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MATH
MATHEMATICS
See also "Statistics".
Credit for MATH 1003
1. Calculus Challenge Exam
This examination which is held in early June is open to students registered in a calculus
course at a high school that has made arrangements with the Department of Mathematics
& Statistics. A fee will be charged.
Students who qualify for credit will receive a certificate entitling them to credit for and
therefore exemption from MATH 1003 when they register at UNB. Upon the student's
acceptance of the credit (3ch), the letter grade of the exam will be recorded on their
transcript.
More information can be obtained from http://www.math.unb.ca or from the Department.
2. Advanced Placement Test
The Science Faculty offers Advanced Placement Tests for some first year science courses,
including MATH 1003, during registration week (early September) each year.
More information can be obtained by consulting the Science section of the calendar or by
contacting the Science Faculty or the Department of Mathematics & Statistics.
Students should note that in the Science Faculty the minimum acceptable grade in a course which
is required by a particular program or is used to meet a prerequisite, is a "C". Any student who fails
to attain a "C" or better in such a course must repeat the course (at the next regular session) until
a grade of "C" or better is attained. Students will not be eligible for graduation until such
deficiencies are removed. The only exception will be granted for a single course with a “D” grade
that is a normal part of the final year of that program, and is being taken for the first time in the
final year
Note: See Courses -> Saint John or Fredericton -> Standard Course Abbreviations in the online undergraduate
calendar for an explanation of abbreviations, course numbers and coding.
MATH 0863 Precalculus Mathematics
0 ch (3C 1T)
A review of high school mathematics topics, including basic properties of number systems,
manipulation of algebraic expressions, equations and inequalities, analytic geometry, linear and
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quadratic functions, polynomial and rational functions, exponential and logarithm functions,
trigonometric functions. Note: This course is designed to serve as preparation for calculus courses
at the university level, such as Math 1003 and Math 1823. It carries no credit for degree programs
at UNB Fredericton.
MATH 1003
Introduction to Calculus I
3 ch (4C)
Functions and graphs, limits, derivatives of polynomial, log, exponential and trigonometric
functions. Curve sketching and extrema of functions. NOTE: Credit may be obtained for only
one of MATH 1003, 1053 or 1823. Prerequisite: A minimum grade of 60% in New Brunswick
high school courses: Trigonometry and 3-space, Advanced Math with an Introduction to
Calculus, or equivalent courses; and a passing score on the Department of Mathematics and
Statistics placement test.
MATH 1013
Introduction to Calculus II
3 ch (4C)
Definition of the integral, fundamental theorem of Calculus, Techniques of integration,
improper integrals. Ordinary differential equations. Taylor polynomials and series. NOTE:
Credit may be obtained for only one of MATH 1013 or 1053. Prerequisite: MATH 1003 or
1053. Note that MATH 1823 does not fully prepare students for MATH 1013; consult the
Department of Mathematics and Statistics for advice.
MATH 1053
Enriched Introduction to Calculus
3 ch (4C)
The syllabus is similar to that for MATH 1003, with more emphasis placed both on the theory
of Calculus and interesting applications. The course will be of special interest to students
with strong Mathematical backgrounds. Any interested student (with or without High School
Calculus) is encouraged to consult with the Mathematics Department. NOTE: Credit may be
obtained for only one of MATH 1003, 1053 or 1823. Prerequisite: A grade of 85% or higher in
a Grade 12 Math course that contains some Calculus, or consent of the Department of
Mathematics and Statistics.
MATH 1063
Enriched Introduction to Calculus II
4 ch (4C)
The syllabus for this course is similar to that of MATH 1013. As with MATH 1053, more
emphasis is placed on theory, mathematical rigor and interesting applications. NOTE: Credit
may be obtained for only one of MATH 1013 or 1063. Prerequisite: A grade of B or higher in
MATH 1053, or MATH 1003 with consent of the Department of Mathematics and Statistics.
