Last updated: June 15, 2015 @ 11:09AM

Thomas Wolf

Howard E. Bell, Ronald A. Kerman, Charles F. Laywine, John P. Mayberry, Eric Muller

S. Ejaz Ahmed, Stephen Anco, Hichem Ben-El-Mechaiekh, Henryk Fukś, Mei Ling Huang, Omar Kihel, Yuanlin Li, Alexander Odesskii, Jan Vrbik, Thomas Wolf

Chantal Buteau, Babak Farzad, William J. Ralph, Xiaojian Xu, Wai Kong (John) Yuen

Thomas A. Jenkyns, Peng Zhang

Dorothy Levay

Dorothy Miners

Lorna Deeth

Margaret Thomson

The Department of Mathematics and Statistics offers a unique program, Mathematics Integrated with Computers and Applications (MICA). This innovative program fully integrates computers and applications into a broad spectrum of courses that range over pure mathematics (the study of mathematics for its own sake), applied mathematics (mathematics for applications) and statistics. With its special focus on technology, the MICA program is especially suited for students desiring careers in applications of mathematics that involve computing. Within the MICA program, students can also form areas of concentration in applied and computational mathematics, mathematics education, pure mathematics or statistics, or they can choose to have no area of concentration.

Students in the MICA program get a solid grounding in mathematical theory and 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 and 2F40 in which students will confront problems from pure and applied mathematics that require experimental and heuristic approaches. In dealing with such problems, students will be expected to develop their own strategies and make their own choices about the best combination of mathematics and computing required in finding solutions.

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.

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.

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 Handbook (brocku.ca/co-op/current-students/co-op-student-handbooks) 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 Handbook (brocku.ca/co-op/current-students/co-op-student-handbooks) 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.

- All students must take three context credits: one Humanities context credit, one Sciences context credit and one Social Sciences context credit. Two credits must be used to satisfy context credit requirements in year 1.
- Students intending to pursue graduate studies in Pure Mathematics will find it essential to have at least MATH 3P97 and 4P03, or MATH 4P11 and 4P13.
- MATH 3P51 and 3P52 are not required for students who fulfill the requirements of the concentration in Mathematics Education, Pure Mathematics or Statistics.
- MATH 1P20 may not be used to satisfy this requirement.
- MATH 2P04, 2P71 or 2P75 recommended in year 2. MATH 3P03, 3P12, 3P60 or 3P75 recommended in year 3.
- Students intending to pursue graduate studies will find it essential to have MATH 3P03 and 3P04.
- In 20 credit degree programs a maximum of eight credits may be numbered 1
*(alpha)*00 to 1*(alpha)*99; at least three credits must be numbered 2*(alpha)*90 or above; at least three credits must be numbered 3*(alpha)*90 or above; and the remaining credits must be numbered 2*(alpha)*00 or above.

In 15 credit degree programs a maximum of eight credits may be numbered 1*(alpha)*00 to 1*(alpha)*99; at least three credits must be numbered 2*(alpha)*90 or above; and the remaining credits must be numbered 2*(alpha)*00 or above.

In some circumstances, in order to meet university degree and program requirements, more than 15 or 20 credits may be taken.

· | MATH 1P01, 1P02, 1P11 and 1P40 |

· | three elective credits (see program note 1) |

· | MATH 2F40, 2P03, 2P08, 2P13, 2P81 and 2P82 |

· | the Humanities context credit, Sciences context credit or Social Sciences context credit (not taken in year 1) |

· | one-half elective credit |

· | MATH 3P06 and 3P12 |

· | one credit from MATH 3P51, 3P52, 3P75, 3P96 |

· | two MATH credits numbered 3(alpha)00 or above (see program note 6) |

· | one elective credit (see program note 6) |

· | Four MATH credits (see program notes 6 and 7) |

· | one elective credit |

· | MATH 1P01, 1P02, 1P11 and 1P40 |

· | three elective credits (see program note 1) |

· | MATH 2F40, 2P03, 2P08, 2P13, 2P81 and 2P82 |

· | SCIE 0N90 |

· | the Humanities context credit, Sciences context credit or Social Sciences context credit (not taken in year 1) |

