UNDERGRADUATE PROGRAM CALENDAR 2004-2005
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UNDERGRADUATE PROGRAM CALENDAR 2004-2005 | ||
Mathematics Courses
MTH 025 Mathematics: Algebra and Introductory Calculus Lect: 4 hrs. Basic algebra, the straight line, graphical solution of a 2x2 system of linear equations and of non-linear equations, algebraic solution of linear systems, functions (quadratic, simple trigonometric, exponential and logarithmic), vectors in the real and complex planes and applications. Trigonometric identities - sine and cosine of the sum and difference of two angles and double angle formulae, graphical and algebraic solution of systems of equations, analytic geometry, conic sections, differential calculus (limits, tangent lines, rates of change, derivatives and applications), integral calculus (antiderivatives, indefinite integrals, areas under a curve, definite integrals and appli-cations). Only available to ATSG students.
MTH 108 Mathematics: Linear Algebra Lect: 3 hrs./Lab: 1 hr. Systems of linear equations, matrices, determinants, vectors, geometry, linear transformations, complex numbers, applications.
MTH 110 Mathematics: Discrete Mathematics I Lect: 3 hrs./Lab: 1 hr This course covers the fundamentals of discrete mathematics with a focus on proof methods. Topics include: naive set theory, notation for modern algebra, propositional and predicate logic from a semantic point of view, proofs, induction, functions, relations, recurrence relations.
MTH 125 Mathematics: Mathematics for the Health Sciences Lect: 4 hrs. Basic Algebra, trigonometric functions, radicals and exponents and a basic introduction calculus.
MTH 128 Mathematics: Introductory Mathematics Lect: 4 hrs. Factoring and Fractions. System of linear equations (2X2, 3X3) and non-linear equations, graphical and algebraic solutions of linear and non-linear equations. Functions (quadratic, simple trigonometric, exponential and logarithmic). Differential Calculus, limits, tangent lines, rates of change, derivatives and applications. Integral Calculus, anti-derivatives, indefinite integrals, areas under a curve, definite integrals and applications. Other topics: graphs of trigonometric functions, fundamental trigonometric identities, trigonometric equations. This course is graded on a pass/fail basis. A PSD grade has no numerical value and is not included in a student’s grade point average; a failure is graded as an “F” and is included in a student’s grade point average.
MTH 130 Mathematics: Calculus I Lect: 3 hrs. Introduction; differentiation; applications of differentiation; Newton’s method; differentials; integration. (formerly first half of MTH 019).
MTH 140 Mathematics: Calculus I Lect: 4 hrs./Lab: 1 hr. Limits, continuity, differentiability, rules of differ-entiation. Absolute and relative extrema, inflection points, asymptotes, curve sketching. Applied max/min problems, related rates. Definite and indefinite integrals, Fundamental Theorem of Integral Calculus. Areas, volumes. Transcendental functions (trigonometric, logarithmic, hyperbolic and their inverses).
MTH 141 Mathematics: Linear Algebra. Review Lect: 4 hrs. Systems of linear equations and matrices. Determinants. Vector spaces. Inner product spaces. Eigenvalues and eigenvectors.
MTH 203 Mathematics: Statistics Lect: 3 hrs. Graphical presentation, frequency distribution, descriptive statistics, probability theory, normal distribution, sampling distribution, binomial distribution, Poisson distribution, t distribution, estimation, hypotheses tests.
MTH 207 Mathematics: Calculus & Computational Methods I Lect: 3 hrs./Lab: 1 hr. Calculus of functions of one variable and related numerical topics. Derivatives of algebraic, trigonometric and exponential functions, techniques of integration, numerical integration. Prerequisite: OAC Calculus.
MTH 210 Mathematics: Discrete Mathematics II Lect: 3 hrs./Lab: 1 hr. This course is a continuation of Discrete Mathematics I. Topics covered include: functions, graphs, induction, recursion, regular expressions, counting and finite fields with applications to cryptography. Prerequisite: MTH 110.
MTH 230 Mathematics: Calculus II Lect: 3 hrs. Appli-cations of integration; integration techniques; introduction to partial differentiation and differential equations. (formerly second half of MTH 019). Prerequisite: MTH 130.
MTH 240 Mathematics: Calculus II Lect: 4 hrs. Integration techniques. L’Hôpital’s Rule. Improper integrals. Partial derivatives. Infinite sequences and series, power series. First-order differential equations, with applications. Prerequisite: MTH 140.
MTH 281 Mathematics: Differential Equations Lect: 3 hrs./Lab: 1 hr. Review of first-order ordinary differential equations and applications; Higher-order linear differential equations; Methods of Undetermined Coefficients and Variation of Parameters; Series solutions; Laplace Transforms; Systems of Differential Equations; Operator Methods; Application of MAPLE to solution of differential equations; Applications of differential equations in automatic control of chemical processes. Prerequisites: MTH 140, MTH 240, MTH 141.
