
MTH 108  Linear Algebra
Systems of linear equations, matrices determinants, vectors, geometry, linear transformations, linear independence, basis, dimension, eigenvalues and eigenvectors, complex numbers, applications.
Weekly Contact: Lecture: 4 hrs. Lab: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

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.
Weekly Contact: Lecture: 3 hrs. Lab: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

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.
Weekly Contact: Lecture: 4 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 131  Modern Mathematics I
Limits and continuity. Differentiation with applications. NewtonRaphson method. Integration; the Fundamental Theorem of Calculus.
Weekly Contact: Lecture: 3 hrs. Lab: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 140  Calculus I
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).
Weekly Contact: Lecture: 4 hrs. Lab: 2 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00
Custom Requisites: Available only to Engineering and Engineering Special Students.

MTH 141  Linear Algebra
Systems of linear equations and matrices. Determinants. Vector spaces. Inner product spaces. Eigenvalues and eigenvectors.
Weekly Contact: Lecture: 4 hrs. Lab: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00
Custom Requisites: Available only to Engineering and Engineering Special students.

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.
Weekly Contact: Lecture: 4 hrs. Tutorial: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 210  Discrete Mathematics II
This course is a continuation of Discrete Mathematics I. Topics include: recursion, induction, introduction to number theory including modular arithmetic and graph theory (time permitting).
Weekly Contact: Lecture: 3 hrs. Lab: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

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. Vectors: geometric and analytic descriptions; dot product, orthogonality and projection; cross product; lines and planes in 3space.
Weekly Contact: Lecture: 3 hrs. Lab: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 240  Calculus II
Integration techniques. L'Hôpital's Rule. Improper integrals. Partial derivatives. Infinite sequences and series, power series. Firstorder differential equations, with applications.
Weekly Contact: Lecture: 4 hrs. Lab: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00
Custom Requisites: Available only to Engineering and Engineering Special Students.

MTH 260  Introduction to Mathematical Inquiry
This course is about proof methodologies and mathematical writing motivated by concepts covered in the prerequisites with a focus on recognizing and writing rigorous mathematical proofs. Topics used as a vehicle for proof writing include set theory, number theory, and analysis. Special emphasis is placed on epsilondelta proofs.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 304  Probability and Statistics I
Topics include: Elements of Probability Theory. Discrete Probability Distribution. (Hypergeometric, Binomial, Poisson). Normal Distribution and its applications. Lognormal Distribution, Multivariate Distributions, Covariance and Correlation, Moment Generating Functions, Central limit theorem and applications. A statistics computer package will be used in this course.
Weekly Contact: Lecture: 3 hrs. Lab: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 310  Calculus and Computational Methods II
Integration techniques, improper integrals, sequences, infinite series, power series. Vectors: geometric and analytic descriptions; dot product, orthogonality and projection; cross product; lines and planes in 3space.
Weekly Contact: Lecture: 4 hrs. Tutorial: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

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.
Weekly Contact: Lecture: 4 hrs. Lab: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

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, finitestate machines, Boolean algebra.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 322  Chaos, Fractals and Dynamics
Fractals; drawing fractals, fractal dimension, Julia sets. Discrete dynamical systems; Logistic equation, perioddoubling bifurcations. The Henon map. Nonlinear ordinary differential equations; phase portraits, stability, periodic orbits, averaging methods and bifurcations. Nonlinear oscillations.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 330  Calculus and Geometry
Derivatives and the chain rule. Multiple integrals, curves and surfaces in 3space. 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.
Weekly Contact: Lecture: 4 hrs. Tutorial: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

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, texponential, 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.
Weekly Contact: Lecture: 3 hrs. Lab: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 404  Probability and Statistics II
Sampling probability distributions ( tstudent, Chisquared and FFisher distribution). Point estimation. Maximum Likelihood estimation. Estimation by confidence intervals. Hypothesis testing. ANOVA one and twoway. Simple linear regression models; multiple regression analysis including variable selection techniques; regression diagnostics. Nonlinear regression. Goodness of fit test. A statistics computer package will be used in this course.
Weekly Contact: Lecture: 3 hrs. Lab: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 40A/B  Thesis
The student will creatively apply the material learned in core courses to a significant problem. A written thesis is required.
Weekly Contact: Lab: 3 hrs./3 hrs.
GPA weight: 2.00
Billing Units: 1/1
Count: 2.00
Consent: Departmental consent required

