THE UNIVERSITY OF MANITOBA
Department of Mathematics:
1000 Level Courses
Faculty of Science
information for prospective students
• published by the Dean’s Office, Faculty of Science •
Introduction
What to do if you lack the prerequisites
The Department of Mathematics offers a wide
variety of 1000 level courses that a student may wish to
take in Year 1. These courses are designed to meet a
variety of needs: to help meet the requirement that all
students take at least a half-course with substantial
university level mathematics content; to meet the
developmental requirements of students with weak
backgrounds in mathematics; and to provide service to
the diverse groups of students who require half-courses
in calculus or linear algebra, whether in preparation for
entry into a professional program or in preparation for
academic programs requiring mathematics.
A listing of these 1000 level courses follows.
These courses are listed under the Department of
Mathematics in the University of Manitoba
Undergraduate Calendar. An abridged copy of the
calendar listings is found in this infosheet; this includes
prerequisites, which are not the same for all courses.
Because there are so many 1000 level courses, choosing
the right course(s) for your needs may seem difficult.
This document will provide guidance to you as you
make your choices. You can obtain help by phoning
(204) 474-8703 or by email:
mathematics_dept@umanitoba.ca.
Some students need to take introductory
calculus, and perhaps MATH 1300 or MATH 1310, to be
eligible to enter certain faculties or programs. A
student in this position, but lacking a grade of 60% or
better in Mathematics (Precalculus) 40S, can proceed as
follows. Register in "Mathematical Skills" (see below) in
Fall Term and earn a "C" or better. Then register in
calculus (and one of MATH 1300 and MATH 1310 if your
program requires it) in Winter Term. The courses MATH
1500 and MATH 1300 will also be taught in May and
June, so another possibility would be to take one of
them in Winter Term and the other in May and June.
The two "special situations" in which Applied
Mathematics 40S can be used as a prerequisite are
these: a student with a grade of 70% or better in
Applied Mathematics 40S can use this (instead of
Mathematics (Precalculus) 40S) as a prerequisite for
either MATH 1300 or MATH 1310. Such students could
(if they need to) take MATH 1300 or MATH 1310,
together with the "Mathematical Skills" course, in Fall
Term, and then (assuming they receive a grade of "C" or
better in Mathematical Skills) take an introductory
calculus course (MATH 1500 or MATH 1520) in Winter
Term.
Prerequisites:
The Mathematical Skills Course
A grade of 60% or better in Precalculus 40S is the
pre-requisite for entry into all 1000 level courses
numbered MATH 1200 and above (with minor
exceptions for MATH 1300 and MATH 1310; see the
section below and the detailed Course Descriptions
beginning on page 5). See Chart 1 on page 3 for more
information.
Note that Applied Mathematics 40S cannot be
substituted for Precalculus 40S for this purpose, except
in two very special situations described below.
The Extended Education Division at the
University of Manitoba offers the non-credit course,
“Mathematical Skills.” This course is designed for, but
not exclusive to, students preparing to enter first year
mathematics courses at the University of Manitoba. For
registration information call Student Services at 4748016 (or Manitoba toll free at: 1-888-261-7011
extension 8016).
Department of Mathematics ⋅ Page 1
THE UNIVERSITY OF MANITOBA
Choosing courses
Students deciding which mathematics courses
to take at University should consider two factors:
•
their aptitude for mathematics and how well they
know their high school mathematics
One's grade in the high school course Mathematics
PreCalculus 40S (or its equivalent from outside
Manitoba) will be a good indication of that. Chart I
on page 3 provides advice on course selection
based on this factor.
•
the program of studies they plan to follow
Chart II on page 4 provides advice based on this
factor. Students should consult the University's
annual Undergraduate Calendar for more detailed
advice concerning their planned programs of study.
MATH 0500
The Department of Mathematics has developed
two new programs available, on a voluntary basis, to all
students registered in Mathematics courses 1200, 1210,
1300, 1310, 1500, 1510, 1520, 1700, and 1710.
The diagnostic test is a voluntary on-line 50question test, whose purpose is to measure your
potential for success in the above Mathematics courses.
The questions test your knowledge and skill in topics
contained in the high school mathematics curriculum,
principally Pre-Calculus 40S. The test provides you with
an assessment of your knowledge and skill level, and
provides advice about actions you should take in order
to increase your chances of success in mathematics
courses.
Access to the Mathematics Diagnostic Test is
gained from your personal WebCT Homepage.
If your results on the diagnostic test indicate that
you would benefit by improving your mathematical
skills, you should purchase a copy of the notes prepared
for this purpose, entitled “Preparing for University
Mathematics”. Enroll in one of sections of the noncredit course MATH 0500 “Preparing for University
Mathematics.” This course will be offered on Saturday
mornings (9:00 am until noon) during the first half of
the school term. Enrollment in each section will be
limited to 25 students. During these sessions a
graduate student from the Department of Mathematics
will serve as a tutor.