· | one-half elective credit |

Spring/Summer Sessions:

· | MATH 0N01 and 2C01 |

Fall Term:

· | MATH 3P06 and 3P12 |

· | one credit from MATH 3P04, 3P08, 3P09, 3P13, 3P51, 3P52, 3P60, 3P72, 3P75, 3P81, 3P82, 3P85, 3P96 |

· | one-half elective credit |

Winter Term:

· | MATH 0N02 and 2C02 |

· | One and one-half credits from MATH 3P04, 3P85, 3P96, 4P07, 4P09, 4P13, 4P84, 4P92, 4P94 |

· | one credit from MATH 4P09, 4P11, 4P84, 4P92, 4P94 |

· | one MATH credit (see program note 6) |

· | one and one-half elective credits |

Spring/Summer Sessions:

· | MATH 0N03 and 2C03 |

Fall Term:

· | One and one-half MATH credits numbered 4(alpha)00 or above |

· | one elective credit |

· | MATH 1P01, 1P02 and 1P40 |

· | MATH 1P11 or 1P12 |

· | three elective credits (see program note 1) |

· | MATH 2F40, 2P03, 2P08, 2P81 and 2P82 |

· | MATH 2P12 or 2P13 |

· | the Humanities context credit, Sciences context credit or Social Sciences context credit not taken in year 1 |

· | one-half elective credit (see program note 5) |

· | SCIE 0N90, MATH 3P81, 3P82, 3P85 and 3P86 |

· | one MATH credit numbered 3(alpha)00 or above (see program note 5) |

· | two elective credits |

Spring/Summer Sessions:

· | MATH 0N01 and 2C01 |

Fall Term:

· | MATH 0N02 and 2C02 |

Winter Term:

· | MATH 4P82, 4P85 |

· | one-half MATH credit (see program note 7) |

· | one elective credit (see program note 7) |

Spring/Summer Sessions:

· | MATH 0N03 and 2C03 |

Fall Term:

· | MATH 4P81, 4P84 |

· | one and one-half MATH credits (see program note 7) |

· | MATH 1P01, 1P02, 1P11 and 1P40 |

· | three elective credits (see program note 1) |

· | MATH 2F40 and 2P03 |

· | one credit from MATH 2P08 and 2P13, MATH 2P08 and 2P12, MATH 2P12 and 2P91, MATH 2P81 and 2P82 |

· | the Humanities context credit, Sciences context credit or Social Sciences context credit not taken in year 1 |

· | one and one-half elective credits |

· | Three MATH credits numbered 3(alpha)00 or above (see program note 6) |

· | two elective credits |

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.

· | MATH 1P01, 1P02, 1P11, 1P40, 1P66 and 1P67 |

· | COSC 1P02 and 1P03 |

· | one Humanities context credit |

Fall Term:

· | MATH 2P03 and 2P81 |

· | COSC 1P50, 2P03 and 2P12 |

· | SCIE 0N90 |

Winter Term:

· | MATH 0N01 and 2C01 |

Spring/Summer Sessions:

· | COSC 2P13 and 2P32 |

· | one Social Sciences context credit |

· | one-half elective credit |

Fall term

· | MATH 0N02 and 2C02 |

Winter Term

· | MATH 2P12 or 2P71 |

· | COSC 3P05 |

· | one elective credit |

Spring/Summer Sessions:

· | MATH 0N03 and 2C03 |

· | MATH 2F40, 2P82, 3P60 and 4P61 |

· | COSC 3P03 and 4F00 |

· | one and one half COSC credits (see program note 7) |

Fall Term:

· | One MATH credit (see program note 7) |

· | one COSC credit (see program note 7) |

· | one-half elective credit (see program note 7) |

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.

To help students meet Primary/Junior Teacher Education admission requirements at Brock University, they should take MATH 2P52.