MATH 1503
Introduction to Linear Algebra
3 ch (3C)
Lines and Planes, The Geometry and Algebra of vectors, Systems of linear equations, Matrix
Algebra, Linear Independence, Linear Transformations, Determinants, Complex numbers,
Eigenvalues, Eigenvectors, Diagonalization, Rotation matrices, Quadratic forms, Least
squares. Prerequisite: A minimum grade of 60% in New Brunswick high school courses:
Trigonometry and 3-space, Advanced Math with an Introduction to Calculus, or equivalent
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courses. Note: Credit will not be given for both Math 1503 and Math 2213.
MATH 1823
Calculus for Management Sciences
3 ch (3C 1T)
Polynomial, logarithmic and exponential functions. Limits and derivatives. Extreme values
and related rates. Simple integration. Differential equations. Throughout stresses
applications to business and economics. NOTE: Credit may be obtained for only one of MATH
1003, 1053 or 1823. Prerequisite: A minimum grade of 60% in New Brunswick high school
courses: Trigonometry and 3-space, Advanced Math with an Introduction to Calculus, or
equivalent courses.
MATH 1833
Finite Mathematics for Management Sciences
3 ch (3C)
Matrices and systems of linear equations. Linear programming concepts; graphical solution
of two variable problems. Permutations and combinations. Elementary probability.
Mathematics of finance. NOTE: Credit for MATH1833 will not be given if the student has
previously taken either MATH 1503 or MATH 2213. Prerequisite: A minimum grade of 60% in
New Brunswick Mathematics 112 GA (Geometry and Applications) and New Brunswick
Mathematics 112 FR (Functions and Relations), or equivalent.
MATH 2003
Intermediate Mathematics I
3 ch (3C 1T)
Analytic geometry and vectors. Parametric curves. Polar, cylindrical and spherical
coordinates. Functions of several variables, partial derivatives, applications to max-min.
Double and triple integrals. Prerequisite: MATH 1013 or MATH 1063. Note: Credit may not
be obtained for both MATH 2003 and MATH 2513.
MATH 2013
Intermediate Mathematics II
3 ch (3C 1T)
Review of first order differential equations. Second order linear O.D.E.'s. Infinite series,
including power series solutions to O.D.E.'s. Line and surface integrals. Theorems of Green
and Stokes. Divergence Theorem. Prerequisite: MATH 2003.
MATH 2203
Discrete Mathematics
3 ch (3C)
Logic, methods of proof, mathematical induction, elementary set theory, functions and
relations. NOTE: This course is designed for students desiring a good grounding in the
foundations of mathematics. Theorems and proofs are an important part of the course.
Credit will not be given for both MATH 2203 and CS 1303. Students majoring in Mathematics
must take MATH 2203. Prerequisite: MATH 1063 or MATH 1013 or permission of instructor.
NOTE: It is strongly recommended that students should have at least a grade of B in MATH
1013 or MATH 1063 to take this course.
MATH 2213
Linear Algebra I
3 ch (3C)
This course introduces the basic concepts of linear algebra, mainly in finite dimensional real
vector spaces. Systems of linear equations, vector and matrix algebra, bases and dimension
of subspaces, row and column spaces, linear transformations and matrix representations,
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inner products, determinants, eigenvectors and diagonalization. Applications as time
permits. Prerequisite: MATH 1013, or MATH 1053, or both MATH 1823 and 1833. This course may
also be taken with the consent of the instructor. Interested first year students are encouraged to
enquire. Note: Credit will not be given for both MATH 1503 and MATH 2213.
MATH 2513
Multivariable Calculus for Engineers
4 ch (4C)
Functions of several variables, partial derivatives, multiple integrals, vector functions,
Green's and Stokes' Theorems.. Prerequisite: MATH 1013 and MATH 1503. Note: Credit
may not be obtained for both MATH 2003 and MATH 2513.
