MATHEMATICS (MATH)
All
MATH/STAT/OPRS courses offered by the Department of Mathematics are approved to
satisfy requirements for the Problem Solving Goal of UNC
MATH 0900. Math
Study Skills and Algebra Review. (1) This course
prepares the student to be successful in college algebra or precalculus. Topics include a review of elementary
algebra, exponents and radicals, polynomial and rational functions, equations
and inequalities. Study skills needed to
be successful in mathematics are an important part of this course. Placement into this course is based on the
score on the Mathematics Placement Exam which is administered by the
Mathematics Department.
MATH 1100. College Algebra. (3) Prerequisite: appropriate score on the Mathematics
Placement Test or placement by the Department. The basic mathematics course for
undergraduates not majoring in Mathematics, Engineering, or the Physical
Sciences. Fundamental concepts of algebra. (Credit may not be given for both
MATH 1100 and 1103; students who already have credit for MATH 1120 or 1241 with
a grade of C or better may not take
1100 for credit.) (Fall, Spring, Summer)
(Evenings)
MATH 1102. Introduction to Mathematical Thinking. (3) Prerequisite: appropriate score on the Mathematics
Placement Test or placement by the Department. An introduction to mathematical
ideas designed primarily for non‑science students. Topics are drawn from
various branches of mathematics which may include algebra, geometry, number
theory, probability, statistics and graph theory. Computers may be used. (Fall, Spring)
MATH 1103. Precalculus Mathematics for Science and
Engineering. (3) Prerequisite: appropriate
score on the Mathematics Placement Test or placement by the Department.
Intended for students who plan to take MATH 1241. Functions and graphs, linear
and quadratic functions, polynomial and rational functions, exponential and
logarithmic functions, trigonometric identities. (Credit may not be given for
both MATH 1100 and 1103; students who already have credit for MATH 1120 or 1241
with a grade of C or better may not
take MATH 1103 for credit.) (Fall,
Spring, Summer) (Evenings)
MATH 1105. Finite Mathematics. (3) Prerequisite: appropriate score on the Mathematics
Placement Test or placement by the Department. Review of high school algebra,
elementary matrix algebra, systems of linear equations and inequalities,
elementary linear programming; probability. (On
demand)
MATH 1120. Calculus. (3)
Prerequisite: appropriate score on the Mathematics Placement Test, MATH 1100 or
1103, or placement by the Department. Intended for students majoring in fields
other than engineering, mathematics or science. Elements of differential and
integral calculus for polynomial, rational, exponential, logarithmic functions,
with applications to business and the social and life sciences. (May not be
taken for credit if credit has been received for MATH 1121 or 1241.) (Fall, Spring, Summer) (Evenings)
MATH 1121. Calculus (ET). (3) Prerequisite: appropriate
score on the Mathematics Placement Test;
MATH 1100 or 1103; or placement by the Department. Intended for students
majoring in Engineering Technology. Elements of differential and integral
calculus for polynomial, rational, exponential, logarathmic and trigonometric
functions, with applications to engineering. May not be taken for credit if
credit has been received for MATH 1120 or 1241. (Fall, Spring) (Evenings)
MATH 1165. Introduction to Discrete Structures. (3) Prerequisite: ITCS 1100 or 1201 and its lab. Propositions
and truth tables, sets, permutations and combinations, relations and functions,
lattices, and trees. (Fall, Spring,
Summer) (Evenings)
MATH 1241. Calculus
I. (3) Prerequisite: appropriate score on the Mathematics Placement
Test; MATH 1103 with a grade of C or better, or placement by the
Department. Designed for students
majoring in Mathematics, Science, or Engineering. Elementary functions, derivatives and their
applications, introduction to definite integrals. (May
not be taken for credit if credit has been received for MATH 1141.) (Fall, Spring, Summer) (Evenings)
MATH 1242. Calculus
II. (3) Prerequisite: MATH 1241 with a grade of C or better. Methods for evaluating definite integrals,
applications of integration, improper integrals, infinite series, Taylor
series, power series, and introduction to differential equations. (May not be taken for credit if credit has