Three credits for a teachable subject at the Junior/Intermediate level (see program note 4). May include MATH 1F92, 1P05, 1P06, 1P66, 2P90, 3P23 and 3P91; MATH 1P11 or 1P12.

For Mathematics as the first teachable subject (a minimum of five credits; see program note 4). An Honours degree in Mathematics is recommended.

For Mathematics as the second teachable subject, a minimum of three credits (see program note 4). For example: MATH 1P01, 1P02, 1P12, 2P90 and one-half MATH 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 Mathematics Department offers a program leading to a Certificate in Statistics normally for those with a degree in Mathematics or a degree in a non-mathematics discipline.

See "Certificate Requirements" under Academic Regulations.

The Certificate in Statistics is awarded upon completion the following courses with a minimum 60 percent overall average:

· | One-half university Calculus credit |

· | MATH 2P12 or 2P13 |

· | MATH 2P81, 2P82, 3P81, 3P82, 3P85, 3P86, 4P81 and 4P82 |

Students may earn a Concentration in Applied and Computational Mathematics by successfully completing the following courses as part of the academic work leading to a BSc (Honours) in Mathematics Integrated with Computers and Applications:

· | MATH 2F40, 3P51 and 3P52 |

· | two and one-half credits from MATH 3P04, 3P08, 3P09, 3P12, 3P60, 3P72, 3P75 |

· | two credits from MATH 3P96, 4P09, 4P84, 4P92, 4P94 |

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 Integrated with Computers and Applications:

· | MATH 2F40, 2P03, 2P08, 2P12, 2P71, 2P90, 3P12, 3P23, 3P91 and 4P90 |

· | one of MATH 3P51, 4P23, 4P96 |

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 Integrated with Computers and Applications

· | MATH 2P04, 2P13, 3P03, 3P04, 3P12 and 3P13 |

· | MATH 2P71 (recommended) or 2P91 |

· | one credit from MATH 3P08, 3P09, 3P51, 3P52, 3P60, 3P72, 3P97, 3P98 |

· | two credits from MATH 4F90, 4P03, 4P11, 4P71, 4P92 |

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 Integrated with Computers and Applications:

· | MATH 2F40, 2P81, 2P82, 3P81, 3P82, 3P85, 3P86, 4P81, 4P82, 4P84 and 4P85 |

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:

· | MATH 1P01, 1P02, 1P40 and 2F40 |

· | MATH 1P11 or 1P12 |

· | one MATH credit numbered 2(alpha)00 or above |

· | one MATH credit numbered 3(alpha)00 or above |

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:

· | MATH 1P11 or 1P12, |

· | MATH 1P66, 1P97, 1P98, 2P90, 3P23 and 3P91 |

· | one-half MATH credit (see program note 4) |

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:

· | MATH 1P01, 1P02, 1P40 and 2P90 |

· | MATH 1P11 or 1P12 |

· | MATH 3P23 or 4P96 |

· | two MATH credits numbered 2(alpha)00 or above |

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

MATH 1F92Describing and comparing 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.

Prerequisite(s): one grade 11 mathematics credit.

Note: designed for non-science majors. Not open to students with credit in any university mathematics or statistics course.

MATH 1P01

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.

Prerequisite(s): two grade 12 mathematics credits including MCV4U or permission of the instructor.

Note: open to all, but primarily intended for mathematics majors and/or future teachers. Students must successfully complete the Mathematics Skills Test.

Completion of this course will replace previous assigned grade and credit obtained in MATH 1P05.

MATH 1P02

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.

Prerequisite(s): MATH 1P01, 1P05 or permission of instructor.

Note: open to all, but primarily intended for mathematics majors and/or future teachers.

Completion of this course will replace previous assigned grade and credit obtained in MATH 1P06.

MATH 1P05

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.

Prerequisite(s): two grade 12 mathematics credits including MCV4U or permission of the instructor.

Note: designed for students in the sciences, computer science, and future teachers. Students must successfully complete the Mathematics Skills Test.

