Requirements and Curriculum
Note: This information reflects the requirements and curriculum printed in the 2007-08 course catalog.
Requirements
Requirements for majors
Math: Plan I (Theory)
220, 240, either 454 or 471, a computer science course numbered 150, 151 or 200, and a minimum of three additional courses in the math department numbered 200 or above, including at least one additional from 365, 454, 456, 459, 471, or 472.
Math: Plan II (Applications)
220, 240, either 454 or 471, a computer science course numbered 150, 151 or 200, and four additional courses in the math department numbered 200 or above.
Math: Plan III (Teaching)
A Plan I mathematics major that includes 321, 365, and 471. Complete one of math 235, 253, 322, 351. Credit hours of required and elective mathematics courses must total a minimum of 30 hours. See education department for secondary education minor requirements.
Mathematics/Statistics
220, 240, 253, 321, 322, 327, 328, and computer science 150, 151 or 200. Mathematics 454 recommended. (A student may not major in both mathematics and mathematics/statistics.)
Required for a mathematics minor
At least 17 hours in mathematics, including 240 and two additional courses numbered 200 or above.
Required for a second teaching area
At least 24 hours, including 151, 152, 220, 240, 321, and 365. Computer science 150, 151 or 200, and education 352 are required.
Suggested patterns for majors planning careers in the following areas:
1. Graduate study in mathematics: Plan I including 253, 321, 351, 454, 456, 459, 471, 472.
2. Statistics: A mathematics/statistics major.
3. Actuarial science: A mathematics/statistics major plus economics 247 and 248, management 353 and 365; and courses in computer science.
4. Computing: 220, 321, 322, 351, 462, 471.
5. Management (accounting, economics): 235, 253, 321, 322, 327, 454.
6. Science: from 253, 321, 322, 327, 328, 351, 452, 454, 456, 462, 471.
First-Year Placement
The mathematics department placement procedure uses high school records, scores on ACT or SAT tests, and a placement test in mathematics as a basis for a recommendation. Students who are well prepared should begin in the calculus sequence, mathematics 151 and 152, or in special cases, 240. Mathematics 130-141 contain various amounts of precalculus material as well as calculus concepts. Students who need calculus, but who also need a review of some algebra or trigonometry, should start with 130 or 140 depending on placement results. Math 123 is only for students who major in elementary education. Math 110 and 115 are designed for students who will not be taking calculus.
Advanced Placement Credit
1. Students can receive credit for calculus courses by scoring a 4 or 5 on the appropriate AP exam,
OR
2. A student who places into math 152 will receive, upon completion of the course with a grade of C or better, Luther College credit for the preceding calculus course, math 151 (if credit has not already awarded through AP or transfer credit).
A student who places into math 240 may petition the head of the math department, upon completion of the course with a grade of C or better, to receive Luther College credit for the preceding calculus course(s), math 151 and/or 152 (if credit has not already awarded through AP or transfer credit). Approval of the petition will depend upon whether the student has previously covered the content of math 151 and/or 152.
Curriculum
110 Finite Mathematics 4 hours
An introduction to topics chosen from logic, problem solving, set operations, counting techniques, probability, linear programming, voting and apportionment methods, graph theory, game theory, statistics, and the mathematics of finance. Recommended for students who wish to take a non-calculus based mathematics class, with emphasis on current applications in the social sciences, business, and life sciences. Prerequisite: high school algebra. (Quant)
115 Introduction to Statistics 4 hours
The course uses real world data sets from the social and natural sciences to help students understand and interpret statistical information. Computer software is used to study data from graphical and numerical perspectives. Topics covered include measures of central tendency and dispersion, probability distributions, sampling methods, point and interval estimation, correlation, regression, contingency tables and tests of hypotheses. Prerequisite: high school algebra. This class does not count towards the mathematics major or minor or the mathematics/statistics major. Prerequisite: high school algebra. (Quant)
123 Mathematics for Elementary School Teachers 4 hours
This course provides pre-service K-8 teachers a strong foundation in the mathematics content areas as described in the NCTM’s Principles and Standards for School Mathematics. The content standards include: Numbers and Operations, Algebra, Geometry, Measurement, Statistics and Probability. This course will engage students in standards-based mathematics learning to prepare them for the pedagogical practices they will learn in ED 323. Prerequisite: one year of high school algebra, one year of high school geometry and admission into the teacher education program. Co-requisite: education 323. (Quant)
130 Precalculus with Derivatives I 4 hours
Algebraic and graphical representations of functions; exponentials; techniques of solving equations and inequalities; modeling; introduction to instantaneous rates of change: limits, derivatives of polynomial functions; continuity. Graphing calculator use is required. (Students who earn credit for 130 may not earn credit for 140.) (Quant)
131 Precalculus with Derivatives II 4 hours
Continuation of topics of Math 130 to rational, logarithmic, and exponential functions and their derivatives; applications. Graphing calculator use is required. (Students who earn credit for 131 may not earn credit for 140.) Prerequisite: 130. (Quant)
139, 239, 339, 439 Special Topics Credit arr.
