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University of Nebraska–Lincoln

Department of Mathematics

What You Need To Know

Bulletin

The full Undergraduate Bulletin.

The department is located on the 2nd and 3rd floors of Avery Hall.

Chair
John Meakin, 206 Avery Hall
Vice Chair
Jamie Radcliffe, 205 Avery Hall
Professors
Avalos, Avramov, Deng, Dunbar, Erbe, Harbourne, Johnson, Lewis, Logan, Meakin, Orr, Peterson, Pitts, Rammaha, Rebarber, Shores, Skoug, J. Walker, M. Walker, R. Wiegand, S. Wiegand, Woodward
Associate Professors
Brittenham, Chouinard, Cohn, Donsig, Hermiller, Hines, Iyengar, Ledder, Marley, Radcliffe
Assistant Professors
Foss, Loladze, Radu, Tenhumberg

Requirements for the Major in Mathematics

A strong mathematics background is essential to an increasing variety of careers. The Department of Mathematics encourages students to select a coherent body of courses in mathematics and in other disciplines that are consistent with their academic goals.

The Department of Mathematics offers four options for the major in mathematics. Each student majoring in mathematics should select an option that meets their academic needs by completing a Program Declaration form in consultation with the Department's Chief Undergraduate Advisor. Ideally, this should be done prior to completing two mathematics courses beyond the calculus sequence. As appropriate, students can change their Program Declaration to select a different option or modify the program of study subject to the approval of the Chief Undergraduate Advisor.

All options for the mathematics major require:

  • A complete calculus sequence: MATH 106, 107, 208 or 108H, 109H, or equivalent.
  • Twenty-four hours (8 courses) selected from the Advanced Mathematics Course List.
  • A minimum cumulative GPA of 2.5 in those courses used to satisfy the Advanced Mathematics course requirements.
  • An approved Program Declaration form.

Program Assessment: In order to assist the department in evaluating its programs, all majors should plan to participate in:

  1. an exit interview
  2. an exit exam

during their last semester before graduation. Please make arrangements with the Chief Undergraduate Advisor.

Option C (Concentration)

This option is ideal for students wishing to combine a strong mathematics education with a coherent body of course work in another discipline. Specific requirements above calculus are as follows:

  • The 8 required mathematics courses must be distributed as follows:
    • MATH 314
    • Either MATH 221 or 380
    • Either MATH 310 or 325
    • At least three Advanced Mathematics courses at the 400 level
    • Two additional Advanced Mathematics courses
  • Any Plan A minor or an approved 18-hour concentration outside of mathematics.
One 400-level course in the area of the concentration may be substituted for one of the required 400-level Advanced Mathematics courses, provided the course makes significant use of advanced mathematics. The Chief Undergraduate Advisor must approve the substitution.
Option E (Education)

This option is ideal for students interested in teaching mathematics at the secondary level. Specific requirements above calculus are as follows:

  • MATH 221, 310, 314, 350, 380, 405, 407, 408
  • An education minor or an approved 18-hour concentration in education
Option R (Research Experience)

This option is recommended for students interested in independent work and for students planning to pursue graduate work in mathematics. Specific requirements above calculus are as follows:

  • The 8 required mathematics courses must be distributed as follows:
    • MATH 221, 310, 314, and 325
    • At least three Advanced Mathematics courses at the 400 level
    • One more Advanced Mathematics course
  • An approved undergraduate research experience. A variety of options exist for meeting this requirement. They include 1) research experiences such as an REU or UCARE that leads to a project paper, 2) a senior honors thesis or a thesis approved for graduation with distinction, or 3) a grade of P in MATH 496, Undergraduate Research Seminar (this course would be in addition to the Advanced Mathematics courses requirement above). To satisfy this requirement, students must file with the Chief Undergraduate Advisor a) a "Research Experience" contract that is approved by the Chief Undergraduate Advisor, and b) the thesis, research papers, or projects as required by the contract. Visit with the Chief Undergraduate Advisor for more information.
Option S (Statistics)

