|
Chair Stephen Anco Professors Emeriti Howard E. Bell, Mei Ling Huang, Ronald A. Kerman, Charles F. Laywine, Eric Muller Professors S. Ejaz Ahmed, Stephen Anco, Hichem Ben-El-Mechaiekh, Henryk Fukś, Omar Kihel, Yuanlin Li, Alexander Odesskii, Jan Vrbik, Thomas Wolf, Chantal Buteau, Xiaojian Xu Assistant Professors Tianyu Guan, William Marshall, Basil Nanayakkara, Pouria Ramazi Adjunct Professors Thomas A. Jenkyns, Peng Zhang Instructor/Manager of Academic Support Dorothy Levay Director, Co-op, Career and Experiential Education Cara Krezek Mathematics Development Programs Co-ordinator Neil Marshall Online Course Developer/Administrator Mark Willoughby |
||||||||||||||||||||||||||||||||||||||||||||||||||||
 |
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Administrative Assistant Jayne Zarecky 905-688-5550, extension 3300 Mackenzie Chown J415 The Department of Mathematics and Statistics offers several programs of study, covering traditional and modern areas of mathematics, statistics, and mathematics education. The BSc Honours in Mathematics and Statistics is a flexible program designed to meet a wide range of interests. There are core courses in calculus, linear algebra, differential equations, probability and statistics, as well as the use of computers to explore and solve mathematical problems. Within this program, students have the option to select a specialized concentration in one of five areas: Applied Mathematics; Pure Mathematics; Mathematics Integrated with Computers and Applications; Mathematics Education; and Statistics. Students also have the opportunity to complete an honours project or thesis under the supervision of a faculty member. Normally the BSc Honours program requires four years to complete. A unique Accelerated Mathematics Studies stream is available for high-achieving students who want to complete the BSc Honours program in three years by following a personalized and accelerated study-plan. Students in this stream will be able to take accelerated reading courses and optional summer courses in mathematics and statistics. For students interested in combining academic studies with real-world work experience, the Department offers Co-op programs in Mathematics or Statistics. Completion requires four and one-half years. Minor programs in either Mathematics or Statistics, as well as a three-year pass program in Mathematics and Statistics are also offered. The Department has a special interest in Mathematics Education and offers several programs and courses specifically for prospective teachers. These include both Concurrent and Consecutive Education programs, as well as Minors for future teachers. Because of the diversity of course options available in all programs, students should discuss their particular interests with faculty before selecting elective courses. |
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
The Accelerated Mathematics Studies stream is designed for students who have exceptional mathematical abilities and who are interested in completing an accelerated BSc Honours program in three years. Strengths of each student will be assessed and a personalized study plan will be created. Enrolment in the stream is limited due to the personalized nature of the program delivery and the individual attention given to students. In addition to the normal application procedures for admission to undergraduate degree studies, students will be assessed on the following criteria:
Evidence of successful engagement in recognized mathematical activities, or completion of advanced mathematical training or any relevant mathematical achievements, together with scores on the entrance placement exam may qualify successful applicants for advanced standing credits. Relevant work-related experience may qualify successful applicants for challenge for credit. Completion of a minimum of 7.0 overall credits and a minimum 85 percent major average is required for progression into year 2. A minimum of 13.0 overall credits and a minimum 85 percent major average in second year courses is required for progression into year 3. |
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Both Co-op programs combine academic and work terms over a period of four and one-half academic years. Students spend at least two years in an academic setting studying core concepts and methodologies in Mathematics and Statistics prior to their first work placement. The study will provide the necessary academic context for the work experience. In addition to the current fees for courses in academic study terms, the students in both co-op programs are assessed an administrative fee for each work term (see the Schedule of Fees). Eligibility to continue in either co-op program is based on a student's major and non-major averages. A student with a minimum 70 percent major average and a minimum 60 percent non-major average may continue. A student with a major average lower than 70 percent will not be permitted to continue in either Co-op program. If a student subsequently raises his/her major average to 70 percent, the student may be readmitted only if approved by the Co-op Admissions Committee. For further information, see the Co-op Programs section of the Calendar. All students in the Co-operative Education programs are required to read, sign and adhere to the terms of the Student Regulations Waiver and Co-op Student Manuals (brocku.ca/co-op/current-students/co-op-student-manuals) as articulated by the Co-op Programs Office. In addition, eligibility to continue in the co-op option is based on the student's major average and non-major average, and the ability to demonstrate the motivation and potential to pursue a professional career. Each four-month co-operative education work term must be registered. Once students are registered in a co-op work term, they are expected to fulfill their commitment. If the placement accepted is for more than one four-month work term, students are committed to complete all terms. Students may not withdraw from or terminate a work term without permission from the Director, Co-op Program Office. Certain courses are required for any degree in Mathematics (see below). Because Mathematics majors need both facility in dealing with mathematical theories and experience in the application of mathematics to real-world problems, each student should discuss his or her particular interests with faculty before selecting elective courses. |
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
The Mathematics and Computer Science Co-op program combines academic and work terms over a period of four and one-half academic years. Students spend one and one-half years in an academic setting studying the fundamentals of Mathematics and Computer Science prior to their first work placement. Successful completion of courses in the core areas of Computer Science and Mathematics provides the necessary academic background for the work experience. In addition to the current fees for courses in academic study terms, Mathematics and Computer Science Co-op students are assessed an administrative fee for each work term (see the Schedule of Fees). Eligibility to continue in the Mathematics and Computer Science Co-op program is based on the student's major and non-major averages. A student with a minimum 70 percent major average and a minimum 60 percent non-major average may continue. A student with a major average lower than 70 percent will not be permitted to continue in the Mathematics and Computer Science Co-op program. If a student subsequently raises his/her major average to 70 percent, the student may be readmitted only if approved by the Co-op Admissions Committee. For further information, see the Co-op Programs section of the Calendar. All students in the Co-operative Education program are required to read, sign and adhere to the terms of the Student Regulations Waiver and Co-op Student Manuals (brocku.ca/co-op/current-students/co-op-student-manuals) as articulated by the Co-op Programs Office. In addition, eligibility to continue in the co-op option is based on the student's major average and non-major average, and the ability to demonstrate the motivation and potential to pursue a professional career. Each four-month co-operative education work term must be registered. Once students are registered in a co-op work term, they are expected to fulfill their commitment. If the placement accepted is for more than one four-month work term, students are committed to complete all terms. Students may not withdraw from or terminate a work term without permission from the Director, Co-op Program Office. The Mathematics and Computer Science Co-op program designation will be awarded to those students who have honours standing and who have successfully completed a minimum of twelve months of Co-op work experience. |
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Year 1
Year 2
Year 3
Year 4
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Year 1
Year 2
Year 3
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Year 1
Year 2
Spring/Summer Sessions:
Year 3 Fall Term:
Winter Term:
Year 4
Spring/Summer Sessions:
Year 5 Fall Term:
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Year 1
