MAA 4226 Advanced Calculus I
- AS 4(4,0) PR: MHF 3302 and
MAC 2313 and MAS 3106 or
C.I.
- Limits, sequences, and continuity,
differentiation and integration.
Derivations of integrals. Infinite series
and convergence. The Balzano-Weierstrass
Theorem and the Heine-Borel Theorem.
Extensions in Euclidian n-space.
- Offered only in the Fall Semester (and some Summer Semesters).
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MAA 4227 Advanced Calculus II
- AS 3(3,0) PR: MAA 4226 or C.I.
- Continuation of MAA 4226.
- Offered only in the Spring semester.
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MAA 5210 Topics in Advanced Calculus
- AS 4(4,0) PR: MAA 4226 or C.I.
- Selected topics in multivariable
calculus, including limits, continuity,
Euler's theorem, the Jacobian, and double
series; extension of single variable
concepts, including uniform convergence
and improper integrals.
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MAA 5405 Complex Variables
- AS 3(3,0) PR: MAC 2313 or C.I.
- Analytic functions. Integration in the
complex plane.
- Laurent series and residue calculus.
Inversion of Laplace transformations.
- Conformal mappings.
- Applications in engineering and the
physical sciences.
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MAA 5416 Foundations of Analysis
- AS 3(3,0) PR: MAA 4226.
- Topological spaces, compactness results,
connectedness, analytical and
differentiable manifolds, topological
groups.
- Lie groups, representation theory for
classical groups, Green, Stoke and Gauss'
theorems.
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MAC 1105 College Algebra
- AS 3(3,0) PR: Intermediate algebra or 2
years of high school algebra or C.I.
- Inequalities. High degree polynomials.
Graphs, rational, logarithmic, and
exponential functions.
- Systems of equations, matrices,
determinants, induction.
- This course prepares students for
higher-level mathematics courses.
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MAC 1114 College Trigonometry
- AS 3(3,0) PR: MAC 1102 or 2 years of high
school algebra or C.I.
- The circle arc length, circular
functions, identities, inverse functions,
applications to simple harmonic motion,
function of angles, complete development
of triangle solving.
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MAC 2233 Concepts of Calculus
- AS 3(3,0) PR: MAC 1105 or C.I.
- The differential and integral calculus of
rational, exponential and logarithmic
functions, with applications to business
analysis.
- Not open to students with credit in
MAC 2253
or MAC 2311.
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MAC 2253 Applied Calculus I
- AS 3(3,0) PR: MAC 1105 and MAC 1114 or
C.I.
- Differential and integral calculus. An
introduction to differential equations
and Laplace Transforms.
- Applications to engineering technology.
- Not open to students with credit in
MAC 2233 or MAC 2311.
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MAC 2254 Applied Calculus II
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MAC 2311 Calculus with Analytic Geometry I
- AS 4(4,0) PR: MAC 1105
and MAC 1114 or
equivalent, or C.I.
- The differential and integral calculus of
algebraic and elementary transcendental
functions with geometric and physical
applications.
- Topics from analytic geometry include
coordinate systems, vectors, lines, conic
sections, transformations of coordinates,
and polar coordinates.
- During the 2nd and 3rd semesters the
topics also include sequences and series,
Taylor series, and the differential and
integral calculus for functions of
several variables.
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MAC 2311H Calculus with Analytic Geometry I
- AS 4(4,0) (Honors): PR: MAC 1105
and MAC 1114 or
equivalent, or C.I.
- Differential and
integral calculus, emphasizing
understanding basic concepts and their
applications.
- Students will complete projects on their
own.
- For honors students from all disciplines.
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MAC 2312 Calculus with Analytic Geometry II
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MAC 2312H Calculus with Analytic Geometry II
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MAC 2313 Calculus with Analytic Geometry III
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MAC 2313H Calculus with Analytic Geometry III
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MAD 4203 Applied Combinatorics
- AS 3(3,0) PR: MAC 2312 and either
MHF 3302 or COT 3100C, or C.I.
- Counting principles; permutations and combinations, multisets, recurrence relations and generating functions; combinatorial designs; the Polya theory of counting.
- Offered only in the Fall semester.
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MAD 4301 Graph Theory
- AS 3(3,0) PR: MAC 2313 and
MHF 3302 or C.I.
- Graph theory; isomorphism, connectivity; traversability, matchings, factorizations, planarity, colorings, and Ramsey number.
- Offered only in the Spring semester.
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MAD 5205 Combinatorics and Graph Theory II
- AS 3(3,0) PR: MAD 4203.
- Polya's theory of counting, Latin squares
and rectangles, block designs, coding
theory, networks, invariants and extremal
graph theory, Ramsey theory,
probabalistic methods, hypergraphs,
applications.
- Offered only in the Spring semester.
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MAP 2302 Differential Equations
- AS 3(3,0) PR: MAC 2313 or C.I.
- Methods of solution for first order
equations.
- Linear equations.
- Laplace transforms.
- Series solutions.
- Selected applications.
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MAP 4103 Mathematical Modeling I
- AS 3(3,0) PR: MAP 2302 or C.I.
- An overview of model construction.
- Model fitting, optimization models,
empirical construction and modeling
dynamic behavior.
- Calculus and ordinary differential
equations required.
- Offered only in the Spring semester.
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MAP 4153 Vector and Tensor Analysis
- AS 3(3,0) PR: MAC 2313 or C.I.
- Vector calculus.
- The theorems of Green, Gauss and Stokes.
Introduction to tensors.
- Application in engineering and physical
sciences.
- Offered only in the Fall semester.
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MAP 4307 Applications of Complex Variables (Advanced Engineering Math Series)
- AS3(3,0) PR: MAP 2302 or C.I.