This option is recommended for students interested in a mathematics major and a strong body of course work in statistics. Specific body of course work in statistics. Specific requirements above calculus are as follows:

  • The 8 required mathematics courses must be distributed as follows:
    • MATH 314 and MATH/STAT 380
    • MATH 310 or 325
    • At least three Advanced Mathematics courses at the 400 level. For the purpose of this requirement, one 400-level statistics course may be substituted for one 400-level Advanced Mathematics course.
    • Two more Advanced Mathematics courses
  • Nine hours of statistics numbered 300 or above in addition to MATH/STAT 380
Under any option, students may substitute a more advanced course in the same area for a required mathematics course. Interested students should visit with the Chief Undergraduate Advisor for more information about this option.

Requirements for the Minor in Mathematics

  1. A complete calculus sequence plus two advanced courses
  2. A complete calculus sequence. Plan B is restricted to students with more than one minor.

Pass/No Pass. For majors or minors, no calculus course can be taken pass/no pass. For the major, at most 3 of the 24 hours of advanced courses may be taken on a pass/no pass basis. For Plan A minor, one advanced course may be taken pass/no pass if approved by the student's major department.

Prerequisites. The prerequisites listed for a course may be replaced by equivalent preparation. A prerequisite for all advanced courses is successful completion of the calculus sequence MATH 106–107–208 (MATH 106H-107H). Additional or specific prerequisites may also be listed. Two courses past calculus are required for all 400-level mathematics courses. Prerequisites for 400-level statistics courses are given with the descriptions. All topics, independent study, reading courses, and seminars require permission before registering. Students with special circumstances in their preparation should confer with the chief adviser or vice chair for guidance in selecting the proper course.

Persons with previous credit in any calculus course may not register for or earn credit in MATH 100A, 101, 102, 103, or 104, without first receiving special written permission from the vice chair.

Graduate Work. The advanced degrees of master of arts, master of science, master of arts (or science) for teachers, and doctor of philosophy, are offered. For details of these programs, see the Graduate Bulletin

Math Courses of Instruction

Courses or special sections bearing a "T" designation are restricted to students in the MAT (MScT) program. See the Graduate Bulletin for further information.

If a course qualifies for Essential Studies (ES) or Integrative Studies (IS), it is noted following the course title and credit hours.

Introductory Mathematics Courses

Mathematics Placement Policy: Students presenting proof of a grade of C (P) or better in the prerequisite course at UNL, UNO, or UNK are exempt from the readiness requirement. Otherwise, readiness is established by having a current, satisfactory score on the department's Mathematics Placement Exam (MPE). For more details, see the current print version of the Schedule of Classes (or see the MPE policy on the department website or the spring or fall pages at UNL's Registration and Records website).

