Last updated: November 23, 2010 @ 03:56PM

Stephen Anco

Professors Emeriti

Howard E. Bell, Charles F. Laywine, John P. Mayberry, Eric MullerStephen Anco, Hichem Ben-El-Mechaiekh, Mei Ling Huang, Ronald A. Kerman, Yuanlin Li, Jan Vrbik, Thomas Wolf

Chantal Buteau, Henryk Fuks, Omar Kihel, Alexander Odesskii, William J. Ralph, Xiaojian Xu, Wai Kong (John) Yuen

Babak Farzad

*Adjunct Professor*

Dorothy Levay, Dorothy Miners

Santo D'Agostino

Margaret Thomson, Josephine (Pina) McDonnell

The Department of Mathematics 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 Mathematics Integrated with Computers and Applications Co-op program combines 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 in Mathematics 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, Mathematics Co-op students are assessed an administrative fee for each work term (see the Schedule of Fees).

Eligibility to continue in Mathematics Integrated with Computers and Applications Co-op program is based on 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 Integrated with Computers and Applications 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.

The Mathematics Integrated with Computers and Applications 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.

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.

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.

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.

- 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 MATH 4P03 and 4P05 or MATH 4P11 and 4P14 and desirable to have all of them.
- 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.
- 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.

· | MATH 1P01, 1P02, 1P12 and 1P40 |

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

· | MATH 2F40, 2P03, 2P08, 2P12, 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 3P51 and 3P52 (see program note 3) |

· | two MATH credits numbered 3(alpha)00 or above |

· | two elective credits (see program note 6) |

· | Four MATH credits (see program notes 2 and 6) |

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

· | MATH 1P01, 1P02, 1P12 and 1P40 |

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

· | MATH 2F40, 2P03, 2P08, 2P12, 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:

· | Three credits from MATH 3P04, 3P08, 3P09, 3P12, 3P13, 3P51, 3P52, 3P60, 3P72, 3P75, 3P81, 3P82 |

Winter Term:

· | MATH 0N02 and 2C02 |

· | Three credits from MATH 3P04, 3P08, 3P09, 3P12, 3P13, 3P51, 3P52, 3P60, 3P72, 3P75, 3P81, 3P82 (not taken in year 3) |

· | two credits from MATH 4P05, 4P07, 4P09, 4P11, 4P13, 4P84, 4P92, 4P93, 4P94 |

Spring/Summer Sessions:

· | MATH 0N03 and 2C03 |

Fall Term:

· | Two credits from MATH 4P05, 4P07, 4P09, 4P11, 4P13, 4P84, 4P92, 4P93, 4P94 (not taken in year 4) |

Year 1

· | MATH 1P01, 1P02, 1P12 and 1P40 |

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

· | MATH 2F40, 2P03, 2P08, 2P12, 2P81 and 2P82 |

· | 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 |

· | one elective credit |

Spring/Summer Sessions:

· | MATH 0N03 and 2C03 |

Fall Term:

· | MATH 4P81, 4P84 |

· | one and one-half MATH credits |

· | MATH 1P01, 1P02, 1P12 and 1P40 |

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

· | MATH 2F40 and 2P03 |

· | one of MATH 2P08 and 2P12, MATH 2P12 and 2P72, MATH 2P81 and 2P82 |

· | |

· | one and one-half elective credits |

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

· | two elective credits (see program note 6) |

Combined major programs have been developed by the Department of Mathematics 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, 1P12 and 1P40 |

· | COSC 1P02, 1P03 and 1P50 |

· | one Sciences context credit |

· | one-half elective credit |

Fall Term:

· | MATH 2P03 and 2P81 |

· | COSC 2P03, 2P12 and 2P90 |

· | SCIE 0N90 |

· | MATH 0N01 and 2C01 |

· | MATH 1P66 and 1P67 |

· | COSC 2P32 |

· | one-half COSC credit |

· | COSC 3F00 |

· | MATH 2F40 and 3F65 |

· | one Humanities context credit |

· | one Social Sciences context credit |

· | MATH 0N02 and 2C02 |

Fall Term:

· | MATH 0N03 and 2C03 |

· | MATH 2P82, 3P60 and 4P61 |

· | COSC 2P13 |

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

Fall Term:

· | One COSC credit (see program note 6) |

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

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

The Department of Mathematics 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 - MATH 2P52.

Three credits for a teachable subject at the Junior/Intermediate level (see program note 4). May include MATH 1F92, 1P05, 1P06, 1P12, 1P66, 2P90, 2P93 and 3P91.

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, 2P93 and one-half MATH credit.

