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MTH
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25A/B
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Algebra and Introductory Calculus-A/B
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Basic algebra, the straight line, 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 linear and non-linear equations, analytic geometry, conic sections, differential calculus (limits, tangent lines, rates of change, derivatives and applications). Only available to Diploma in Arts students.
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Lect: 4 hrs.
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Course Weight: 2.00
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Systems of linear equations, determinants, vectors, geometry, linear transformations, matrices and graphs, number fields, applications.
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Lect: 3 hrs./Lab: 1 hr.
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Course Weight: 1.00
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MTH
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110
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Discrete Mathematics I
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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.
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Lect: 3 hrs./Lab: 1 hr.
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Course Weight: 1.00
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MTH
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125
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Mathematics for the Health Sciences
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Mathematics for The Health Sciences: Basic Algebra, trigonometric functions, radicals and exponents, exponential and logarithmic functions, and a basic introduction to statistics.
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Lect: 4 hrs.
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Course Weight: 1.00
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MTH
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128
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Introductory Mathematics
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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.
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Lect: 4 hrs.
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Course Weight: 0.00
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MTH
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131
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Modern Mathematics I
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Differentiation; applications of differentiation; Newton's method; differentials; integration; applications of integration; Linear Algebra: systems of linear equations, Gauss elimination, matrices; vectors, dot product, cross product.
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Lect: 4 hrs./Lab: 1 hr.
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Course Weight: 1.00
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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).
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Lect: 4 hrs./Lab: 1 hr.
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Course Weight: 1.00
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Review. Systems of linear equations and matrices. Determinants. Vector spaces. Inner product spaces. Eigenvalues and eigenvectors. (1 hr. Lab every other week).
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Lect: 4 hrs./Lab: 0.5 hrs.
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| Antirequisite: MTH 126
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Course Weight: 1.00
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Graphical presentation, frequency distribution, descriptive statistics, probability theory, normal distribution, sampling distribution, binomial distribution, Poisson distribution, t distribution, estimation, hypotheses tests.
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Lect: 3 hrs.
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| Prerequisites: CHY 102, MTH 140, MTH 141, PCS 125, PCS 211, CPS 125, CVL 206, MTH 240, and MTL 200
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Course Weight: 1.00
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MTH
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207
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Calculus and Computational Methods I
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Calculus of functions of one variable and related numerical topics. Derivatives of algebraic, trigonometric and exponential functions, techniques of integration, numerical integration.
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Lect: 3 hrs./Lab: 1 hr.
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Course Weight: 1.00
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MTH
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210
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Discrete Mathematics II
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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.
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Lect: 3 hrs./Lab: 1 hr.
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| Prerequisite: MTH 110
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Course Weight: 1.00
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MTH
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231
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Modern Mathematics II
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Applications of integration and integration techniques. Introduction to partial derivatives. Introduction to ordinary differential equations. Sequences and series, convergence, Taylor series. Elementary Linear Algebra: lines and planes in 3-space, determinants.
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Lect: 4 hrs./Lab: 1 hr.
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| Prerequisite: MTH 131
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Course Weight: 1.00
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Integration techniques. L'Hopital's Rule. Improper integrals. Partial derivatives. Infinite sequences and series, power series. First-order differential equations, with applications.
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Lect: 4 hrs.
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| Prerequisite: MTH 140, CHY 102, and PCS 125
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Course Weight: 1.00
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MTH
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281
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Differential Equations
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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.
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Lect: 3 hrs./Lab: 1 hr.
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| Prerequisites: CHY 102, CPS 125, PCS 125, CHE 222, CHY 211, PCS 211, MTH 140, MTH 141, and MTH 240
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Course Weight: 1.00
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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.
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Lect: 3 hrs./Lab: 1 hr.
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| Prerequisite: MTH 281
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Course Weight: 1.00
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MTH
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304
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Probability and Statistics I
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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.
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Lect: 3 hrs./Lab: 1 hr.
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| Prerequisites: MTH 108 and MTH 310
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Course Weight: 1.00
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MTH
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309
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Differential Equations
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Ordinary differential equations with applications, Laplace transforms, linear systems of differential equations with applications.