100A [100x]Intermediate Algebra3 One year high school algebra and appropriate score on the Math Placement Exam. Credit earned in MATH 100A will not count toward degree requirements. A review of the topics in a second-year high school algebra course taught at the college level. Topics include: real numbers, 1st and 2nd degree equations and inequalities, linear systems, polynomials and rational expressions, exponents and radicals. There is a heavy emphasis on problem solving strategies and techniques throughout the course.
101 [101x]College Algebra3 Appropriate placement exam score and either two years of high school algebra or a grade of P, C, or better in MATH 100A. Real numbers, exponents, factoring, linear and quadratic equations, absolute value, inequalities, functions, graphing, polynomial and rational functions, exponential and logarithmic functions, systems of equations.
102 [102x]Trigonometry2 One year high school geometry and either two years high school algebra, one semester high school precalculus, and a qualifying score on the Math Placement Exam; or a grade of C, P, or better in MATH 101. Credit towards the degree may be earned in only one of MATH 102 or 103. Trigonometric functions, identities, trigonometric equations, solution of triangles, inverse trigonometric functions, and graphs.
103College Algebra and Trigonometry5 Appropriate placement exam score, one year high school geometry, and two years high school algebra. For students with previous college math courses, permission is also required. First and second degree equations and inequalities, absolute value, functions, polynomial and rational functions, exponential and logarithmic functions, trigonometric functions and identities, laws of sines and cosines, applications, polar coordinates, systems of equations, graphing, conic sections.
104Calculus for Managerial and Social Sciences3 [ES] Appropriate placement exam score or a grade of P (pass), or C or better in MATH 101. Credit for both MATH 104 and 106 is not allowed. Rudiments of differential and integral calculus with applications to problems from business, economics, and social sciences.
Students with adequate high school preparation (equivalent to MATH 101 and 102) should begin with MATH 106, which is the first course in a three-semester calculus sequence. Students who have had some calculus in high school may be eligible for advanced placement and should contact the Department of Mathematics and Statistics for further information. MATH 104 is recommended for students in managerial and social sciences.
106 [106x]Analytic Geometry and Calculus I5 [ES][IS] One year high school geometry; two years algebra and one year precalculus-trig in high school, or MATH 102 or 103 or equivalent. Math Placement Policy applies. Credit for both MATH 104 and 106 is not allowed. Functions of one variable, limits, differentiation, exponential, trigonometric and inverse trigonometric functions, maximum-minimum, and basic integration theory (Riemann sums) with some applications.
106BCalculus I for Biology and Medicine5 [ES][IS] One year high school geometry; two years high school algebra and one year high school precalculus-trigonometry, or MATH 102 or 103 or equivalent. Math Placement Policy applies. Credit toward the degree may be earned in only one of: MATH 104, 106, 106B, or 108H. MATH 106B serves as a prerequisite for other courses in place of MATH 106 or 108H. Functions of one variable, limits, differentiation, integration theory, fundamental theorem of calculus, with applications in the life sciences.
107 [107x]Analytic Geometry and Calculus II5 [ES][IS] A grade of P (pass), C or better in MATH 106. Integration theory; techniques of integration; applications of definite integrals; basics of ordinary differential equations; series, Taylor series.