Year 2
Year 3
Spring/Summer Sessions:
Year 4 Fall Term:
Winter Term:
Spring/Summer Sessions:
Year 5 Fall Term:
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Year 1
Year 2
Year 3
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Combined major programs have been developed by the Department of Mathematics and Statistics in co-operation with each of these departments: Biological Sciences, Chemistry, Computer Science, Economics and Physics. Program requirements are listed in the calendar sections of the co-major discipline. Students may take a combined major in Mathematics and a second discipline. For requirements in the other discipline, the student should consult the relevant department/centre. It should be noted that not all departments/centres provide a combined major option. |
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Students admitted to the Mathematics and Computer Science Co-op program must follow an approved program pattern. The most common pattern is listed below. For other approved patterns, consult the Co-op Office. Year 1
Year 2 Fall Term:
Winter Term:
Spring/Summer Sessions:
Year 3 Fall term
Winter Term
Spring/Summer Sessions:
Year 4
Year 5 Fall Term:
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
The Department of Mathematics and Statistics has identified courses that are particularly appropriate for students preparing to become teachers at either the elementary or secondary levels. Students should consult the Chair in the selection of courses. |
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Three credits for a teachable subject at the Junior/Intermediate level. May include MATH 1P05, 1P06, 1P11 or 1P12, 1P66, 2P90, 3P23, 3P91, and STAT 1F92. |
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
For Mathematics as the first teachable subject (a minimum of five credits). An Honours degree in Mathematics is recommended. For Mathematics as the second teachable subject, a minimum of three credits. For example: MATH 1P01, 1P02, 1P12, 2P90 and one-half MATH or STAT credit; MATH 3P23 or 4P96. |
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
The Department of Mathematics and Statistics and the Faculty of Education co-operate in offering two Concurrent BSc (Honours)/BEd programs. The Mathematics BSc (Honours)/BEd programs combines the BSc Honours program or BSc Integrated Studies Honours program with the teacher education program for students interested in teaching at the Intermediate/Senior level (grades 7-12) and at the Junior/Intermediate level (grades 4-10). Refer to the Education - Concurrent BSc (Honours)/BEd (Intermediate/Senior) or Education - Concurrent BSc Integrated Studies (Honours)/BEd (Junior/Intermediate) program listings for further information. |
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
The Concentration in Applied Mathematics program is designed for students who want a solid foundation in mathematics, statistics and computing along with exposure to modern topics like mathematics of networks, dynamical systems, cryptography, soliton theory, and mathematical physics. Graduates of this program will be able to pursue a variety of jobs in industries such as energy, aerospace and telecommunications, health/medical technology, mathematical software, and also will be well prepared to undertake graduate studies in applied mathematics or computational science or mathematical physics. Students may earn a Concentration in Applied Mathematics by successfully completing the following courses as part of the academic work leading to a BSc (Honours) in Mathematics and Statistics:
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
The Concentration in Mathematics Education program is for the modern teacher who wants to harness the technology that is transforming the teaching and learning of mathematics in the twenty-first century. Graduates of this program will answer the Ontario government's call for mathematics educators who are experts in teaching with a variety of technological tools. Future teachers will obtain a strong background in traditional mathematics such as calculus, algebra and geometry, and also will study the historical and contemporary contributions of mathematics to civilization. In addition, students will learn how technology can be used to create interactive learning environments, to model the real world, and to visualize information. This unique program provides several courses designed specifically for future mathematics teachers. Students may earn a Concentration in Mathematics Education by successfully completing the following courses as part of the academic work leading to a BSc (Honours) in Mathematics and Statistics:
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
Concentration in Mathematics Integrated with Computers and Applications (MICA) |
|
|||||||||||||||||||||||||||||||||||||||||||||||||||
|
The Concentration in Mathematics Integrated with Computers and Applications (MICA) program, focusing on technology, is ideal for students desiring careers in the application of mathematics to science, industry and finance. Graduates of this program have gone on to obtain Masters degrees in areas such as finance and computational mathematics. Students receive a solid grounding in mathematical theory and also learn how to use computer and information technology to apply and present what they have learned. The core of the MICA program consists of MATH 1P40, 2P40 and 3P40 in which students confront real world problems requiring them to create mathematical models and run computer simulations. In solving such problems, students are encouraged to develop their own strategies for using the best combination of mathematics and computing. Students may earn a Concentration in Mathematics Integrated with Computers and Applications by successfully completing the following courses as part of the academic work leading to a BSc (Honours) in Mathematics and Statistics:
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
The Concentration in Pure Mathematics program provides students with breadth and depth of knowledge of concepts, methodologies, techniques and aptitudes needed to become a professional mathematician. In addition to the core courses required by all concentrations, it includes advanced courses in central areas of algebra and analysis, as well as choice of electives in mathematical specialties of particular interest to the students. Suited for those who intend to pursue further studies in pure or applied mathematics as it includes foundational courses commonly required for admission to graduate programs in the mathematical sciences. Also serves those joining the work force through the development of logical reasoning, computational preferences, analytical and problem-solving skills and creative thinking. Students may earn a Concentration in Pure Mathematics by successfully completing the following courses as part of the academic work leading to a BSc (Honours) in Mathematics and Statistics:
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
The Concentration in Statistics program gives a student the opportunity to prepare for advanced study of statistics. Mathematical statistics theory and practical applications of statistical inferences, statistical models, stochastic models, experimental design, sampling and other methods. Development of the student's abilities in logical reasoning, creative thinking, problem solving, case studies and computation skills. Application of statistical knowledge to many areas, such as actuarial science, biological science, business, economics, education, engineering, agriculture and public health. After graduation, students can advance to graduate studies, or find jobs with employers such as Statistics Canada, hospitals, financial institutions, insurance companies and various business. Students may earn a Concentration in Statistics by successfully completing the following courses as part of the academic work leading to a BSc (Honours) in Mathematics and Statistics:
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Students in other disciplines may obtain a Minor in Mathematics within their degree program by completing the following courses with a minimum 60 percent average:
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Students in other disciplines may obtain a Minor in Statistics within their degree program by completing the following courses with a minimum 60 percent average:
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Students intending to become elementary teachers, who are in another discipline, can obtain a Minor in Elementary Teaching Mathematics within their degree program by completing the following courses with a minimum 60 percent overall average:
Students intending to become secondary teachers, who are in another discipline, can obtain a Minor in Secondary Teaching Mathematics within their degree program by completing the following courses with a minimum 60 percent overall average:
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Note that not all courses are offered in every session. Refer to the applicable term timetable for details. # Indicates a cross listed course * Indicates primary offering of a cross listed course |