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Lect: 3 hrs./Lab: 1 hr.
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| Prerequisites: CHY 102, CPS 125, MTH 140, MTH 141, PCS 125, MTL 200, PCS 211, PCS 213, MTH 240 and (AER 222 or MEC 222)
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Course Weight: 1.00
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MTH
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310
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Calculus and Computational Methods II
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Integration techniques, improper integrals, sequences, infinite series, power series, partial derivatives, maxima and minima.
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Lect: 3 hrs./Lab: 1 hr.
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| Prerequisite: MTH 207
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Course Weight: 1.00
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MTH
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312
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Differential Equations and Vector Calculus
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Second and higher order 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.
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Lect: 4 hrs.
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| Prerequisites: CHY 102, PCS 125, PCS 211, CPS 125, ELE 202, PCS 224, MTH 140, MTH 141, and MTH 240
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Course Weight: 1.00
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MTH
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314
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Discrete Mathematics for Engineers
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Sets and relations, proposition and predicate logic, functions and sequences, elementary number theory, mathematical reasoning, combinatorics, graphs and trees, finite-state machines, Boolean algebra.
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Lect: 3 hrs.
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| Prerequisites: CHY 102, PCS 125, PCS 211, ELE 202, PCS 224, CPS 125, MTH 140, MTH 141, and MTH 240
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Course Weight: 1.00
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MTH
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322
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Chaos, Fractals and Dynamics
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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.
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Lect: 3 hrs.
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| Prerequisite: MTH 231
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Course Weight: 1.00
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MTH
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330
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Calculus and Geometry
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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.
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Lect: 4 hrs.
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| Prerequisites: MTH 231 or (MTH 108 and MTH 310)
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Course Weight: 1.00
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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.
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Lect: 4 hrs./Lab: 1 hr.
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| Prerequisites: CHY 102, MTH 140, MTH 141, PCS 125, PCS 211, CPS 125, CVL 206, CVL 207, MTL 200, and MTH 240
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Course Weight: 1.00
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MTH
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380
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Probability and Statistics I
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Probability and Statistics I: Descriptive statistics. Probability (Laws of probability. Conditional probability. Discrete probability distributions (binomial, hypergeometric, Poisson). Continuous probability distributions, Normal, t-exponential, x^2. 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.
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Lect: 3 hrs.
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Course Weight: 1.00
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MTH
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401
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Differential Equations
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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.
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Lect: 3 hrs.
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| Prerequisites: MTH 207 and MTH 310
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Course Weight: 1.00
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MTH
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404
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Probability and Statistics II
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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.
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Lect: 3 hrs.
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| Prerequisite: MTH 304
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Course Weight: 1.00
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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.
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Lect: 3 hrs./Lab: 1 hr.
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| Prerequisite: MTH 110
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Course Weight: 1.00
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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, x^2 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).
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Lect: 3 hrs./Lab: 1 hr.
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| Prerequisites: CHY 102, CPS 125, MTH 140, PCS 125, MTL 200, PCS 211, PCS 213, MTH 141, MTH 240 and (AER 222 or MEC 222)
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Course Weight: 1.00
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MTH
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430
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Dynamic Systems Differential Equations
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First-order differential equations with applications; linear higher-order differential equations with applications; simultaneous Eigenvalues and Eigenvectors.
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Lect: 3 hrs.
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| Prerequisite: MTH 131
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Course Weight: 1.00
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MTH
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480
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Probability and Statistics II
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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.
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Lect: 3 hrs.
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| Prerequisite: MTH 380
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Course Weight: 1.00
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MTH
|
500
|
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Introduction to Stochastic Processes
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Probability of a function of several variables, martingales, conditional expectations, maximum likelihood estimators, random walks, stochastic processes (stationary and ergodic). Applications of statistical processes in science.
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Lect: 3 hrs.
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| Prerequisite: MTH 480
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Course Weight: 1.00
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MTH
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501
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Numerical Analysis I
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Numerical Analysis I: Errors and floating point arithmetic. Solutions of non-linear equations including fixed point integration. 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.