MATH 2623
Introduction to Mathematical Thinking
3 ch (3C)
An introduction to mathematical thinking. Content varies, and is focused on presenting
mathematics as a living, creative discipline. A sample of topics: patterns and symmetry,
tiling, non-Euclidean geometry, chaos and fractals, planetary motion, binary numerals, prime
numbers, Fibonacci numbers, voting systems, the calendar. Not available for credit to
students with a Major in Mathematics/Statistics. Prerequisite: Successful completion of at
least one year of a university program.
Fundamental Principles of Elementary School
3 ch (3C 1L)
Mathematics
This course is intended for students who anticipate a career as an elementary or middle
school teacher. The course focuses on topics taken from the K-8 curriculum with extensions
beyond classroom topics to show the 'how' and 'why' behind school mathematics. The major
topics are problem solving, number concepts, number and relationship operations, patterns
and relations, shape and space, as well as data management and probability. Intended for
students registered in arts programs. Not available for credit to students who would have
6ch of Level 1000 mathematics in their degree programs. Antirequisite: MATH 3633.
Prerequisite: Successful completion of at least one year of a university program.
MATH 2633
MATH 3003
Applied Analysis
3 ch (3C)
Vector spaces of functions, convergence in normed linear spaces, orthogonal polynomials,
Fourier series, Fourier transform, Fast Fourier transform, introduction to wavelets, and
selected applications. Prerequisites: MATH 2013 or MATH 3503, and MATH 2213 or MATH
1503 (MATH 3213 recommended). NOTE: Credit will not be given for both MATH 3003 and
MATH 3113.
MATH 3033
Group Theory
3 ch (3C)
Groups are the mathematical objects used to describe symmetries. This course covers the
fundamentals of group theory, together with applications selected from geometry, advanced
algebra and physical sciences. Prerequisites: MATH 2203 or CS 1303, and MATH 2213 or
MATH 1503 (MATH 3213 recommended). Other interested students are encouraged to seek
consent of the instructor.
MATH 3043
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Ordinary Differential Equations
3 ch (3C)
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First order equations, linear systems, variation of parameters, method of undetermined
coefficients, Laplace transforms, power series solutions, fundamental matrix solution.
Existence and uniqueness of solutions, properties of linear systems, eigenvalue problems,
vector fields, phase-plane analysis, Liapunov method. Prerequisite: MATH 2013 or MATH
2513. NOTE: Credit cannot be obtained for both Math 3043 and Math 3503.
MATH 3063
Geometry
3 ch (3C)
Axiomatic systems, non-Euclidian geometry, transformations in geometries, topological
properties of figures. Recommended for Education students or prospective Mathematics
teachers. Prerequisite: MATH 1503 or MATH 2213, or permission of the instructor.
Interested students are encouraged to enquire.
MATH 3073
Partial Differential Equations
3 ch (3C)
Methods of solution for first order equations. Classification of second order equations.
Characteristics. Analytic and numerical methods of solution for hyperbolic, elliptic and
parabolic equations. Prerequisite: MATH 2013 or both MATH 2513 and 3503.
MATH 3093
Elementary Number Theory
3 ch (3C)
Primes, unique factorization, congruences, Diophantine equations, basic number theoretic
functions. Recommended for Education students or prospective Mathematics teachers.
MATH 3103
Analysis I
3 ch (3C)
The real number system, elementary set theory, metric spaces, sequences and series,
continuity. Prerequisites: MATH 2013, 2203, and MATH 2213 or 1503.
MATH 3113
Analysis II
3 ch (3C)
Differential calculus, integration, sequences and series of functions, completeness of basis,
convergence of Fourier Series, Fourier Transforms. Additional topics may include differential
forms or wavelets and wavelet transforms. Prerequisite: MATH 3103. NOTE: Credit will not
be given for both MATH 3003 and MATH 3113.
