# Minor Statistics (24 credits)

Offered by: Mathematics and Statistics     Degree: Bachelor of Science

### Program Requirements

The Minor may be taken in conjunction with any primary program in the Faculty of Science. Students should declare their intention to follow the Minor Statistics at the beginning of the penultimate year and must obtain approval for the selection of courses to fulfil the requirements for the Minor from the Departmental Chief Adviser (or delegate).

All courses counted towards the Minor must be passed with a grade of C or better. Generally, no more than 6 credits of overlap are permitted between the Minor and the primary program. However, with an approved choice of substantial courses, the overlap restriction may be relaxed to 9 credits for students whose primary program requires 60 credits or more, and to 12 credits when the primary program requires 72 credits or more.

#### Required Courses (15 credits)

* MATH 223 may be replaced by MATH 235 and MATH 236. In this case the complementary credit requirement is reduced by 3 credits.

• MATH 222 Calculus 3 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Taylor series, Taylor's theorem in one and several variables. Review of vector geometry. Partial differentiation, directional derivative. Extreme of functions of 2 or 3 variables. Parametric curves and arc length. Polar and spherical coordinates. Multiple integrals.

Terms: Fall 2015, Winter 2016

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• Prerequisite: MATH 141. Familiarity with vector geometry or Corequisite: MATH 133
• Restriction: Not open to students who have taken CEGEP course 201-303 or MATH 150, MATH 151 or MATH 227
• MATH 223 Linear Algebra (3 credits) *

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Review of matrix algebra, determinants and systems of linear equations. Vector spaces, linear operators and their matrix representations, orthogonality. Eigenvalues and eigenvectors, diagonalization of Hermitian matrices. Applications.

Terms: Fall 2015, Winter 2016

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• Fall and Winter
• Prerequisite: MATH 133 or equivalent
• Restriction: Not open to students in Mathematics programs nor to students who have taken or are taking MATH 236, MATH 247 or MATH 251. It is open to students in Faculty Programs
• MATH 323 Probability (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Sample space, events, conditional probability, independence of events, Bayes' Theorem. Basic combinatorial probability, random variables, discrete and continuous univariate and multivariate distributions. Independence of random variables. Inequalities, weak law of large numbers, central limit theorem.

Terms: Fall 2015, Winter 2016

Instructors: William J Anderson (Fall)

• Prerequisites: MATH 141 or equivalent.
• Restriction: Intended for students in Science, Engineering and related disciplines, who have had differential and integral calculus
• Restriction: Not open to students who have taken or are taking MATH 356
• MATH 324 Statistics (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.

Terms: Fall 2015, Winter 2016

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• Fall and Winter
• Prerequisite: MATH 323 or equivalent
• Restriction: Not open to students who have taken or are taking MATH 357
• You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.
• MATH 423 Regression and Analysis of Variance (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Least-squares estimators and their properties. Analysis of variance. Linear models with general covariance. Multivariate normal and chi-squared distributions; quadratic forms. General linear hypothesis: F-test and t-test. Prediction and confidence intervals. Transformations and residual plot. Balanced designs.

Terms: Fall 2015

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• Fall
• Prerequisites: MATH 324, and MATH 223 or MATH 236
• Restriction: Not open to students who have taken or are taking MATH 533.

#### Complementary Courses (9 credits)

9 credits selected from:

• CHEM 593 Statistical Mechanics (3 credits)

Offered by: Chemistry (Faculty of Science)

### Overview

Chemistry : Intermediate topics in statistical mechanics, including: modern and classical theories of real gases and liquids, critical phenomena and the renormalization group, time-dependent phenomena, linear response and fluctuations, inelastic scattering, Monte Carlo and molecular dynamics methods.

Terms: Winter 2016

Instructors: David M Ronis (Winter)

• Winter
• Term paper
• Prerequisite: CHEM 345. Recommended: CHEM 365
• GEOG 351 Quantitative Methods (3 credits)

Offered by: Geography (Faculty of Science)

### Overview

Geography : Multiple regression and correlation, logit models, discrete choice models, gravity models, facility location algorithms, survey design, population projection.

Terms: Winter 2016

Instructors: Sebastien Breau (Winter)

• Winter
• 3 hours
• Prerequisite: MATH 203 or permission of instructor
• You may not be able to get credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.
• MATH 427 Statistical Quality Control (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Introduction to quality management; variability and productivity. Quality measurement: capability analysis, gauge capability studies. Process control: control charts for variables and attributes. Process improvement: factorial designs, fractional replications, response surface methodology, Taguchi methods. Acceptance sampling: operating characteristic curves; single, multiple and sequential acceptance sampling plans for variables and attributes.

