bibrahim/traindata huggingface dataset:
PR: MATH 2320
 
MATH 3320 Abstract Algebra
is an introduction to groups and group homomorphisms including cyclic groups, cosets, Lagrange's theorem, normal subgroups and quotient groups, introduction to rings and ring homomorphisms including ideals, prime and maximal ideals, quotient rings, integral domains and fields.
PR: MATH 2320
 
MATH 3321 Applied Algebra
- inactive course.
 
MATH 3331 Projective Geometry
includes course topics: projective space, the principle of duality, mappings in projective space, conics and quadrics.
PR: MATH 2051
 
MATH 3340 Introductory Combinatorics
includes topics: distributions, the binomial and multinomial theorems, Stirling numbers, recurrence relations, generating functions and the inclusion-exclusion principle. Emphasis will be on applications.
PR: MATH 2320
 
MATH 3370 Introductory Number Theory
examines perfect numbers and primes, divisibility, Euclidean algorithm, greatest common divisors, primes and the unique factorization theorem, congruences, cryptography (secrecy systems), Euler-Fermat theorems, power residues, primitive roots, arithmetic functions, Diophantine equations, topics above in the setting of the Gaussian integers.
PR: MATH 2320
 
MATH 4000 Lebesgue Integration
includes a review of the Riemann integral, functions of bounded variation, null sets and Lebesgue measure, the Cantor set, measurable sets and functions, the Lebesgue integral in R1 and R2, Fatou's lemma, Monotone and Dominated Convergence Theorems, Fubini's Theorem, an introduction to Lebesgue-Stieltjes measure and integration.
CR: the former Pure Mathematics 4400
PR: MATH 3001
 
MATH 4001 Functional Analysis
includes metric and normed spaces, completeness, examples of Banach spaces and complete metric spaces, bounded linear operators and their spectra, bounded linear functionals and conjugate spaces, the fundamental theorems for Banach spaces including the Hahn–Banach Theorem, topology including weak and weak* topologies, introduction to Hilbert spaces.
CR: the former Pure Mathematics 4302
PR: MATH 3001
 
MATH 4100 Applied Functional Analysis
- inactive course.
 
MATH 4102 Stochastic Methods in Applied Mathematics
- inactive course.
 
MATH 4130 Introduction to General Relativity
- inactive course.
 
MATH 4130 Introduction to General Relativity
studies both the mathematical structure and physical content of Einstein’s theory of gravity. Topics include the geometric formulation of special relativity, curved spacetimes, metrics, geodesics, causal structure, gravity as spacetime curvature, the weak-field limit, geometry outside a spherical star, Schwarzschild and Kerr black holes, Robertson-Walker cosmologies, gravitational waves, an instruction to tensor calculus, Einstein’s equations, and the stress-energy tensor.
CO: MATH 4230
EQ: Physics 4220
PR: MATH 3202 and one of Physics 3220 or MATH 4230 or permission of the Head of Department.
 
MATH 4131 Numerical Linear Algebra
- inactive course.
 
MATH 4132 Introduction to Optimization
- inactive course.
 
MATH 4133 Numerical Optimization
is numerical methods for functions of one variable, for functions of several variables including unrestricted search, sequential uniform search, irregular search, non-gradient methods, gradient methods with and without constraints, geometric programming, selection of other topics from dynamic programming, integer programming, etc., solution of applied problems by numerical optimization.
PR: MATH 3132
 
MATH 4140 Introduction to Mathematical Control Theory
- inactive course.
 
MATH 4160 Partial Differential Equations I
covers two point boundary value problems, Fourier series, Sturm-Liouville theory, canonical forms, classification and solution of linear second order partial differential equations in two independent variables, separation of variable, integral transform methods.
PR: MATH 2260 (or the former MATH 3260) and 3202
 
MATH 4161 Integral Equations
- inactive course.
 
