Department of Mathematics at FAS, AUB
 
Undergraduate Courses 

COURSES / PROGRAMS

Mathematics

  • MATH 101 Calculus and Analytic Geometry I 3.1; 3 cr.
    Limits, continuity, differentiation with application to curve plotting; Rolle's theorem; integration with application to area, distance, volume, arc-length; fundamental theorem of calculus, transcendental functions. Each Semester
  • MATH 102 Calculus and Analytic Geometry II 3.1; 3 cr.
    Methods of integration, improper integrals, polar coordinates, conic sections, analytic geometry in space, parametric equations, and vector functions and their derivatives.
    Prerequisite: MATH 101. Each Semester
  • MATH 201 Calculus and Analytic Geometry III 3.1; 3 cr.
    Multivariable functions, partial derivatives, cylindrical and spherical coordinates, multiple integrals, sequences and series, and integration in vector fields.
    Prerequisite: MATH 102. Each Semester
  • MATH 202 Differential Equations 3.0; 3 cr.
    Surface integrals, Stokes theorem, divergence theorem; first-order differential equations, linear
    differential equations, series solutions, Bessel’s and Legendre’s functions, Laplace transform, and
    systems. Prerequisite: MATH 201. Each Semester
  • MATH 203 Mathematics for Social Sciences I 3.0; 3 cr.
    Polynomials, factoring, first and second-degree equations, inequalities, absolute value, straight lines, Gaussian elimination, functions, graphs, exponential and logarithmic functions differentiation. Not open to students with prior credit in MATH 101 or its equivalent. Annually.
  • MATH 204 Mathematics for Social Sciences II 3.0; 3 cr.
    Matrix operations, inverses, determinants, set operations, permutations, combinations, probability, rate of change, techniques of integration, differential equations, graphs of multivariate functions, partial derivatives, and optimization.
    Prerequisite: MATH 101 or MATH 203. Annually.
  • MATH 210 Introduction to Analysis 3.0; 3 cr.
    The real numbers, completeness, sequences, some basic topology of the real line, compact sets, Heine-Borel theorem, continuous functions, intermediate value theorem, uniform continuity, extreme values, differentiation, mean-value theorem, Taylor's theorem, integration, sequences and series of functions.
    Prerequisite: MATH 201. Annually.
  • MATH 211 Discrete Structures 3.1; 3 cr.
    Logical reasoning, sets, relations and functions; mathematical induction, counting, and simple
    finite probability theory; analysis of algorithms, complexity; recurrence relations and difference
    equations; truth tables and switching circuits; graphs and trees; strings and languages. This course
    is equivalent to CMPS 211. Annually.
  • MATH 212 Introductory Partial Differential Equations 3.0, 3 cr.
    Partial differential equations as mathematical models in science, Fourier series, Fourier inversion,
    Gibbs phenomenon, applications of Fourier series to partial differential equations (heat equation,
    Laplace equation, wave equation), Sturm-Liouville Systems, Fourier and Laplace transforms and
    applications to partial differential equations, pointwise and uniform convergence of sequences and
    series of functions. Prerequisites: MATH 201, MATH 202. For non-Math majors. No credit given for MATH
    212 and MATH 224.
  • MATH 213 Higher Geometry 3.0; 3 cr.
    Topics chosen from isometries of Euclidean space, inversion, elements of differential geometry, the Frenet frame, curvature, torsion, the pseudo-sphere, hyperbolic geometry, and affine and projective geometry. Biennially.
  • MATH 214 Topology I 3.0; 3 cr.
    Topological spaces, continuous functions, separation axioms, compactness, connectedness, metrizable spaces, and finite product spaces.
    Prerequisite: MATH 210. Annually.
  • MATH 216 Topology II 3.0; 3 cr.
    A senior level course covering more advanced topics in topology.
    Prerequisite: consent of instructor. Biennially.
  • MATH 218 Elementary Linear Algebra with Applications 3.0; 3 cr.
    An introduction to linear algebra at a less theoretical level than MATH 219. Systems of linear equations and Gaussian elimination, vectors in Rn, matrices, determinants, vector spaces, subspaces and dimension, orthogonal projection and least-squares approximation, eigenvalues, eigenvectors, and selected applications . Students cannot receive credit for both MATH 219 and MATH 218. Annually.
