Preparation
for the Major: Mathematics 131, 132.
Preparation
for the Major: Mathematics 131, 132. In order to be considered for acceptance in the program, the student should have an average of 70 or more in Math 131 and 132, and a grade of at least 65 in each of these courses with the Deparment agreement.
Proposed
changes on program study:Required Courses:
Math 231, 232, 233, 234, 238, 330, 332, 333, 334, 335, 337, 338, 411, 433, Stat231, Stat332, Comp232, Phys211, Phys231.
Elective Courses(15 Credits of the following):
Math 331, 339, 430, 431, 432, 434, 435, 436, 437, 438, Phys232.
Required Courses(34 Credits):
Math 231, 232, 233, 234, 238, 333, 334, 335, 337, 411, 433, Phys231.
Elective Courses(6 Credits of the following):
Math 330, 331, 332, 338, 339, 430, 431, 432, 434, 435, 436, 437, 438.
Proposed
Course Description : Math 131: Calculus and Analytic Geometry I
Differential calculus including analytic geometry, functions and limits, trigonometric and rational functions, derivatives, techniques and applications of differentiation. Integral calculus including definite and indefinite integrals and applications.
[2 lectures + 2 discussions]
Math 132: Calculus and Analytic Geometry II
Logarithmic , exponential, inverse trigonometric functions, hyperbolic and inverse hyperbolic functions. Techniques of integration. Analytic geometry including conic sections , polar and parametric coordinates. (Prerequisite: Math 131) [2 lectures + 2 discussions]
Sets, Introduction to symbolic logic, linear equations, solving two equations with two variables, linear programming , data description, Measures of location. Mathematics, Variation, correlation, consumer mathematics.
Prerequisite: No credits for student with High School Scientific Stream.
Math 231: Calculus and Analytic Geometry III
Convergence of infinite sequences and series including Taylor and power series.
Vectors, curves and surfaces in space. Functions of several variables, partial derivatives, maxima and minima of functions of several variables, Lagrange multipliers. Multiple integrals including change of variables. (Prerequisite: Math 132) [3 regular classes]
Review of vector algebra; vector functions of a single variable, planar motion in polar coordinates; vector field, divergence, curl, the Laplacian and vector identities; line, surface and volume integrals; generalized orthogonal coordinates, applications. (Prerequisite: Math 231) [3]
Math 233 Introduction to Set Theory and Symbolic Logic
Mathematical reasoning and basic concepts of symbolic logic; sets, relations, functions; natural numbers; finite and infinite sets, cardinal numbers. (Prerequisite: Math 132) (4 regular classes)
Math 234 Introduction to Linear Algebra
Matrices and systems of linear equations, matrix algebra determinants and Cramer's rule, vector spaces and linear transformations, eigenvalues and eigenvectors, inner product spaces and matrix norm. (Prerequisite: Math 132)
Math 235: Mathematics For Business Students
Linear Equations, Systems of Linear Equations, Matrices, Markov Chain Linear Programming, Non-Linear Functions , Mathematics of Finance, Annuities, Introduction to Differential Calculus with applications. Prerequisite: (135 or High School Scientific Stream)
Math 237 Calculus for Business Students
Exponential and logarithmic functions, Trigonometric functions, Derivatives and higher derivatives. Introduction to differential equations, Functions with several variables, Partial differentiation, Integration and application of derivatives and definite integrals. (Prerequisite: Math 235 )
Math 238 Ordinary Differential Equations
Exact differential equations, first and second order linear differential equations, method of undetermined coefficients and variation of parameter, existence and uniqueness of solutions of first order differential equations, series solutions, Laplace transform. Linear systems of differential equations. (Prerequisite: Math 132). No credit will be given to students that passed math 246.
