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Bachelor of Arts (Honours) Economics - Mathematical Economics

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  • Academic Title
    Bachelor of Arts (Honours) Economics - Mathematical Economics
  • Course description
    B.A. (Honours) Economics - Mathematical Economics
    The B.A. (Honours) Economics - concentration in Mathematical Economics is a three-year program consisting of 90 course credits. Four-year students have additional requirements detailed below.

    Requirements of the program are:
    Required courses     48 credits
    Elective courses within the program     15 credits
    Free electives     27 credits

    Requirements for the B.Sc.
    :

    All the requirements of the BA(Honours) Economics - Mathematical Economics
    Plus:     three-year students lacking the MAT 191/192 program prerequisite will have the credits necessary to complete these courses added to their degree program
    Plus:     an additional program pre-requisite of Physics 191 and Physics 192 or equivalent; students lacking these courses must make them up from among their free electives
    Plus:     among the 27 credits of free electives, at least three lecture courses in science (total 9 credits) to be taken from among the offerings in Chemistry, Biology, Biochemistry, Physics or Computer Science.

    Mathematics 100a      Excursions in Modern Mathematics      3-3-0
    An introduction to modern applied mathematics: social choice, management science, growth, symmetry, and descriptive statistics. Not intended as a numeracy course, nor for the remediation of algebraic shortcomings: computational complexity is minimal, and math prerequisites are absent. Instead, the methodology of mathematics is addressed: the use of unambiguous language and simplification to model practical problems, the types of answers the discipline can provide, and the notions of generalization and "open" problems. The course will allow the student to develop a sense of the nature of mathematics as a discipline, and an appreciation of its role in the modern world.
    Note: Science students must enroll in Mathematics 110 instead of this course. Students may only receive credit for one of MAT 100 or MAT 110.

    Mathematics 101b     Further Excursions in Mathematics     3-3-0
    Further topics in modern applied mathematics. A continuation of the style and subjects in Mathematics 100, this course is also not intended to redress deficiencies in numeracy, nor does it have any mathematical prerequisites. Topics may include growth models, game theory, linear programming, fractal geometry, coding theory, non-Euclidean geometry and selected current readings.
    Note: Science students must enroll in Mathematics 111b instead of this course. Students may only receive credit for one of MAT 101 and MAT 111.

    Mathematics 104a     History of Mathematics     3-3-0
    This course is designed to help history, philosophy, and education students come to a deeper understanding of the mathematical side of culture by means of writing short essays. Mathematics majors acquire a philosophical and cultural understanding of their subject by means of doing actual mathematics problems from different eras. Topics may include perfect numbers, Diophantine equations, Euclidean construction and proofs, the circle area formula, the Pell equation, cubic equations, the four square theorem, quaternions, and Cantor's set theory. The philosophical themes of infinity and Platonism recur repeatedly throughout the course.

    Mathematics 105a     Introduction to Discrete Mathematics     3-3-0
    Combinatorics. Propositional logic. Induction. Sets. Quantifiers. Recursion relations.

    Mathematics 106a     Advanced Calculus I     3-3-0
    Sequences and series. Taylor series and polynomials. Power Series. Functions of 2 and 3 variables. Partial Derivatives, directional derivatives, differentials. Lagrange multipliers. Multiple integrals and applications.
    Prerequisite: Mathematics 192b or a grade of at least 80% in Mathematics 199b.

    Mathematics 107b     Advanced Calculus II     3-3-0
    Vector-valued functions, parametric curves, arc length, curvature. Change of Variables and Jacobians. Line intergrals. Surface integrals. Green's theorem. Divergence theorem. Stoke's theorem. Differential operator.
    Prerequisite: Mathematics 106a, Mathematics 108a

    Mathematics 108a     Matrix Algebra     3-3-0
    Operations on matrices, transpose and inverse. Systems of linear equations. Determinants. Linear transformations. Eigenvalue and eigenvectors. Vector spaces. Bases and dimension. Rank and nullity. Applications.

    Mathematics 109b     Linear Algebra     3-3-0
    Diagonalization. Inner product spaces. Gram-Schmidt process. Change of basis. Complex vector spaces. Systems of differential equations. Applications.
    Prerequisite: Mathematics 108a

    Mathematics 110a     Excursions in Modern Mathematics     3-3-0
    This is the same course as Mathematics 100 but it is intended that science students would enroll in this course and complete assignments that are more appropriate to their needs.
    NOTE: Students may only receive credit for one of MAT 100 or MAT 110.