been received for MATH 1242.) (Fall, Spring, Summer) (Evenings)
MATH 2050. Topics in Mathematics. (2‑3) Prerequisite: consent of the Department. Topics in
mathematics elected to supplement regular offerings at the 2000 level. (May or
may not count for a Math core course for the ITCS major.) May be repeated for
additional credit with the approval of the Department. (On demand)
MATH 2103. Problem Solving in Mathematics Using Computers
and Calculators in the Classroom. (3)
Prerequisite: MATH 2101 with a grade of C
or better. Calculators in the mathematics curriculum; microcomputer hardware
and courseware in mathematics; LOGO; probability; data collection, analysis,
and interpretation. May not be used to satisfy requirement for a major or minor
in Mathematics. (Fall, Spring, Summer)
(Evenings)
MATH 2164. Matrices and Linear Algebra. (3) Prerequisite: MATH 1120 or 1241 with a grade of C or better or consent of the
Department. Matrix algebra, systems of linear equations, vector spaces, linear
transformations, determinants, inner products, eigenvalues. (Fall, Spring, Summer) (Evenings)
MATH 2171. Differential Equations. (3) Prerequisite: MATH 1242 with a grade of C or better. An introduction to ordinary
differential equations including first order equations, general theory of
linear equations, series solutions, special solutions, special equations such
as Bessel's equation, and applications to physical and geometric problems. (Fall, Spring, Summer) (Evenings)
MATH 2241. Calculus
III. (3) Prerequisite: MATH 1242 with a grade of C or better. Functions of two or more variables, vectors
in two and three dimensions, partial derivatives, optimization, double and
triple integrals and their applications.
(May not be taken for credit if credit has been received for MATH
2141.) (Fall, Spring, Summer)
(Evenings)
MATH 2242. Calculus
IV. (3) Prerequisite: MATH 2241 with a grade of C or better. Parametric curves and surfaces, vector
fields, line and surface integrals; Green’s theorem, Divergence theorem,
Stoke’s theorem and applications.
Fourier series and its applications.
(Fall, Spring) (Evenings)
MATH 2340. Number Concepts and Relationships. (3) Prerequisite: MATH 1100 or MATH 103 with a grade of C or
better or consent of the Department. A
study of integers, rationals, and real numbers; conjectures and intuitive
proofs in a number theory; number sequences, patterns, functions; algebraic
concepts and skills. An emphasis on the
development of problem-solving strategies and abilities. (May not be taken for
the major of minor). (Spring)
MATH 2341. Algebra and Algebraic Structures. (3) Prerequisites: MATH 2340 with a grade of C or better or
MATH 2102 with a grade of C or better or consent of the Department. A study of functions and their properties
arising from a variety of problem situations.
Representations of real-world relationships with physical models,
charts, graphs, equations, and inequalities.
Properties of real and complex numbers.
Concrete examples of algebraic structures such as groups, rings, fields,
and vector spaces. (Fall)
MATH 2342. Data Analysis and Probability. (3) Prerequisite: STAT 1220 or STAT 1222 with a grade of C or
better or consent of the Department.
Introduction to the statistical process.
Collection of data from experiments and surveys; organizing,
representing, and interpreting data; formulating arguments based on analysis. Plan and conduct experiments and simulations
to determine experimental probabilities.
Develop counting techniques and other methods to determine
probabilities. (May not be taken for the major or minor). (Spring)
MATH 2343. Geometry
and Measurement. (3) Prerequisite: MATH
1100 or MATH 1103 with a grade of C or
better or consent of the Department. A
study of properties and relationships of shape, size, and symmetry in two and three
dimensions. Explore concepts of motion
in two and three dimensions through transformations. Present written and oral arguments to justify
conjectures and generalizations. Become
familiar with the historical development of Euclidean geometry. (May not be
taken for the major or minor). (Fall)
MATH 3050. Selected Topics in Mathematics. (2‑3) Prerequisite: consent of the Department. Topics selected
to supplement regular offerings at the 3000 level in mathematics or statistics.
May be repeated for credit with the approval of the Department. (On demand)
MATH 3116. Graph Theory. (3) Prerequisite: MATH 2164 or consent of the Department.