Math 246: Differential Equations and Linear Algebra
Exact differential equations, first and second order linear differential equations, method of undetermined coefficients and variation of parameter, series solutions, Laplace transform. Matrices, determinants, systems of equations, vector spaces, linear transformations, eigenvalues, eigenvectors. Linear systems of differential equations. (Prerequisite: Math 132). No credit will be given to students that passed math 238.
Floating point representation, solution of linear and nonlinear systems of equations, polynomial interpolation, numerical differentiation and integration. (Prerequisite: math 246 or math 234, Comp 132 or Comp 221)
Math 331: Introduction to Number Theory
Integers, integers modulo n, division and Euclidean algorithms, prime factorization, divisibility, congruencies, the distribution of primes, quadratic residues, Diophantine equations (Prerequisite: Math 233)
Math 332: Mathematical Methods
Fourier series, partial differential equations and boundary value problems, separation of variables; complex functions including analytic functions and conformal mappings; Legendre and Bessel functions and some applications. (Prerequisite Math 246 or Math 238).
The real number system, continuity , continuity on sets, limits of sequences, theorems on continuous functions on intervals, uniform continuity, Cauchy sequences, the Heine. Borel theorem, differentiability, inverse functions, the Darboux and Riemann integrals for functions on R. (Prerequisite: Math 233).
Math 334: Advanced Calculus II:
Euclidean spaces, elementary topology of n, differentiation of real valued functions, Riemann multiple integrals, Jacobian and change of variable, sequences and series of functions, uniform convergence, differentiation and integration of series of functions; complete metric spaces, contractions and fixed point theorems. (Prerequisite: Math 333)
Complex numbers, limits and continuity of complex functions, analytic functions, complex integration, series expansion of elementary functions, complex integration, calculus of residues, integrals over the real axis.
(Prerequisite: math 233)
An introduction to algebraic structure, groups, permutation groups, subgroups, normal subgroups, quotient groups; group homomorphisms and group isomorphism; Direct sums Rings, ideals and ring homomorphisms, prime and maximal ideals.
(Prerequisite: math 233)
Math 338: Abstract Algebra II:
Polynomial rings, unique factorization domains and Euclidean domains, quotient rings; field extensions, finite fields and geometric constructions. (Prerequisite: math 337)
Math 339: Non-Euclidean Geometry
Axioms of Euclidean geometry, the parallel axiom, finite geometries, Hilbert's axioms and Neutral Geometry, Hyperbolic geometry , spherical geometry, Geometraic Transformations.
(Prerequisite: Math 233)
Numerical solution of initial and boundary value problems for ordinary and partial differential equations, finite difference methods, convergence, stability and consistency finite element method.
(Prerequisite: math 330, math 332)
Math 431: Advanced Linear Algebra
Linear transformation, inner product, existence and uniqueness of determinant, rational and Jordan canonical forms, dual vector spaces, classification of quadratic and Hermitian forms, multilinear algebra, direct sums and tensor products.
(Prerequisite: math 337, math 234)
Topological spaces, semimetrizable topologies; continuity, homeomorphism and topological properties; subspaces and product spaces; separation axioms; compactness and connectedness. (Prerequisite: math 333)
Math 433 Topological Structures
Product and quotient spaces; nets and filters; variousforms of compactness and connectedness. (Prerequisite: math 432)
Measure theory including outer measure, completion of measure and construction of metric outer measure; Integration including measurable functions, integrals of simple functions, elementary properties of integrals, Lebesgue integral on the real line; metric spaces including Lp spaces, complete metric spaces, the Stone Weierstrass theorem. (Prerequisite: math 334)
Harmonic functions, integrands with branch points, Rouch`s theorem; conformal mapping, Schwarz-Christoffel transformation, the Riemann mapping theorem; infinite products, Weierstass and Mittag-Leffler expansions; analytic continuation. (Prerequisite: math 335)
Math 436: Mathematical Modeling
Discrete dynamics, growth and decay problems , nonlinear differential equations, discrete non-linear models. (Prerequisite: math 332)
