MATHEMATICS

Most college level mathematics courses have as prerequisite High School Math 536, or equivalent. The first mathematics course students take at Vanier depends on their high school mark. Students are advised to consult the placement chart.

Courses in the pre-university program should be selected in accordance with the following guidelines:

a) Science Students
All science students are required to take Calculus I (201-NYA), Calculus II (201-NYB), and Linear Algebra (201-NYC). Students with a grade between 60% and 69% in Math 536 should first take Introduction to College Mathematics (201-HSG-05). Additional courses such as 201-HTH, 201-HTG, 201-HTJ, and 201-HTK may be selected depending on the student's interest. However, 201-HTJ is strongly recommended for students intending to study Engineering or the Physical Sciences at university.

b) Social Science
Mathematics has become an important tool for students in all areas of the social sciences. Complementary Topics in QM (Statistics) (201-300) is a required course for students planning to major in Psychology. Other students will find that statistics and the mathematics program recommended for commerce students provides a strong foundation for university studies.

c) Commerce
Calculus I (201-103), Calculus II (201-203), and Linear Algebra (201-105) are prerequisites for admission to most Quebec University Commerce Programs.

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201-007-50
FUNCTIONS I
Prerequisite: Math 314
Class: 6 hrs./wk.
This course is equivalent to High School Math 436. Topics are selected from basic algebra, relations, and functions. They include: variables, polynomials, operations on polynomials, factoring, simplification of algebraic expressions, solution of quadratic equations, relations, functions, Cartesian coordinate system, slope, and line.

201-009-50
FUNCTIONS II
Prerequisite: Math 436 or equivalent
Class: 5 hrs./wk.
This course is equivalent to High School Math 536. Topics are selected from functions, trigonometry, exponents and logarithms. They include: degrees, radians, arc length, trigonometric values with and without calculators, identities (including double angle formulas), simplification of trigonometric expressions, sine and cosine laws, graphing, properties and graphs of logarithmic and exponential functions, graphing of quadratic, absolute value, square root functions, circle, parabola.

201-103-VA (Social Science/Commerce), 201-NYA-05 (Science)
CALCULUS I
Credits: 2.66
Prerequisite: Math 536 or equivalent
Recommended: Science students with a grade between 60% and 69% in Math 536 or equivalent should first take 201-HSG-05.
Class: 5 hrs./wk.
Note: Science students and Social Science/Commerce students will register in separate sections.
This course provides an understanding of the fundamental notions of differential calculus. It introduces the concept of limit, continuity and the derivative with its applications.

201-105-VA (Social Science/Commerece), 201-NYC-05 (Science)
LINEAR ALGEBRA
Credits: 2.66
Prerequisite: Math 536 or equivalent
Class: 5 hrs./wk.
Note: Science students and Social Science/Commerce students will register in separate sections.
The aim of this course is to teach the student to understand and perform computations involving vectors, matrices, and systems of linear equations. The properties of geometrical vectors in two and three dimensions will be used to motivate similar results in higher dimensions. Systems of equations will be studied in terms of lines, planes, and hyperplanes. Dot products, cross products, and determinants will be used extensively.

201-122-VA
APPLIED MATHEMATICS
Credits: 2.66
Prerequisite: Math 536 or equivalent
Class: 4 hrs./wk.
For students in the Computer Science Technology program.
The student will become acquainted with the principal mathematical concepts used in this field. Topics include: exponential and logarithmic functions, calculus of errors, vectors, matrices, systems of linear equations, linear programming, and combinations.

201-171-92
MATHEMATICAL MODELS I
Credits: 2.66
Prerequisite: Math 436 or equivalent
Class: 5 hrs./wk.
For students in the Industrial Electronics and Digital Systems Technology programs.
This course will emphasize the application of several mathematics topics such as: vectors, complex numbers, exponentials, and logarithms, together with some trigonometry.

201-203-77 (Social Science/Commerce), 201-NYB-05 (Science)
CALCULUS II
Credits: 2.66
Prerequisite: 201-103 or 201-NYA
Class: 5 hrs./wk.
Note: Science students and Social Science/Commerce students will register in separate sections.
This course deals primarily with integral calculus and its applications. Other topics include a further development of limits (l'Hôpital's Rule), sequences and series, the solution of simple differential equations, and numerical integration.

201-HTK-05
LINEAR ALGEBRA II
Credits: 2.66
Prerequisite: 201-105
Class: 5 hrs./wk.
Linear algebra has a wide range of applications in physical sciences, life sciences, social science, and business. This course will investigate some of the general concepts which give the subject its power and flexibility; for example, linear transformations, characteristic vectors, preferred coordinate systems, orthogonal transformations, convexity, and so forth. Possible applications include: linear programming, stochastic processes, and differential equations.

201-217-78
BIOMETRY
Credits: 2.00
Prerequisite: Math 436 or equivalent
Class: 4 hrs./wk.
For students in the Natural Science Technology program, ecology option.
This course deals with statistical methods applied to biological research, descriptive statistics, probability, the binomial theorem, Poisson, chi-square, normal, t and F distributions, analysis of variance, correlation, and regression.