Graphs as mathematical models. Planarity, colorability, connectivity, trees.
Applications and algorithms for networks, matching problems and areas of
computer science. (Fall) (Alternate years)
MATH 3122. Probability and Statistics I. (3) Prerequisite: MATH 2241 with a grade of C or better. Sample spaces, random
variables, moment generating functions, some standard distributions,
multivariate distributions, laws of large numbers, limit theorems. (Fall) (Evenings)
MATH 3123. Probability and Statistics II. (3) Prerequisite: MATH/STAT 3122. Estimation, bias,
consistency, efficiency, maximum likelihood estimates, sufficient statistics,
testing, the power function, chi‑square test, Kolmogorov‑Smirnov
test. Credit for mathematics major not
given for both MATH 3125 and MATH/STAT 3123. (Spring) (Evenings)
MATH 3128. Actuarial
Science I. (3) Prerequisites: MATH 3122 or
the consent of the Department. The
mathematical theory of compound interest.
The theory and application of contingency mathematics in the life and
casualty areas. Probabilistic and
deterministic models for annuities and pensions. (Spring)
MATH 3129. Actuarial
Science II. (3) Prerequisites: MATH 3128
or the consent of the Department.
Deterministic and probabilistic models for annuities and pensions,
additional models of risks and financial
transactions. (Fall)
MATH 3141. Advanced Calculus of One Variable. (3) Prerequisites: MATH 2241 and 2164 with grades of C or better. Topology of the real line;
continuity, uniform continuity, differentiability, integration, sequences and
series of functions. (Fall) (Evenings)
MATH 3142. Advanced Calculus of Several Variables. (3) Prerequisite: MATH 3141. Continuity and differentiability
of functions of several variables, inverse and implicit function theorems,
integration, Fubini's theorem, change of variables, the classical integral
theorems of Gauss, Green and Stokes and their generalizations. (Spring) (Evenings)
MATH 3146. Introduction to Complex Analysis. (3) Prerequisite: MATH 2241 with a grade of C or better. Analytic functions, complex
integration, calculus of residues, conformal mapping. (Spring) (Alternate years)
MATH 3163. Introduction to Modern Algebra. (3) (W) Prerequisite: MATH 1242 and MATH 2164 with a grade of C or better or consent of the
Department. Examples and elementary properties of basic algebraic structures,
especially groups. The course emphasizes the writing of proofs of elementary
theorems. (Fall, Spring) (Evenings)
MATH 3166. Combinatorics. (3) Prerequisites: MATH 2164. Combinatorial modeling,
generating functions, recurrence relations, inclusion‑exclusion principle
and problems from recreational mathematics. (Spring)
(Alternate years)
MATH 3171. Applied Mathematics. (3) Prerequisites: MATH 2241 and 2171 with grades of C or better. Separation of variables
techniques for the classical partial differential equations of mathematical
physics; Fourier series; Sturm‑Liouville theory. (Fall) (Evenings)
MATH 3176. Numerical Analysis. (3) Prerequisites: ITCS 1100 or 1201 and its lab, MATH 2241
and 2171. Numerical solution of initial value and boundary value problems in
ordinary differential equations, direct and iterative methods of solving
systems of equations. Selected problems will be programmed for computer
solution. (Spring) (Alternate years)
MATH 3181. Fundamental Concepts of Geometry. (3)
Prerequisite: MATH 2164 with a grade of C or better. Foundations of geometry,
transformations, comparison of Euclidean and non‑ Euclidean geometries. (Fall, Spring) (Evenings)
MATH 3551. Mathematics Cooperative Education Experience.