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Lect: 4 hrs.
|
| Prerequisites: MTH 108 and MTH 207
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Course Weight: 1.00
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MTH
|
503
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Operations Research I
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Linear Programming and the Simplex Algorithm. Sensitivity analysis, duality, and the dual simplex algorithm. Transportation and Assignment Problems, Network models. Integer programming.
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Lect: 3 hrs.
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Course Weight: 1.00
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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.
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Lect: 3 hrs./Lab: 2 hrs.
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| Prerequisite: MTH 310
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Course Weight: 1.00
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MTH
|
510
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Numerical Analysis
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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.)
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Lect: 3 hrs.
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| Prerequisites: CHY 102, CPS 125, MTH 140, PCS 125, MTL 200, (PCS 211 or PCS 213), MTH 141, MTH 240, (MTH 309 or MTH 340), (AER 222 or CVL 206) and MEC 222
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Course Weight: 1.00
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MTH
|
514
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Probability and Stochastic Processes
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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.
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Lect: 3 hrs.
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| Prerequisites: ELE 302, COE 318, COE 328, MTH 312, MTH 314, ELE 401, ELE 404, and COE 428
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Course Weight: 1.00
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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.
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Lect: 3 hrs./Lab: 1 hr.
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| Prerequisite: MTH 108
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Course Weight: 1.00
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MTH
|
599
|
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Foundations of Mathematical Thought
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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.
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UL
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Lect: 3 hrs.
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| Restriction: Computer Engineering, Chemical Engineering Coop, Computer Science, Electrical Engineering, Industrial Engineering, Mechanical Engineering, Chemistry, Biology, Contemporary Science
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Course Weight: 1.00
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MTH
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601
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Numerical Analysis II
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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.
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Lect: 4 hrs.
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| Prerequisite: MTH 501
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Course Weight: 1.00
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MTH
|
603
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Operations Research II
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Nonlinear programming, decision making, inventory models, Markov chains, queuing theory, dynamic programming, Simulation.
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Lect: 3 hrs.
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| Prerequisite: MTH 503
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Course Weight: 1.00
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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.
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Lect: 3 hrs./Lab: 1 hr.
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| Prerequisite: MTH 110
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Course Weight: 1.00
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| back to top | |
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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.
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Lect: 3 hrs./Lab: 1 hr.
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| Prerequisite: MTH 108
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Course Weight: 1.00
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| back to top | |
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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.
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Lect: 3 hrs./Lab: 1 hr.
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| Prerequisites: MTH 108 and MTH 207
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Course Weight: 1.00
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| back to top | |
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An advanced course in Fourier Methods dealing with the application of Fourier series, Fourier transforms, convolution, correlation, discrete and fast Fourier transforms.
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Lect: 3 hrs.
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| Prerequisites: MTH 108 and MTH 207
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Course Weight: 1.00
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MTH
|
712
|
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Differential Equations II
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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.
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Lect: 3 hrs.
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| Prerequisite: MTH 401
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Course Weight: 1.00
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| back to top | |
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MTH
|
714
|
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Logic and Computability
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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.
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Lect: 3 hrs./Lab: 1 hr.
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| Prerequisites: MTH 110 and MTH 405
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Course Weight: 1.00
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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.
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Lect: 3 hrs./Lab: 1 hr.
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| Prerequisite: MTH 210
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Course Weight: 1.00
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| back to top | |
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MTH
|
814
|
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Computational Complexity
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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.
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Lect: 3 hrs./Lab: 1 hr.
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| Prerequisites: MTH 110 and MTH 405
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Course Weight: 1.00
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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).
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Lect: 3 hrs./Lab: 1 hr.
|
| Prerequisite: MTH 110
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Course Weight: 1.00
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| back to top | |
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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.
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Lect: 3 hrs./Lab: 1 hr.
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| Prerequisites: MTH 108 and MTH 210
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Course Weight: 1.00
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Continuous and discrete image representation. Sampling and reconstruction. Quantization. Convolution. Transforms: Fourier, Sine, Cosine, wavelet. Time/Frequency domains. Image enhancement/restoration. Edge detection, feature extraction, segmentation, registration.
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Lect: 3 hrs./Lab: 1 hr.
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| Prerequisite: MTH 710
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Course Weight: 1.00
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COURSES