MTH 282 Mathematics: Vector Calculus Lect: 3 hrs./Lab: 1 hr. Scalar and vector fields. Gradient, divergence and curl operators. Line, surface and volume integrals. Theorems of Green, Gauss and Stokes. Introduction to Transport equations with applications. Prerequisite: MTH 281.
MTH 304 Mathematics: Probability and Statistics I Lect: 3 hrs./Lab: 1 hr. Brief Introduction to Statistics. Description of Numerical Data. Elements of Probability Theory. Discrete Probability Distribution. (Hyper-geometric, Binomial, Poisson). Normal Distribution and its applications. Sampling Distributions. The t-distribution and the X² distribution. Confidence Interval and Hypothesis Testing concerning the mean, variance and proportion of a single population. Confidence Interval and Hypothesis Testing concerning the mean and proportion of two populations. The F-distribution. SAS will be used in this course. Precursor: MTH 108, MTH 310.
MTH 309 Mathematics: Differential Equations Lect: 3 hrs./Lab: 1 hr. Ordinary differential equations with applications, series solutions, Laplace transforms, linear systems of differential equations with applications. Fourier series. Introduction to Series Solutions of Linear Equations. Precursor: MTH 141. Prerequisite: MTH 240.
MTH 310 Mathematics: Mathematics Lect: 3 hrs/ Lab: 1 hr. Integration techniques, improper integrals, sequences, infinite series, power series, partial derivatives, maxima and minima, first order differential equations. Prerequisite: MTH 207.
MTH 312 Mathematics: Differential Equations and Vector Calculus Lect: 4 hrs. Second order differential equations, systems of differential equations. Applications to electric circuits. Directional derivative. Line, surface and volume integrals. Green’s theorem, Stoke’s theorem and divergence theorem. Vector fields, coordinate systems. Prerequisites: MTH 140, MTH 240, MTH 141.
MTH 314 Mathematics: Discrete Mathematics for Engineers Lect: 3 hrs. Sets and relations, proposition and predicate logic, functions and sequences, elementary number theory, mathematical reasoning, combinatorics, graphs and trees, finite-state machine, Boolean algebra. Prerequisites: CPS 125, MTH 140, MTH 240, MTH 141.
MTH 340 Mathematics: Calculus III Lect: 4 hrs./Lab: 1 hr. Additional applications of Integration. Partial differentiation. Unconstrained extrema and the Hessian matrix. Constrained extrema and Lagrange multipliers. Curves and Surfaces. Multiple integration. Line and surface integrals. Theorems of Gauss, Green and Stokes. Fourier series. Laplace transforms and their application to second-order and other differential equations. Prerequisite: MTH 240.
MTH 380 Mathematics: Probability and Statistics I Lect: 3 hrs. Brief Introduction to Statistics. Description of Numerical Data. Probability. Discrete Probability Distributions. Normal Distribution and its applications. Sampling Distributions. Large Sample Estimation. Large Sample Tests of Hypotheses. Inference from Small Samples. A statistics computer package will be used in this course.
MTH 401 Mathematics: Differential Equations Lect: 3 hrs. First-order differential equations with applications. Linear higher-order differential equations with applications. Laplace transform methods. Simultaneous Differential Equations. Use of Maple to solve differential equations. Precursor: MTH 310. Prerequisite: MTH 207.
MTH 404 Mathematics: Probability and Statistics II Lect: 3 hrs. A continuation of the introductory topics covered in MTH 304. Contingency Tables. Goodness of fit tests. Type I and Type II errors. Correlation. Regression. ANOVA One and two-way. A statistics computer package may be used in this course. Prerequisite: MTH 304.
MTH 405 Mathematics: Formal Languages Lect: 3 hrs./Lab: 1 hr. This is a first course in automata theory and formal languages. Topics include: regular grammars and finite state automata, context-free grammars and pushdown automata, pumping lemmas, Turing machines and computable languages, Chomsky hierarchy, Church’s thesis, halting problem, NP-completeness. Prerequisite: MTH 110.
MTH 410 Mathematics: Statistics Lect: 3 hrs./Lab: 1 hr. Description of numerical data. Elements of probability theory. Discrete probability distributions (hypergeometric, binomial, Poisson). Normal distribution. t-distribution. X² distribution. Confidence interval and hypothesis testing concerning mean, variance and proportion for one and two populations. F-distribution. Correlation. Simple linear regression (if time permits). Prerequisites: MTH 141, MTH 240.