107HHonors Calculus II5–7 [ES][IS] By invitation only. This is an accelerated calculus course that covers approximately half of MATH 107 and all of MATH 208.
108HHonors Accelerated Calculus I5 or 7 [ES][IS] Good standing in the University Honors Program or by invitation. Accelerated calculus course covering MATH 106 and approximately one-half of MATH 107.
109HHonors Accelerated Calculus II5 or 7 [ES][IS] Good standing in the University Honors Program or by invitation; MATH 108H. Covers second half of MATH 107 and all of MATH 208.
189HUniversity Honors Seminar5 or 7 [ES][IS] Good standing in the University Honors Program or by invitation; placement score on the Math Placement Examination (MPE) or the MATH 104 level or above. University Honors Seminar 189H is required of all students in the University Honors Program. Topics vary.
198HFreshman Seminar1–3 Open only to students in the Honors Program or by invitation.
200/800Mathematics for Elementary School Teachers3 Undergraduates must be admitted to Teachers College or the child development program of HRFS; successful completion of the PPST; and removal of any mathematics entrance deficiencies. Graduate students are admitted by permission. All mathematics entrance deficiencies must be removed before taking this course. Fundamental mathematical concepts basic to the understanding of arithmetic.
201/801Geometry for Elementary School Teachers3 Completion of MATH 200 with a grade of C, P or better. Undergraduates must be admitted to Teachers College or the child development program of HRFS. Graduate students are admitted by permission. Fundamental mathematical concepts basic to the understanding of elementary geometry will be presented in this course.
203Contemporary Mathematics3 [ES][IS] Sophomore standing and removal of all entrance deficiencies in mathematics. Not open to students with credit or concurrent enrollment in MATH 104, 105, 106, or STAT 180. Applications of quantitative reasoning and methods to problems and decision making in the areas of management, statistics, and social choice. Topics include networks, critical paths, linear programming, sampling, central tendency, inference, voting methods, power index, game theory, and fair division problems.
208 [208x]Analytic Geometry and Calculus III4 [ES][IS] A grade of P, C or better in MATH 107. Vectors and surfaces, parametric equations and motion, functions of several variables, partial differentiation, maximum-minimum, Lagrange multipliers, multiple integration, vector fields, path integrals, Green's Theorem, and applications.
208H Honors: Analytic Geometry and Calculus III4 [ES][IS] Good standing in the University Honors Program or by invitation. For course description, see MATH 208.
260Introduction to the Foundations of Mathematics3 [IS] MATH 106. Not open to mathematics majors except for dual matriculants in Teachers College. Elementary logic, inductive and deductive reasoning, methods of proof.
300Mathematics Matters3 Admissions to the College of Education and Human Sciences and removal of any mathematics entrance deficiencies. Credit towards the degree may be earned in only one of: MATH 200 or MATH 300. Designed for elementary education majors with mathematics as an area of concentration. Numbers and operations. Develop an understanding of mathematics taught in the elementary school.
301Geometry Matters3 MATH 200 or MATH 300, with a grade of C or Pass or better. Credit towards the degree may be earned in only one of: MATH 201 or MATH 301. Designed for elementary education majors with mathematics as an area of concentration. Geometry and measurement. Develop an understanding of geometry as taught in the elementary school.
350Concepts in Geometry3 MATH 260. Not open to mathematics majors except those with dual matriculation in Teachers College. Modern elementary geometry, plane transformations and applications, the axiomatic approach, Euclidean constructions. Additional topics will vary.