MATH 3213
Linear Algebra II
3 ch (3C)
Finite and infinite dimensional vector spaces over general fields. Subspaces, independent
and spanning sets, dimension, linear operators, determinants, inner product spaces. As time
permits, applications selected from least squares approximation, Markov chains, data
compression, traffic flow, robotics, genetics, graph theory, cryptography. Prerequisite: MATH
2213 or MATH 1503 or consent of the instructor.
MATH 3243
Complex Analysis
3 ch (3C)
Complex analytic functions, contour integrals and Cauchy's theorems; Taylor's, Laurent's and
Liouville's theorems; residue calculus. Prerequisites: MATH 2003, MATH 2013 or equivalent.
MATH 3333
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Combinatorial Theory
3 ch (3C)
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Topics selected from: Principle of inclusion and exclusion, Mobius inversion, generating
functions, systems of distinct representatives, Ramsey's Theorem, duality in external
problems, duality in programming, dynamic programming, block designs, introduction to
matroid theory, signal-flow graphs. (The course is also of interest to students in Computer
Science and Engineering.) Prerequisite: MATH 1003, 1823 or 1833.
MATH 3343
Networks and Graphs
3 ch (3C)
Graphs, Euler paths, tournaments, factors, spanning trees, applications, electric networks
and Kirchhoff's laws, matroids, kernels, Grundy function and application to game theory,
Menger's theorem, flows in networks, flow algorithms. Prerequisite: MATH 1003, 1823 or
1833 and MATH 2203 or CS 1303.
MATH 3353
Computational Algebra
3 ch (3C)
Topics in abstract algebra are approached from the perspective of what can be computed
using such software packages as Maple, Macaulay and GAP. The topics covered will be
selected from: Grobner bases, resultants, solving polynomial equations, invariant theory of
finite groups, and the exact solution of differential equations. The course work will include a
mixture of problem sets emphasizing theory and practical lab assignments. Prerequisites:
one of MATH 1013 or MATH 1063, and one of MATH 1503 or MATH 2213.
MATH 3363
Finite Mathematics (A)
3 ch (3C)
Applications of algebraic and combinatorial methods to a selection of problems from coding
theory, computability, information theory, formal languages, cybernetics and the social and
physical sciences. Prerequisite: 12 ch in Math and/or Stat.
MATH 3373
Introduction to Game Theory (O)
3 ch (3C)
Strategic games, n-person games in normal form, dominated strategies, Nash equilibrium, mixed
strategies and mixed strategy equilibrium, games with perfect information, games with imperfect
information, Bayesian games, extensive games. The course introduces basic non-cooperative game
theory and analytical tools for decision makers (consumers, firms, politicians, governments). It is
suitable for Mathematics, Economics, Computer Science, Management Science, Political Science,
Social Science and Science students or any student with a minor in such disciplines, in particular
those in the Mathematics/Statistics-Economics option. Note: this course is cross-listed as ECON
4673. Students cannot obtain credit for both MATH 3373 and ECON 4673 (or 5673).Prerequisites:
MATH 1823 and MATH 1833; or MATH 1003 and MATH 1013; or MATH 1053 and MATH 1063; or
ECON 3013; or permission of the instructor.
MATH 3413
Introduction to Numerical Methods
3 ch (3C)
Intended for Mathematics, Science or Engineering students. Error analysis, convergence and
stability. Approximation of functions by polynomials. Numerical quadrature and
differentiation. The solution of linear and nonlinear equations and the solution of ordinary
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differential equations. This course will emphasize the understanding of numerical algorithms
and stress applications in the applied sciences, as well as the influence of finite precision and
arithmetic on computational results. Note: This course is cross-listed as CS 3113. Credit will
not be given for both MATH 3413 and CS 3113. Prerequisites: CS 1003 or CS 1073; and MATH
2213 or MATH 1503.