    Mathematics 111b     Further Excursions in Mathematics     3-3-0
    This is the same course as Mathematics 101b but it is intended that science students would enroll in this course and complete assignments that are more appropriate to their needs.
    Note: See Mathematics 101b. Students may only receive credit for one of MAT 101 and MAT111.

    Mathematics 114b     Modern Geometry: Euclidean to Fractal     3-3-0
    Particularly recommended for elementary and high-school teachers. Euclidean, elliptic and hyberbolic geometries, and applications: modern graphics, fractal images and the work of analytical artists like M.C. Escher.
    This course must be taken concurrently with Mathematics 184b.
    Prerequisite: Mat 105
    Corequisite: Mat 184b

    Mathematics 115b     Further Discrete Mathematics     3-3-0
    Complex Numbers. More recurrence. Equivalence relations. Relations and functions. Graph theory. Cardinality.
    Prerequisite: Mathematics 105a

    Mathematics 125a     Number Theory     3-3-0
    A classical discipline, number theory has become the spectacularly successful language of modern aryptography and coding theory. This course is a gently introduction to the classical theory and modern applications. Topics may include: unique factorization and congruences, group of integers module n and its units, Fermat's little theorem, Fermat's last theorem, Euler's function, Wilson's theorem, Chinese remainder theorem, quadratic repricocity, Gaussian integers.
    Prerequisite: Mathematics 105

    Mathematics 172a     Mathematical Economics I     3-3-0
    Application of matrix algebra and multivariate calculus to model-building and problem- solving in Economics
    Prerequisites: Economics 102, 103
    See EMA262A
    Students may not take this course for credit if they have received credit for EMA262a.

    Mathematics 177a     Introduction to Mechanics     3-3-0
    Statics: equilibrium of bodies subject to many forces. Kinematics; rectilinear, plane, circular and simple harmonic motion. Dynamics: conservation of mechanical energy and momentum; place and circular motion of particles; rotation of macroscopic bodies. Elasticity: elastic moduli. Hydrostatics and hydrodynamics.
    Prerequisite: Physics 191a or equivalent
    Corequisite: Mathematics 106a
    See Physics 117a
    Students may not take this course for credit if they have received credit for Physics 117a.

    Mathematics 184b     Modern Geometry by Laboratory Explorations     1-0-3
    Geometry explorations using Geometer's Sketchpad software. Projects will enhance the learning of the curriculum of the course MAT 114 which must be taken concurrently.
    Corequisite: Mat 114b

    Mathematics 190ab     Precalculus Mathematics     3-3-0
    Review of algebra. Sets, Functions, graphs. Slope and equation of a straight line. Equation of a circle. Exponential and logarithm functions with applications. Arithmetic and geometric progressions. Permutations and Combinations.
    Students who have received credit for an equivalent course taken elsewhere may not register for this course.
    Mathematics 191a     Enriched Calculus I     3-3-0
    Elementary functions, limits, continuity. The derivative, differentiability, mean value theorem. Maxima and minima, Fermat's theorem, extreme value theorem, related rates, L'Hospital's rule. Applications. Riemann sums, definite integral. Emphasis is on an analytical understanding. This course must be taken concurrently with Mathematics 081a.
    This course is for students who lack collegial Mathematics 103 or the equivalent.
    This course is required for all students in Mathematics, Physics and Computer Science.
    Students who have received credit for an equivalent course taken elsewhere may not register for this course.
    Credit will be given for only one of Mathematics 191a, 193ab, and 198ab.

    Mathematics 081a     Enriched Calculus Laboratory I     1-0-3
    A series of problems sessions and/or Calculus laboratory projects utilizing Computer Algebra Systems (CAS) technology. This course is designed to enhance the material covered in Mathematics 191a, and must be taken concurrently.

    Mathematics 192b     Enriched Calculus II     3-3-0
    Area. The definite integral. The Fundamental Theorem of Calculus. Techniques of integration. Volumes, centers of mass, moments of inertia, arclength and other applications of integration. Mean value theorem for integrals. Emphasis is on analytical understanding.
    This course must be taken concurrently with Mathematics 082b.
    Prerequisite: Mathematics 191a or a grade of at least 70% in Mathematics 198a or 80% in Mathematics 193ab.
    This course is for students who lack Collegial Mathematics NYB or the equivalent.
    This course is required for all students in Mathematics, Physics and Computer Science.
    Students who have received credit for an equivalent course taken elsewhere may not register for this course.
    Credit will be given for only one of Mathematics 191a, 193ab, and 198a.

