|
|
|
The student will creatively apply the material learned in core courses to a significant problem. A written thesis is required.
|
|
|
|
Lab: 3 hrs.
|
|
|
|
Departmental consent required
|
|
GPA Weight: 2.00
|
|
Billing Units: 1/1
|
| back to top | |
|
|
|
|
Systems of linear equations, determinants, vectors, geometry, linear transformations, matrices and graphs, number fields, applications.
|
|
|
|
Lect: 3 hrs./Lab: 1 hr.
|
|
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
110
|
|
Discrete Mathematics I
|
|
|
This course covers the fundamentals of discrete mathematics with a focus on proof methods. Topics include: propositional and predicate logic, notation for modern algebra, naive set theory, relations, functions and proof techniques.
|
|
|
|
Lect: 3 hrs./Lab: 1 hr.
|
|
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
125
|
|
Mathematics for Professional Programs
|
|
|
Basic Algebra, finite series, coordinate geometry, trigonometric functions, radicals and exponents, exponential and logarithmic functions, and a basic introduction to statistics.
|
|
|
|
Lect: 4 hrs.
|
|
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
128
|
|
Introductory Mathematics
|
|
|
Factoring and Fractions. Functions (linear, quadratic, simple trigonometric, exponential and logarithmic). Differential calculus: limits, tangent lines, rates of change, derivatives and applications. Other topics: fundamental trigonometric identities, trigonometric equations. This course is graded on a pass/fail basis.
|
|
|
|
Lect: 4 hrs.
|
|
|
|
|
|
GPA Weight: 0.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
131
|
|
Modern Mathematics I
|
|
|
Limits and continuity. Differentiation with applications. Newton-Raphson method. Integration; the Fundamental Theorem of Calculus.
|
|
|
|
Lect: 3 hrs./Lab: 1 hr.
|
|
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
|
|
Limits, continuity, differentiability, rules of differentiation. 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).
|
|
|
|
Lect: 4 hrs./Lab: 2 hrs.
|
|
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
|
|
Systems of linear equations and matrices. Determinants. Vector spaces. Inner product spaces. Eigenvalues and eigenvectors.
|
|
|
|
Lect: 4 hrs./Lab: 1 hr.
|
|
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
207
|
|
Calculus and Computational Methods I
|
|
|
Calculus of functions of one variable and related numerical topics. Derivatives of algebraic, trigonometric and exponential functions. Differentiation techniques and applications of derivatives. Techniques of integration, numerical integration.
|
|
|
|
Lect: 3 hrs./Lab: 1 hr.
|
|
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
210
|
|
Discrete Mathematics II
|
|
|
This course is a continuation of Discrete Mathematics I. Topics include: recursion, induction, regular expressions and finite state automata, efficiency of algorithms, graph theory, introduction to number theory and counting.
|
|
|
|
Lect: 3 hrs./Lab: 1 hr.
|
| Prerequisite: MTH 110
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
231
|
|
Modern Mathematics II
|
|
|
Implicit functions and differentiation. Related rates, concavity, inflection points and asymptotics. Optimization. L'Hôpital's rule. Applications of integration. Techniques of integration. Numerical integration. Functions of 2 or more variables, partial derivatives.
|
|
|
|
Lect: 3 hrs./Lab: 1 hr.
|
| Prerequisite: MTH 131
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
|
|
Integration techniques. L'Hôpital's Rule. Improper integrals. Partial derivatives. Infinite sequences and series, power series. First-order differential equations, with applications.
|
|
|
|
Lect: 4 hrs./Lab: 1 hr.
|
| Prerequisite: MTH 140
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
304
|
|
Probability and Statistics I
|
|
|
Topics include: 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.
|
|
|
|
Lect: 3 hrs./Lab: 1 hr.
|
| Prerequisites: MTH 310 or MTH 240 or MTH 231
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
310
|
|
Calculus and Computational Methods II
|
|
|
Integration techniques, improper integrals, sequences, infinite series, power series, partial derivatives, maxima and minima.