MATH 3473
Mathematical Modelling (A)
3 ch (3C)
This course is intended to develop skills in translating a problem in the real world to a well
formulated mathematical problem. The basic techniques and tools for model formulation,
model analysis, numerical simulation and model interpretation will be offered. Project topics
will be chosen from Biology, Physics, Chemistry, Mechanics, Engineering, Economics and
elsewhere. Prerequisites: Math 1013 and permission of the instructor.
MATH 3503
Differential Equations for Engineers
3 ch (3C 1T)
Nonhomogeneous differential equations, undetermined coefficients, variation of
parameters, systems of 1st and 2nd order ordinary differential equations, Laplace
transforms, Fourier series. Prerequisite: MATH 1503 or 2213. Co-requisite MATH 2513 or
MATH 2003. NOTE: Credit cannot be obtained for both MATH 3503 and MATH 3043.
MATH 3543
Differential Geometry for Geomatics Engineers
4 ch (4L 1T)
Basic analytic geometry, spherical trigonometry, geometry of curves in space, measurements
on surfaces, Gaussian surface geometry. Prerequisites: MATH 2513.
MATH 3623
History of Mathematics (A)
3 ch (3C) [W]
A non-technical survey of the development of mathematics from primitive peoples through
Indian, Oriental, Babylonian, Egyptian and Greek cultures. More emphasis will be placed on
Western European and post-Renaissance mathematics, and recent (post-1940) history. An
attempt is made to discuss each new mathematical contribution in light of both past
mathematics and social scientific forces of the day. Some background in Mathematics
necessary. Prerequisite: 12 ch in Math and/or Stat.
MATH 3633
Fundamental Principles of School Mathematics I.
3 ch (3C)
A course for undergraduate students who anticipate a career as teachers. Topics build
around the K-12 syllabus, with extensions beyond the classroom, to show the 'how' and
'why' behind school mathematics. Mathematical language; real numbers and other
mathematical structures; Euclidean geometry; functions; mathematical connections;
problem solving. Prerequisite: 6 ch of university mathematics.
MATH 3803
Introduction to the Mathematics of Finance
3 ch (3C)
Measurement of interest, compound interest, annuities, amortization schedules and sinking
funds,bonds. Prerequisite: MATH1013 or a grade of B or better in MATH 1823.
MATH 3813
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Mathematics of Finance II (O)
3 ch (3C)
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A more advanced study of the topics in MATH3803 including varying and continuous
annuities and yield rates. Prerequisite: MATH3803 with a grade of B or better.
MATH 3843
Introduction to Life Contingencies
3 ch (3C)
Survival distributions, general life insurances and life annuities, reserves. Joint annuities and
last survivor annuities. Prerequisite: One term of statistics and MATH 3803.
MATH 4023
Functional Analysis
3 ch (3C)
Normed spaces, the Hahn-Banach theorem, uniform boundedness theorem. The contraction
mapping theorem. Existence and uniqueness for nonlinear differential equations. Further
topics may include Wavelets or Banach spaces. Prerequisite: Any two of MATH 3003, 3103,
3113, or permission of the instructor.
MATH 4043
Advanced Algebra (A)
3 ch (3C)
Prime fields and characteristic, extension fields, algebraic extensions, theory of finite fields,
Galois theory, and topics which may include some of: rings, topological algebra, multilinear
and exterior algebra, quadratic forms. Prerequisites: MATH 3033.
MATH 4063
Advanced Geometry (Exotic Spaces) (O)
3 ch (3C)
A deeper investigation of Euclidean and Non-Euclidean spaces of any dimension. Topics
selected from: axiom systems, linear and affine transformations, conformal and linear
models for Euclidean and hyperbolic spaces and their isometry groups, basic theory of
convexity, combinatorial properties of polytopes. Prerequisites: One of MATH 2213, MATH
2003, MATH 2513, or MATH 3063.