The Department of Mathematics 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 another 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 university Calculus credit |

· | MATH 2P12, 2P81, 2P82, 3P81, 3P82, 3P85, 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 4P05, 4P07, 4P09, 4P84, 4P93, 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, 2P93, 3P12, 3P90 and 3P91 |

· | MATH 3P51 or 3P93 |

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 (with the possible exception of MATH 2P72):

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

· | MATH 2P71 (recommended) or 2P72 |

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

· | two credits from MATH 4F90, 4P03, 4P11, 4P14, 4P71, 4P92, 4P93 |

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, 1P12, 1P40 and 2F40 |

· | 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 1P12, 1P66, 1P97, 1P98, 2P90, 2P93 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, 1P12, 1P40, 2P90 and 2P93 |

· | 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 with an emphasis 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 a 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, continuity, derivatives and differentiability, implicit differentiation, linear approximation, max and min, related rates, curve sketching, l'Hospital's rule, antiderivatives, integrals, FTC without proof, integration by substitution. Use of Maple.

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 a 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. 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 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 1P12

Introduction to finite dimensional real vector spaces; systems of linear equations: matrix operations and inverses, determinants. Vectors in R

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

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.

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 popular growth.

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.

Prerequisite(s): MATH 1P66.

Note: designed for students in Computer Science.

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

MATH 2F05

First and second order differential equations, vector functions, curves, surfaces; tangent lines and tangent planes, linear approximations, local extrema; cylindrical and spherical co-ordinates; gradient, divergence, curl; double and triple integrals, line and surface integrals; Green's theorem, Stokes' theorem, Gauss' theorem; elementary complex analysis. Emphasis on applications to physical sciences. Use of Maple.

Prerequisite(s): MATH 1P02 or 1P06.

Students will not receive earned credit in MATH 2F05 if MATH 2P03 has been successfully completed.

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 and 1P40 or permission of the instructor.

MATH 2P03

Multivariable integration, polar, cylindrical and spherical coordinates, vector algebra, parameterized curves and surfaces, vector calculus, arc length, curvature and torsion, projectile and planetary motion, line integrals, vector fields, Green's theorem, Stokes' theorem, the use of computer algebra systems to manipulate vectors, plot surfaces and curves, determine line integrals and analyze vector fields.

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

MATH 2P04

Sets; mappings, count ability; 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 equationsd 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

Finite dimensional real vector spaces and inner product spaces; matrix and linear transformation; eigenvalues and eigenvectors; the characteristic equation and roots of polynomials; diagonalization; complex vector spaces and inner product spaces; selected applications; use of a computer algebra system and selected applications.

Prerequisite(s): MATH 1P12.

MATH 2P13

Vector spaces over fields; linear transformations; diagonalization and the Cayley-Hamilton theorem; Jordan canonical form; linear operators on inner product spaces; the spectral theorem; bilinear and quadratic forms.

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 2P72

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 1P12.

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 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

Transforming random variables, central limit theorem, law of large numbers. Random sample; sample mean and variance. Sampling from normal population: chi-square, t and F distributions, sample median and order statistics. Point and interval estimation of population parameters: method of moments, maximum-likelihood technique, consistent, unbiased and efficient estimators, confidence intervals. Hypotheses testing: type I and II errors, most powerful tests. Use of SAS, Maple or other statistical packages.

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 2P93

Triumphs in mathematical thinking emphasizing many cultures up to 1000 AD. Special attention is given to analytical understanding of mathematical problems from the past, with reference to the stories and times behind the people who solved them. Students will be encouraged to match 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 2P51.

MATH 2P95

Scales and termperaments, 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 1P12 or permission of the instructor.

Completion of this course will replace previous assigned grade and credit obtained in MATH 2P31.

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 3F65

Applied probability, Markov chains, Poisson and exponential processes, renewal theory, queuing theory, applied differential equations. Networks, graph theory, reliability theory, NP-completeness.

Prerequisite(s): MATH 1P01 or 1P97; MATH 1P12, 1P66 and 1P67.

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 2F05 or 2P03.

MATH 3P08

Linear second-order differential equations. Integral transform methods, series solutions, special functions (Gamma, Bessel, Legendre). Boundary value problems; introduction to Sturm-Liouville theory and series expansions by orthogonal functions. Emphasis on applications to physical sciences. Use of Maple.

Prerequisite(s): MATH 2F05 or 2P08.

MATH 3P09

First-order equations and method of characteristics. Second-order linear equations, initial and boundary value problems for the heat equation, wave equation, and Laplace equation. Fourier series, cylindrical (Bessel) and spherical (Legendre) harmonic series. Eigenfunction problems and normal modes. Nonlinear wave equations. Emphasis on applications to physical sciences. Use of Maple.

Prerequisite(s): MATH 2F05 or 2P08.