MTH 410  Statistics
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, tdistribution, Exponential distribution, x² distribution. Confidence interval and hypothesis testing concerning mean, variance and proportion for one and two populations. Fdistribution. Correlation. Simple linear regression (if time permits).
Weekly Contact: Lecture: 3 hrs. Lab: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 425  Differential Equations and Vector Calculus
Review of firstorder ordinary differential equations and applications; Higherorder linear differential equations; Laplace Transforms and ODEs. Scalar and vector functions and fields, Directional Derivative, coordinate systems, divergence and curl of vector fields; line, surface and multiple integrals, Divergence theorem; Green's and Stokes' theorems; Applications.
Weekly Contact: Lecture: 4 hrs. Lab: 2 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 430  Dynamic Systems Differential Equations
Firstorder differential equations, first order systems, linear systems; numerical methods and applications. Nonlinear systems, discrete dynamical systems. Linear Algebra; Eigenvalues and eigenvectors.
Weekly Contact: Lecture: 4 hrs. Tutorial: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 480  Probability and Statistics II
A continuation of the introductory topics covered in MTH 380. ANOVA One and twoway. Correlation. Regression. Contingency Tables. Goodness of fit tests. A statistics computer package will be used in this course.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 500  Introduction to Stochastic Processes
Topics include: Conditional expectation. Markov chains. Poisson process and Compound Poisson process. Continuoustime Markov processes. Discretetime martingales. Continuoustime martingales. Brownian motion. Stochastic integration and introduction to stochastic differential equations.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 501  Numerical Analysis I
Errors and floating point arithmetic. Solutions of nonlinear 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.
Weekly Contact: Lecture: 3 hrs. Lab: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 503  Intro Linear Programming and Applications
Linear Programming Formulations, Simplex Algorithm, Weak and Strong Duality, Complementary Slackness Conditions, PrimalDual Algorithms, Applications, Integer Programming Formulations, Cutting Planes, BranchandBound.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 510  Numerical Analysis
Review of Taylor's formula, truncation error and round off error. Solutions of Non linear Equations in one variable. Linear Equations. LUdecomposition. Eigenvalues and eigenvectors. Jacobi, GaussSeidel methods. Interpolation and curve fitting. Numerical integration. Numerical solution of ordinary differential equations. (Initial value problems.)
Weekly Contact: Lecture: 3 hrs. Lab: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

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)
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00
Liberal Studies: UL
Custom Requisites: Not available to Faculty of Engineering and Architecture Students (with the exception of Architecture) nor Faculty of Science Students.

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.
Weekly Contact: Lecture: 3 hrs. Lab: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 525  Analysis
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.
Weekly Contact: Lecture: 3 hrs. Lab: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 540  Geometry
Projective plane and 3space. Crossratio, perspectivity, conics and quadrics, poles and polars. Line geometry in projective 3space. 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.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 560  Problem Solving
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.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

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 prerequisites but a previous course in Philosophy or other course requiring logical reasoning is recommended.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00
Liberal Studies: UL
Custom Requisites: Not available to Faculty of Engineering and Architecture nor Faculty of Science Students with the exception of Architecture.