MATH 4100
Honours Project
6 ch [W]
Mathematics Honours students must complete a project under the supervision of a faculty
member. The project is to include a written report and an oral presentation. Prior to being
admitted into MATH 4100, the student must have been admitted to the Honours Program
and have submitted an acceptable project proposal to the department. Normally students
would begin preparation and research for the project during their third year of study, submit
the proposal by October of their fourth (final) year of study, and complete the written and
oral presentation by the end of the winter term, to graduate in May of that year.
MATH 4103
Measure Theory and Wavelets
3 ch (3C)
Brief review of Riemann integration. Algebras of sets, outer measure, measure, measurable
sets, measurable functions, the Lebesgue integral, properties of the Lebesgue integral,
abstract measure spaces, integrals and derivatives, sequences of integrals, Fubini's theorem.
Properties of Fourier transforms, multiresolution analysis, Daubechies wavelets.
Prerequisite: One of MATH 3003, MATH 3103, or permission of the instructor.
MATH 4123
Advanced Linear Algebra (O)
3 ch (3C)
The theory of vector spaces and linear transformations, dual spaces, multilinear maps
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(including tensors and determinants); further topics chosen from canonical forms, metric
vector spaces, algebras, etc. Prerequisites: MATH 3213.
MATH 4142 Introduction to Dynamical Systems (O) 3ch (3C)
Many of the processes studied in science, engineering and economics are described by
nonlinear differential equations. This course introduces qualitative methods to find essential
information about the solutions of nonlinear equations without necessarily attempting to find
the solution completely. Topics include flows, stability, phase plane analysis, limit cycles,
bifurcations, chaos, attractors, maps, fractals. Applications throughout. Prerequisites: Math
3043, or both Math 2513 and Math 3503, or permission of the
instructor.
MATH 4153
Topology (A)
3 ch (3C)
A continuation of the topological concepts introduced in MATH 3103. Basic results in pointset topology. Prerequisites: MATH 3103.
MATH 4413
Fluid Mechanics (A)
3 ch (3C)
Derivation of the Equations of Motion: Euler's equations, rotation and vorticity, NavierStokes equations. Potential Flow: complex potentials, harmonic functions, conformal
mapping, potential flow in three dimensions. Slightly Viscous Flow: boundary layers and
Prandtl boundary layer equations. Gas Flow in one dimension: characteristics and shocks.
Prerequisite: MATH 2003-2013 or equivalent.
MATH 4423
Mathematical Theory of Control (A)
3 ch (3C)
Topics selected according to the interests of students and faculty which may include the
following: optimal control of linear systems, Pontryagin's maximum principle, controlability,
observability, distributed parameter systems, differential games, stochastic systems.
Prerequisite: MATH 2013 or equivalent.
MATH 4433
Calculus of Variations (A)
3 ch (3C)
Introduction to functionals and function spaces. Variation of a functional. Euler's equations,
necessary condition for an extremum, case of several variables, invariance of Euler's
equation, fixed end point problem for unknown functions, variational problems in
parametric form, functionals depending on high order derivatives. Prerequisite: MATH 2013
or equivalent.
MATH 4443
Introduction to Quantum Field Theory
3 ch (3C)
Relativistic quantum mechanics. The negative energy problem. Classical field theory,
symmetries and Noether's theorem. Free field theory and Fock space quantization. The
interacting field: LSZ reduction formula, Wick's theorem, Green's functions, and Feynman
diagrams. Introduction to Quantum electrodynamics and renormalization. This course is
cross-listed as PHYS 4938. Credit cannot be obtained for both Math 4443 and PHYS 4953.
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Prerequisites: MATH 3003, PHYS 3051, and one of MATH 3043, 3503, PHYS 3011, 3031, or
permission of instructor.
MATH 4453
Special Functions (A)
3 ch (3C)
Covers in depth those functions which commonly occur in Physics and Engineering, namely,
the Gamma, Beta, Bessel, Legendre, hypergeometric, Hermite and Laguerre functions.