MATH 3P12

Group theory with applications. Topics include modular arithmetic, symmetry groups and the dihedral groups, subgroups, cyclic groups, permutation groups, group isomorphism, frieze and crystallographic groups, Burnside's theorem, cosets and Lagrange's theorem, direct products and cryptography.

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

MATH 3P13

Further topics in group theory: normal subgroups and factor groups, 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 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 and 1P12 or permission of the instructor.

MATH 3P72

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

Prerequisite(s): MATH 2F05 or 2P03; MATH 2P72 (2P60).

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 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 1P12 and 2P82; MATH 2F05 or MATH 2P03 and 2P08.

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.

MATH 3P85

Review of distributional theory. Convergence types. Some special and limiting distributions. Review of point and interval estimations. Efficiency, sufficiency, robustness and completeness. Bayesian estimations, credible intervals, prediction intervals. Basic theory of hypotheses testing: Neyman-Pearson lemma, likelihood ratio test, chi-square test, Test of stochastic independence. Normal models: quadratic forms, noncentral chi-square and noncentral

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 3P90

Topics in Euclidean and non-Euclidean geometry chosen from the classification of isometries in selected geometries, projective geometry, finite geometries and axiometic systems for plane Euclidean geometry.

Prerequisite(s): MATH 1P12 and 2P90 (2P50).

Completion of this course will replace previous assigned grade and credit obtained in MATH 3P50.

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), BA (Honours)/BEd (Junior/Intermediate), BSc (Honours)/BEd (Junior/Intermediate) and students in minor programs for teachers with a minimum of 9.0 overall credits.

Prerequisite(s): three MATH credits.

MATH 3P93

The development of modern mathematics from medieval times to the present. The course includes 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, 1P12 and 2P93.

Completion of this course will replace previous assigned grade and credit obtained in MATH 3P51.

MATH 3P97

Introduction to metric and topological spaces; connectedness, completeness, countability axioms, separation pro-perties, 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 4P05

Wavelets as an orthonormal basis for R

Prerequisite(s): MATH 2P08, 2P12 and 3P03.

Completion of this course will replace previous assigned grade and credit obtained in MATH 4P04.

MATH 4P07

Topics may include ordinary differential equations: existence and uniqueness theory, strange attractors, chaos, singularities. Partial differential equations: Cauchy-Kovalevski theorem, well-posedness of classical linear heat equation and wave equation, weak solutions, global existence, uniqueness and asymptotic behaviour.

Prerequisite(s): MATH 3P08.

Completion of this course will replace previous assigned grade and credit obtained in MATH 4F08.

MATH 4P09

(also offered as PHYS 4P09)

Introduction to solitons. Travelling waves, nonlinear wave and evolution equations (Korteweg de Vries, Bousinesq, nonlinear Schrodinger, sine-Gordon), soliton solutions and their interaction properties, Lax pairs and construction of single and multisoliton solutions.

Prerequisite(s): one of MATH 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.

Completion of this course will replace previous assigned grade and credit obtained in MATH 4F10.

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.

Completion of this course will replace previous assigned grade and credit obtained in MATH 4F10.

MATH 4P14

Topics may include modules, homological algebra, group algebra, algebraic geometry, lattice theory, graph theory and logic.

Prerequisite(s): MATH 3P13 or permission of the Department.

Completion of this course will replace previous assigned grade and credit obtained in MATH 4F10 or 4P12.

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.

Restriction: permission of the Department.

Note: while no specific course is an essential prerequisite, students should have competence in abstraction equivalent to that obtained by successful completion of MATH 3P12.

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 the binomial distribution, contingency tables, Kolmogorov Smirnov statistics, nonparametric analysis of variance, nonparametric regression, comparisons with parametric methods. 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 4P92

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

Restriction: permission of the Department.

Completion of this course will replace previous assigned grade and credit obtained in MATH 4F91.

MATH 4P93

Topics may include point set topology, differential geometry, algebraic topology and dynamical systems.

Prerequisite(s): MATH 3P97 or permission of the Department.

Completion of this course will replace previous assigned grade and credit obtained in MATH 4F91.

MATH 4P94

(also offered as PHYS 4P94)

Review of Special Relativity and Minkowski space-time. Introduction to General Relativity theory including gravitation and the space-time metric, light cones, horizons, asymptotic flatness; energy-momentum of particles and light rays (geodesics). Static black holes (Schwarzschild metric), properties of light rays and particle orbits. Rotating black holes (Kerr metric).

Prerequisite(s): MATH 2F05, PHYS 2P20 and 2P50 or permission of the instructor.

CO-OP COURSES

MATH 0N01First co-op work placement (4months) 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

Provide student 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

Provide 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

Provide student 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

Provide students with the opportunity to apply what they've learned in their academic studies through areer-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

Provide 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.