140 Precalculus with Derivatives I and II 4 hours
Algebraic and graphical representations of functions: polynomial, rational, exponential, and logarithmic; techniques of solving equations and inequalities; modeling; introduction to instantaneous rates of change: limits, derivatives; continuity; applications of derivatives. Graphing calculator use is required. (Students who earn credit for 140 may not earn credit for 130 or 131.) (Quant)
141 Calculus I with Algebra and Trigonometry 4 hours
Continuation of topics of Math 131 or 140: trigonometric functions and their derivatives, chain rule, the mean value theorem, Riemann sum approximation for integrals, definite integrals, antiderivatives, applications. Graphing calculator use is required. (Students who earn credit for 141 may not earn credit for 151.) Prerequisite: 131 or 140 or consent of instructor. (Quant)
151 Calculus I 4 hours
Topics related to instantaneous rates of change: functions, limits, continuity, derivatives, mean value theorem, applications; antiderivatives, definite integrals. Graphing calculator use is required. (Students who earn credit for 151 may not earn credit for 130, 140, or 141.) Prerequisite: a minimum of 1–1/2 years of algebra, 1/2 year of trigonometry, 1 year of geometry. (Quant)
152 Calculus II 4 hours
Applications of the definite integral, techniques of integration, differential equations, power series, Taylor series, and an introduction to computer algebra systems. Prerequisite: 141 or 151 or consent of instructor. (Quant)
185 First-year Seminar 4 hours
A variety of seminars for first-year students offered each January term.
220 Discrete Structures 4 hours
Propositional and predicate logic, methods of proof, induction, recursion and recurrence relations, sets and combinatorics, binary relations (including equivalence relations and partial orderings), functions, Boolean algebra and computer logic, and finite state machines. Prerequisites: mathematics 152 or above or computer science 150, 151, or 220, or consent of instructor. (Same as computer science 220.) (Quant)
235 Operations Research 4 hours
Model building. Analytic tools useful to management chosen from linear programming, simplex algorithm, sensitivity analysis, duality; integer linear programming; goal programming; dynamic programming; networks, PERT-CPM, maximum flow, shortest path; simulation; nonlinear programming. Offered alternate years. Prerequisite: 140 or 151. (Quant)
240 Linear Algebra 4 hours
Matrices, abstract vector spaces, subspaces, spanning sets, linear independence, bases, linear transformations, isomorphisms, eigenvalues and eigenvectors, inner product spaces. Prerequisite: 152, or consent of instructor. (Quant)
253 Multivariable Calculus 4 hours
Vector valued functions: limits, continuity, derivatives, and integrals. Length of space curves, tangents and normals to curves. Functions of several variables: limits, continuity, partial derivatives, directional derivatives, the gradient, tangent plane approximation and differentials, extreme value, multiple integrals, vector fields, line integrals, Green’s theorem, surface integrals, Stokes’ theorem, the divergence theorem. Prerequisite: 240. (Quant)
260 Elementary Number Theory 4 hours
Divisibility theory in the integers, prime numbers, Euclidean algorithm, Diophantine equations, congruences, divisibility tests, Euler’s theorem, public key cryptography, primitive roots, quadratic reciprocity law. Usually offered in alternate years. Prerequisites: 220 or 240. (Quant)
321 Probability and Statistics I 4 hours
Axioms and laws of probability, independence, conditional probability, combinatorics, discrete and continuous random variables, mathematical expectation, central limit theorem, descriptive statistics, confidence intervals. Only one of 321, 322, and 328 may apply toward the math major. Prerequisite: 152. (Quant)
322 Probability and Statistics II 4 hours
Sampling distribution theory, theory of estimation and hypothesis testing, confidence intervals, inferences for means and proportions, correlation and regression, chi-square tests. Only one of 321, 322, 328 may apply toward the math major. Prerequisite: 321. (Quant)
327 Applied Statistics I 4 hours
Regression Analysis: Least square estimates, simple linear regression, multiple linear regression, hypothesis testing and confidence intervals for linear regression models, prediction intervals, and ANOVA. Model diagnostics including tests of constant variance assumptions, serial correlation, and multicollinearity. Time series: Linear time series, moving average, autoregressive and ARIMA models. Estimation and forcasting. Forcast errors and confidence intervals. Prerequisite: college-level statistics course. (Quant)