Additional or alternative special functions may be included. Applications to Physics and
Engineering will be discussed. Prerequisite: MATH 3043 or MATH 3503 or equivalent.
MATH 4473
Introduction to Differential Geometry (A)
3 ch (3C)
Geometry of embedded curves and surfaces, n-dimensional manifolds, tensors, Riemannian
geometry. Prerequisites: MATH 2013 or equivalent.
MATH 4483
Introduction to General Relativity (A)
3 ch (3C)
Along with quantum theory, general relativity is one of the central pillars of modern
theoretical physics with wide-ranging implications for astrophysics and high energy
physics. The essential idea is that gravitation is a manifestation of the curvature of spacetime
rather than a force in the Newtonian sense. This course will provide students with a basic
working understanding of general relativity and an introduction to important applications such
as black holes and cosmology. Contents: review and geometric interpretation of special
relativity, foundations of general relativity, linearized gravity and classical tests, black holes,
cosmology. Note: this course is cross-listed as PHYS 4983. Credit cannot be obtained for both
Math 4483 and PHYS 4983. Prerequisites: MATH 4473 or permission of instructor.
MATH 4503
Numerical Methods for Differential Equations
3 ch (3C)
The numerical solution of ordinary differential equations, and partial differential equations
of elliptic, hyperbolic and parabolic type. The course is a basic introduction to finite
difference methods, including the associated theory of stability, accuracy and convergence.
Students will gain practical experience using state-of-the-art numerical solvers and
visualization tools, while solving practical problems from the physical and biological sciences.
Cross-listed as CS 4115. Prerequisites: One of: MATH 3043, MATH 3073, MATH 3413, MATH
3503, CS 3113, CHE 3418, or ME 3522.
MATH 4563
Mathematical Biology (A)
3 ch (3C)
Overview of the field of Mathematical Biology. Development, simulation and analysis of
mathematical models describing biological systems. Equal emphasis is placed on developing
simple models and case studies of successful models. The principal mathematical tools are
differential and difference equations, finite mathematics, probability and statistics. This course
is intended for students in their third or fourth year having an interest in biological research.
Prerequisites: a course in statistics, MATH 2003 or 2013 or equivalent, or permission of the
instructor. This course is cross-listed as BIOL 4563. Credit may not be obtained for both
MATH 4563 and BIOL 4563.
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MATH 4633
Calculus Revisited
3 ch (3C)
A course for high school mathematics teachers. The course is built around a set of
optimization problems, whose solution requires review of topics in first and second year
calculus and linear algebra. Connections are made with topics in the Common Atlantic High
School Mathematics Curriculum. Prerequisite: Permission of Instructor.
MATH 4643
Formal Languages
3 ch (3C)
Brief history of structural linguistics. Introduction to mathematical methods of linguistics.
Finite state automata, regular languages. Computability. Chomsky hierarchy. Phrasestructure grammars. Artificial intelligence problem. Critiques of structural linguistics.
Prerequisite: Permission of the instructor. MATH 2203 or CS2333 recommended.
MATH 4853
Mathematics of Financial Derivatives (A)
3 ch (3C)
Basics of options, futures, and other derivative securities. Introduction to Arbitrage. Brief
introduction to partial differential equations. Stochastic calculus and Ito's Lemma. Option
pricing using the Black-Scholes model. Put-call parity and Hedging. Pricing of European and
American call and put options. Numerical methods for the Black-Scholes model: binary trees,
moving boundary problems, and linear complementarity. The barrier, and other exotic
options. Prerequisites: CS 1073 or experience with a computer programming language, and
either MATH 3503 and STAT 2593, or MATH 2013, 2213, and STAT 3083.
MATH 4903
Independent Study in Mathematics
3 ch
Topics to be chosen jointly by student, advisor, and Department Chair. May be taken for
credit more than once. Title of topic chosen will appear on transcript. Prerequisite:
Permission of Department.
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