MATH 4162 Numerical Methods for Differential Equations
covers numerical solution of initial value problems for ordinary differential equations by single and multi-step methods, Runge-Kutta, and predictor-corrector; numerical solution of boundary value problems for ordinary differential equations by shooting methods, finite differences and spectral methods; numerical solution of partial differential equations by the method of lines, finite differences, finite volumes and finite elements.
PR: MATH 3132 and 4160
 
MATH 4170 Partial Differential Equations II
covers first order equations, Cauchy problems, Cauchy-Kowalewska theorem, second order equations, canonical forms, wave equations in higher dimensions, method of spherical means, Duhamel's principle, potential equation, Dirichlet and Neuman problem, Green's function and fundamental solution, potential theory, heat equation, Riemann's method of integration, method of plane and Riemann waves for systems of PDEs of the first order.
PR: MATH 4160
PR: MATH 4160
 
MATH 4180 Introduction to Fluid Dynamics
covers basic observations, mass conservation, vorticity, stress, hydrostatics, rate of strain, momentum conservation (Navier-Stokes equation), simple viscous and inviscid flows, Reynolds number, boundary layers, Bernoulli's and Kelvin's theorems, potential flows, water waves, thermodynamics.
CR: ONAE 4020
EQ: Physics 4205
PR: MATH 2260 (or the former MATH 3260) and 3202
 
MATH 4190 Mathematical Modelling
is intended to develop students' skills in mathematical modelling and competence in oral and written presentations. Case studies in modelling will be analysed. Students will develop a mathematical model and present it in both oral and report form.
CR: MATH 4191
PR: MATH 3100, 3161, 4160, and a technical writing course offered by a Science department (MATH 2130 is recommended).
 
MATH 419A and 419B Applied Mathematics Honours Project
is a two-semester course that requires the student, with supervision by a member of the Department, to prepare a dissertation in an area of Applied Mathematics. In addition to a written project, a one hour presentation will be given by the student at the end of the second semester.
CH: 6
CR: the former AMAT 4199
PR: registration in an Honours or Joint Honours program in Applied Mathematics.
 
MATH 4230 Differential Geometry
covers both classical and modern differential geometry. It begins with the classical theory of curves and surfaces, including the Frenet-Serret relations, the fundamental theorem of space curves, curves on surfaces, the metric, the extrinsic curvature operator and Gaussian curvature. The modern section studies differentiable manifolds, tangent vectors as directional derivatives, one-forms and other tensors, the metric tensor, geodesics, connections and parallel transport, Riemann curvature and the Gauss-Codazzi equations.
PR: MATH 3202
 
MATH 4240 Differential and Integral Calculus on Manifolds
- inactive course.
 
MATH 4250 Reinforcement Learning
considers a mathematical framework in which an agent (such as a person or a robot) learns which actions to take in an environment in order to maximize a specific reward signal. The course provides an introduction to reinforcement learning, including tabular solution methods, dynamic programming, Monte Carlo methods, temporal-difference learning, planning methods and approximate solution methods.
PR: MATH 2051, MATH 3132, Statistics 2550
 
MATH 4252 Quantum Information and Computing
MATH 4252 Quantum Information and Computing
covers postulates of quantum mechanics, matrix theory, density matrices, qubits, qubit registers, entanglement, quantum gates, superdense coding, quantum teleportation, quantum algorithms, open systems, decoherence, physical realization of quantum computers.
EQ: Physics 4852
PR: MATH 2051 or Physics 3820
 
MATH 4280-4289 Special Topics in Pure and Applied Mathematics
will have the topics to be studied announced by the Department. Consult the Department for a list of titles and information regarding availability.
PR: permission of the Head of the Department
 
MATH 4300 General Topology
is an introduction to point-set topology, centering on the notions of the topological space and the continuous function. Topological properties such as Hausdorff, compactness, connectedness, normality, regularity and path-connectedness are examined, as are Urysohn’s metrization theorem and the Tychonoff theorem.
PR: MATH 3300 or 3000
 
MATH 4301 Algebraic Topology
- inactive course.
 
MATH 4310 Complex Function Theory
examines topology of C, analytic functions, Cauchy's theorem with proof, Cauchy integral formula, singularities, argument principle, Rouche's theorem, maximum modulus principle, Schwarz's lemma, harmonic functions, Poisson integral formula, analytic continuation, entire functions, gamma function, Riemann-Zeta function, conformal mapping.
PR: MATH 3210
 
MATH 4320 Ring Theory
examines factorization in integral domains, structure of finitely generated modules over a principal ideal domain with application to Abelian groups, nilpotent ideals and idempotents, chain conditions, the Wedderburn-Artin theorem.
PR: MATH 3320
 
