MATHS 108, or permission of the department chairperson.
Not open to students who have credit in MATHS 201, 202, or 203. Open only to special education majors.

215 Discrete Systems. (4)
Topics from discrete mathematics, including formal logic, methods of proof, set theory, relations, recursion, combinatorics, and graph theory. A systematic development of number systems via equivalence classes is included as an application of these topics.
Prerequisite: MATHS 162 or 165 or permission of the department chairperson.

221 Probability and Statistics. (3) 
Elementary probability theory, random variables, discrete and continuous probability distributions. Theory and applications of descriptive and inferential statistics. Statistical software and graphing calculator use is integrated throughout the course.  Prerequisite: MATHS 162 or 165 or permission of the department chairperson.

222 Statistical Studies. (1) 
Continuation of MATHS 221 focusing on a few additional topics.  A major component is the design, implementation, analysis, and presentation of statistical studies. Technology is an integral part, including statistical software and graphing calculators.  Prerequisite: MATHS 221 or permission of the department chairperson.

250 Pre-College Mathematics from an Advanced
Viewpoint.  (3) 
In-depth treatment of concepts underlying common topics in the middle and high school mathematics curriculum. Topics include number systems, polynomial and transcendental functions, analytic geometry, theory of equations, and measurement.  Prerequisite: MATHS 150, 166, 215.  
Open only to mathematics teaching majors.

267 Calculus 3. (4)
Multidimensional calculus and its applications. Topics include three-dimensional vector calculus, Gauss's theorem, Green's theorem, and Stoke's theorem. Includes the use of graphing calculators and computer software.
Prerequisite: MATHS 166.

271 Mathematics Contest Problem Solving. (1)
Advanced mathematics problem-solving strategies for individuals and groups. Designed to prepare participants for the Putnam Exam and other collegiate mathematics contests. 
Open to all students.
A total of 2 hours of credit may be earned, but no more than 1 in any one semester or term.

298 Undergraduate Colloquium. (1)
A series of brief introductions to the mathematical landscape including glimpses of mathematics in the workplace. Topics are drawn from all areas of the mathematical sciences.
A total of 3 hours of credit may be earned, but no more than 1 in any one semester or term.

299X Experimental/Developmental Topics. (1-6)
Topics relevant to the discipline. Course titles will be announced before each semester.
A total of 6 hours of credit may be earned.

310 Topics in Algebra for the Elementary and Middle School Teacher. (3) 
Development of algebraic concepts including variables, functions, and matrices, and applications of these topics in the elementary and middle school curriculum.  
Prerequisite: MATHS 202 with a C- or better grade.

311 Algebraic Structures. (3)
Consideration of the basic algebraic structures: groups, rings, integral domains, and fields. Examples of these structures and elementary proof will be emphasized as will polynomials over rings, integral domains, and the fields of real and complex numbers.
Prerequisite: MATHS 215, 217.

316 Topics in Number Theory for the Elementary and Middle School Teacher. (3) 
The study of a collection of topics from the theory of numbers that have specific applications in the elementary and middle school curriculum.  
Prerequisite: MATHS 202 with a C- or better grade.

320 Probability. (4)
Probability theory for discrete and continuous sample spaces, random variables, density functions, distribution functions, marginal and conditional distributions, mathematical expectation, moment-generating functions, common distributions, sampling distribution theory, central limit theorem, t, chi-square, and F distributions.
Prerequisite: MATHS 166, 215.

321 Mathematical Statistics. (4)
Point and interval estimation, maximum likelihood, Neyman-Pearson Lemma, likelihood ratio tests, classical tests of significance, goodness-of-fit, contingency tables, correlation, regression, nonparametric methods, Bayesian methods.
Prerequisite: MATHS 320.

330 Technology in Elementary and Middle School Mathematics. (3)  
The use of technology in elementary and middle school mathematics, such as spreadsheets, calculators, algebraic or geometric modeling tools, educational software, and World Wide Web applications.  
Prerequisite: MATHS 202 with C- or better grade.

331 Technology in the Teaching of Secondary
Mathematics. (3) 
The use of technology in the teaching of secondary and middle school mathematics, such as spreadsheets, calculators, algebraic or geometric modeling tools, educational software, and World Wide Web applications.  
Prerequisite: MATHS 250; admission to Teacher Education; permission to enroll in 300/400-level professional education courses.