MATH 221, 221H, and any 300- or 400-level course taught in the Department of Mathematics may be substituted for MATH 208 as meeting the ES requirement for Area B.

Advanced Mathematics Courses

221/821Differential Equations3 [IS] A grade of "P" or "C" or better in MATH 208. Not open to MA or MS students in mathematics or statistics. First- and second-order methods for ordinary differential equations including: separable, linear, Laplace transforms, linear systems, and some applications.
221HDifferential Equations3 [IS] Admission to the University Honors Program or by invitation. First- and second-order methods for ordinary differential equations including: separable, linear, Laplace transforms, linear systems, and some applications.
310Introduction to Modern Algebra3 [IS] Introduction to groups, rings, and fields as a natural extension of elementary number theory and the theory of equations. Particular emphasis is placed on the study of polynomials with coefficients in the rationals, reals, or complex numbers.
310HIntroduction to Modern Algebra3[IS] Admission to the University Honors Program or by invitation. Introduction to groups, rings, and fields as a natural extension of elementary number theory and the theory of equations. Particular emphasis is placed on the study of polynomials with coefficients in the rationals, reals, or complex numbers.
314/814Applied Linear Algebra (Matrix Theory)3 Not open to MA or MS students in mathematics or statistics. Fundamental concepts of linear algebra from the point of view of matrix manipulation with emphasis on concepts that are most important in applications. Topics include solving systems of linear equations, vector spaces, inner products, determinants, eigenvalues, similarity of matrices, and Jordan Canonical Form.
314HApplied Linear Algebra (Matrix Theory)3[IS] Admission to the University Honors Program or by invitation. Fundamental concepts of linear algebra from the point of view of matrix manipulation with emphasis on concepts that are most important in applications. Topics include solving systems of linear equations, vector spaces, inner products, determinants, eigenvalues, similarity of matrices, and Jordan Canonical Form.
322/822Advanced Calculus3 Not open to MA or MS students in mathematics or statistics. Uniform convergence of sequences and series of functions, Green's theorem, Stoke's theorem, divergence theorem, line integrals, implicit and inverse function theorems, and general coordinate transformations.
324/824Introduction to Partial Differential Equations3 MATH 221. Not open to MA or MS students in mathematics or statistics. Derivation of the heat, wave, and potential equations; separation of variables method of solution; solutions of boundary value problems by use of Fourier series, Fourier transforms, eigenfunction expansions with emphasis on the Bessel and Legendre functions; interpretations of solutions in various physical settings.
325Elementary Analysis3[IS] An introductory course emphasizing mastery of basic calculus concepts and the development of skill in constructing proofs. Topics include mathematical induction, completeness of the real numbers, sequences and series, limits and continuity, derivatives, uniform convergence, Taylors theorem, integration and the fundamental theorem of calculus.
340/840Numerical Analysis I,Computer Science 340/8403 CSCE 150 or 155. Credit cannot be given for both MATH 340 and ENGM 480. Not open to MA or MS students in mathematics or statistics. Algorithm formulation for the practical solution of problems such as interpolation, roots of equations, differentiation and integration. Includes analysis of effects of finite precision.
380Statistics and Applications, STAT 3803 MATH 107. For course description, see STAT 380.
405/805Discrete and Finite Mathematics3 [IS] MATH 314 is desirable but not required. Credit is not allowed for both MATH 105 and MATH 405, or for both CSCE 235 and MATH 405. Not open to math majors except for dual matriculants in Teachers College. Not open to MA or MS students in mathematics or statistics. Graphs and networks, map coloring, finite differences, Pascal's triangle, the Pigeonhole Principle, Markov chains, linear programming, Game Theory.
407Mathematics for High School Teachers I3 MATH 208 and 310. Analysis of the connection between college mathematics and high school algebra and precalculus.
408Mathematics for High School Teachers II3 MATH 310 and 350. Analysis of the connections between college mathematics and high school algebra and geometry.
417/817 [817T]Introduction to Modern Algebra I3 [IS] MATH 310 is advisable for most students. Topics from elementary group theory and ring theory, including fundamental isomorphism theorems, ideals, quotient rings, domains, Euclidean or principal ideal rings, unique factorization, modules and vector spaces, including direct sum decompositions, bases, and dual spaces.
418/818Introduction to Modern Algebra II3 MATH 417/817. Topics from field theory including Galois theory and finite fields and from linear transformations including characteristic roots, trace and transpose, and determinants.
423/823Introduction to Complex Variable Theory3 Complex numbers, functions of complex variables, analytic functions, complex integration, Cauchy's integral formulas, Taylor and Laurant series, calculus of residues and contour integration, conformal mappings, harmonic functions, and some applications. This is an advanced introductory course for engineering, physical sciences, and mathematics majors.
425/825 [825T]Mathematical Analysis I3 [IS] Real number system, topology of Euclidean space and metric spaces, compactness, sequences, series, convergence and uniform convergence, and continuity and uniform continuity.