Terms: Fall 2015

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• Prerequisites: MATH 323 + MATH 324
• MATH 447 Introduction to Stochastic Processes (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Conditional probability and conditional expectation, generating functions. Branching processes and random walk. Markov chains, transition matrices, classification of states, ergodic theorem, examples. Birth and death processes, queueing theory.

Terms: Winter 2016

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• Winter
• Prerequisite: MATH 323
• Restriction: Not open to students who have taken or are taking MATH 547.
• MATH 523 Generalized Linear Models (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Modern discrete data analysis. Exponential families, orthogonality, link functions. Inference and model selection using analysis of deviance. Shrinkage (Bayesian, frequentist viewpoints). Smoothing. Residuals. Quasi-likelihood. Contingency tables: logistic regression, log-linear models. Censored data. Applications to current problems in medicine, biological and physical sciences. R software.

Terms: Winter 2016

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• Winter
• Prerequisite: MATH 423
• Restriction: Not open to students who have taken MATH 426
• MATH 525 Sampling Theory and Applications (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Simple random sampling, domains, ratio and regression estimators, superpopulation models, stratified sampling, optimal stratification, cluster sampling, sampling with unequal probabilities, multistage sampling, complex surveys, nonresponse.

Terms: Fall 2015

Instructors: Russell Steele (Fall)

• Prerequisite: MATH 324 or equivalent
• Restriction: Not open to students who have taken MATH 425
• MATH 545 Introduction to Time Series Analysis (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Stationary processes; estimation and forecasting of ARMA models; non-stationary and seasonal models; state-space models; financial time series models; multivariate time series models; introduction to spectral analysis; long memory models.

Terms: This course is not scheduled for the 2015-2016 academic year.

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• Prerequisite: MATH 324 or MATH 357 or equivalent
• MATH 556 Mathematical Statistics 1 (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Distribution theory, stochastic models and multivariate transformations. Families of distributions including location-scale families, exponential families, convolution families, exponential dispersion models and hierarchical models. Concentration inequalities. Characteristic functions. Convergence in probability, almost surely, in Lp and in distribution. Laws of large numbers and Central Limit Theorem. Stochastic simulation.

Terms: Fall 2015

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• Fall
• Prerequisite: MATH 357 or equivalent
• MATH 557 Mathematical Statistics 2 (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Sampling theory (including large-sample theory). Likelihood functions and information matrices. Hypothesis testing, estimation theory. Regression and correlation theory.

Terms: Winter 2016

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• Winter
• Prerequisite: MATH 556
• PHYS 362 Statistical Mechanics (3 credits)

Offered by: Physics (Faculty of Science)

### Overview

Physics : Quantum states and ensemble averages. Fermi-Dirac, Bose-Einstein and Boltzmann distribution functions and their applications.

Terms: Winter 2016

Instructors: Mark Sutton (Winter)

• Winter
• 3 hours lectures
• Prerequisites: MATH 248 or equivalents, PHYS 253.
• Restriction: Honours students, or permission of the instructor
• Restriction: Not open to students taking or having passed PHYS 333
• PHYS 559 Advanced Statistical Mechanics (3 credits)

Offered by: Physics (Faculty of Science)

### Overview

Physics : Scattering and structure factors. Review of thermodynamics and statistical mechanics; correlation functions (static); mean field theory; critical phenomena; broken symmetry; fluctuations, roughening.

Terms: Fall 2015

Instructors: Walter Reisner (Fall)

• Fall
• 3 hours lectures
• Restriction: U3 Honours students, graduate students, or permission of the instructor
• SOCI 504 Quantitative Methods 1 (3 credits)

Offered by: Sociology (Faculty of Arts)

### Overview

Sociology (Arts) : Analysis of quantitative information, especially in large, survey-type, data sets. Use of computer programs such as SPSS and SAS. Topics include: cross tabulations with an emphasis on multi-dimensional tables, multiple correlation and regression, and, the relationship between individual and aggregate level statistical analyses. Special reference to demographic techniques.

Terms: Winter 2016

Instructors: Thomas Soehl (Winter)

• Prerequisites: SOCI 350 and SOCI 461 or equivalents

No more than 6 credits may be taken outside the Department of Mathematics and Statistics.

Further credits (if needed) may be freely chosen from the required and complementary courses for majors and honours students in Mathematics, with the obvious exception of courses that involve duplication of material.

Faculty of Science—2015-2016 (last updated May. 28, 2015) (disclaimer)