335 Mathematical Models. (3)
Construction of mathematical models for use with problems in physics, chemistry, biology, and economics. Emphasizes the construction and interpretation of models. Existing computer software will be used.
Prerequisite or parallel: MATHS 166, 217.

345 Survey of Geometries. (4) 
A comparative study of Euclidean and non-Euclidean geometries, their respective histories and technologies, and their applications in mathematics, the sciences, and modern life.  
Prerequisite: MATHS 166, 215, 217.

360 Topics in Geometry for the Elementary and Middle School Teacher. (3) 
Investigation of selected topics in geometry and measurement, from both historical and contemporary perspectives, with applications in the elementary and middle school curriculum.  Prerequisite: MATHS 202 with a C- or better grade.

368 Unpaid Professional Experience in Mathematical Sciences. (1-8)
Supervised unpaid work and learning experience as a practicing mathematician, statistician, or actuarial scientist. Practical problem-solving experience will be gained through an internship, practicum, or other such situation.  Offered credit/no credit only.
Prerequisite: permission of the department chairperson.
A total of 8 hours of credit may be earned in MATHS 368 and 369 combined.

369 Paid Professional Experience in Mathematical
Sciences. (1-8)
Supervised paid work and learning experience as a practicing mathematician, statistician, or actuarial scientist. Practical problem-solving experience will be gained through an internship, practicum, or other such situation.  Offered credit/no credit only. 
Prerequisite: permission of the department chairperson.
A total of 8 hours of credit may be earned in MATHS 368 and 369 combined.

371 Intermediate Analysis. (3)
Introduction to basic concepts of analysis: the real numbers, sequences, continuous functions, the derivative, and the Riemann integral.
Prerequisite: MATHS 166, 215, or permission of the department chairperson.

377 Complex Analysis. (3)
Algebra and geometric representation of complex numbers, properties of complex analytic functions, contour integration, power series and Laurent series, poles and residues, conformal mapping, and applications.
Prerequisite: MATHS 267 or permission of the department chairperson.

390 Honors Colloquium in Mathematics. (1-6)  
Selected topics in mathematics with emphasis on individualized study.  
A total of 6 hours of credit may be earned.

395 Teaching and Learning Mathematics in the Secondary School. (3)
Examination of national and state mathematics standards, curricular materials, and methods for teaching mathematics to secondary school students. Issues related to mathematics curriculum, instruction, and assessment of secondary school students. Class ideas applied in teaching situations.
Prerequisite: MATHS 311, 345, 393, a minimum grade-point average of 2.5 in all mathematics courses that are to be applied to the major, and admittance to teacher education and permission to enroll in 300/400-level professional education courses.
Parallel: EDSEC 380.

411 Abstract Algebra 1. (3) 
The theory of groups, including subgroups, cyclic groups, normal subgroups, cosets, Lagrange’s Theorem, quotient structures, homomorphisms, automorphisms, group actions, Sylow’s Theorems, structure of finite abelian groups, generators and relations.  
Prerequisite: MATHS 311 or permission of the department chairperson.

412 Abstract Algebra 2. (3) 
An introduction to the theory of rings, including integral domains, division rings, and fields. Quotient fields of integral domains.  Homomorphisms, ideals, and quotient structures. Factorization in commutative rings. Polynomial rings and field extensions.  Aspects of Galois theory.  
Prerequisite: MATHS 411 or permission of the department chairperson.

415 Mathematics of Coding and Communication. (3)
Exploration of applications of number theory, group theory, and linear algebra to areas such as cryptography and error-correcting codes; applications of graph theory to resource allocation and route planning; other possible topics selected by the instructor.
Prerequisite: MATHS 311 or permission of the department chairperson.

416 Theory of Numbers. (3)
Topics include the division algorithm; positional notation; divisibility; primes; congruences; divisibility criteria; the sigma, divisor, and phi functions; diophantine equations; linear, polynomial, and simultaneous congruences; theorems of Fermat, Euler, Lagrange, and Wilson; quadratic reciprocity.
Prerequisite: MATHS 215 or permission of the department chairperson.