|
|
|
|
Lect: 3 hrs./Lab: 1 hr.
|
| Prerequisite: MTH 207
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
312
|
|
Differential Equations and Vector Calculus
|
|
|
Second and higher order differential equations with Laplace Transforms, systems of differential equations, Fourier series and applications to electric circuits. Directional derivative. Line, surface and volume integrals. Green's theorem, Stoke's theorem and divergence theorem. Vector fields, coordinate systems.
|
|
|
|
Lect: 4 hrs./Lab: 1 hr.
|
| Prerequisites: MTH 141 and MTH 240
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
314
|
|
Discrete Mathematics for Engineers
|
|
|
Sets and relations, proposition and predicate logic, functions and sequences, elementary number theory, mathematical reasoning, combinatorics, graphs and trees, finite-state machines, Boolean algebra.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisites: MTH 141 and MTH 240
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
322
|
|
Chaos, Fractals and Dynamics
|
|
|
Fractals; drawing fractals, fractal dimension, Julia sets. Discrete dynamical systems; Logistic equation, period-doubling bifurcations. The Henon map. Nonlinear ordinary differential equations; phase portraits, stability, periodic orbits, averaging methods and bifurcations. Nonlinear oscillations.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisite: (MTH 231 or MTH 310 or MTH 240) and (MTH 108 or MTH 141)
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
330
|
|
Calculus and Geometry
|
|
|
Derivatives and the chain rule. Multiple integrals, curves and surfaces in 3-space. Div, grad and curl operators, line and surface integrals, theorems of Green, Gauss and Stokes. Linear Algebra: linear transformations, matrix representations and change of coordinates.
|
|
|
|
Lect: 4 hrs.
|
| Prerequisites: MTH 231 or MTH 310 or MTH 240 or ECN 230
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
380
|
|
Probability and Statistics I
|
|
|
Probability and Statistics I: Descriptive statistics. Probability (Laws of probability. Conditional probability. Discrete probability distributions (binomial, hypergeometric, Poisson). Continuous probability distributions, Normal, t-exponential, x². Applications of discrete and continuous distributions. Sampling distributions (sample mean, sample proportion, difference between two samples, difference between two sample proportions). Sampling distribution concerning mean variance and proportion for one or two populations. Estimation for large and small samples. Hypothesis testing concerning mean, variance and proportion for one or two populations, (large samples and small samples) including paired data testing.
|
|
|
|
Lect: 3 hrs./Lab: 1 hr.
|
|
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
404
|
|
Probability and Statistics II
|
|
|
Topics include: Multivariate Distributions. ANOVA one- and two-way. Simple linear regression models; multiple regression analysis including variable selection techniques; regression diagnostics, goodness of fit test. Non-linear regression. A statistics computer package may be used in this course.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisite: MTH 304 or MTH 380, Antirequisite: MTH 480
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
|
|
Statistics: Description of numerical data. Elements of probability theory. Discrete probability distributions (hypergeometric, binomial, geometric and Poisson distribution). Continuous probability distributions; uniform on an interval, Normal distribution, t-distribution, Exponential 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).
|
|
|
|
Lect: 3 hrs./Lab: 1 hr.
|
| Prerequisites: MTH 141 and MTH 240
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
425
|
|
Differential Equations and Vector Calculus
|
|
|
Review of first-order ordinary differential equations and applications; Higher-order linear differential equations; solution methods series solutions; Laplace Transforms and ODEs. Scalar and vector functions and fields, Chain rule, Directional Derivative, coordinate systems, divergence and curl of vector fields; line, surface and multiple integrals, Divergence theorem; Green's and Stokes' theorems; Applications. Introduction to a computer algebra system.
|
|
|
|
Lect: 4 hrs./Lab: 2 hrs.
|
| Prerequisites: MTH 140 and MTH 141 and MTH 240
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
430
|
|
Dynamic Systems Differential Equations
|
|
|
First-order differential equations, first order systems, linear systems; numerical methods and applications. Non-linear systems, discrete dynamical systems. Linear Algebra; Eigenvalues and eigenvectors.