Courses included in the program
A three credit course, also called a half course,
runs over one term. A six credit course or full course
spans two terms. The courses marked with an * are also
available en français at Collège universitaire de SaintBoniface. (Credit hours are indicated in parenthesis.)
MATH 1010 Applied Finite Mathematics (3)
MATH 1020 Mathematics and Art (3)
MATH 1190 Topics in Mathematics (6)
MATH 1200 Elements of Discrete Mathematics* (3)
MATH 1210 Techniques of Classical & Linear Algebra (3)
MATH 1300 Vector Geometry & Linear Algebra* (3)
MATH 1310 Matrices for Management & Social Sciences (3)
MATH 1500 Introduction to Calculus* (3)
MATH 1510 Applied Calculus I (3)
MATH 1520 Introductory Calculus for Management &
Social Sciences (3)
MATH 1700 Calculus II* (3)
MATH 1710 Applied Calculus II (3)
Notes on Courses
MATH 1010, MATH 1020 and MATH 1190
The courses MATH 1010, Applied Finite
Mathematics, MATH 1020, Mathematics in Art, and
MATH 1190, Topics in Mathematics, are general interest
courses. Students without a strong mathematics
background, or without prerequisites for other
mathematics courses, are encouraged to take either
MATH 1010, MATH 1020 or MATH 1190 to fulfill the
University requirements that all students must have 3
credit hours in a course with a substantial mathematical
content. (MATH 1020 is taught with School of Art FA
1020 and has limited enrollment.) Students entering
any program that uses mathematics are urged to select
courses from those with course numbers MATH 1200 or
higher. NOTE: Students holding credit in MATH 1200
or higher cannot take these three courses.
Department of Mathematics ⋅ Page 2
THE UNIVERSITY OF MANITOBA
CHART I: Choosing University Mathematics courses based on Senior 4 courses
Mathematics
Pre-Calculus 40S
mark in percentage
(or equivalent)
Best choice of University mathematics course
No Pre-Calculus 40S or
less than 60%
You can take MATH 1010, MATH 1020 or MATH 1190. To take any other
University mathematics course, take the Math Skills course from Continuing
Education (a non-degree, non-credit course) or take/repeat Pre-calculus 40S
through a school division or by correspondence.
60% - 69%
You are eligible to take any of the first year mathematics courses, but are
likely to experience some difficulties with many parts of these courses. You
may benefit from taking the Mathematical Skills course from Continuing
Education before attempting any course numbered MATH 1200 or above.
Alternately, some of the introductory courses (MATH 1310, MATH 1500 and
MATH 1520) have "developmental" sections, in which there are extra classes
devoted to review. You should consider enrolling in a developmental
section.
70% - 79%
You are eligible to take any of the first year Mathematics courses but some
concern about your basic mathematical skills may still be appropriate. You
might choose to enroll in a "developmental" section (see above).
80% - 100%
You are eligible to take any of the first year Mathematics courses. Assuming
you have good study skills and work habits, you should succeed in any
introductory course.
Applied Mathematics 40S
mark in percentage
70 - 100%
You can take MATH 1010, MATH 1020, MATH 1190, MATH 1300 or MATH
1310. To take any other University mathematics course, take the Math Skills
course from Continuing Education, or Pre-Calculus 40S through a school
division or by correspondence.
Department of Mathematics ⋅ Page 3
THE UNIVERSITY OF MANITOBA
CHART II: Choosing your mathematics course by your intended program of study
ABBREVIATIONS: In what follows, "MATH 13A0" means either MATH 1300 or MATH 1310; "MATH 15A0" means one of MATH 1500,
MATH 1510 or MATH 1520; and "MATH 17A0" means one of MATH 1700 or MATH 1710.