Completion of this course will replace previous assigned grade and credit obtained in MATH 1P01.

MATH 1P06

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.

Prerequisite(s): MATH 1P01 or 1P05.

Note: designed for students in the sciences, computer science, and future teachers.

Completion of this course will replace previous assigned grade and credit obtained in MATH 1P02.

MATH 1P11

Review of linear systems and matrix algebra. General determinants and applications. Complex numbers. Vector geometry in R2 and 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.

Prerequisite(s): two grade 12 mathematics credits including MCV4U.

MATH 1P12

Systems of linear equations with applications. Matrix algebra. Determinants.Vector geometry in R

Prerequisite(s): one grade 12 mathematics credit or permission of instructor.

Students will not receive earned credit for MATH 1P12 if MATH 1P11 has been successfully completed.

MATH 1P20

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, conic sections, exponential functions, logarithmic functions, polar co-ordinates, mathematical induction, binomial theorem, vectors and matrices.

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.

MATH 1P40

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.

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.

MATH 1P66

Introduction to mathematical abstraction, logic and proofs including mathematical induction.

Prerequisite(s): one grade 12 mathematics credit.

Note: MCB4U recommended. Students may not concurrently register in MATH 2P04, 2P13 or 2P71.

Students will not receive earned credit for MATH 1P66 if MATH 2P04, 2P13 or 2P71 have been successfully completed.

MATH 1P67

Development and analysis of algorithms, complexity of algorithms; recursion solving recurrence relations; relations and functions.

Restriction: open to COSC (single or combined), BCB, CAST, CNET majors and APCO minors.

Prerequisite(s): MATH 1P66.

MATH 1P97

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.

Prerequisite(s): one grade 12 mathematics credit

Note: may be available on site, online or blended. 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.

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.

Prerequisite(s): one grade 12 mathematics credit or MATH 1P20.

Note: designed for students in Biological Sciences, Biotechnology, Business, Earth Sciences, Economics, Environmental Geoscience and Medical Sciences. Not open to students with credit in any university statistics course.

MATH 2F40

Theory and application of mathematical models; discrete dynamical systems; time series and their application to the prediction of weather and sunspots; Markov chains; empirical models using interpolation and regression; continuous stochastic models; simulation of normal, exponential and chi-square random variables; queuing models and simulations, use of a computer algebra system.

Prerequisite(s): MATH 1P02 or 1P06; MATH 1P40 or permission of the instructor.

MATH 2P03

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.

Prerequisite(s): MATH 1P02, 1P06 or permission of the instructor.

MATH 2P04

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.

Prerequisite(s): MATH 2P03.

MATH 2P08

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.

Prerequisite(s): MATH 1P02, 1P06 or permission of the instructor.

MATH 2P12

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.

Prerequisite(s): MATH 1P11 or 1P12.

MATH 2P13

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.

Prerequisite(s): MATH 2P12.

MATH 2P52

Mathematical concepts and ideas in number systems; geometry and probability arising in the Primary and Junior school curriculum.

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.

MATH 2P71

Counting, inclusion and exclusion, pigeonhole principle, permutations and combinations, derangements, binomial expansions, introduction to discrete probability; to graph theory, Eulerian graphs, Hamilton Cycles, colouring, planarity, trees.

Prerequisite(s): two 4U mathematics credits or permission of the instructor.

MATH 2P75

Applications of mathematics to financial markets. Models for option pricing, rates of interest, price/yield, pricing contracts and futures, arbitrage-free conditions, market risk, hedging and sensitivities, volatility; stock process as random walks and Brownian motions; Black-Scholes formula; finite difference methods and VaR.

Prerequisite(s): MATH 1P97 and 1P98.

MATH 2P77

Introduction to 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.

Prerequisite(s): two 4U mathematics credits or permission of the instructor.

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. Some common discrete and continuous distributions: Binomial, Poisson, hypergeometric, normal, uniform and exponential. Use of SAS, Maple or other statistical packages.

Prerequisite(s): MATH 2P03 or permission of the instructor.