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 finiteelement methods. Optimization methods: linear programming, the simplex method and nonlinear programming. The Matlab software will be used in assignments as a numeric and symbolic tool.
Weekly Contact: Lecture: 3 hrs. Lab: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 601  Numerical Analysis II
Numerical solutions for initial value and boundary value problems for ordinary differential equations. RungeKutta, Multistep, Hybrid methods. Convergence criteria. Error analysis aspects. Shooting, finite difference, RayleighRitz methods. Matrix eigenvalue problem. Jacobi, Givens, Householder, Power methods. Numerical double interpolation and multiple integration. Nonlinear systems of equations. Numerical solutions to partial differential equations. This course will include laboratory classes using electronic calculators and computer terminals.
Weekly Contact: Lecture: 4 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 603  NonLinear Programming and Applications
Quadratic Optimization, NonLinear Optimization, Optimality Conditions, KarushKuhnTucker Theorem, Numerical Methods (Descent Direction, Newton's), Portfolio Optimization, Markowitz Efficient Frontier, Capital Market Line, Sharpe Ratio.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 607  Graph Theory
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.
Weekly Contact: Lecture: 3 hrs. Tutorial: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 609  Number Theory
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 Phifunction 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.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 617  Algebra
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.
Weekly Contact: Lecture: 3 hrs. Tutorial: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 630  Mathematical Biology
Linear differential equations, RouthHurwitz criteria, firstorder systems. Local stability in the firstorder nonlinear systems, phaseplane analysis, periodic solutions, bifurcations, global stability, Liapunov functions, persistence and extinction theory. Harvesting a single population, predatorprey models, competition models, spruce budworm models, chemostat models, epidemic models, HodgkinHuxley, FitzhughNagumo models and/or models of molecular events.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 640  Complex Analysis
Arithmetic of Complex numbers. DeMoivre's theorem. Roots and Powers of complex numbers. Functions of a complex variable. Limits and continuity. CauchyRiemann equations. Exponential, trigonometric, hyperbolic and logarithmic functions. Analytic functions. Integration in the complex plane. Residue theorem. Applications.
Weekly Contact: Lecture: 3 hrs. Tutorial: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

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.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00
Consent: Departmental consent required

MTH 655  Financial Innovations
This course covers the most recent technological innovations in finance. Topics include: blockchain technology, concept of money, digital money, cryptocurrencies, smart contracts, natural language processing, artificial neural networks (feedforward, recursive, associative memory, selforganizing, etc.) and elements of fuzzysets theory, adaptive neurofuzzy interference systems.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 660  Fixed Income Modelling
This course develops and studies techniques and models that are used in the analysis of fixed income securities. Topics include: extracting yield curves from bond prices, economics of the term structure of interest rates, types of fixed income securities, one and multifactor diffusion models, HeathJarrowMorton models, measurement and management of interest rate risk, defaultable bonds and credit derivatives and stock and currency derivatives when interest rates are stochastic.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 665  Mathematical Game Theory
Games and solution concepts, Nash's theorem, LemkeHowson algorithm, extensive games, stochastic repeated game Baysian games, coalition games combinatorial games, network games and quality of equilibria, mechanism design, elections and arrow's theorem.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

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.
Weekly Contact: Lecture: 3 hrs. Lab: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

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.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 710  Fourier Analysis
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.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

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. SturmLiouville theory and Green's formula. Techniques will include separation of variables, canonical transformations and integral transform methods.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

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.
Weekly Contact: Lecture: 3 hrs. Tutorial: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 718  Design and Codes
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.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

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.
Weekly Contact: Lecture: 3 hrs. Lab: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

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.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

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.
Weekly Contact: Lecture: 3 hrs. Lab: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 810  Selected Topics in Mathematics
An advanced level course taught by regular faculty members from the department. Topics offered are determined by faculty expertise available. Registration may be limited to fourthyear students.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00
Consent: Departmental consent required

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, NPcompleteness, Cook's theorem, hierarchy results, circuit complexity, probabilistic algorithms, models for parallel computation.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 816  Cryptography
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.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 817  Combinatorics
Elementary principles of counting, partitions, and applications. Generating functions, recurrence equations. Groups of permutations and their applications to counting. Designs and matroids.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

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.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

MTH 820  Image Analysis
Continuous and discrete image representation. Sampling and reconstruction. Quantization. Spatial domain and intensity transformations. Convolution. Image enhancement/restoration. Edge detection, feature extraction, segmentation, registration.
Weekly Contact: Lecture: 3 hrs. Lab: 1 hr.
GPA weight: 1.00
Billing Units: 1
Count: 1.00

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; RiemannStieljes integral and the Riemann integral; Riesz's representation theorem.
Weekly Contact: Lecture: 3 hrs.
GPA weight: 1.00
Billing Units: 1
Count: 1.00