|
|
|
|
Lect: 4 hrs.
|
| Prerequisites: (MTH 108 and (MTH 231 OR MTH 310)) or ECN 230
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
480
|
|
Probability and Statistics II
|
|
|
A continuation of the introductory topics covered in MTH 380. ANOVA One and two-way. Correlation. Regression. Contingency Tables. Goodness of fit tests. A statistics computer package will be used in this course.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisite: MTH 380, Antirequisite: MTH 404
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
500
|
|
Introduction to Stochastic Processes
|
|
|
Topics include: Measure and probability. Conditional expectation. Discrete time martingales. Markov Processes. Martingales in continuous time and Brownian motion. Stochastic integration and introduction to stochastic differential equations. Poisson process.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisite: MTH 404 or MTH 480 or ECN 702
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
501
|
|
Numerical Analysis I
|
|
|
Errors and floating point arithmetic. Solutions of non-linear equations including fixed point iteration. Matrix computations and solutions 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.
|
|
|
|
Lect: 3 hrs./Lab: 1 hr.
|
| Prerequisite: ECN 230 or MTH 231 or (MTH 108 and MTH 310); Antirequisite: MTH 510
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
503
|
|
Operations Research I
|
|
|
Linear Programming and the Simplex Algorithm. Sensitivity analysis, duality, and the dual simplex algorithm. Transportation and Assignment Problems, Network models. Integer programming.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisites: (MTH 108 or MTH 141) and (MTH 231 or MTH 240 or MTH 310)
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
510
|
|
Numerical Analysis
|
|
|
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.)
|
|
|
|
Lect: 3 hrs./Lab: 1 hr.
|
| Prerequisites: MTH 141 and MTH 240
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
511
|
|
Limitations of Measurement
|
|
|
Measurements are made to make a judgment about something. It can be to judge the accuracy of data, to accept or reject a product or to determine the price charged in everyday commerce. The judgment made can only be as sound as the measurement is reliable. The error in making a measurement limits its usefulness. This course will introduce basic concepts associated with measurement and the uncertainty in measurement, including the source of error in measurement. Examples taken from the physical, biological and medical sciences will illustrate how the limitations of measurements can alter people's perceptions and the impact this can have on issues such as government policies and medical treatments. (Formerly SCI 500)
|
|
UL
|
|
Lect: 3 hrs.
|
| Not available to Faculty of Engineering and Architecture Students (with the exception of Architecture) nor Faculty of Science Students.
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
514
|
|
Probability and Stochastic Processes
|
|
|
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.
|
|
|
|
Lect: 3 hrs./Lab: 1 hr.
|
| Prerequisites: MTH 312
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
|
|
Axioms of the real number system. Elementary point topology. Sequences and series of numbers. Limits and Continuity. Differentiation and Taylor's theorem. Sequences and Series of functions. Introduction to Riemann integration. Implicit and inverse function theorems and applications.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisite:MTH 210
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
|
|
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.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisite: MTH 108 or MTH 141
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
|
|
Introduction to techniques in problems solving; heuristics of problem solving; direct proof and proof by contradiction; problems in elementary number theory; principle of mathematical induction and the pigeonhole principle; zeros of polynomials; inequalities.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisite: MTH 210
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
599
|
|
Foundations of Mathematical Thought
|
|
|
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
|
|
Lect: 3 hrs.
|
| Not available to Faculty of Engineering and Architecture nor Faculty of Science Students with the exception of Architecture.