- Analytic functions and complex
integration.
- Residue integration, Taylor and Laurent
series, conformal mapping and the
application of complex analysis to
Potential Theory.
- Offered only in the Spring semester.
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MAP 4308 Fourier Methods (Advanced Engineering Math Series)
- AS 3(3,0) PR: MAP 2302
- Fourier series, integrals and transforms.
- Partial differential equations or
vibrating membranes and heat flow.
- No credit for mathematics majors.
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MAP 4363 Applied Boundary Value Problems I
- AS3(3,0) PR: MAP 2302 or C.I.
- Systems of linear equations.
- Fourier series.
- The eigenvalue problem of
Sturm-Liouville.
- The method of Green's functions.
- Offered only in the Fall semester.
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MAP 4364 Applied Boundary Value Problems II
- AS 3(3,0) PR: MAP 4363 or C.I.
- Legendre polynomials and Bessel
functions.
- The theory of Sturm-Liouville.
- Separation of variables.
- Applications involving the wave equation,
heat equation and equation of Laplace.
- Offered only in the Spring semester.
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MAP 5385 Applied Numerical Mathematics
- AS 3(3,0) PR: MAP 2302 or C.I.
- Classical topics or numerical analysis
and their applications, Romberg
integration.
- Richardson extrapolation, Gaussian
quadrature schemes.
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MAP 5396 Splines and Data Fitting
- AS 3(3,0) PR: MAS 3106, MAS 3113, MAP 2302, or C.I.
- Univariate splines and their application
to data fitting.
- Applications to regression analysis,
differential and integral equations.
- Algorithms to use different types of
splines in computation.
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MAP 5404 Ordinary Differential Equations and Applications
- AS 3(3,0) PR: MAP 2302, Differential
Equations; or C.I.
- Existence and uniqueness of solutions of
differential equations, systems of
ordinary differential equations,
autonomous systems, phase plane analysis,
stability, bifurcations.
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MAP 5407 Applied Mathematics I
- AS 3(3,0) PR: MAP 2302 or C.I.
- Fourier series, calculus of variations.
Hamilton's principle, eigenvalues and
stationary points, Rayleigh-Ritz method,
partial differential equations, and
approximation methods.
- May be taken after Applied Math II.
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MAP 5426 Special Functions
- AS 3(3,0) PR: MAP 2302 or C.I.
- Series and integral representations,
generating functions, recurrence
relations and orthogonality properties of
the special functions.
- Emphasis on Bessel, Legendre and
hypergeometric functions.
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MAP 5514 Linear and Nonlinear Waves I
- AS 3(3,0) PR: MAP 2302, MAP 4363; or C.I.
- Equations of motion in inviscid and
viscous fluids, energy equation and
energy flux, linear theory of gravity and
capilliary-gravity waves, variational
principles for water waves.
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MAS 3105 Elementary Linear and Matrix Algebra
- AS 4(4,0) PR: MAC 3312 or C.I.
- Matrices, determinants, vector spaces in
Rn, linear independence, basis, solutions
of systems, range of linear
transformations, eigenvectors, Jordan
Form, matrix functions, quadratic forms.
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MAS 3106 Linear Algebra
- AS 4(4,0) PR: MHF 3302 and MAS 3105 or
C.I.
- Abstract vector spaces, linear
transformations, isomorphisms, projections,
eigenvalues and eigenvectors, diagonalization,
Jordan canonical Form, inner products
- Offered only in the Spring semester.
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MAS 3203 Introduction to Number Theory
- AS 3(3,0) PR: MHF 3302 or C.I.
- Inductive reasoning
- Prime numbers and factorization
- The division algorithm and congruences.
- Euler's phi function and other multiplicative functions.
- Offered only in the Spring semester.
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MAS4146 Linear Systems (Advanced Engineering Math Series)
- AS 3(3,0) PR: MAP 2302
- Systems, eigenvalue problems and
diagonalization.
- Vector calculus, line/surface integrals
and integral theorems.
- No credit for mathematics majors.
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MAS 4301 Algebraic Structures
- AS 3(3,0) PR: MHF 3302 and
MAS 3106 or C.I.
- An introduction to groups, rings and
fields.
- Offered only in the Fall semester.
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MGF 1106 Finite Mathematics
- AS 3(3,0) PR: Intermediate algebra or 2
years of high school algebra or C.I.
- Introduction to logical structure, sets,
probability, arrays, games.
- This course is intended for students who
are not planning to take further courses
in mathematics.
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MHF 3302 Logic and Proof in Mathematics
- AS 3(3,0) PR: MAC 2311 , CR: MAC 2312, or C.I.
- Basic mathematical logic.
- Methods of proof in mathematics.
- Application of proofs to elementary
mathematical structures.
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MHF 4404 History of Mathematics
- AS 3(3,0) PR: MAC 2312 or C.I.
- A chronological study of the evolution of
mathematical thought from primitive
counting through modern ideas of the 20th
century.
- Recommended for prospective teachers in
mathematics.
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MTG 4212 Modern Geometries
- AS 4(4,0) PR: MAC 2311 or C.I.
- Axiomatic systems for finite geometries
- Euclidean geometry of polygons and the circle
- Non-Euclidean geometry
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MTG 4302 Introduction to Topology
- AS 3(3,0) PR: MHF 3302 and MHF 3302, or C.I.
- Metric spaces
- Topological spaces
- Continuity, compactness, connectedness
- Offered only in the Spring semester.
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MTG 5256 Differential Geometry
- AS 3(3,0) PR: MAA 4227 or C.I.
- Differentiable manifolds
- Tangent space and tangent bundle
- Vector fields
- Lie derivatives
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