Recommended courses
(see Remark 1 on next page)
Intended program of study
Required courses for entry to program
Faculty of Agricultural & Food
Sciences
See Faculty of Agricultural and Food Sciences
section of the Undergraduate Calendar
Faculty of Arts
3 credit hours from list of approved
mathematics courses (see Faculty of Arts
section of the Undergraduate Calendar)
MATH 1010 or MATH 1190
Faculty of Arts
(Honours Economics)
6 credit hours from MATH 13A0, MATH 15A0 or
MATH 17A0 (see Remark 3 on next page)
MATH 1300 and MATH 1500
Faculty of Engineering
MATH 1210, MATH 1510 and MATH 1710
MATH 1210, MATH 1510 and
MATH 1710
Clayton H. Riddell
Faculty of Environment, Earth
and Resources
(Geophysics Honours)
MATH 1210, MATH 15A0 and MATH 17A0,
(see Remarks 3 and 4 on next page)
MATH 1210, MATH 1500 and
MATH 1700
Faculty of Management
(non Actuarial pattern)
MATH 15A0 (see Remarks 3 and 4 on next
page)
MATH 1520
Faculty of Management
(Actuarial pattern)
MATH 15A0
(see Remarks 3 and 4 on next page)
MATH 1300, MATH 1500 and
MATH 1700
Faculty of Pharmacy
MATH 15A0
MATH 1500
Faculty of Science
(Honours Biological Sciences)
(see note following Chart I)
MATH 1200, MATH 1300 or MATH
1500 (see Remark 1 on next page)
Faculty of Science
(Biochemistry, Chemistry)
MATH 15A0 and MATH 17A0
(see Remarks 3 and 4 on next page)
MATH 1500 and MATH 1700
Faculty of Science
(Computer Science)
MATH 13A0 and MATH 15A0
(see Remark 3 on next page)
MATH 1300 and MATH 1500
Faculty of Science
(Mathematics major)
MATH 13A0, MATH 15A0 and MATH 17A0
(see Remarks 3 and 4 on next page)
MATH 1300, MATH 1500 and
MATH 1700; perhaps also MATH
1200
Faculty of Science
(Physics)
MATH 13A0, MATH 15A0 , MATH 17A0 and
MATH 1200 is required for the Major
(see Remarks 3 and 4 on next page)
MATH 1300, MATH 1500 and
MATH 1700
Faculty of Science
(Statistics major)
MATH 1200, MATH 13A0, MATH 15A0 and
MATH 17A0 (see Remarks 3 and 4 on next
page)
MATH 1300, MATH 1500 and
MATH 1700
Fine Arts
3 credit hours
MATH 1020
Department of Mathematics ⋅ Page 4
THE UNIVERSITY OF MANITOBA
Remarks
1. Recommendations are indicated where there is a
choice among required courses or where it is
advisable that a course be taken in first year.
Students intending to enter a specific faculty and/or
major program within that Faculty are urged to
consult the University of Manitoba Undergraduate
Calendar and/or representatives of the
Faculty/program in question, for more information.
2. MATH 1500 and MATH 1510 are always
interchangeable as prerequisites for later courses in
Mathematics, as are MATH 1700 and MATH 1710.
Other departments and faculties may not provide
similar flexibility in the use of our courses as
prerequisites and corequisites for their courses and
programs. You are advised to consult their
prerequisite and corequisite requirements as
described in the University of Manitoba
Undergraduate Calendar.
3. Students planning to study Linear Algebra beyond
Year I are advised to elect MATH 1300. Students
who intend to take more than 3 credit hours of
Year I calculus are advised to take MATH 1500, or
MATH 1510, rather than MATH 1520.
4. MATH 1510 has the high school course Physics 40S
as a prerequisite. MATH 1710 has the University
physics course PHYS 1050 as a corequisite.
Examples drawn from physics will be used in these
courses.
5. For details regarding Mathematics prerequisites for
entry to the Honours and Major programs see the
University Undergraduate Calendar.
Course descriptions
This is an abridged version of course descriptions of the
1000 level Mathematics courses found in the University
of Manitoba Undergraduate Calendar. A complete list of
all undergraduate mathematical sciences courses which
are presently approved by Academic Senate is available
in the University of Manitoba Undergraduate Calendar.
NOTE: Unless otherwise specified, a minimum grade of
“C” must be achieved for any course stipulated as
prerequisite to a further course in Mathematics.
MATH 1010 Applied Finite Mathematics (3)L
For students needing to fill the requirement of a
university level mathematics course. This course
introduces students to modern applications of
discrete mathematics. Topics include: mathematics
of finance, linear programming, graph theory and
game theory. This course cannot be used as part of
an Honours, Major, General or Minor program in
the Mathematical Sciences.
MATH 1020 Mathematics in Art (3)
For students needing to fill the requirement of a
university level mathematics course. It introduces
students to mathematical methods and principles in
works of art in relation to Euclidean and nonEuclidean geometrics. Topics include: linear
perspective; shapes, patterns and balance;
proportion, ratio and harmony; symmetry,
geometry, and the study of different surfaces. This
course has limited enrollment. It may not be used as
part of an Honours, Major, General or Minor
program in the Mathematical Sciences.
MATH 1190 Topics in Mathematics (6)
This course is designed to give students in various
faculties a measure of insight into modern
mathematics. Topics are taken from number
systems, geometry and combinatorics. This is a
terminal course and may not be used as a
prerequisite for other Mathematics courses. It may
not be used as part of an Honours, Major, General
or Minor program in the Mathematical Sciences.