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
600
|
|
Computational Methods In Mathematics
|
|
|
Topics include: Statistical simulation of random variables and stochastic differential equations. Numerical solutions for partial differential equations, finite differences and finite-element methods. Optimization methods: linear programming, the simplex method and non linear programming. The Matlab software will be used in assignments as a numeric and symbolic tool.
|
|
|
|
Lect: 3 hrs./Lab: 1 hr.
|
| Prerequisite: MTH 501 or MTH 510
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
601
|
|
Numerical Analysis II
|
|
|
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.
|
|
|
|
Lect: 4 hrs.
|
| Prerequisites: MTH 501 or MTH 510
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
603
|
|
Operations Research II
|
|
|
Nonlinear programming, decision making, inventory models, Markov chains, queuing theory, dynamic programming, Simulation.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisite: MTH 503
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
|
|
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, intractability and random algorithms.
|
|
|
|
Lect: 3 hrs.
|
|
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
|
|
Division Algorithm, The greatest common divisor, Euclidean Algorithm and Diophantine Equations; Prime numbers and Fundamental Theorem of arithmetic; The theory of congruences; Linear congruences and The Chinese Remainder Theorem; Special congruences: Fermat's little theorem, Wilson's theorem; Euler's Phi-function and Euler's generalization of Fermat's little theorem; Applications: RSA cryptosystem; Legendre's symbol and its properties; Euler's criterion; Quadratic reciprocity law; Some nonlinear Diophantine equations; Representation of integers as sums of squares.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisite: MTH 108 or MTH 141
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
|
|
Sets; Binary operations; functions; partitions and equivalence relations; definition and examples of groups; elementary properties of groups; order of group elements; properties of the order of group elements; cyclic groups; subgroups, counting cosets and Lagrange's theorem; homomorphisms; quotient groups; the fundamental homomorphism theorem and its consequences; Definition and elementary properties of rings; integral domains.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisite:MTH 210
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
630
|
|
Mathematical Biology
|
|
|
Linear differential equations, Routh-Hurwitz criteria, first-order systems. Local stability in the first-order nonlinear systems, phase-plane analysis, periodic solutions, bifurcations, global stability, Liapunov functions, persistence and extinction theory. Harvesting a single population, predator-prey models, competition models, spruce budworm models, chemostat models, epidemic models, Hodgkin-Huxley, Fitzhugh-Nagumo models and/or models of molecular events.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisites: (MTH 231 or MTH 310 or MTH 240) and (MTH 430 or MTH 309 or MTH 425 or MTH 312) and (MTH 108 or MTH 141)
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
|
|
Arithmetic of Complex numbers. 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. Analytic functions. Integration in the complex plane. Residue theorem. Applications.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisites: MTH 312 or MTH 330 or MTH 425
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
642
|
|
Data Analytics: Advanced Methods
|
|
|
This course builds on the previous Basic Methods course and covers more advanced concepts including classification and clustering algorithms, decision trees, linear and logistic regression, time series analysis, and text analytics. The course will provide applied knowledge on how to analyze large scale network data produced through social media. In this context topics include network community detection, techniques for link analysis, information propagation on the web and information analysis of social media.
|
|
|
|
Lect: 3 hrs.
|
|
|
|
Departmental consent required
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
700
|
|
Financial Mathematics I
|
|
|
Topics include: Introduction to the fundamental topics in financial mathematics including fixed income instruments and derivative pricing. Stochastic calculus, martingales and Ito's formula are the main modeling tools used in the course. Pricing and hedging for a wide range of option contracts and future derivatives are developed for several models and by means of analytical and numerical techniques.
|
|
|
|
Lect: 3 hrs./Lab: 1 hr.