    Mathematics 082b     Enriched Calculus Laboratory II     1-0-3
    A series of problems sessions and/or Calculus laboratory projects utilizing Computer Algebra Systems (CAS) technology. This course is designed to enhance the material covered in Mathematics 192b, and must be taken concurrently.
    Prerequisite: Mathematics 191a

    Mathematics 193ab     Calculus I (for Business and Economics students)     3-3-0
    Functions. Limits and continuity. Slope of tangent line. Derivative of a function. Derivatives of polynomial, exponential and logarithmic functions. Rules for sums, products, quotients. Chain rule. Maxima and minima. Introduction to integration: antiderivatives and area.
    Pre or Co-requisite: Mathematics 190a, CEGEP Math NYA or the equivalent
    Credit will be given for only one of Mathematics 191a, 193ab and 198ab.
    Students who have received credit for an equivalent course taken elsewhere may not register for this course.

    Mathematics 195ab     Calculus II (for Business and Economics Students)     3-3-0
    Review and extension of differentiation and integration. Implicit differentiation. Integration by substitution and parts. Separable first order differential equations. Riemann sums. Applications to areas, finance, etc. Introduction to matrix algebra.
    Prerequisite: Mathematics 193b or CEGEP Math NYA or the equivalent.
    Credit will be given for only one of Mathematics 192b, 195ab and 199b.
    Students who have received credit for an equivalent course taken elsewhere may not register for this course.

    Mathematics 198a     Calculus I (for Life Sciences)     3-3-0
    Elementary functions, limits, tangent line approximations. The derivative, and differentiation rules. Continuous optimization in one variable. Applications to Biology, Chemistry, Medicine and Environmental Science. The emphasis is on conceptual understanding and computational competency. This course must be taken concurrently with Mathematics 088ab.
    This course is intended for students who lack collegial Mathematics NYA or the equivalent.
    Students who have received credit for an equivalent course taken elsewhere may not register for this course.
    Credit will be given for only one of Mathematics 191a, 193ab, and 198ab.

    Mathematics 088a     Calculus (for Life Sciences) Laboratory I     1-0-3
    A series of problems sessions and/or Calculus laboratory projects utilizing Computer Algebra Systems (CAS) technology. This course is designed to enhance the material covered in Mathematics 198ab, and must be taken concurrently.

    Mathematics 199b     Calculus II (for Life Sciences)     3-3-0
    The definite integral, area, integration by substitution and parts. Applications to Biology, Chemistry, Medicine and Environment Science. Separable and linear differential equations. The emphasis is on conceptual understanding and computational competency.
    This course must be taken concurrently with Mathematics 089b.
    Prerequisite: Mathematics 198ab or 191a or the equivalent.
    This course is intended for students who lack collegial Mathematics NYB or the equivalent.
    Students who have received credit for an equivalent course taken elsewhere may not register for this course.
    Credit will be given for only one of Mathematics 192b, 195ab, and 199b.

    Mathematics 089b     Calculus (for Life Sciences) Laboratory II     1-0-3
    A series of problems sessions and/or Calculus laboratory projects utilizing Computer, Algebra Systems (CAS) technology. This course is designed to enhance the material covered in Mathematics 199b, and must be taken concurrently.
    Prerequisite: Mathematics 198ab or 191a or the equivalent.

    Mathematics 210a     Ordinary Differential Equations     3-3-0
    Techniques for solving first and second order linear differential equations. Systems of first order equations. Power series solutions for second order equations including the method of Frobenius. Various applications of differential equations.
    Prerequisite: Mathematics 106
    See Physics 270
    Students may not take this course for credit if they have received credit for Physics 270

    Mathematics 211b     Mathematical Methods of Physics     3-3-0
    Discussion of series solutions in connection with the gamma function and Bessel, Legendre and hypergeometric functions. Laplace transform with applications. Elementary trigonometric Fourier series and boundary value problems. Certain partial differential equations of physics.
    Prerequisites: Mathematics 210a
    See Physics 271
    Students may not take this course for credit if they have received credit for Physics 271

    Mathematics 213a     Introduction to Probability     3-3-0
    Discrete and continuous distributions. Moments, mean and variance. Moment generating functions. Multivariate distributions. Laws of large numbers. Sampling distributions. Central Limit Theorem.
    Prerequisite: Mathematics 106a

    Mathematics 214b     Introduction to Mathematical Statistics     3-3-0
    Further sampling distributions: Chi-square, t and F. Estimation, confidence intervals. Hypothesis testing, theory and practice. Regression and correlation. Analysis of Variance. Nonparametric methods.
    Prerequisite: Mathematics 213a

    Mathematics 215a     Real Analysis I     3-3-0
    Real number system. Completeness theorem. Sequences of real numbers. Bolzano- Weierstrass Theorem. Cauchy sequences. Series of real numbers. Limits. Continuous functions. Differentiation. Mean-Value Theorem. L'Hospital's rule. Riemann integration. Fundamental Theorem of Calculus.
    Prerequisite: Mathematics 107b.