  • MATH 219 Linear Algebra I 3.0; 3 cr.
    A rigorous introduction to linear algebra, with emphasis on proof and conceptual reasoning. Vector spaces, linear transformations and their matrix representation, linear independence, bases and dimension, rank-nullity, systems of linear equations, brief discussion of inner products, projections, orthonormal bases, change of basis, determinants, eigenvalues, eigenvectors, and spectral theorem. Students cannot receive credit for both MATH 219 and MATH 218. Annually.
  • MATH 220 Linear Algebra II 3.0; 3 cr.
    A deeper study of determinants, inner product spaces, and eigenvalue theory. Adjoints and the spectral theorem, primary decomposition, quotient spaces, diagonalization, triangularization, rational and Jordan forms, connection with modules over a PID, dual spaces, bilinear forms, and tensors.
    Prerequisite: MATH 241 or consent of instructor. Biennially.
  • MATH 223 Advanced Calculus 3.0; 3 cr.
    Metric spaces, normed vector spaces, the derivative as a linear transformation, chain rule, vector versions of mean-value theorem, Taylor's formula, inverse and implicit function theorems, divergence, curl, differential forms, Stokes's theorem, and notions of differential geometry.
    Prerequisite: MATH 210 or MATH 224, and MATH 218 or MATH 219. Biennially.
  • MATH 224 Fourier Series and Applications 3.0; 3 cr.
    Uniform and absolute convergence of infinite series and integrals, Laplace's method and Stirling's formula, Sturm-Liouville systems, Gram-Schmidt orthogonalization, orthogonal polynomials, Fourier series, Fourier integrals, Parseval and Plancherel theorems, and some partial differential equations.
    Prerequisite: MATH 201 and MATH 210. Annually. No credit given for MATH 212 and MATH 224.
  • MATH 225 Wavelets and Applications 3.0; 3 cr.
    Discrete Fourier Transform, Fast Fourier Transform, Wavelets on the Integers, Applications to Signal and Image Processing.
    Prerequisite: MATH 224. Biennially
  • MATH 227 Introduction to Complex Analysis 3.0; 3 cr.
    Complex numbers, analytic functions, integration in the complex plane, Cauchy's integral theorem, Taylor series, Laurent series, singularities, residues, and contour integration.
    Prerequisite: MATH 201 and consent of instructor. Annually.
  • MATH 233 Advanced Probability and Random Variables 3.0; 3 cr.
    Same description as STAT 233. Annually.
  • MATH 234 Introduction to Statistical Inference 3.0; 3 cr.
    Same description as STAT 234. Annually.
  • MATH 238 Applied Probability Models 3.0; 3 cr.
    Same description as STAT 238. Annually.
  • MATH 241 Introduction to Abstract Algebra 3.0; 3 cr.
    Groups, subgroups, homomorphisms, normal subgroups and quotient groups, permutation groups, orbits and stabilizers, statement of Sylow theorems, rings, ideals, homomorphisms and quotient fields, and Euclidean and principal ideal domains.
    Prerequisite: MATH 219 or MATH 218 with a good understanding of proof, or consent of instructor. Annually.
  • MATH 242 Topics in Algebra 3.0; 3 cr.
    Topics chosen among: fields and Galois theory, group theory, ring theory, modules over a PID, and other topics as determined by the instructor.
    Prerequisite: MATH 241. Biennially.
  • MATH 251 Numerical Computing 3.0; 3 cr.
    Techniques of numerical analysis: number representations and round-off errors, root finding, approximation of functions, integration, solving initial value problems, Monte-Carlo methods. Implementations and analysis of the algorithms will be stressed. Projects using MATLAB or a similar tool will be assigned.
    Prerequisites: CMPS 200 and MATH 201. Annually.
  • MATH 261 Number Theory 3.0; 3 cr.
    Prime factorization, the Euclidean algorithm, congruences, quadratic reciprocity, some Diophantine equations, binary quadratic forms, and continued fractions.
    Prerequisite: MATH 219 or consent of instructor. Annually.
  • MATH 271 Set Theory 3.0; 3 cr.
    Operations on sets and families of sets, ordered sets, transfinite induction, axiom of choice and equivalent forms, and ordinal and cardinal numbers. Biennially.
  • MATH 281 Numerical Linear Algebra 3.0; 3 cr.
    Equivalent to CMPS 281. Biennially.
  • MATH 293/294 Senior Tutorial Courses 3.0; 3 cr.
    Prerequisite: senior standing.
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