|
| Prerequiste: MTH 500
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
707
|
|
Modelling and Searching Networks
|
|
|
Review of graph theory. Binomial random graph model. First and second moment method; martingales. Overview of models such as preferential attachment, ranking, geometric, and copying models. Introduction to graph searching. Topics from graph searching such as Cops and Robbers games, graph cleaning, Seepage, and firefighting.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisites: MTH 607 and (MTH 380 or MTH 304 or MTH 410)
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
|
|
An advanced course in Fourier Methods dealing with the application of Fourier series, Fourier transforms, convolution, correlation, discrete and fast Fourier transforms. Continuous and discrete signal representation and processing.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisites: (MTH 108 or MTH 141) and (MTH 231 or MTH 207 or MTH 240)
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
712
|
|
Partial Differential Equations
|
|
|
Topics include: Overview of modeling with partial differential equations; boundary value problems of applied mathematics including such partial differential equations as the heat equation, Laplace's equation and the Helmholtz equation. Sturm-Liouville theory and Green's formula. Techniques will include separation of variables, canonical transformations and integral transform methods.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisite: (MTH 309 or MTH 430) and (MTH 330)
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
714
|
|
Logic and Computability
|
|
|
Propositional and predicate calculus, first order theories, undecidability. Resolution and Horn clauses, logic programming (Prolog). Effective computability and halting problem. Applications of logic to problems in computability.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisites: MTH 110 or MTH 314
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
|
|
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.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisite: MTH 110 or MTH 314
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
719
|
|
Applied Linear Algebra
|
|
|
Emphasis on the interplay between theory, application and numerical techniques. Review of vector spaces, complexity of algorithms and numerical techniques, applications of eigenvalues and eigenvectors. Singular value decomposition. Markov chains and probability matrices. Linear Transformations. Inner product spaces. Concepts will be illustrated through applications as chosen by the instructor. Lab work done with an appropriate software package.
|
|
|
|
Lect: 3 hrs./Lab: 1 hr.
|
| Prerequisite: MTH 108 or MTH 141 or MTH 430
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
732
|
|
Introduction to Fluid Dynamics
|
|
|
We derive equations governing fluid flows from the basic physical conservation laws. Exact analytic solutions to various elementary flow problems are obtained. We consider viscous flow, irrotational flow, boundary layers and water waves. Flow instability will also be examined. Mathematical results are related to phenomena observed in aerodynamics, flow through conduits and geophysical flows.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisite: MTH 330 and MTH 712
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
800
|
|
Financial Mathematics II
|
|
|
This course covers fixed income derivatives and the quantitative aspects of risk and portfolio management in modern finance. It introduces single factor interest rate models and pricing and covers analysis of risk measures and their properties, market, credit risk and an overview of other types of risks. The course also develops portfolio optimization techniques. Case studies and preparation for financial certification programs (FRM and PRM) are also included.
|
|
|
|
Lect: 3 hrs./Lab: 1 hr.
|
| Prerequisite: MTH 700
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
814
|
|
Computational Complexity
|
|
|
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.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisite: MTH 110 or MTH 314
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
|
|
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.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisite: MTH 110 or MTH 314
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
|
|
Elementary principles of counting, partitions, and applications. Generating functions, recurrence equations. Groups of permutations and their applications to counting. Designs and matroids.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisites: (MTH 108 or MTH 141) and (MTH 231 or MTH 207or MTH 140)
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
818
|
|
Topics in Algebra
|
|
|
Permutation groups, group actions and applications in combinatorics. Commutative rings, polynomial rings, and finite fields. Basic concepts and the Fundamental Theorem of Galois theory. Finite and infinite Abelian groups and decomposition theorems. Modules. Rings with chain conditions. Advanced topics in linear algebra, canonical forms.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisite: MTH 617
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
|
|
Continuous and discrete image representation. Sampling and reconstruction. Quantization. Spatial domain and intensity transformations. Convolution. Image enhancement/restoration. Edge detection, feature extraction, segmentation, registration.
|
|
|
|
Lect: 3 hrs./Lab: 1 hr.
|
| Prerequisites: (MTH 108 or MTH 141) and (MTH 231 or MTH 310 or MTH 240)
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
|
MTH
|
825
|
|
Topics in Analysis
|
|
|
Vector and normed spaces; Spaces of continuous functions and bounded variation. Banach spaces; Functions of bounded variations and their characterizations; Riemann-Stieljes integral and the Riemann integral; Riesz's representation theorem.
|
|
|
|
Lect: 3 hrs.
|
| Prerequisite: MTH 525
|
|
|
|
GPA Weight: 1.00
|
|
Billing Units: 1
|
| back to top | |
|