Note: may be taken concurrently with MATH 2P03.

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.

Prerequisite(s): MATH 2P81.

MATH 2P90

The development of Euclidean and non-Euclidean geometry from Euclid to the 19th century. The deductive nature of plane Euclidean geometry as an axiomatic system, the central role of the parallel postulate and the general consideration of axiomatic systems for geometry in general and non-Euclidean geometry in particular. Introduction to transformation geometry. Use of Geometer's Sketchpad.

Prerequisite(s): one MATH credit.

Completion of this course will replace previous assigned grade and credit obtained in MATH 2P50.

MATH 2P91

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.

Prerequisite(s): MATH 1P11 or 1P12; MATH 2P12.

Completion of this course will replace previous assigned grade and credit obtained in MATH 2P72.

MATH 2P95

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.

Prerequisite(s): one of MATH 1P01, 1P02, 1P05, 1P06, 1P97; MATH 1P11 or 1P12 or permission of the instructor.

MATH 2P97

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.

Prerequisite(s): MATH 1P01 or 1P05; MATH 1P11 or 1P12; MATH 2P71 or 2P81 or permission of instructor.

Note: recommended to students wishing to participate in mathematical problem solving competitions.

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.

Prerequisite(s): MATH 1F92 or 1P98.

MATH 3P03

Approximation of functions by algebraic and trigonometric polynomials (Taylor and Fourier series); Weierstrass approximation theorem; Riemann integral of functions on R

Prerequisite(s): MATH 2P04.

MATH 3P04

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.

Prerequisite(s): MATH 2P03.

MATH 3P06

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.

Prerequisite(s): MATH 2P03.

MATH 3P08

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.

Prerequisite(s): MATH 2P08.

MATH 3P09

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.

Prerequisite(s): MATH 2P08.

MATH 3P12

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.

Prerequisite(s): MATH 2P12 or permission of the instructor.

MATH 3P13

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.

Prerequisite(s): MATH 3P12.

MATH 3P23

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.

Prerequisite(s): one MATH credit.

Completion of this course will replace previous assigned grade and credit obtained in MATH 2P93.

MATH 3P51

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.

Prerequisite(s): MATH 2F40 and 2P03.

Completion of this course will replace previous assigned grade and credit obtained in MATH 3F40.

MATH 3P52

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.

Prerequisite(s): MATH 2F40 and 2P03.

Completion of this course will replace previous assigned grade and credit obtained in MATH 3F40.

MATH 3P60

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.

Prerequisite(s): MATH 1P02 or 1P06; MATH 1P11 or 1P12; MATH 2P12 or permission of the instructor.

MATH 3P72

Problems and methods in non-linear optimization. Classical optimization in R

Prerequisite(s): MATH 2P03 and 2P91 (2P72).

MATH 3P73

(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.

Prerequisite(s): MATH 2P91 (2P72) or ECON 3P91.

MATH 3P75

Probability, Brownian motion, martin-gales, Markov processes, differential equations, finite difference and tree models used in financial mathematics of options; stocks; one-dimensional Ito processes, Black-Scholes for both constant and non-constant inputs, continuous time hedging, valuing American and exotic options.

Prerequisite(s): MATH 1P11 or 1P12; MATH 2P03, 2P08, 2P12 and 2P82.

MATH 3P81

Analysis of variance; single-factor experiments; randomized block designs; Latin squares designs; factorial designs; 2

Prerequisite(s): MATH 2P82.

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, selected topics. Use of SAS, Maple or other statistical packages.

Prerequisite(s): MATH 2P12 and 2P82 or permission of the instructor.

Note: MATH 3P82 has been approved by VEE (Validation by Education Experience) Administration Committee of the Society of Actuaries. To receive VEE credit, candidates will need a minimum grade of 70 percent.

MATH 3P85

Multivariate, marginal and conditional distributions, independence, expectation, covariance, conditional expectation. Functions of random variables, transformation techniques, order statistics. Some 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.

Prerequisite(s): MATH 2P82.

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.

