Logic, sets and functions, algorithms, mathematical reasoning, counting, relations, graphs, trees, Boolean Algebra, computation, modeling.

in each case with at least 60%, and 1.0 courses with at least 60% in each from:

or the former Applied Mathematics 1411A/B,

or the former Applied Mathematics 1412A/B,

or the former Applied Mathematics 1414A/B, or the former Applied Mathematics 1413.

This course provides an introduction to logical reasoning and proofs. Topics include sets, counting (permutations and combinations), mathematical induction, relations and functions, partial order relations, equivalence relations, binary operations, elementary group theory and applications to error-correcting codes.

the former Applied Mathematics 1412A/B, the former Applied Mathematics 1414A/B, the former Applied Mathematics 1413, in each case with a minimum mark of 60%; or permission of the department.

with a minimum mark of 60% can be used in place of

This course presents an introduction to the mathematical foundations of computer science, with an emphasis on mathematical reasoning, combinatorial analysis, discrete structures, applications and modeling, and algorithmic thinking. Topics include sets, functions, relations, algorithms, number theory, matrices, mathematical reasoning, counting, graphs and trees.

Matrix operations, systems of linear equations, linear spaces and transformations, determinants, eigenvalues and eigenvectors, applications of interest to Engineers including diagonalization of matrices, quadratic forms, orthogonal transformations; introduction to MATLAB with applications from linear algebra.

Ontario Secondary School MHF4U or MCV4U, or

the former Applied Mathematics 1412A/B, the former Applied Mathematics 1413.

Introduction to complex numbers, limits, continuity, differentiation of functions of one variable with applications, extreme values, l’Hospital’s rule, antiderivatives, definite integrals, the Fundamental Theorem of Calculus, the method of substitution.

Ontario Secondary School MCV4U or equivalent, or

the former Applied Mathematics 1413, the former Applied Mathematics 1414A/B.

Techniques of integration, areas and volumes, arclength and surfaces of revolution, applications to physics and engineering, first order differential equations, parametric curves, polar coordinates, sequences and series, vectors and geometry, vector functions, partial differentiation with applications.

or Calculus1500A/B, or the former Applied Mathematics 1412A/B.

A continuation for Engineering Science 1036A/B. Data organization and manipulation; abstract data types and their implementations in the C programming language; lists, stacks, queues, trees; pointers; recursion; file handling and storage. Intended for students in the Faculty of Engineering.

Review of limits and derivatives of exponential, logarithmic and rational functions. Trigonometric functions and their inverses. The derivatives of the trig functions and their inverses. L'Hospital's rules. The definite integral. Fundamental theorem of Calculus. Simple substitution. Applications including areas of regions and volumes of solids of revolution.

An enriched version of Calculus 1000A/B. Basic set theory and an introduction to mathematical rigour. The precise definition of limit. Derivatives of exponential, logarithmic, rational trigonometric functions. L'Hospital's rule. The definite integral. Fundamental theorem of Calculus. Integration by substitution. Applications.

Applications of integration, integration using mathematical software packages. Scaling and allometry. Basic probability theory. Fundamentals of linear algebra: vectors, matrices, matrix algebra. Difference and differential equations. Each topic will be illustrated by examples and applications from the biological sciences, such as population growth, predator-prey dynamics, age-structured populations.

or the former Applied Mathematics 1412A/B.

the former Physics 1029A/B, and the former Physics 1302A/B;

Explore foundational topics in astronomy, biology, chemistry, computer science, earth science, mathematics, and physics through an integrated questions-based approach. Small-group interactions and interdisciplinary laboratory experiments are designed to foster teamwork, interdisciplinary thinking, and the development problem-solving and critical-thinking skills.

Enrolment in Year 1 of the Western Integrated Science program and a minimum of 60% in each of

For students requiring the equivalent of a full course in calculus at a less rigorous level than Calculus 1501A/B.  Integration by parts, partial fractions, integral tables, geometric series, harmonic series, Taylor series with applications, arc length of parametric and polar curves, first order linear and separable differential equations with applications.

Properties and applications of vectors; matrix algebra; solving systems of linear equations; determinants; vector spaces; orthogonality; eigenvalues and eigenvectors.

One or more of Ontario Secondary School MCV4U,

A continuation for both Computer Science 1025A/B and Computer Science 1026A/B. Data organization and manipulation; abstract data types and their implementations in a modern programming language; lists, stacks, queues, trees; recursion; file handling and storage.

(in each case with a mark of at least 65%).

Students who intend to pursue a degree in Actuarial Science, Applied Mathematics, Astronomy, Mathematics, Physics, or Statistics should take this course. Techniques of integration; The Mean Value Theorem and its consequences; series, Taylor series with applications; parametric and polar curves with applications; first order linear and separable differential equations with applications.

or the former Computer Science 2101A/B, in each case with at least 65%, and 1.0 course with at least 60% in each from:

the former Applied Mathematics 1411A/B, the former Applied Mathematics 1412A/B, the former Applied Mathematics 1414A/B, the former Applied Mathematics 1413; or 2)

COMPSCI 2214A/B

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