MTH 480 Mathematics: Probability and Statistics II Lect: 3 hrs. A continuation of the introductory topics covered in MTH 380. Contingency Tables. Goodness of fit tests. Type I and Type II errors. Correlation. Regression. ANOVA One and two-way. A statistics computer package will be used in this course. Prerequisite: MTH 380.
MTH 501 Mathematics: Numerical Analysis I Lect: 4 hrs. Errors and floating point arithmetic. Solutions of non-linear equations including fixed point integration and Bairstow-Lin’s method. Matrix computations and solution of systems of linear equations. Interpolation. Finite difference methods. Least squares fit. Cubic spline interpolation. Numerical integration. Numerical solution of ordinary differential equations. Taylor series method. Euler method. This course will include laboratory classes using electronic calculators and computer terminals. Prerequisites: MTH 108, MTH 207.
MTH 503 Mathematics: Operations Research I Lect: 3 hrs. Linear Programming and the Simplex Algorithm. Sensitivity analysis, duality, and the dual simplex algorithm. Transportation and Assignment Problems, Network models. Integer programming.
MTH 505 Mathematics: Calculus III Lect: 3 hrs./Lab: 2 hrs. Multiple Integrals, curves and surfaces in 3-space. Div, grad and curl operators, line and surface integrals, theorems of Green, Gauss, and Stokes, numerical methods, integral transforms. Prerequisite: MTH 310.
MTH 510 Mathematics: Numerical Analysis Lect: 3 hrs. Review of Taylor’s formula, truncation error and roundoff error. Solutions of Non linear Equations in one variable. Linear Equations. LU-decompostion. Eigenvalues and eigenvectors. Jacobi, Gauss-Seidel methods. Interpolation and curve fitting. Numerical integration. Numerical solution of ordinary differential equations. (Initial value problems.) Prerequisites: CPS 125, MTH 141, MTH 309, or MTH 340.
MTH 514 Mathematics: Probability and Stochastic Processes Lect: 3 hrs. Introduction to probability theory and stochastic processes. Topics covered include: elements of probability theory, conditional probability sequential experiments, random variables and random vectors, probability density, function cumulative density functions, functions of random variables, expected values of random variables, transform methods in random variable, reliability of systems, joint and marginal probability, correlation, confidence intervals, stochastic processes, stationary and ergodic processes, power spectral density, sample processes. Prerequisite: All required second year electrical/computer engineering courses.
MTH 540 Mathematics: Geometry Lect: 3 hrs./Lab: 1 hr. Projective plane and 3-space. Cross-ratio, perspectivity, conics and quadrics, poles and polars. Line geometry in projective 3-space. Euclidean, elliptic and hyperbolic interpretation of projective results. Inversive geometry and the complex projective line. Classification of motions in the Euclidean, elliptic, Gaussian and hyperbolic cases. Prerequisite: MTH 108.
MTH 599 Mathematics: Foundations of Mathematical Thought Lect: 3 hrs. A one semester course on the nature of mathematical thought. Mathematics is commonly believed to enjoy a degree of certainty which sets it apart from other disciplines. Moreover, this certainty is often confused with veracity, and a science gains respectability as its quantitative component increases. This course will explore the nature and extent of this certainty in mathematics. There are no specific pre-requisites but a previous course in Philosophy or other course requiring logical reasoning is recommended. (UL)
MTH 601 Mathematics: Numerical Analysis II Lect: 4 hrs. Numerical solutions for initial value and boundary value problems for ordinary differential equations. Runge-Kutta, Multi-step, Hybrid methods. Convergence criteria. Error analysis aspects. Shooting, finite- difference, Rayleigh-Ritz methods. Matrix eigenvalue problem. Jacobi, Givens, Householder, Power methods. Numerical double interpolation and multiple integration. Non-linear systems of equations. Numerical solutions to partial differential equations. This course will include laboratory classes using electronic calculators and computer terminals. Prerequisite: MTH 501.
MTH 603 Mathematics: Operations Research II Lect: 3 hrs. Nonlinear programming, decision making, inventory models, Markov chains, queuing theory, dynamic programming, Simulation. Prerequisite: MTH 503.
MTH 607 Mathematics: Graph Theory Lect: 3 hrs./Lab: 1 hr. Introduction to graph theory and its applications with an emphasis on algorithmic structure. Topics may include graphs, digraphs and subgraphs, representation of graphs, breadth first and depth first search, connectivity, paths, trees, circuits and cycles, planar graphs flows and networks, matchings, colourings, hypergraphs, intract-ability and random algorithms. Prerequisite: MTH 110 or Departmental Approval.