MATH 4321 Group Theory
examines permutation groups, Sylow theorems, normal series, solvable groups, solvability of polynomials by radicals, introduction to group representations.
PR: MATH 3320
 
MATH 4331 Galois Theory
covers irreducible polynomials, field extensions, Galois groups, and the solution of equations by radicals.
PR: MATH 2051 and MATH 3320
 
MATH 4340 Combinatorial Analysis
continues most of the topics started in 3340 with further work on distributions, recurrence relations and generating functions. Generating functions are used to solve recurrence relations in two variables. Also included is a study of Polya's theorem with applications.
PR: MATH 2000 and 3340
 
MATH 4341 Combinatorial Designs
MATH 4341 Combinatorial Designs
includes the study of finite fields, Latin squares, finite projective planes and balanced incomplete block designs.
PR: MATH 3320 or 3340
 
MATH 4370 Number Theory
is continued fractions, an introduction to Diophantine approximations, selected Diophantine equations, the Dirichlet product of arithmetic functions, the quadratic reciprocity law, and factorization in quadratic domains.
PR: MATH 3370
 
MATH 4375 History of Mathematics
- inactive course.
 
MATH 439A and 439B Pure Mathematics Honours Project
is a two-semester course that requires the student, with supervision by a member of the Department, to prepare a dissertation in an area of Pure Mathematics. Although original research by the student will not normally be expected, the student must show an ability and interest to learn and organize material independently. A one-hour presentation will be given by the student at the end of the second semester.
CH: 6
CR: the former MATH 4399
PR: registration in an Honours or Joint Honours program in Pure Mathematics
13.9.2 Statistics Courses
In accordance with Senate's Policy Regarding Inactive Courses, the course descriptions for courses which have not been offered in the previous three academic years and which are not scheduled to be offered in the current academic year have been removed from the following listing. For information about any of these inactive courses, please contact the Head of the Department.
Statistics courses are designated by STAT. Where the 4 digit course number is the same, students can receive credit for only one course with subject names MATH, AMAT, PMAT, STAT.
 
STAT 1500 Introduction to Data Science
aims to teach fundamentals of data science. Emphasis will be placed on data visualization, data wrangling and summarizing data, statistical estimation and testing, regression modeling, supervised and unsupervised statistical learning. Standard data science software will be used to demonstrate the techniques.
PR: 3 credit hours in Mathematics or Statistics courses, or a combination of placement test and high school Mathematics scores acceptable to the Department
 
STAT 1510 Statistical Thinking and Concepts
examines the basic statistical issues encountered in everyday life, such as data collection (both primary and secondary), ethical issues, planning and conducting statistically-designed experiments, understanding the measurement process, data summarization, measures of central tendency and dispersion, basic concepts of probability, discrete probability models, understanding sampling distributions, the central limit theorem based on simulations (without proof), linear regression, concepts of confidence intervals and testing of hypotheses. Statistical software will be used to demonstrate each technique.
CO: Mathematics 1000
CR: cannot receive credit for STAT 1510 if completed with, or subsequent to, STAT 2500, 2550 or the former 2510
 
STAT 2410 Introduction to Probability Theory
covers combinatorial analysis, axioms of probability, conditional probability, independence, random variables, distribution function, mathematical expectation, Chebyshev’s inequality, joint distribution of two random variables, binomial and related distributions, Poisson, gamma, beta, normal, student t and F distributions, functions of random variables, convergence in probability, convergence in distribution, central limit theorem.
CR: STAT 3410
OR: one 90 minute tutorial period per week
PR: MATH 2000
 
STAT 2500 Statistics for Business and Arts Students
covers descriptive statistics (including histograms, stem-and-leaf plots and box plots), elementary probability, random variables, the binomial distribution, the normal distribution, sampling distribution, estimation and hypothesis testing including both one and two sample tests, paired comparisons, correlation and regression, related applications.
CR: STAT 2550, the former 2510, Psychology 2910, 2925 and the former 2900
LH: one 90 minute lab per week. Statistical computer package will be used in the laboratory, but no prior computing experience is assumed
PR: 3 credit hours in Mathematics or Statistics courses, or a combination of placement test and high school Mathematics scores acceptable to the Department
 