Prerequisite(s): MATH 2P12 and 2P82 or permission of the instructor.

MATH 3P91

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.

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.

MATH 3P95

(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.

Prerequisite(s): MATH 2P03 and 2P08.

Note: MATH 2P12 is recommended.

Completion of this course will replace previous assigned grade and credit obtained in MATH (PHYS) 4P64.

MATH 3P96

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.

Prerequisite(s): MATH 2P03, 2P12 and 2P81.

MATH 3P97

Introduction to metric and topological spaces; connectedness, completeness, countability axioms, separation properties, covering properties, metrization of topological spaces.

Prerequisite(s): MATH 2P04; MATH 2P12 and 2P13 or MATH 3P12 and 3P13.

MATH 3P98

Introduction to the theory of normed linear spaces, fixed-point theorems, Stone-Weierstrass approximation on metric spaces and preliminary applications on sequence spaces.

Prerequisite(s): MATH 3P97.

MATH 4F90

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.

MATH 4P03

Lebesgue integration on R

Prerequisite(s): MATH 3P03.

MATH 4P06

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.

Restriction: permission of the instructor.

MATH 4P09

(also offered as PHYS 4P09)

Introduction to solitons. 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.

Prerequisite(s): one of MATH 3P08, 3P09, 3P51, 3P52.

MATH 4P11

Advanced topics from group theory. Topics may include the Sylow theorems, free groups, nilpotent and solvable groups and some simple Lie groups.

Prerequisite(s): MATH 3P13.

MATH 4P13

Advanced topics from ring theory. Topics may include radicals, Wedderburn-Artin theorems, modules over rings and some special rings.

Prerequisite(s): MATH 3P13.

MATH 4P23

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.

Prerequisite(s): MATH 1P02 or 1P06; MATH 1P11 or 1P12; MATH 3P23 (2P93).

Completion of this course will replace previous assigned grade and credit obtained in MATH 3P93.

MATH 4P61

(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.

Restriction: open to COSC (single or combined) majors.

Prerequisite(s): MATH 1P67.

Note: MATH students may take this course with permission of Department.

MATH 4P71

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.

Prerequisite(s): MATH 2P71 or permission of the instructor.

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.

Prerequisite(s): MATH 3P85 or permission of the instructor.

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.

Prerequisite(s): MATH 3P85 or permission of the instructor.

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.

Prerequisite(s): MATH 3P85 or permission of the instructor.

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.

Prerequisite(s): MATH 3P85 or permission of the instructor.

MATH 4P90

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.

Prerequisite(s): MATH 1P11 or 1P12; MATH 2P90.

Completion of this course will replace previous assigned grade and credit obtained in MATH 3P90.

MATH 4P92

Topics may include algebraic number theory, analytic number theory and cryptography.

Restriction: permission of the Department.

Prerequisite(s): MATH 1P11 or 1P12; one of MATH 2P12, 2P71, 2P81, 3P12.

MATH 4P94

(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).

Prerequisite(s): MATH 2P03, 2P08, 3P06, PHYS 2P20 and 2P50 or permission of the instructor.

MATH 4P96

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.

Prerequisite(s): MATH 1P40 and two and one-half MATH credits or permission of the instructor.

CO-OP COURSES

MATH 0N01First co-op work placement (4 months) with an approved employer.

Restriction: open to MATH and MICA Co-op students.

MATH 0N02

Second co-op work placement (4 months) with an approved employer.

Restriction: open to MATH and MICA Co-op students.

MATH 0N03

Third co-op work placement (4 months) with an approved employer.

Restriction: open to MATH and MICA Co-op students.

MATH 0N04

Optional co-op work placement (4 months) with an approved employer.

Restriction: open to MATH and MICA Co-op students.

MATH 0N05

Optional co-op work placement (4 months) with an approved employer.

Restriction: open to MATH and MICA Co-op students.

MATH 2C01

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.

MATH 2C02

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.

MATH 2C03

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.

MATH 2C04

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.

MATH 2C05

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.