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Students must check to ensure that prerequisites are met. Students may be deregistered, at the request of the instructor, from any course for which prerequisites and/or restrictions have not been met. MATHEMATICS COURSES Introductory Statistics (also offered as STAT 1F92) Description and comparison of data sets, linear regression analysis, basic probability theory, discrete probability distributions, binomial and normal distributions, Central Limit Theorem, confidence intervals and hypothesis tests on means and proportions, properties of t-, F- and chi-squared distributions, analysis of variance, inference on regression. Emphasis on interpretation of numerical results for all topics. Use of Minitab. Lectures, 3 hours per week. Prerequisite(s): one grade 11 mathematics credit. Note: designed for non-science majors. Concurrent enrolment in MATH/STAT 1P98 or in MATH/STAT 1P99 is not permitted and credits will not be counted. Major credit will not be granted to Mathematics majors. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Completion of this course will replace previously assigned grade and credit obtained in MATH/STAT 1P98 and 1P99. Calculus Concepts I Differential calculus emphasizing on concepts and the use of both theory and computers to solve problems. Precalculus topics, limits, continuity and the intermediate value theorem, derivatives and differentiability, implicit differentiation, linear approximation, mean value theorem with proof and applications, max and min, related rates, curve sketching, l'Hospital's rule, antiderivatives, Riemann sums, FTC with proof, integration by substitution. Use of Maple. Lectures, 4 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): two grade 12 mathematics credits including MCV4U or permission of the instructor. Note: intended for mathematics majors and/or future teachers. Students must successfully complete the Mathematics Skills Test. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Completion of this course will replace previous assigned grade and credit obtained in MATH 1P05. Calculus Concepts II Integral calculus emphasizing concepts, theory and computers to solve problems. Further integration techniques. Applications to areas between curves, volumes, arc length and probabilities. Multivariable calculus: partial derivatives, optimization of functions of two variables. Sequences and series: convergence tests, Taylor and Maclaurin series and applications. Differential Equations: direction fields, separable equations, growth and decay, the logistic equation, linear equations. Use of Maple. Lectures, 4 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 1P01, 1P05 or permission of instructor. Note: intended for mathematics majors and/or future teachers. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Completion of this course will replace previous assigned grade and credit obtained in MATH 1P06. Applied Calculus I Differential calculus emphasizing problem solving, calculation and applications. Precalculus topics, limits and asymptotic analysis, continuity, derivatives and differentiability, implicit differentiation, linear approximation. Applications: slope, rates of change, maximum and minimum, convexity, curve sketching, L'Hospital's rule. Antiderivatives, integrals, fundamental theorem of calculus, integration by substitution. Use of a computer algebra system. Lectures, 4 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): grade 12 Mathematics MHF4U or MATH 1P20. Note: designed for students in the sciences, computer science, and future teachers. Students must successfully complete the Mathematics Skills Test. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Completion of this course will replace previous assigned grade and credit obtained in MATH 1P01. Applied Calculus II Integral calculus emphasizing problem solving, calculations and applications. Further techniques of integration. Areas between curves, volumes, arc length and probabilities. 1st order differential equations. Sequences and series: convergence tests, Taylor and Maclaurin series and applications. Use of computer algebra system. Lectures, 4 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 1P01 or 1P05. Note: designed for students in the sciences, computer science, and future teachers. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Completion of this course will replace previous assigned grade and credit obtained in MATH 1P02. Linear Algebra I Review of linear systems and matrix algebra. General determinants and applications. Complex numbers. Vector geometry in R2 to R3. Dot product, norm and projections, cross product, lines and planes. Finite-dimensional vector spaces (real and complex). Linear transformations from Rn to Rm; rank and kernels. Eigenvalues. Use of a computer algebra system. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): two grade 12 mathematics credits including MCV4U. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Applied Linear Algebra Systems of linear equations with applications. Matrix algebra. Determinants. Vector geometry in R2 and R3 dot product, norm and projections, cross product, lines and planes. Complex numbers. Euclidean n-space. Linear transformations from Rn to Rm. Focus on applications of linear algebra to sciences and integrated use of a computer algebra system. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): one grade 12 mathematics credit or permission of instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Students will not receive earned credit for MATH 1P12 if MATH 1P11 has been successfully completed. Introduction to Mathematics Essential mathematics skills required for university mathematics courses. Sets, real and complex numbers, solutions of inequalities and equations, functions, inverse functions, composition of functions, polynomial functions, rational functions, trigonometry, trigonometric functions, trigonometric identities, exponential functions, logarithmic functions, mathematical induction, binomial theorem, vectors and matrices. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): one grade 11 mathematics credit. Note: not open to students with credit in any university calculus course. Cannot be used toward a Mathematics teachable subject at Brock. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Mathematics Integrated with Computers and Applications I Exploration of ideas and problems in algebra, differential equations, and dynamical systems using computers. Topics include number theory, integers mod p, roots of equations, fractals, predator-prey models and the discrete logistic equation for population growth. Lectures, 2 hours per week; lab, 2 hours per week. Restriction: open to MATH (single or combined), MATH (Honours)/BEd (Intermediate/Senior) majors and minors until date specified in Registration guide. Prerequisite(s): MATH 1P01 or 1P05. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Mathematical Reasoning Introduction to mathematical reasoning, logic and proofs including mathematical induction. Basics of set theory. Lectures, 3 hours per week. Prerequisite(s): MATH 1P20 or one grade 12 mathematics credit. Note: MCB4U recommended. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Mathematics for Computer Science Development and analysis of algorithms, complexity of algorithms, recursion solving recurrence relations and relations and functions. Lectures, 3 hours per week. Prerequisite(s): MATH 1P66. Corequisite(s): COSC 1P03. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Mathematics in Culture Role of mathematics in past and contemporary cultures including applications to science, society and the arts. Topics may include the stock market, social media, cryptography, history of numbers, statistics in newspapers, game theory, music, epidemics, and mathematics in movies and television. Lectures, 3 hours per week. Restriction: not open to Mathematics (single or combined) majors. Note: major credit will not be granted to Mathematics majors. Cannot be used toward a Mathematics teachable subject for programs at Brock. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Calculus With Applications Lines, polynomials, logarithms and exponential functions; two-sided limits; rates of change using derivatives; max and min of functions using derivatives; higher derivatives and concavity; area under a curve using integrals; optimization of functions of two variables using partial derivatives; growth and decay using differential equations; applications to many different disciplines; use of computer algebra systems. Lectures, 4 hours per week. Restriction: not open to Mathematics (single or combined) majors. Prerequisite(s): MATH 1P20 or one grade 12 mathematics credit. Note: designed for students in Biological Sciences, Biotechnology, Business, Earth Sciences, Economics, Environmental Geoscience, Geography and Medical Sciences. Not open to students with credit in any university calculus course. Major credit will not be granted to Mathematics majors. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Practical Statistics (also offered as STAT 1P98) Descriptive statistics; probability of events; counting rules; discrete and continuous probability distributions: binomial, Poisson and normal distributions; Central Limit Theorem; confidence intervals and hypothesis testing; analysis of variance; contingency tables; correlation and regression; emphasis on real-world applications throughout; use of statistical computer software. Lectures, 3 hours per week. Restriction: not open to Mathematics (single or combined) majors. Prerequisite(s): one grade 12 mathematics course or MATH 1P20. Note: designed for students in Biological Sciences, Biotechnology, Business, Earth Sciences, Economics, Environmental Geoscience and Medical Sciences. Concurrent enrolment in MATH/STAT 1P99 or in MATH/STAT 1F92 is not permitted and credit will not be counted. Major credit will not be granted to Mathematics majors. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Completion of this course will replace previous assigned grade and credit obtained in MATH/STAT 1P99 and 1F92. Applied Statistics for Life Sciences (also offered as STAT 1P99) Visualization and interpretation of life science data using histograms, frequency tables, correlation and regression, and a variety of statistical measures; basic concepts of probability; applications of the binomial, Poisson and normal distributions; confidence intervals for proportions and means; hypothesis testing; contingency tables; introduction to ANOVA; emphasis on interpretation and use of Microsoft Excel software throughout. Lectures, 3 hours per week. Prerequisite(s): one grade 12 mathematics course or MATH 1P20 Note: designed for students in the Life and Applied Health Sciences. Concurrent enrolment in MATH/STAT 1P98 or in MATH/STAT 1F92 is not permitted and credit will not be counted. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Completion of this course will replace previous assigned grade and credit obtained in MATH/STAT 1P98 and 1F92. Multivariable Calculus Functions of two and three variables, partial derivatives, gradient, critical points, maxima and minima, Taylor expansion, inverse and implicit function theorems. Cartesian, polar, cylindrical and spherical coordinates. Curves and surfaces, parametric representation, tangent space. Two- and three-dimensional integration, line and surface integrals. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 1P02, 1P06 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Basic Concepts of Analysis Sets; mappings, countability; properties of the real number system; inner product, norm, and the Cauchy-Schwarz inequality; compactness and basic compactness theorems (Cantor's theorem, the Bolzano-Weierstrass theorem, the Heine-Borel theorem); connectedness; convergence of sequences; Cauchy sequences; continuous and uniformly continuous functions. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 2P03. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Ordinary Differential Equations Linear and nonlinear differential equations. Basic existence and uniqueness theory. Analytical and numerical solution methods; asymptotic behaviour. Qualitative analysis of autonomous systems including periodic cycles and steady-states. Examples of conservative systems and dissipative systems. Modelling and applications of differential equations. Use of Maple. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 1P02, 1P06 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Linear Algebra II General vector spaces. Basis and dimension. Row and column spaces. Rank and nullity; the dimension theorem. Real inner product spaces. Angles and orthogonality. Orthonormal bases. Gram-Schmidt process. Eigenvalues, eigenvectors and diagonalization. Linear transformations. Applications to differential equations and least square fitting. Use of a computer algebra system. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 1P11 or 1P12. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Linear Algebra III - Advanced Review and further study of vector spaces over arbitrary fields. General linear transformations. Kernel and range. Invertibility. Matrices of linear transformations. Similarity. Isomorphism. Complex vector spaces and inner product spaces. Unitary, normal, symmetric, skew-symmetric and Hermitian operators. Orthogonal projections and the spectral theorem. Bilinear and quadratic forms. Jordan canonical form. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 2P12. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Mathematics Integrated with Computers and Applications II Theory and applications of mathematical modelling and simulation. Topics may include discrete dynamical systems, Monte-Carlo methods, stochastic models, the stock market, epidemics, analysis of DNA, chaotic dynamical systems, cellular automata and predator-prey. Lectures, lab, 4 hours per week. Prerequisite(s): MATH 1P02 or 1P06; MATH 1P40 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Completion of this course will replace previous assigned grade and credit obtained in MATH 2F40. Principles of Mathematics for Primary and Junior Teachers Mathematical concepts and ideas in number systems; geometry and probability arising in the Primary and Junior school curriculum. Lectures, seminar, 4 hours per week. Restriction: students must have a minimum of 5.0 overall credits. Note: designed to meet the mathematics admission requirement for the Primary/Junior Pre-service program of the Faculty of Education at Brock University. Not open to students holding credit in any grade 12 or university mathematics course. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Introductory Financial Mathematics Mathematical models arising in finance and insurance. Compound interest, the time-value of money, annuities, mortgages, insurance, measures of risk. Introduction to stocks, bonds and options. Lectures, lab, 4 hours per week. Prerequisite(s): one of MATH 1P01, 1P05, 1P97, MATH/STAT 1P98. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Probability (also offered as STAT 2P81) Probability, events, algebra of sets, independence, conditional probability, Bayes' theorem; random variables and their univariate, multivariate, marginal and conditional distributions. Expected value of a random variable, the mean, variance and higher moments, moment generating function, Chebyshev's theorem. Common discrete and continuous distributions: Binomial, Poisson, hypergeometric, normal, uniform and exponential. Use of SAS, Maple or other statistical packages. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 1P02, 1P06 or permission of the instructor. Note: may be taken concurrently with MATH 2P03. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Mathematical Statistics I (also offered as STAT 2P82) Random sampling, descriptive statistics, Central Limit Theorem, sampling distributions related to normality; point estimation: measurements for estimation performance, methods of moments, maximum likelihood, ordinary/weighted least squares; confidence intervals, testing procedures, and their relation for population means, difference between means, variances, ratio of variances, proportions and difference between proportions. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH/STAT 2P81. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Euclidean and Non-Euclidean Geometry I Development of Euclidean and non-Euclidean geometry from Euclid to the 19th century. Deductive nature of plane Euclidean geometry as an axiomatic system, central role of the parallel postulate and general consideration of axiomatic systems for geometry in general and non-Euclidean geometry in particular. Introduction to transformation geometry. Use of Geometer's Sketchpad. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): one MATH or STAT credit. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Discrete Optimization Problems and methods in discrete optimization. Linear programming: problem formulation, the simplex method, software, and applications. Network models: assignment problems, max-flow problem. Directed graphs: topological sorting, dynamic programming and path problems, and the travelling salesman's problem. General graphs: Eulerian and Hamiltonian paths and circuits, and matchings. Lectures, 3 hours per week; lab, 1 hour per week. Prerequisite(s): MATH 1P11 or 1P12 Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Completion of this course will replace previous assigned grade and credit obtained in MATH 2P72. Introduction to Combinatorics Counting, inclusion and exclusion, pigeonhole principle, permutations and combinations, derangements, binomial expansions. Introduction to discrete probability and graph theory, Eulerian graphs, Hamilton Cycles, colouring, planarity, and trees. Lectures, 3 hours per week; tutorial, 1 hour per week. Prerequisite(s): two 4U mathematics credits or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Completion of this course will replace previous assigned grade and credit obtained in MATH 2P71. Introduction to Network Analysis Complex networks and their properties, random graphs, network formation models. Webgraph: models, search engines, page-ranking algorithms. Community clustering, community structure. Opinion formation, on-line social networks. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): two 4U mathematics credits or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Completion of this course will replace previous assigned grade and credit obtained in MATH 2P77. Mathematics and Music Scales and temperaments, history of the connections between mathematics and music, set theory in atonal music, group theory applied to composition and analysis, enumeration of rhythmic canons, measurement of melodic similarity using metrics, topics in mathematical music theory, applications of statistics to composition and analysis. Lectures, 3 hours per week; lab/tutorial 1 hour per week. Prerequisite(s): one of MATH 1P01, 1P02, 1P05, 1P06, 1P97; MATH 1P11 or 1P12 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Problem Solving Solving mathematical problems using insight and creative thinking. Topics may include pigeonhole principle, finite and countable sets, probability theory, congruences and divisibility, polynomials, generating functions, inequalities, limits, geometry, and mathematical games. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 1P01 or 1P05; MATH 1P11 or 1P12; MATH 2P92 (2P71) or MATH/STAT 2P81 or permission of instructor. Note: recommended to students wishing to participate in mathematical problem solving competitions. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Applied Statistics (also offered as STAT 2P98) Single-factor and factorial experimental design methods; nested-factorial experiments. Simple and multiple linear regression methods, correlation analysis, indicator regression; regression model building and transformations. Contingency tables, binomial tests, nonparametric rank tests. Simple random and stratified sampling techniques, estimation of sample size and related topics. Use of SAS, Maple or other statistical packages. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH/STAT 1F92 or 1P98. Note: major credit will not be granted to Mathematics majors. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Real Analysis Approximation of functions by algebraic and trigonometric polynomials (Taylor and Fourier series); Weierstrass approximation theorem; Riemann integral of functions on Rn, the Riemann-Stieltjes integral on R; improper integrals; Fourier transforms. Lectures, 3 hours per week; tutorial, 1 hour per week. Prerequisite(s): MATH 2P04. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Complex Analysis Algebra and geometry of complex numbers, complex functions and their derivatives; analytic functions; harmonic functions; complex exponential and trigonometric functions and their inverses; contour integration; Cauchy's theorem and its consequences; Taylor and Laurent series; residues. Lectures, 3 hours per week; tutorial, 1 hour per week. Prerequisite(s): MATH 2P03. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Vector Calculus and Differential Geometry Vector fields, vector algebra, vector calculus; gradient, curl and divergence. Polar, cylindrical and spherical coordinates. Green's, Stokes' and divergence theorems. Introduction to differential geometry of surfaces. Topics may include differential forms, exterior calculus, frames, Gauss-Bonnet theorem. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 2P03. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Advanced Differential Equations Linear second-order differential equations and special functions. Introduction to Sturm-Liouville theory and series expansions by orthogonal functions. Boundary value problems for the heat equation, wave equation and Laplace equation. Green's functions. Emphasis on applications to physical sciences. Use of Maple. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 2P08. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Partial Differential Equations Survey of linear and nonlinear partial differential equations. Analytical solution methods. Existence and uniqueness theorems, variational principles, symmetries, and conservation laws. Emphasis on applications to physical sciences. Use of Maple. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 2P08. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Applied Algebra Group theory with applications. Topics include modular arithmetic, symmetry groups and the dihedral groups, subgroups, cyclic groups, permutation groups, group isomorphism, Burnside's theorem, cosets and Lagrange's theorem, direct products and cryptography, normal subgroups and factor groups. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 2P12 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Abstract Algebra Further topics in group theory: homomorphisms and isomorphism theorems, structure of finite abelian groups. Rings and ideals; polynomial rings; quotient rings. Division rings and fields; field extensions; finite fields; constructability. Lectures, 3 hours per week; lab/tutorial 1 hour per week. Prerequisite(s): MATH 3P12. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Great Moments in Mathematics I Triumphs in mathematical thinking emphasizing many cultures up to 1000 AD. Analytical understanding of mathematical problems from the past, referencing the stories and times behind the people who solved them. Matching wits with great mathematicians by solving problems and developing activities related to their discoveries. Lectures, 4 hours per week. Prerequisite(s): one MATH or STAT credit. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Completion of this course will replace previous assigned grade and credit obtained in MATH 2P93. Mathematics Integrated with Computers and Applications III Concepts and programming of contemporary models and simulations used in mathematics and sciences. Lectures, lab, 4 hours per week. Prerequisite(s): MATH 1P11 or 1P12; MATH 2P03 and COSC 2P95. Note: students will develop a final project in their own discipline. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Completion of this course will replace previous assigned grade and credit obtained in MATH 2F40. Visual and Interactive Mathematics Techniques in the visual representation of mathematical data and the interactive presentation of mathematical ideas. Topics may include modelling and simulation, visualization of real world data, interactive learning environments, and interactive websites. Lectures, lab, 4 hours per week. Prerequisite(s): MATH 1P02 or 1P06; MATH 1P11 or 1P12; MATH 2P40 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Completion of this course will replace previous assigned grade and credit obtained in MATH 2F40. Applied Mathematics with Maple Blending mathematical concepts with computations and visualization in Maple. Modelling of physical flows, waves and vibrations. Animation of the heat equation and wave equation; applications including vibrations of rectangular and circular drums, heat flow and diffusion, sound waves. Eigenfunctions and convergence theorems for Fourier eigenfunction series. Approximations, Gibbs phenomena, and asymptotic error analysis using Maple. Lectures, lab, 4 hours per week. Prerequisite(s): MATH 2P03 and 2P12; MATH 2P08 or 2P40. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Partial Differential Equations in C++ Analytic solution of first order PDEs (characteristic ODE systems and their analytic solution) and the numerical solution of first and second order PDEs (discretization, derivation and comparison of different finite difference equations, stability analysis, boundary conditions), the syntax of the C++ programming language, projects in C++ solving PDEs numerically. Lectures, lab, 4 hours per week. Prerequisite(s): MATH 2P03 and 2P12; MATH 2P08 or 2P40. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Numerical Methods Survey of computational methods and algorithms; basic concepts (algorithm, computational cost, convergence, stability); roots of functions; linear systems; numerical integration and differentiation; Runge-Kutta method for ordinary differential equations; finite-difference method for partial differential equations; fast Fourier transform; Monte Carlo methods. Implementation of numerical algorithms in a scientific programming language. Lectures, 3 hours per week; lab, 1 hour per week. Prerequisite(s): MATH 1P02 or 1P06; MATH 1P11 or 1P12; MATH 2P12 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Continuous Optimization Problems and methods in non-linear optimization. Classical optimization in Rn: inequality constraints, Lagrangian, duality, convexity. Non-linear programming. Search methods for unconstrained optimization. Gradient methods for unconstrained optimization. Constrained optimization. Dynamic programming. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 2P03 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Game Theory (also offered as ECON 3P73) Representation of Games. Strategies and payoff functions. Static and dynamic games of complete or incomplete information. Equilibria concepts: Nash, Bayesian Nash and Perfect Bayesian Nash equilibria. Convexity concepts, fixed points for correspondences and minimax. Core and Shapley value of a game. Refinements and Applications. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): one of MATH 2P91 (2P72), ECON 3P91 or 3Q91. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Theory of Financial Mathematics Mathematical models arising in modern investment practices. Compound interest, annuities, the time-value of money, Markowitz portfolio theory, efficient frontier, random walks, Brownian processes, future contracts, European and American options, and put-call parity. Introduction to Black-Scholes. Lectures, lab, 4 hours per week. Prerequisite(s): MATH/STAT 2P82. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Experimental Design (also offered as STAT 3P81) Analysis of variance; single-factor experiments; randomized block designs; Latin squares designs; factorial designs; 2f and 3f factorial experiments; fixed, random and mixed models; nested and nested-factorial experiments; Taguchi experiments; split-plot and confounded in blocks factorial designs; factorial replication; regression models; computational techniques and use of SAS, Maple or other statistical packages; related topics. Lectures, 3 hours per week; lab, 1 hour per week. Prerequisite(s): MATH/STAT 2P82. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Regression Analysis (also offered as STAT 3P82) Simple and multiple linear regression and correlation, measures of model adequacy, residual analysis, weighted least squares, polynomial regression, indicator variables, variable selection and model building, multicollinearity, time series, additional topics. Use of SAS, Maple or other statistical packages. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 1P11 or 1P12; MATH/STAT 2P82 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Mathematical Statistics II (also offered as STAT 3P85) Multivariate, marginal and conditional distributions, independence, expectation, covariance, conditional expectation. Functions of random variables, transformation techniques, order statistics. Special and limiting distributions. Proof of central limit theorem. Point estimation: efficiency, consistency, law of large numbers, sufficiency, Rao-Blackwell theorem MVUE. Interval estimation. Hypothesis testing: Neyman-Pearson theory, likelihood ratio test, Bayesian inference. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 2P03 and MATH/STAT 2P82 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Applied Multivariate Statistics (also offered as STAT 3P86) Matrix algebra and random vector, sample geometry and random sampling, multivariate normal distribution, inference about mean, comparison of several multivariate means, multivariate linear regression model, principle components, factor analysis, covariance analysis, canonical correlation analysis, discrimination and classification, cluster analysis, computational techniques and use of SAS, Maple or other statistical packages and related topics. Lectures, 3 hours per week; lab 1 hour per week. Prerequisite(s): MATH 1P11 or 1P12; MATH/STAT 2P82 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Mathematics at the Junior/Intermediate/Senior Level A treatment of mathematics and its teaching and learning at the junior, intermediate and senior levels. A major portion of the course will involve directed projects. Lectures, seminar, 4 hours per week. Restriction: open to MATH (Honours) BSc/BEd (Intermediate/Senior) majors, Elementary and Secondary Teaching Mathematics minors with a minimum of 9.0 overall credits. Prerequisite(s): three MATH credits. Note: Mathematics Integrated with Computers and Applications with a Concentration in Mathematics Education may register. Contact Department. Students in other programs will require permission of the Department. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Symmetry Groups, Matrix Representations and Applications Symmetry groups, their invariants and matrix representations. Permutation groups, rotation groups. Representations of discrete and continuous groups by linear transformations (matrices). General properties and constructions of group representations. Representations of specific groups. Lie groups and Lie algebras. Applications in various areas of Mathematics and Theoretical Physics. Prerequisite(s): MATH 2P12 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Introduction to Mathematical Physics (also offered as PHYS 3P95) Topics may include Calculus of variations, Lagrangian and Hamiltonian mechanics, field theory, differential forms, vector and polyvector fields, tensor fields, Lie derivative, connection, Riemannian metric, Lie groups and algebras, manifolds, and mathematical ideas of quantum mechanics. Applications to theoretical physics. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 2P03 and 2P08. Note: MATH 2P12 is recommended. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Completion of this course will replace previous assigned grade and credit obtained in MATH (PHYS) 4P64. Computational Ergodic Theory and Dynamical Systems Orbits of maps, counting and invariant measures, shift transformation, ergodicity and Birkhoff ergodic theorem, central limit theorem for dynamical systems, Poincare recurrence theorem, entropy and data compression, Lyapunov exponent, invariant subspaces, construction of stable and unstable manifolds for maps, symbolic dynamics and topological entropy. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 2P03, 2P12 and MATH/STAT 2P81. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Introductory Topology Introduction to metric and topological spaces; connectedness, completeness, countability axioms, separation properties, covering properties, metrization of topological spaces. Lectures, 4 hours per week. Prerequisite(s): MATH 3P03 or Permission of the Instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Functional Analysis Introduction to the theory of normed linear spaces, fixed-point theorems, Stone-Weierstrass approximation on metric spaces and preliminary applications on sequence spaces. Lectures, 4 hours per week. Prerequisite(s): MATH 2P12 and MATH 3P03 or Permission of the Instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Honours Project Independent project in an area of pure or applied mathematics, or mathematics education. Restriction: open to MATH (single or combined) majors with either a minimum of 14.0 credits, a minimum 70 percent major average and a minimum 60 percent non-major average or approval to year 4 (honours) and permission of the instructor. Note: carried out under the supervision of a faculty member. The supervisor must approve the topic in advance. Presentation of the project is required. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Advanced Real Analysis Lebesgue integration on Rn; differentiation and absolute continuity; Fubini's theorem; Lp spaces, elementary theory of Banach and Hilbert spaces. Lectures, 3 hours per week. Prerequisite(s): MATH 3P03. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Special Topics Advanced topics selected from ring theory, homological algebra, algebraic geometry, number theory, point-set topology, differential geometry, algebraic topology, ordinary or partial differential equations, dynamical systems or any other field of mathematics. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Restriction: permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Solitons and Nonlinear Wave Equations (also offered as PHYS 4P09) Linear and nonlinear travelling waves. Nonlinear evolution equations (Korteweg de Vries, nonlinear Schrodinger, sine-Gordon). Soliton solutions and their interaction properties. Lax pairs, inverse scattering, zero-curvature equations and Backlund transformations, Hamiltonian structures, and conservation laws. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): one of MATH 3P08, 3P09, 3P51, 3P52. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Topics in Groups Advanced topics from group theory. Topics may include isomorphism theorems, Sylow theorems, finite abelian groups, free groups, nilpotent and solvable groups and some simple Lie groups. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 3P12. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Topics in Rings and Modules Advanced topics from ring theory. Topics may include radicals, Wedderburn-Artin theorems, modules over rings and some special rings. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 3P13. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Great Moments in Mathematics II Development of modern mathematics from medieval times to the present. Fibonacci's calculation revolution, the disputes over cubic equations, Pascal and probability, Fermat's last theorem, Newton and Calculus, Euler and infinite series, set theory and the possibilities of inconsistencies in mathematics. Lectures, 4 hours per week. Prerequisite(s): MATH 1P02 or 1P06; MATH 1P11 or 1P12; MATH 3P23 (2P93). Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Completion of this course will replace previous assigned grade and credit obtained in MATH 3P93. Theory of Computation (also offered as COSC 4P61) Regular languages and finite state machines: deterministic and non-deterministic machines, Kleene's theorem, the pumping lemma, Myhill-Nerode Theorem and decidable questions. Context-free languages: generation by context-free grammars and acceptance by pushdown automata, pumping lemma, closure properties, decidability. Turing machines: recursively enumerable languages, universal Turing machines, halting problem and other undecidable questions. Lectures, 3 hours per week. Restriction: open to COSC (single or combined), BCB, CAST, CNET, GAMP and NEUR Neurocomputing stream majors. Prerequisite(s): MATH 1P67 (minimum 60 percent). Note: MATH students may take this course with permission of Mathematics Department. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Combinatorics Review of basic enumeration including distribution problems, inclusion-exclusion and generating functions. Polya theory. Finite fields. Orthogonal Latin squares, affine and projective planes. Coding theory and cryptography. Lectures, 3 hours per week; tutorial, 1 hour per week. Prerequisite(s): MATH 2P92 (2P71) or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Sampling Theory (also offered as STAT 4P81) Theory of finite population sampling; simple random sampling; sampling proportion; estimation of sample size; stratified random sampling; optimal allocation of sample sizes; ratio estimators; regression estimators; systematic and cluster sampling; multi-stage sampling; errors in surveys; computational techniques and use of SAS, Maple or other statistical packages and related topics. Lectures, 3 hours per week; lab, 1 hour per week. Prerequisite(s): MATH/STAT 3P85 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Nonparametric Statistics (also offered as STAT 4P82) Order statistics, rank statistics, methods based on binomial distribution, contingency tables, Kolmogorov Smirnov statistics, nonparametric analysis of variance, nonparametric regression, comparisons with parametric methods. Computational techniques and use of SAS, Maple or other statistical packages. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH/STAT 3P85 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Topics in Stochastic Processes and Models (also offered as STAT 4P84) Topics may include general stochastic processes, Markov chains and processes, renewal process, branching theory, stationary processes, stochastic models, Monte Carlo simulations and related topics. Use of SAS, Maple or other statistical packages. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH/STAT 3P85 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Topics in Advanced Statistics (also offered as STAT 4P85) Topics may include advanced topics in stochastic processes and models, queueing theory, time series analysis, multivariate analysis, Bayesian statistics, advanced methods and theory in statistical inference, and related topics. Use of SAS, Maple or other statistical packages. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH/STAT 3P85 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Euclidean and Non Euclidean Geometry II Topics in Euclidean and non-Euclidean geometry chosen from the classification of isometries in selected geometries, projective geometry, spherical geometry, finite geometries and axiomatic systems for plane Euclidean geometry. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 1P11 or 1P12; MATH 2P90. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Completion of this course will replace previous assigned grade and credit obtained in MATH 3P90. Topics in Number Theory and Cryptography Topics may include algebraic number theory, analytic number theory and cryptography. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Restriction: permission of the Department. Prerequisite(s): MATH 1P11 or 1P12; one of MATH 2P12, 2P81, 2P92 (2P71), 3P12. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Relativity Theory and Black Holes (also offered as PHYS 4P94) Review of Special Relativity and Minkowski space-time. Introduction to General Relativity theory; the space-time metric, geodesics, light cones, horizons, asymptotic flatness; energy-momentum of particles and light rays. Curvature and field equations. Static black holes (Schwarzschild metric), properties of light rays and particle orbits. Rotating black holes (Kerr metric). Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 2P03, 2P08, 3P06, PHYS 2P20 and 2P50 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Technology and Mathematics Education Topics may include contemporary research concerning digital technologies, such as computer algebra systems and Web 2.0, in learning and teaching mathematics, design of educational tools using VB.NET, HTML, Geometer's Sketchpad, Maple, Flash, critical appraisal of interactive learning objects in mathematics education. Lectures, 2 hours per week; lab/tutorial, 2 hours per week. Prerequisite(s): MATH 1P40 and two and one-half MATH or STAT credits or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. STATISTICS COURSES Introductory Statistics (also offered as MATH 1F92) Description and comparison of data sets, linear regression analysis, basic probability theory, discrete probability distributions, binomial and normal distributions, Central Limit Theorem, confidence intervals and hypothesis tests on means and proportions, properties of t-, F- and chi-squared distributions, analysis of variance, inference on regression. Emphasis on interpretation of numerical results for all topics. Use of Minitab. 3 hours per week Prerequisite(s): one grade 11 mathematics credit. Note: designed for non-science majors. Concurrent enrolment in MATH/STAT 1P98 or in MATH/STAT 1P99 is not permitted and credits will not be counted. Major credit will not be granted to Mathematics majors. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Completion of this course will replace previously assigned grade and credit obtained in MATH/STAT 1P98 and 1P99. Practical Statistics (also offered as MATH 1P98) Descriptive statistics; probability of events; counting rules; discrete and continuous probability distributions: binomial, Poisson and normal distributions; Central Limit Theorem; confidence intervals and hypothesis testing; analysis of variance; contingency tables; correlation and regression; emphasis on real-world applications throughout; use of statistical computer software. Lectures, 3 hours per week. Restriction: not open to Mathematics (single or combined) majors. Prerequisite(s): one grade 12 mathematics course or MATH 1P20. Note: designed for students in Biological Sciences, Biotechnology, Business, Earth Sciences, Economics, Environmental Geoscience and Medical Sciences. Concurrent enrolment in MATH/STAT 1P99 or in MATH/STAT 1F92 is not permitted and credit will not be counted. Major credit will not be granted to Mathematics majors. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Completion of this course will replace previous assigned grade and credit obtained in MATH/STAT 1P99 and MATH/STAT 1F92. Applied Statistics for Life Sciences (also offered as MATH 1P99) Visualization and interpretation of life science data using histograms, frequency tables, correlation and regression, and a variety of statistical measures; basic concepts of probability; applications of the binomial, Poisson and normal distributions; confidence intervals for proportions and means; hypothesis testing; contingency tables; introduction to ANOVA; emphasis on interpretation and use of Microsoft Excel software throughout. Lectures, 3 hours per week. Note: designed for students in the Life and Applied Health Sciences. Concurrent enrolment in MATH/STAT 1P98 or in MATH/STAT 1F92 is not permitted and credit will not be counted. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Completion of this course will replace previous assigned grade and credit obtained in MATH/STAT 1P98 and 1F92. Probability (also offered as MATH 2P81) Probability, events, algebra of sets, independence, conditional probability, Bayes' theorem; random variables and their univariate, multivariate, marginal and conditional distributions. Expected value of a random variable, the mean, variance and higher moments, moment generating function, Chebyshev's theorem. Common discrete and continuous distributions: Binomial, Poisson, hypergeometric, normal, uniform and exponential. Use of SAS, Maple or other statistical packages. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 1P02, 1P06 or permission of the instructor. Note: may be taken concurrently with MATH 2P03. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Mathematical Statistics I (also offered as MATH 2P82) Random sampling, descriptive statistics, Central Limit Theorem, sampling distributions related to normality; point estimation: measurements for estimation performance, methods of moments, maximum likelihood, ordinary/weighted least squares; confidence intervals, testing procedures, and their relation for population means, difference between means, variances, ratio of variances, proportions and difference between proportions. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH/STAT 2P81. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Applied Statistics (also offered as MATH 2P98) Single-factor and factorial experimental design methods; nested-factorial experiments. Simple and multiple linear regression methods, correlation analysis, indicator regression; regression model building and transformations. Contingency tables, binomial tests, nonparametric rank tests. Simple random and stratified sampling techniques, estimation of sample size and related topics. Use of SAS, Maple or other statistical packages. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH/STAT 1F92 or 1P98. Note: major credit will not be granted to Mathematics majors. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Experimental Design (also offered as MATH 3P81) Analysis of variance; single-factor experiments; randomized block designs; Latin squares designs; factorial designs; 2f and 3f factorial experiments; fixed, random and mixed models; nested and nested-factorial experiments; Taguchi experiments; split-plot and confounded in blocks factorial designs; factorial replication; regression models; computational techniques and use of SAS, Maple or other statistical packages; related topics. Lectures, 3 hours per week; lab, 1 hour per week. Prerequisite(s): MATH/STAT 2P82. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Regression Analysis (also offered as MATH 3P82) Simple and multiple linear regression and correlation, measures of model adequacy, residual analysis, weighted least squares, polynomial regression, indicator variables, variable selection and model building, multicollinearity, time series, additional topics. Use of SAS, Maple or other statistical packages. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 1P11 or 1P12; MATH/STAT 2P82 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Mathematical Statistics II (also offered as MATH 3P85) Multivariate, marginal and conditional distributions, independence, expectation, covariance, conditional expectation. Functions of random variables, transformation techniques, order statistics. Special and limiting distributions. Proof of central limit theorem. Point estimation: efficiency, consistency, law of large numbers, sufficiency, Rao-Blackwell theorem MVUE. Interval estimation. Hypothesis testing: Neyman-Pearson theory, likelihood ratio test, Bayesian inference. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH 2P03 and MATH/STAT 2P82 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Applied Multivariate Statistics (also offered as MATH 3P86) Matrix algebra and random vector, sample geometry and random sampling, multivariate normal distribution, inference about mean, comparison of several multivariate means, multivariate linear regression model, principle components, factor analysis, covariance analysis, canonical correlation analysis, discrimination and classification, cluster analysis, computational techniques and use of SAS, Maple or other statistical packages and related topics. Lectures, 3 hours per week; lab 1 hour per week. Prerequisite(s): MATH 1P11 or 1P12; MATH/STAT 2P82 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Honours Project Independent project in an area of pure or applied mathematics,or mathematics education. Restriction: open to MATH (single or combined) majors with either a minimum of 14.0 credits, a minimum 70 percent major average and a minimum 60 percent non-major average or approval to year 4 (honours) and permission of the instructor. Note: carried out under the supervision of a faculty member. The supervisor must approve the topic in advance. Presentation of the project is required. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Completion of this course will replace previous assigned grade and credit obtained in MATH 4F90. Sampling Theory (also offered as MATH 4P81) Theory of finite population sampling; simple random sampling; sampling proportion; estimation of sample size; stratified random sampling; optimal allocation of sample sizes; ratio estimators; regression estimators; systematic and cluster sampling; multi-stage sampling; errors in surveys; computational techniques and use of SAS, Maple or other statistical packages and related topics. Lectures, 3 hours per week; lab, 1 hour per week. Prerequisite(s): MATH/STAT 3P85 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Nonparametric Statistics (also offered as MATH 4P82) Order statistics, rank statistics, methods based on binomial distribution, contingency tables, Kolmogorov Smirnov statistics, nonparametric analysis of variance, nonparametric regression, comparisons with parametric methods. Computational techniques and use of SAS, Maple or other statistical packages. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH/STAT 3P85 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Topics in Stochastic Processes and Models (also offered as MATH 4P84) Topics may include general stochastic processes, Markov chains and processes, renewal process, branching theory, stationary processes, stochastic models, Monte Carlo simulations and related topics. Use of SAS, Maple or other statistical packages. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH/STAT 3P85 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Topics in Advanced Statistics (also offered as MATH 4P85) Topics may include advanced topics in stochastic processes and models, queueing theory, time series analysis, multivariate analysis, Bayesian statistics, advanced methods and theory in statistical inference, and related topics. Use of SAS, Maple or other statistical packages. Lectures, 3 hours per week; lab/tutorial, 1 hour per week. Prerequisite(s): MATH/STAT 3P85 or permission of the instructor. Note: this course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. CO-OP COURSES Co-op Work Placement I First co-op work placement (4 months) with an approved employer. Restriction: open to MATH and MICA Co-op students. Co-op Work Placement II Second co-op work placement (4 months) with an approved employer. Restriction: open to MATH and MICA Co-op students. Co-op Work Placement III Third co-op work placement (4 months) with an approved employer. Restriction: open to MATH and MICA Co-op students. Co-op Work Placement IV Optional co-op work placement (4 months) with an approved employer. Restriction: open to MATH and MICA Co-op students. Co-op Work Placement V Optional co-op work placement (4 months) with an approved employer. Restriction: open to MATH and MICA Co-op students. Co-op Reflective Learning and Integration I Provides students with the opportunity to apply what they've learned in their academic studies through career-oriented work experiences at employer sites. Restriction: open to MATH and MICA Co-op students. Prerequisite(s): SCIE 0N90. Corequisite(s): MATH 0N01. Note: students will be required to prepare learning objectives, participate in a site visit, write a work term report and receive a successful work term performance evaluation. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Co-op Reflective Learning and Integration II Provides students with the opportunity to apply what they've learned in their academic studies through career-oriented work experiences at employer sites. Restriction: open to MATH and MICA Co-op students. Prerequisite(s): SCIE 0N90. Corequisite(s): MATH 0N02. Note: students will be required to prepare learning objectives, participate in a site visit, write a work term report and receive a successful work term performance evaluation. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Co-op Reflective Learning and Integration III Provides students with the opportunity to apply what they've learned in their academic studies through career-oriented work experiences at employer sites. Restriction: open to MATH and MICA Co-op students. Prerequisite(s): SCIE 0N90. Corequisite(s): MATH 0N03. Note: students will be required to prepare learning objectives, participate in a site visit, write a work term report and receive a successful work term performance evaluation. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Co-op Reflective Learning and Integration IV Provides students with the opportunity to apply what they've learned in their academic studies through career-oriented work experiences at employer sites. Restriction: open to MATH and MICA Co-op students. Prerequisite(s): SCIE 0N90. Corequisite(s): MATH 0N04. Note: students will be required to prepare learning objectives, participate in a site visit, write a work term report and receive a successful work term performance evaluation. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. Co-op Reflective Learning and Integration V Provides students with the opportunity to apply what they've learned in their academic studies through career-oriented work experiences at employer sites. Restriction: open to MATH and MICA Co-op students. Prerequisite(s): SCIE 0N90. Corequisite(s): MATH 0N05. Note: students will be required to prepare learning objectives, participate in a site visit, write a work term report and receive a successful work term performance evaluation. This course may be offered in multiple modes of delivery. The method of delivery will be listed on the academic timetable, in the applicable term. |
||||||||||||||||||||||||||||||||||||||||||||||||||||
 |
||||||||||||||||||||||||||||||||||||||||||||||||||||
2021-2022 Undergraduate Calendar
Last updated: August 16, 2021 @ 07:44AM