STAT 2501 Further Statistics for Business and Arts Students
covers power calculation and sample size determination, analysis of variance, multiple regression, nonparametric statistics, time series analysis, introduction to sampling techniques.
CR: STAT 2560, Psychology 2911, 2950, and the former 2901
LH: one 90 minute lab per week. Statistical computer package will be used in the laboratory.
PR: STAT 2500 or the former 2510
 
STAT 2550 Statistics for Science Students
is an introduction to basic statistics methods with an emphasis on applications to the sciences. Material includes descriptive statistics, elementary probability, binomial distribution, Poisson distribution, normal distribution, sampling distribution, estimation and hypothesis testing (both one and two sample cases), chi-square test, one way analysis of variance, correlation and simple linear regression.
CR: Engineering 4421, STAT 2500, the former STAT 2510, Psychology 2910, Psychology 2925, and the former Psychology 2900
LH: one 90 minute lab per week. Statistical computer package will be used in the laboratory, but no prior computing experience is assumed.
PR: Mathematics 1000 or the former 1081
 
STAT 2560 Further Statistics for Science Students
covers estimation and hypothesis testing in the two-sample and paired sample cases, one way and two way analysis of variance, simple and multiple linear regression, chi-square tests, non-parametric tests including sign test, Wilcoxon signed rank test and Wilcoxon rank test.
CR: STAT 2501, Psychology 2911, 2950, and the former 2901
EQ: the former STAT 2511
LH: one 90 minute lab per week. Statistical computer packages will be used in the laboratory, but no prior computing experienced is assumed.
PR: STAT 2500 or 2550, Mathematics 1000
 
STAT 3411 Statistical Inference I
examines sampling distributions, order statistics, confidence interval, hypotheses testing, chi-square tests, maximum likelihood estimation, maximum likelihood estimation, Rao-Cramér inequality and efficiency, maximum likelihood tests, sufficiency, completeness and uniqueness, exponential class of distributions, likelihood ratio test and Neyman-Pearson lemma.
OR: one and a half hour tutorial period weekly
PR: STAT 2410 or 3410
 
STAT 3520 Experimental Design I
STAT 3520 Experimental Design I
is an introduction to basic concepts in experimental design, including principles of experimentation; single factor designs such as completely randomized designs; randomized block designs; Latin square designs; Graeco Latin square designs; multiple comparison tests; analysis of covariance; balanced incomplete block designs; factorial designs; fixed, random and mixed effects models.
CR: Psychology 3900 and 3950
PR: Mathematics 2050 and either STAT 3411 or both Mathematics 1001 and one of STAT 2501 or 2560 or the former 2511
 
STAT 3521 Regression
covers inferences in linear regression analysis including estimation, confidence and prediction intervals, hypotheses testing and simultaneous inference; matrix approach to regression analysis, multiple linear regression, multicollinearity, model building and selection, polynomial regression, qualitative predictor variables.
PR: Mathematics 2050 and either STAT 3411 or both Mathematics 1001 and one of STAT 2501 or 2560 or the former 2511
 
STAT 3540 Time Series I
is an introduction to basic concepts of time series analysis such as stationarity and nonstationarity, components of time series, transformation of nonstationary series using regression, decomposition methods and differencing, autocovariance and autocorrelation functions, moving average (MA), autoregressive (AR), and ARMA representation of stationary time series including stationarity and invertibility conditions; partial autocorrelation function; properties of MA(q), AR(p) and ARMA(p, q) models, model identification, parameter estimation, model diagnostics and selection, forecasting, integrated ARMA process. Applications to real time series.
PR: either STAT 3411 or both Mathematics 1001 and one of STAT 2501 or 2560 or the former 2511
 
STAT 3570 Reliability and Quality Control
covers an introduction to reliability, parallel and series systems, standard parametric models, estimation of reliability, quality management systems, introduction to statistical process control, simple quality control tools, process control charts for variables and attributes, process capability, cumulative sum chart, exponentially weighted moving average chart, acceptance sampling plans, measurement system analysis, continuous improvement and six sigma methodology.
PR: either STAT 3411 or both Mathematics 1001 and one of STAT 2501 or 2560 or the former 2511
 
STAT 3585 Computational Statistics
is an introduction to modern computational statistics, using a programming language which implements S. Emphasis will be placed on the development of algorithms and programs for generating random numbers, numerical techniques and programs for graphical exploratory data analysis, implementing specialized statistical procedures, Monte Carlo simulation and resampling.
PR: STAT 2410, STAT 2560
 