MATH 1200 Elements of Discrete Mathematics (3)
Sequences and series, trigonometry, complex
numbers, algebra of polynomials, approximation of
zeros of functions, linear difference equations.
Prerequisite: a minimum grade of 60% in Math PreCalculus 40S (300), or grade of “C” or better in the
Mathematical Skills course taught by the Continuing
Education Division. Not to be held with MATH 1210.
Department of Mathematics ⋅ Page 5
THE UNIVERSITY OF MANITOBA
MATH 1210 Techniques of Classical & Linear
Algebra(3)L
An introduction to a variety of practical algebraic
concepts and skills necessary for the study of
calculus and advanced engineering mathematics.
The emphasis of this course is in the development
of methodology and algebraic skill necessary for
successful completion of subsequent engineering
mathematics courses. Applications in this course
make it especially suitable for students intending to
take programs in Engineering. Not to be held with
MATH 1200, 1300, or MATH 1310. Prerequisite: a
minimum grade of 60% in Math Pre-Calculus 40S
(300) or a grade of “C” in the Mathematical Skills
course taught by the Continuing Education Division.
MATH 1300 Vector Geometry and Linear Algebra (3)L
An introduction to vectors, matrices, systems of
linear equations and three-dimensional geometry.
Not to be held with MATH 1210 or MATH 1310.
Prerequisite: a minimum grade of 60% in Math PreCalculus 40S (300), or a minimum grade of 70% in
Applied Math 40S, or grade of “C” in he
Mathematical Skills course taught by the Continuing
Education Division.
MATH 1310 Matrices for Management & Social
Sciences (3)L
Matrix methods with examples relevant to the
Management and Social Sciences. Topics include
vectors, matrices, systems of linear equations and
determinants; applications include economic
models, the simplex method for linear
programming, Markov chains, and game theory.
Not to be held with MATH 1210 or MATH 1300.
Prerequisite: a minimum grade of 60% in Math PreCalculus 40S (300), or a minimum grade of 70% in
Applied Math 40S , or a grade of “C” in the
Mathematical Skills course taught by the Continuing
Education Division.
MATH 1500 Introduction to Calculus (3)L
Differentiation and integration of elementary
functions, with applications to maxima and minima,
rates of change, area and volume. Not to be held
with MATH 1510 or MATH 1520. Prerequisite: a
minimum grade of 60% in Math Pre-Calculus 40S
(300) or a grade of “C” in the Mathematical Skills
course taught by the Continuing Education Division.
MATH 1510 Applied Calculus (3)L
Functions and graphs, limits and continuity,
differentiation of functions defined explicitly and
implicitly; applications of derivatives to velocity and
acceleration, related rates, maxima and minima;
differentials, indefinite and definite integrals.
Physical applications in this course make it
especially suitable for students intending to take
programs in engineering. Not to be held with MATH
1500 or MATH 1510. Prerequisites: a minimum
grade of 60% in Math Pre-Calculus 40S (300) or a
grade of “C” in the Mathematical Skills course
taught by the Continuing Education Division, Physics
40S (300) or a pass in PHYS 0900.
MATH 1520 Introductory Calculus for
Management and Social Sciences (3)L
Differentiation and integration of functions of one
variable and partial differentiation of functions of
several variables. Emphasizes applications in the
areas of management and social science. Not to be
held with MATH 1500 or MATH 1510. Prerequisite:
a minimum grade of 60% in Math Pre-Calculus 40S
(300) or equivalent or a pass in the Mathematical
Skills course taught by the Continuing Education
Division.
MATH 1700 Calculus II (3)L
Theory and techniques of integration, curve
sketching, volume, arc length, surface area and
partial derivatives. Not to be held with MATH 1710.
Prerequisites: MATH 1500 or MATH 1510.
Department of Mathematics ⋅ Page 6
THE UNIVERSITY OF MANITOBA
MATH 1710 Applied Calculus II (3)L
Applications of integration to volumes, centres of
mass, moments of inertia, work and fluid pressure;
differentiation of trigonometric exponential and
logarithmic functions; techniques of integration,
polar co-ordinates. Physical applications in this
course make it especially suitable for students
intending to take programs in engineering. Not to
be held with MATH 1700. Prerequisite: MATH 1500
or MATH 1510. Corequisite: PHYS 1050.
For further information
Please contact:
Department of Mathematics
342 Machray Hall, The University of Manitoba
Winnipeg MB R3T 2N2
Telephone: (204) 474-8703
FAX: (204) 474-7611
e-mail: mathematics_dept@Umanitoba.ca
website: umanitoba.ca/science/mathematics/
Note: In the event of any inconsistencies between the
information provided in this Infosheet and the
University's annual Undergraduate Calendar, the
Calendar entry shall prevail. The effective date of
information provided in this Infosheet is
September 2011.
Department of Mathematics ⋅ Page 7