328 Applied Statistics II 4 hours
Design and analysis of experiments. Analysis of variance techniques. Fixed, random, and mixed models. Repeated Measures. Only one of 321, 322, and 328 may apply toward the math major. Prerequisite: 327. (Quant)
351 Ordinary Differential Equations 4 hours
An introduction to first and second order differential equations, existence and uniqueness theorems, higher order linear differential equations, Laplace transforms, power series solutions, boundary value problems, systems of linear differential equations, and applications in the physical, biological, and social sciences. Prerequisite: 240. (Quant)
365 Geometry 4 hours
Elements of Euclidean and non-Euclidean geometries: incidence, betweenness, separation, congruence, and parallel postulates. Geometry of physical space. Historical development. A proof oriented course. Prerequisite: 220, 240. (Quant)
380 Internship Credit arr.
On-the-job learning experience. The plan must be presented for departmental approval before the experience begins.
385 Seminar Credit arr.
395 Independent Study 1, 2 or 4 hours
452 Partial Differential Equations 4 hours
An introduction to initial and boundary value problems associated with certain linear partial differential equations (e.g., Laplace, heat and wave equations). Fourier series methods, including the study of best approximation in the mean and convergence, will be a focus. Sturm-Liouville problems and associated eigenfunctions will be included. Numerical methods, such as finite difference, finite element, and finite analytic, may be introduced, including the topics of stability and convergence of numerical algorithms. Prerequisites: 351. (Quant)
454 Principles of Real Analysis 4 hours
The mathematics of real functions, emphasizing rigorous analytical proofs; sets, real number properties, cardinality, topology of the reals, limits of a function, continuity, differentiation, integration, sequence, series. Prerequisite: 220, 240. (Quant)
456 Functions of a Complex Variable 4 hours
Extending calculus to functions of a complex variable. Complex numbers, limits, derivatives, Cauchy-Riemann equations, analytic functions, contour integrals, Cauchy integral formula. Taylor series, Laurent series, residues, conformal mappings, and applications. Offered in alternate years. Prerequisite: 253. (Quant)
459 Topology 4 hours
An introduction to general, or point-set, topology. Topological spaces and continuous functions. Order, metric, product, and subspace topologies. Limit points, connectedness, compactness, countability axioms, separation axioms, Urysohn lemma and metrization theorem. Usually offered in alternate years. Prerequisite: 220, 240. (Quant)
462 Numerical Analysis 4 hours
Roots of equations and solutions of systems of linear equations, interpolation and approximation, differences and numerical integration, and numerical solutions of ordinary differential equations. Offered in alternate years. Prerequisite: 240, computer science 150. (Same as computer science 462.) (Quant)
471 Abstract Algebra I 4 hours
Introduction to the basic structures of abstract algebra: groups, subgroups, cosets, isomorphisms, factor groups, homomorphisms, rings, integral domains, fields, ideals, and polynomial rings. Prerequisite: 220, 240. (Quant)
472 Abstract Algebra II 4 hours
Topics may include simple groups, Sylow theorems, divisibility in integral domains, generators and relations, field extensions, splitting fields, solvability by radicals, Galois theory, symmetry, and geometric constructions. Offered on demand. Prerequisite: 471. (Quant)
485 Seminar Credit arr.
490 Senior Project 1, 2, or 4 hours
493 Senior Honors Project 4 hours
A yearlong independent research project. Applications are completed on the “Honors Program” form available at the registrar’s office, requiring the signatures of a faculty supervisor, the department head, the honors program director, and the registrar. Interdisciplinary projects require the signatures of two faculty supervisors. The project must be completed by the due date for senior projects. The completed project is evaluated by a review committee consisting of the faculty supervisor, another faculty member from the major department, and a faculty member from outside the major department. All projects must be presented publicly. Only projects awarded an “A-” or “A” qualify for “department honors” designation. The honors project fulfills the all-college senior project requirement.