STAT 4402 Stochastic Processes
STAT 4402 Stochastic Processes
covers the Poisson process, renewal theory, Markov chains, and some continuous state models including Brownian motion. Applications are considered in queuing, reliability, and inventory theory. Emphasis is on model building and probabilistic reasoning.
CR: Mathematics 4102
PR: STAT 2410 or 3410
 
STAT 4410 Statistical Inference II
covers decision theory, uniformly minimum variance estimators, sufficiency and completeness, likelihood theory and maximum likelihood estimation, other estimation methods including best linear unbiased estimation, estimating equations and Bayesian estimation, hypothesis testing and interval estimation, and applications of statistical inference methods under regression models and analysis of variance models.
PR: Mathematics 2051, STAT 3411
 
STAT 4504 Biostatistics
provides an overview of statistical principles and methods in epidemiology. Emphasis will be placed on study designs, measures of risk and disease-exposure association, inference for measures of association, confounding, causal inference, analysis of binary responses, count, and time-to-event.
PR: STAT 2550 and STAT 3411
 
STAT 4520 Experimental Design II
is an introduction to factorial experiments including mixed effects models, unbalanced data in factorial designs, two level and three level factorial experiments, blocking and confounding in factorial designs, fractional factorial experiments, unreplicated factorial experiments, response surface designs, robust parameter designs, nested and split plot designs.
PR: STAT 3520
 
STAT 4530 Survey Sampling
covers basic concepts, simple random sampling, unequal probability sampling and the Horvitz-Thompson principle, sufficiency, design and modelling in sampling, ratio and regression estimators, stratified and cluster sampling, methods for elusive and/or hard- to-detect populations.
PR: STAT 3411
 
STAT 4540 Time Series
examines the analysis of time series in the time domain and is an introduction to frequency domain analysis. Topics covered include integrated ARMA processes, seasonal time series models, intervention analysis and outlier detection, transfer function models, time series regression and GARCH models, vector time series models, state space models and the Kalman Filter. Spectral decomposition of a time series is introduced. Emphasis is on applications and examples with a statistical software package.
PR: STAT 3411 and 3540
 
STAT 4550 Non-parametric Statistics
covers inferences concerning location based on one sample, paired samples or two samples, inferences concerning scale parameters, goodness-of-fit tests, association analysis, tests for randomness.
PR: one of STAT 3520 or 3521 or STAT 3411
 
STAT 4560 Continuous Multivariate Analysis
STAT 4560 Continuous Multivariate Analysis
examines the multivariate normal distribution and its marginal and conditional distributions, distributions of non-singular and singular linear combinations, outline of the Wishart distribution and its application, in particular, to Hotelling’s T-squared statistic for the mean vector, connection between likelihood ratio and Hotelling’s T- squared statistics, a selection of techniques chosen from among MANOVA, multivariate regression, principal components, factor analysis, discrimination and classification, clustering.
PR: Mathematics 2051, STAT 2410 or 3410, and one of STAT 3411, 3520, or 3521
 
STAT 4561 Categorical Data Analysis
is an analysis of cross-classified categorical data with or without explanatory variables, chi-square test, measures of association, multidimensional contingency tables, hypotheses of partial and conditional independence, log-linear models for Poisson, multinomial and product-multinomial sampling schemes, concept of ordinal categorical models, logit models, likelihood estimation, selection of suitable log-linear and logit models.
PR: STAT 3520 or 3521
 
STAT 4581 Quantitative Methods in Biology
- inactive course.
 
STAT 4590 Statistical Analysis of Data I
examines the statistical analysis of real life univariate data using computational and statistical methods including descriptive statistics, chi-square tests, non-parametric tests, analysis of variance, linear, logistic and log-linear regressions. Other statistical techniques such as integrated autoregressive moving average modelling and forecasting or quality control methods may be introduced depending on the nature of the data.
LH: one 90 minute lab per week
PR: one of STAT 3520, 3521 or 3540
 
STAT 459A and 459B Statistics Honours Project
is a two-semester course that requires the student, with supervision by a member of the Department, to prepare a dissertation in an area of Statistics. In addition to a written project, a presentation will be given by the student at the end of the second semester.
CH: 6
CR: the former STAT 4599
PR: registration in an Honours or Joint Honours program in Statistics