426/826Mathematical Analysis II3 MATH 425/825. Differentiation, the mean value theorem, Riemann and Riemann-Stieltjes integrals, functions of bounded variation, equicontinuity, function algebras, and the Weierstrass and Stone-Weierstrass theorems.
427/827Mathematical Methods in the Physical Sciences3 MATH 221. Not open to mathematics majors. Not open to MA or MS students in mathematics. Matrix operations, transformations, inverses, orthogonal matrices, rotations in space. Eigenvalues and eigenvectors, diagonalization, applications of diagonalization. Curvilinear coordinate systems, differential operations in curvilinear coordinate systems, Jacobians, changes of variables in multiple integration. Scalar, vector and tensor fields, tensor operations, applications or tensors. Complex function theory, integration by residues, conformal mappings.
428/828Principles of Operations Research3 [IS] MATH 314 and either STAT 380 or IMSE 321 or equivalent. An introduction to the techniques and applications of operations research. The topics will include linear programming, queueing theory, decision analysis, network analysis, and simulation.
430/830Ordinary Differential Equations I3 [IS] MATH 221 and 322. The Picard existence theorem, linear equations and linear systems, Sturm separation theorems, boundary value problems, phase plane analysis, stability theory, limit cycles and periodic solutions.
431/831Ordinary Differential Equations II3 MATH 430. A continuation of MATH 430.
432/832Linear Optimization3 [IS] MATH 314/814. Mathematical theory of linear optimization, convex sets, simplex algorithm, duality, multiple objective linear programs, formulation of mathematical models.
433/833Nonlinear Optimization3 MATH 314/814. Mathematical theory of constrained and unconstrained optimization, conjugate direction and quasi-Newton methods, convex functions, Lagrange multiplier theory, constraint qualifications.
439/839Mathematical Models in Biology3 MATH 107 or permission. MATH 439/839 has a small laboratory component. Discrete and continuous models in ecology, population models, predation and food webs, the spread of infectious diseases and life hostories. Prbability and random processes in nature, elementary models for molecular events, and pharmacokinetics.
441/841Approximation of Functions Computer Science 441/8413 A programming language, MATH 221 and 314. Polynomial interpolation, uniform approximation, orthogonal polynomials, least-first-power approximation, polynomial and spline interpolation, approximation and interpolation by rational functions.
442/842Methods of Applied Mathematics I3 MATH 221 and 314, or their equivalents. Derivation, analysis, and interpretation of mathematical models for problems in the physical and applied sciences. Scaling and dimensional analysis. Asymptotics, including regular and singular perturbation methods and asymptotic expansion of integrals. The calculus of variations.
443/843Methods of Applied Mathematics II3 MATH 442 or permission. Application of partial differential equation models to problems in the physical and applied sciences.. Topics include derivation of partial differential equations, the theory of continuous media, linear and nonlinear wave propagation, diffusion, transform methods, and potential theory.
445/845Introduction to the Theory of Numbers I3 Arithmetic functions, congruences, reciprocity theorem, primitive roots, diophantine equations and continued fractions.
447/847Numerical Analysis II Computer Science 447/8473 CSCE 340, MATH 221 and 314. Numerical matrix methods and numerical solutions of ordinary differential equations.
450/850Combinatorics3 MATH 310 or 314. Theory of enumeration and/or existence of arrangements of objects: Pigeonhole principle, inclusion-exclusion, recurrence relations, generating functions, systems of distinct representatives, combinatorial designs and other applications.
452/852Graph Theory3 MATH 310 or 314. Theory of directed and undirected graphs, including trees, circuits, subgraphs, matrix representations, coloring problems, and planar graphs. Emphasis on methods which can be implemented by computer algorithms. Selected applications.
456/856Differential Geometry I3 MATH 221, 314, and 322. Introduction to a selection of topics in modern differential manifolds, vector bundles, vector fields, tensors, differential forms, Stoke's theorem, Riemannian and semi-Riemannian metrics, Lie Groups, connections, singularities. Applications include gauge field theory, catastrophe theory, general relativity, fluid flow.
457/857Differential Geometry II3 MATH 456. A continuation of MATH 456.
465/865 [865T]Introduction to Mathematical Logic I Computer Science 465/8653 Semantical and syntactical developments of propositional logic, discussion of several propositional calculi, applications to Boolean algebra and related topics, semantics and syntax of first-order predicate logic including Godel's completeness theorem, the compactness theorem.
871 [871T]General Topology I3
872General Topology II3 MATH 871.

Seminars, Independent Study, Topics and Reading Courses

398Special Topics in Mathematicsarr Permission.
399Independent Study in Mathematicsarr Prior arrangement with and permission of individual faculty member.
399HHonors Course1–4 For candidates for degrees with distinction, with high distinction, or with highest distinction in the College of Arts and Sciences.
495 /895Honors Seminar1–3 per sem, max 6 MATH 208 and permission.
496/896Seminar in Mathematics1–3 per sem, max 6 Permission.
497/897Reading Course1–4 Open to graduate students and, with permission, to seniors and especially qualified juniors.
899Masters Thesis6–10

Refer to the Graduate Bulletin for 900-level courses.