    Mathematics 216b     Real Analysis II     3-3-0
    The generalized Riemann interal (improper integrals). Sequences and series of functions. Pointwise and uniform convergence. Power series. Taylor series. Classical theorems (integration, differentiation, Weierstrass M-test. Cauchy-Hadamard theorem). Equicontinuity. Ascoli-Arzela theorem. Stone-Weierstrass approximation theorem).
    Prerequisite: Mathematics 215a
    Offered alternately with Mathematics 217b

    Mathematics 217b     Complex Analysis     3-3-0
    Sequences and series of complex numbers. Functions. Limits. Continuous functions. Analytic functions. Cauchy-Riemann equations. Contour integration. Cauchy's theorem. Cauchy integral formula. Taylor and Laurent series. Singularities and residues.
    Prerequisite: Mathematics 215a.
    Offered alternately with Mathematics 216b

    Mathematics 221a     Introduction to Modern Algebra I     3-3-0
    Introduction to the theory of groups. Symmetries of a square. The dihedral groups. Cyclic groups, permutation groups. Isomorphisms, external and internal direct sums. Cosets and Lagrange's theorem. Factor groups.
    Prerequisite: Mathematics 105ab, Mathematics 109b

    Mathematics 222b     Introduction to Modern Algebra II     3-3-0
    Additional topics from group theory. Introduction to Ring Theory. Integral Domains and Fields. Factorization of Polynomials. Finite Fields. Introduction to Algebraic Coding Theory.
    Prerequisite: Mathematics 221a

    Mathematics 224     Cryptography     3-3-0
    Cryptography is a key technology in electronic security systems. The aim of this course is to explain the basic techniques of modern cryptography and to provide the necessary mathematical background. Topics may include: the classical encryption schemes, perfect secrecy, DES, prime number generation, public-key encryption, factoring, digital signatures, quantum computing.
    Prerequisites: Mathematics 105, 108
    Professor Brüstle

    Mathematics 225b     Numerical Methods     3-3-0
    Numerical techniques for problem solving in Mathematics, Computer Science and Physics. Error analysis, roots of equations, QR-algorithm, interpolation, Numerical approaches to differentiation, integration and solutions of differential equations.
    Prerequisites: Computer Science 111ab. Mathematics 107, 108.
    Note: See CSC 275 and Phy 275.
    Students may not take this course for credit if they have received credit for Computer Science 275 or Physics 275.

    Mathematics 226a     Mathematical Problem Solving     3-3-0
    A course designed to foster problem solving abilities in mathematics. New mathematical concepts will be introduced to the student through solving specific problems. Problems will be taken from Putnam and Mathematics Olympiad competitions and from actuarial examinations.
    Prerequisites: Mathematics 107, 108

    Mathematics 271b     Econometrics II     3-3-0
    Ordincary least-square estimation and hypothesis testing using matrix algebra. The topics include: generalised least squares estimation, distributed (eg. models, two-stage) least squares estimation, and the Granger causality test.
    See EMA 361b
    Students may not take this course for credit if they have received credit for EMA 361b.

    Mathematics 272b     Mathematical Economics II     3-3-0
    The application of differential and difference equations, and mathematical programming, to model building and problem solving in Economics.
    See EMA 362b
    Students may not take this course for credit if they have received credit for EMA 362b.

    Mathematics 275b     Theoretical Aspects of Computer Science     3-3-0
    The course will include several of the following topics: Computational models; Computational complexity; Finite-state machines; Context-free languages; Pushdown automata; Turing machines; Undecidable problems.
    Prerequisite: Math 105
    See Computer Science 305b
    Students may not take this course for credit if they have received credit for Computer Science 305b.

    Mathematics 277a     Design and Analysis of Algorithms     3-3-0
    This course is intended to make students familiar with most of the existing techniques for problem solving. It starts with an introduction to algorithms efficiency, solving recurrence relations and basic data structures. Then different techniques for algorithms design are discussed; the divide-and-conquer technique, the greedy technique and its applications to graph algorithms, dynamic programming, backtracking and genetic algorithms. At the end, students are briefly introduced to the vase area of "difficult" problems, or NP-complete.
    Prerequisite: Computer Science 204 and Mathematics 105.
    See Computer Science 217a.
    Students may not take this course for credit if they have received credit for Computer Science 217a.