201-257-82
STATISTICS
Credits: 2.66
Prerequisite: 201-122
Class: 4 hrs./wk.
For students in the Computer Science Technology program.
Topics include: descriptive statistics, probability, statistical inference, correlation coefficients, chi-square test, and an introduction to time series.

201-271-92
MATHEMATICAL MODELS II
Credits: 2.66
Prerequisite: 201-171
Class: 5 hrs./wk.
For students in the Industrial Electronics and Digital Systems Technology programs.
This course demonstrates the use of calculus in the solution of problems in electronics. Topics include: techniques in differentiation, first and second derivative applications, maxima and minima, simple differential equations, and integrals.

201-300-94 
COMPLEMENTARY TOPICS IN QUANTITATIVE METHODS
Credits: 2.00
Prerequisite: 360-300-91
Class: 3 hrs./wk.
Required for students majoring in Psychology.
The objective of this course is to cover those topics in statistics which are not covered in Quantitative Methods (360-300-91). Topics include: probability, random variables, hypothesis testing, confidence intervals, and chi-square tests.

201-HTJ-77
CALCULUS III
Credits: 2.66
Prerequisite: 201-NYB
Recommended co-requisite: 201-NYC
Class: 5 hrs./wk.
The topics developed are applied widely in the physical sciences and elsewhere. They may include: hyperbolic functions and their inverses, functions of several variables, partial derivatives, increments, the chain rule, multiple integration with applications, differential equations, solutions of certain first and second order equations with applications, and the Laplace transform with applications.

Note: Students planning to enter University Engineering or Physical Science Programs are strongly urged to take this course.

201-HTH-05
PROBABILITY AND STATISTICS
Credits: 2.66
Prerequisite: 201-NYA
Recommended co-requisite: 201-NYB
Class: 5 hrs./wk.
This course is offered for students who know Calculus (differentiation and integration). It deals with sample spaces, combinatorics, discrete and continuous random variables, the most important probability distributions, descriptive and inferential statistics.

201-HTG-05
NUMERICAL METHODS
Credits: 2.66
Prerequisite: 201-NYA, 201-NYC
Class: 5 hrs./wk.
This course studies methods for finding the approximate solutions to mathematical problems, and the evaluation of these approximate solutions by computer. Topics will be chosen from the following: approximating roots of functions, matrices and linear equations, numerical integration, statistical, and Monte Carlo methods.

201-HTL-05
DIFERENTIAL EQUATIONS
Credits: 2.66
Prerequisite: 201-NYB
Class: 5 hrs./wk.

201-702-85
INTRODUCTION TO APPLIED MATHEMATICS
Credits: 2.66
Prerequisite: Math 436 or equivalent
Class: 5 hrs./wk.
This course is designed for students in the Building Systems Engineering Technology and Architectural Technology programs.

Topics most relevant to the student's technology program will be chosen from among the following: logarithmic functions and their applications, systems of equations and their applications, complex numbers and their applications, and vector analysis. Emphasis will be placed on applying mathematics to a variety of concrete situations.

201-HSG-05
INTRODUCTION TO COLLEGE MATHEMATICS
Credits: 2.66
Prerequisite: High School Math 536 or equivalent
For Science students who obtained between 60% and 69% in High School Math 536 or equivalent.
Class: 5 hrs./wk.
The purpose of this course is to lay the foundations for successful studies in College Science programs.

Core topics include: analytic geometry, polynomials and their roots, exponential and logarithmic functions, trigonometry and trigonometric functions. Some of the following topics may be added: conics, complex numbers, mathematical induction, combinatorics, and the Binomial Theorem.

Algebraic skills will be reinforced throughout the course.



COMPLEMENTARY
COURSES

201-HTA-03
MATHEMATICS IN EVERYDAY LIFE (BLOCK 2)
Credits: 2.00
Class: 3 hrs./wk.
This course is intended to give students the tools necessary to apply mathematics to situations in their everyday life. Topics include ratio and percent, discounts and markups, interest, mortgages, and annuities. Students will learn to use their calculator efficiently and to analyze information given by banks and the media.

201-HSC-03
MATHEMATICAL TOOLS FOR USE IN THE LIFE SCIENCES
(BLOCK 2)
Credits: 2.00
Class: 3 hrs./wk.
The topics in this course will be directly related to those used by nurses in the practice of their profession. Students will solve problems on the calculation of dose and dosage, flow rates, concentration and dilutions. Students will study basic statistics and use their knowledge to analyze tables and other statistical information found in medical journals.

201-HSB-03
DRAWING AND GEOMETRY
IN ART
Credits: 2.00
Class: 3 hrs./wk. Students will explore geometric drawing with different tools: grids, ruler, compass, setsquare, protractor and, as well, graphic software (e.g. Cabri). During this journey through the World of Geometry, they will meet puzzles on grids, triangles with their linear and circular curiosities, "golden" figures, regular polygons and flower-petals, fractal objects such as Sierpinski's triangle and Koch's snowflake, exotic curves as conics (parabola, ellipse, hyperbola), cardioids (hearts), astroids (stars). Finally students will practice periodical drawings, analyse Escher's works and create their own tessellation (periodical covering) of the plane.