MTH 609 Mathematics: Number Theory Lect: 3 hrs./Lab: 1 hr. Linear congruencies and systems, primitive roots and prime certificates, applications to data encryption for security. Legendre and Jacobi symbols. Euler and Mobius functions, quadratic reciprocity, sums of two, three and four squares, quadratic forms and class groups, partitions, efficient algorithms and their computer implementation. Prerequisite: MTH 108.
MTH 640 Mathematics: Complex Analysis Lect: 3 hrs./Lab: 1 hr. DeMoivre’s theorem. Roots and Powers of complex numbers. Functions of a complex variable. Limits and continuity. Cauchy-Riemann equations. Exponential, trigonometric, hyperbolic and logarithmic functions. Conformal transformations. Integration in the complex plane. Residue theorem and some of its applications. Laplace and Fourier transforms. Prerequisite: MTH 108, MTH 207.
MTH 710 Mathematics: Fourier Analysis Lect: 3 hrs. An advanced course in Fourier Methods dealing with the application of Fourier series, Fourier transforms, convolution, correlation, discrete and fast Fourier transforms. Precursor: MTH 207. Prerequisites: MTH 207, MTH 108.
MTH 712 Mathematics: Differential Equations II Lect: 3 hrs. Series solutions of differential equations. Bessel’s equation and Bessel functions. Legendre’s differential equation. Derivation of some partial differential equations (P.D.E.). Solution of P.D.E.’s using separation of variables. Prerequisite: A first course in differential equations.
MTH 714 Mathematics: Logic & Computability Lect: 3 hrs./Lab 1 hr. Propositional and predicate calculus, first order theories, models and review of semantics of logic, resolution proof, completeness, consistency, independence, undecideability. Logic programming. Effective computability, evidence for Church’s Thesis. Review of Turing machines, reducibility, halting problem, Rice’s theorem, decideability of various formal language problems. Prerequisite: MTH 110, MTH 405.
MTH 718 Mathematics: Design and Codes Lect: 3 hrs./Lab: 1 hr. Students will learn the basics of design theory, with particular emphasis on error correcting and detecting codes. Such codes are widely used in network communications. The student will also be exposed to other applications of design such as scheduling and routing problems. Topics covered are introduction to codes Hamming distance, minimum distance; Error correction and detection. Perfect codes. Dual codes; Finite geometries Linear codes; Designs Latin squares and Transversal Designs. Shannon’s Theorem. Authentication codes. Threshold schemes. One time pad; Block Designs from geometries. Triple systems. Block designs and their codes. Scheduling problems; Codes Assumus Mattson Theorem. Hamming designs/codes. Reed Muller codes. Golay codes. Codes from triple systems. Prerequisite: MTH 210 (Discrete Mathematics II).
MTH 814 Mathematics: Computational Complexity Lect: 3 hrs./Lab: 1 hr. Order of Growth notation, time and space complexities of DTMs and NDTMs, intractability, basic complexity classes, P=NP?, reducibility and completeness, NP-completeness, Cook’s theorem, hierarchy results, circuit complexity, probabilistic algorithms, models for parallel computation. Prerequisites: MTH 110, MTH 405.
MTH 816 Mathematics: Cryptography Lect: 3hrs./Lab: 1 hr. This course will consider the mathematics of modern cryptographic schemes, including commonly used public and private key systems. The main uses; authentication, validation and encryption will be discussed. System vulnerabilities will also be considered. Topics covered include: Introduction to Ciphers. Authentication, validation and encryption. Public vs. private keys. Finite fields. Properties of a good cipher; Simple Ciphers ROT n, Matrix schemes. Probabilistic attacks, brute force; Authentication and Validation MD5, Digital Signatures, integrity checks, hash functions; Private key encryption Block ciphers, 3DES, IDEA, AES (Rijndael); Public key encryption RSA, Rabin-Williams, Integer Factorization problem (IFP). DSA, Diffie, Hellman, Discrete logarithm problem (DFP). ECC, Elliptic Curves, Elliptic curve discrete logarithm problem (ECDLP) (if time permits).
Prerequisite: MTH 110.
MTH 817 Mathematics: Combinatorics Lect: 3 hrs./Lab: 1 hr. Elementary principles of counting: permutations, combinations, circular arrangements. Partitions; derangements, number of integer solutions of a Diophantine equation with unit coefficients; Bell numbers. Introduction to the generating function method, exponential generating functions. Solutions of recurrence equations. Principle of inclusion and exclusion; Stirling numbers. groups of permutations and applications to counting problems; orbit numbers, Polya’s counting formula. Designs, latin squares, orthogonal Latin squares. Hadamard matrices. Matroids. Other optional topics may include: posets and Zorn’s lemma, Ramsey’s Theorem, finite geometries. Prerequisites: MTH 108, MTH 210, or departmental approval.