(O) Prerequisites: Sophomore standing, a 3.0
GPA in MATH/STAT/OPRS courses and consent of the Department of Mathematics. The
student will be employed in a manner that affords him/her the opportunity of
using and enhancing mathematical knowledge and skills through practical
experience. After completing MATH 3551, the student must take MATH 3652. MATH
3551 may be repeated with consent of the Department. (On demand)
MATH 3652. Mathematics Cooperative Education Seminar. (1) Prerequisite: MATH 3551. The student will give an
exposition of his/her work experience in MATH 3551. An exposition of underlying
theoretical concepts and related ideas may also be required. (On demand)
MATH 3688. Mathematics Awareness Seminar. (O) Prerequisite: sophomore standing. Visiting speakers,
discussion of internships, cooperative education and job opportunities; selected topics in mathematics. (Fall)
MATH 3689. Mathematics Project Seminar. (1) (O) Prerequisite: senior standing. Oral presentation by the
student on an area of mathematics or a mathematical problem. (Fall, Spring)
MATH 3691. Seminar. (1‑6) Prerequisite: consent of the Department. Readings, study
and discussion designed to develop the student's ability to study independently
and to present results properly. (On
demand)
MATH 3790. Junior Honors Seminar. (3) Prerequisite: consent of the Department. May be repeated
once for additional credit with approval of the Department. (On demand)
MATH 3791. Senior Honors Tutorial. (3) Prerequisite: consent of the Department. Individual
tutorials in which the student will pursue independent study and research in
any area of mathematics under the direction of one or more faculty members. The
project of the student will be planned to culminate in a research paper of
original or expository nature. May be repeated for additional credit with the
approval of the Department. (On demand)
MATH 4000. Topics in Foundations or History of Mathematics.
(2‑3) Prerequisite: consent of the
Department. Topics in the foundations or the history of mathematics selected to
supplement regular course offerings in this area of mathematics. May be
repeated for credit with approval of the Department. Credit for the M.A. degree
in Mathematics requires approval of the Department. (On demand)
MATH 4040. Topics in Analysis. (2‑3) Prerequisite: consent of the Department. Topics in
analysis selected to supplement regular course offerings in this area of
mathematics. May be repeated for credit with the approval of the Department.
Credit for the M.A. degree in Mathematics requires approval of the Department. (On demand)
MATH 4060. Topics in Algebra. (2‑3) Prerequisite: consent of the Department. Topics in algebra
selected to supplement regular course offerings in this area of mathematics.
May be repeated for credit with the approval of the Department. Credit for the
M.A. degree in Mathematics requires approval of the Department. (On demand)
MATH 4080. Topics in Geometry and Topology. (3) Prerequisite: consent of the Department. Topics in
geometry or topology selected as to supplement regular course offerings in this
area of mathematics. May be repeated for credit with approval of the
Department. Credit for M.A. degree in Mathematics requires approval of the
Department. (On demand)
MATH 4109. History
of Mathematical Thought. (3) Prerequisite:
MATH 1241 or consent of the Department. A study of the development of
mathematics in its historical setting from the earliest beginnings to modern
times. Not approved for the M.A. in mathematics degree. (Fall) (Evenings)
MATH 4161. Number Theory. (3) Prerequisite: MATH 3163 with a grade of C or better or consent of the
Department. A study of the elements of classical number theory including
divisibility, congruences, diophantine equations, prime numbers and their
distribution, quadratic reciprocity, number‑theoretic functions, and
famous unsolved problems. Not approved for the M.A. in mathematics degree. (Spring) (Alternate years)
MATH 4163. Modern Algebra. (3) Prerequisite: MATH 3163 or consent of the Department.
Groups, rings, integral domains, and fields. (Fall) (Alternate years)
MATH 4164. Abstract Linear Algebra. (3) Prerequisite: MATH 3163 and 2164 or consent of the
Department. Vector spaces over arbitrary fields, linear transformations,
canonical forms, and multilinear algebra. (Spring)
(Alternate years)
MATH 4181. Introduction to Topology. (3) Prerequisite: MATH 2164 with a grade of C or better.
Topics from set theory and point set topology such as cardinality, order,
topological spaces, metric spaces, separation axioms, compactness and
connectedness. (Fall) (Alternate years)
MATH 4691. Seminar. (1‑6) Prerequisite: consent of the Department. Individual or
group investigation and exposition of selected topics in mathematics. (On demand)
MATH 4692. Seminar. (1‑6) Prerequisite: consent of the Department. A continuation of
MATH 4691. (On demand