422 Theory of Sampling and Surveys. (3)
Survey designs; simple random, stratified, cluster, and systematic sampling; ratio estimates; regression estimates; cost and variance functions.
Prerequisite: MATHS 321 or its equivalent.

428 Regression and Time Series Models. (3) 
Addresses regression topics that include simple and multiple linear regression, polynomial regression, regression diagnostics, and forecasting. Introduces time series topics that include exponential smoothing, auto-regressive, integrated, moving average (ARIMA) models, and forecasting.  
Prerequisite: MATHS 321 or equivalent.

429 Analysis of Variance in Experimental Design Models. (3)
Multivariate normal distribution; quadratic forms; linear models; simple random, randomized block, Latin squares, factorial, split-plot, balanced incomplete block design; analysis of covariance; confounding; multiple comparison tests.
Prerequisite: MATHS 321 or its equivalent.

441 Geometry and Topology. (3)
Introduction to geometric topology, including piecewise linear structures, Euler's formula, surfaces and solids, knots, graphs, and other topics.
Prerequisite: MATHS 217, 267; or permission of the department chairperson.

445 Differential Geometry. (3) 
Fundamentals of differential geometry, as an extensive study of curves and surfaces in 3-space. Includes the use of computer visualization and emphasizes the importance of differential geometry in areas like relativity theory and modern physics.  Prerequisite: MATHS 267 or permission of the department chairperson.

452 Mathematics of Life Contingencies 1. (4)
Survival distributions, life tables; the mathematics of life insurance, life annuities, net premiums, and net premium reserves.
Prerequisite: MATHS 321, 351, and a minimum grade-point average of 2.5 in all mathematics courses that are to be applied to the major.

453 Mathematics of Life Contingencies 2. (4)
Mathematics of multiple life functions, multiple decrement models, valuation theory for pension plans, insurance models including expenses, nonforfeiture benefits, and dividends.
Prerequisite: MATHS 452.

454 Mathematics of Investments. (4) 
Mathematical analysis and actuarial principles of investments and asset management.  
Prerequisite: MATHS 320, 351; or permission of the department chairperson.

456 Introduction to Operations Research. (3) 
Optimization techniques of linear programming, dynamic programming, and integer programming. Optimal solutions of PERT-CPM networks. Optimal decision strategies.  
Prerequisite: MATHS 162 or 166, 217, or permission of the department chairperson.

460 History of Mathematics. (3)
The development of mathematics from prehistoric times to the seventeenth century. Topics may include number concepts and numeration, algebra, geometry, trigonometry, analytic geometry, and calculus.
Prerequisite: MATHS 161 or 165.

473 Boundary Value Problems. (3)
Fourier Series and integrals, heat and wave equations in one dimension, Laplace's equation in two dimensions, problems in higher dimensions, numerical methods of solving boundary value problems.
Prerequisite: MATHS 374.

475 Topics in Partial Differential Equations. (3)
Classical solution techniques for liner PDEs. Topics include first- and second-order equations, method of characteristics, special functions, orthogonal polynomials, transforms, Green's functions, and fundamental solutions. A computer algebra system is utilized.
Prerequisite: MATHS 374, 267; or permission of the department chairperson.

497 Student-Faculty Colloquium. (1-6)
Participatory colloquium experience for motivated students. A contemporary topic of broad mathematical interest is chosen each semester. Each student is paired with a faculty member. These pairs work together to develop and present components of the semester-long course.
Prerequisite: MATHS 267 or permission of the department chairperson.
A total of 6 hours of credit may be earned.

498 Senior Seminar. (2) 
Development of a broad, connected, contemporary perspective of mathematics and its applications. Includes a variety of readings, special lectures, and discussions. Each student will participate in a substantial project, presented both in oral and written forms.  Prerequisite: senior standing or permission of the department chairperson.  
Open only to mathematical sciences majors.

499 Reading and Honors. (1-8)
Juniors and seniors, with the approval of the mathematical sciences department, may enroll for special advanced work not offered in courses at the 300- and 400-levels.
Prerequisite: approval of the department chairperson.
A total of 8 hours of credit may be earned.
Open only to juniors and seniors.

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