    Mathematics 278b     Advanced Mechanics     3-3-0
    Dynamics of macroscopic bodies. Newtonian gravitation: planetary orbits; tides. Elasticity; the flexure of elastic bodies. Relativistic dynamics of particles. The Lagrangian and Hamilton's Principle.
    Prerequisite: Physics 117a, Mathematics 210a
    Offered alternate years
    See Physics 218b
    Students may not take this course for credit if they have received credit for Physics 218b.

    Mathematics 279b     Scientific Programming     3-3-3
    This course is designed as an introduction to programming languages and environments suitable for the numerically intensive applications in the natural sciences and mathematics. Examples will be given to illustrate the use of Fortran in numerical calculations. Other examples will be tackled using the Maple language initially developed to handle problems in symbolic computation.
    Prerequisite: CSC 204, Math 191, Math 192
    See Computer Science 208b, Physics 278B
    Students may not take this course for credit if they have received credit for Computer Science 208b or Physics 278b.

    Mathematics 301b     Vector Analysis     3-3-0
    Algebra of vectors. Vector-valued functions. Vector differential and integral calculus. Theorems of Gauss, Green and Stokes. Differential forms. Differentiability in Rn. Inverse function theorem.
    Prerequisite: Mathematics 107b.

    Mathematics 302b     Tensor Analysis     3-3-0
    General curvilinear coordinates. Differential forms. Bilinear forms and tensors of rank two. Tensor algebra and tensor calculus.
    Prerequisite: Mathematics 301a.

    Mathematics 305b     Calculus of Variations     3-3-0
    Euler-Lagrange equations for constrained and unconstrained single and double integral variational problems. Parameter-invariant single integrals. General variational formula. The canonical formalism. Hilbert's independent integral. Hamilton-Jacobi equation and the Cavatheodory complete figure. Fields and the Legendre and Weierstrass sufficient conditions.
    Prerequisites: Mat 107, Mat210
    See Physics 276
    Students may not take this course for credit if they have received credit for Physics 276

    Mathematics 306b     Differential Geometry     3-3-0
    Curves in 3-space. Euclidean motions, surface theory. Introduction to differential manifold, Guassian and mean curvature, imbedding conditions. Geodesics, parallel transport and the Gauss-Bonet Theorem.
    Prerequisite: Mat 107, Mat 210

    Mathematics 321a     Graph Theory     3-3-0
    An introduction to the combinatorial, algorithmic and algebraic aspects of graph theory.
    Prerequisite: Mat 105
    Note: See CSC371. Students may not take this course for credit if they have received credit for CSC371.

    Mathematics 331b     Metric Spaces and Topology     3-3-0
    Sets, functions, images and preimages. Topological spaces, metric spaces. Open and closed sets, accumulation points, continuous functions, homeomorphisms. Some topological properties, particularly connectedness and compactness.
    Pre-requisite: Mathematics 215a, or consent of the instructor.

    Mathematics 333b     Infinite Abelian Groups     3-3-0
    Structure of finite abelian groups, examples of infinite abelian groups, torsion and torsion- free groups, divisible groups, pure subgroups, algebraically compact groups, classification of torsion-free groups of rank 1. Generalizations of group concepts to modules over a principal ideal ring.
    Prerequisite: Mathematics 221a, 222b

    400 level courses are for Honours students only

    Mathematics 450a, 451b     Topics in Algebra I and II     3-3-0
    A selection is made to suit the interests of students from such topics as: ring theory, introduction to homological algebra, introduction to group representations or commutative algebra.
    Prerequisite: Mathematics 109b, 222b or consent of instructor.
    Offered by arrangement.

    Mathematics 452a     Topics in Analysis I     3-3-0
    Normed spaces, Banach and Hilbert spaces, Hilbert space operators, Normed algebras, Stone-Weierstrass theorem. Special function spaces.
    Prerequisite: Mathematics 216b.

    Mathematics 453b     Topics in Analysis II     3-3-0
    Theory of integration. Measurable functions, measures and integrable functions. Lebesque spaces. Models of convergence. Decomposition and generation of measures. Product measures.
    Prerequisite: Mathematics 216b.
    Offered by arrangement.
    Mathematics 454a, 455b     Topology Offered by arrangement.  
      
    Mathematics 456a     Independent Studies I     3-0-0
    Open to final year honours students by arrangement with the department.

    Mathematics 457b     Independent Studies II     3-0-0
    See Mathematics 456a.

    Cognate Courses:
    Philosophy 151 may count as a cognate for the Honours or Major program.

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