Differential Calculus (Honours Version)

1998/99 CALENDAR COPY:*
Axioms for real numbers, limits, continuity and differentiability. This
course covers slightly fewer topics than AS/SC/AK/MATH1300 3.0, but
covers them
in greater depth. It should be taken by all those planning an Honours degree
in Mathematics or a Specialized Honours degree in Statistics.*

MATH1000 aims to develop the students' ability to think and write clearly, logically and precisely, and to read a mathematical text with understanding. One goal is learning how to write proofs. (Of course, we will not spend all our time proving things!)

It is declared policy of the Mathematics Department to take into
account, in the grading of MATH1000 and MATH1010,
the ``newness'' to students of such ``pure'' mathematics courses,
in order to encourage interested students to
take them. Therefore, although the honours courses are more
"theoretical", students who are willing to put a serious effort
into them should find it *neither easier nor harder* to
get a high mark (A, B+) in MATH1000/1010 than to get the
same mark in MATH1300/1310.

The text will be the most recent edition of Salas and Hille,
*Calculus: One and Several Variables*.

*Prerequisite: *AS/SC/MATH1500 3.0 or

AS/SC/MATH1515 3.0
or OAC Calculus or equivalent.

*Degree credit exclusions: *AS/SC/MATH1013 3.0,

AS/SC/AK/MATH1300 3.0, AS/SC/MATH1505 6.0,

AS/MATH1530 3.0, AS/AK/MATH1550 6.0,

AS/ECON1530 3.0, AK/MATH1410 6.0.

**Coordinator: ** Richard Ganong

**AS/SC/MATH1010 3.0 WIntegral Calculus (Honours
Version)**

1998/99 CALENDAR COPY:*Riemann integral, fundamental theorems of calculus, transcendental
functions, integration techniques, sequences, series. This course covers
fewer topics than AS/SC/AK/MATH1310 3.0,
but covers them in greater depth. It
should be taken by all those planning an Honours degree in Mathematics or a
Specialized Honours degree in Statistics.*

See description of MATH1000 for remarks on content, grades policy, textbook, and method of determining the student's grade.

*Prerequisite: *MATH1000 3.0 or permission of the department.

*Degree credit exclusions: *AS/SC/MATH1014 3.0,

AS/SC/AK/MATH1310 3.0, AS/SC/MATH1505 6.0,

AS/SC/AK/MATH3110 3.0, AK/MATH1410 6.0.

**Coordinator: ** Richard Ganong

**AS/SC/MATH1013 3.0 FW
Applied Calculus I**

1998/99 CALENDAR COPY:*The
first half of this course deals with differentiation and the second half
with integration. Topics include derivatives of algebraic and transcendental
functions, indefinite integrals, techniques of integration, the definite
integral and its interpretation as an area.*

Three lecture hours. ``Mathlab'' help will be available.

The grade will be based 50% on term tests (3) and 50% on final exam.

The text will be
D. Varberg and E.J. Purcell, *Calculus*.

(Both the 6th and the 7th edition are acceptable.)

*Prerequisite: *AS/SC/MATH1500 3.0 or

AS/SC/MATH1515 3.0
or OAC Calculus.

*Degree credit exclusions: *AS/SC/MATH1000 3.0,

AS/SC/AK/MATH1300 3.0, AS/SC/MATH1505 6.0,

AS/MATH1530 3.0, AS/AK/MATH1550 6.0,

AS/ECON1530 3.0, AK/MATH1410 6.0.

**Coordinators:** Fall: Peter A. Taylor

Winter: L. Steven Hou

**AS/SC/MATH1014 3.0 W
Applied Calculus II**

1998/99 CALENDAR COPY:*Applications
of differential and integral calculus (e.g., maxima and minima,
areas, volumes of revolution, moments and centroids, etc.), indeterminate
forms, improper integrals, Taylor series, simple ordinary differential
equations and an introduction to multivariate calculus.*

This course is a sequel to MATH1013.

For the textbook and further comments, see the description of MATH1013 above.

*Prerequisites: *One of AS/SC/MATH1000 3.0, AS/SC/

MATH1013 3.0, AS/SC/AK/MATH1300 3.0, or, for non-

Science students only, six credits in the form of: AS/MATH

1530 3.0 and AS/MATH1540 3.0, or AS/MATH1550 6.0,

or AS/ECON1530 3.0 and AS/ECON1540 3.0.

*Degree credit exclusions: *AS/SC/MATH1010 3.0,

AS/SC/AK/MATH1310 3.0, AS/SC/MATH1505 6.0,

AK/MATH1410 6.0.

**Coordinator: ** Peter A. Taylor

**AS/SC/MATH1016 1.0 F
Applied Mathematics Module I**

1998/99 CALENDAR COPY:*Designed for
students in Applied Mathematics to complement and enrich the
material in AS/SC/
MATH1013 3.0. The module treats the theory in
greater depth, and explores extended applications and modelling.*

One lecture hour per week.

*Prerequisite: *OAC Calculus or

AS/SC/MATH1500 3.0 or
AS/SC/MATH1515 3.0.

*Corequisite: *AS/SC/MATH1013 3.0

(not acceptable as a
prerequisite).

**Coordinator: ** Kim Maltman

**SC/MATH1017 1.0 W
Applied Mathematics Module II**

1998/99 CALENDAR COPY:*Designed for
students in Applied Mathematics to complement and enrich the
material in AS/SC/ MATH1014 3.0. The module treats the theory in
greater depth, and explores extended applications and modelling.*

One lecture hour per week.

*Prerequisites: *AS/SC/MATH1013 3.0 and MATH1016 1.0.

*Corequisite: *AS/SC/MATH1014 3.0

(not acceptable as a
prerequisite).

**Coordinator: ** Peter A. Taylor

**AS/SC/MATH1025 3.0 W
Applied Linear Algebra**

1998/99 CALENDAR COPY:*Topics include polar coordinates
in Euclidean 3-space, general matrix
algebra, determinants, vector space concepts for Euclidean n-space (e.g.,
linear dependence and independence, basis, dimension, linear
transformations, etc.), an introduction to eigenvalues and eigenvectors.*

The text will be Anton and Rorres,
*Elementary Linear Algebra, Applications
Version* (7th ed).

The final grade will be based on term tests (50%) and on a final exam (50%).

Note that MATH1540 3.0 may not be taken for credit by anyone taking, or anyone who has taken, MATH1025.

*Prerequisite: *AS/SC/MATH1525 3.0

or OAC Algebra and Geometry.

*Degree credit exclusions: *AS/SC/MATH2000 6.0,

AS/SC/MATH2021 3.0,
AS/SC/AK/MATH2221 3.0,

AK/MATH2220 6.0.

**Coordinator: ** Walter Tholen

**AS/SC/AK/MATH1090 3.0 FW
Introduction to Sets and Logic**

(formerly MATH1120 3.0) 1998/99 CALENDAR COPY:*Sets,
functions, relations, induction, proof techniques, logic and logic
circuits, basic combinatorics and some basic graph theory.*

*Important Notes:* 1. This year, this
course will be in a somewhat experimental, transitional
stage. There will be two versions of it, one tailored to the needs of
students majoring in Computer Science, the other geared to a
more general audience (including Mathematics majors).

2. **Computer Science majors (or students
having computer science as one of their majors or as a potential major)
MAY NOT ENROL in Section C**. This section of the course *will
not* fulfill Computer Science requirements.

3. **Mathematics majors
should enrol only in Section C
of the course** (provided that they do not have computer science as a present
or possible future major). Students majoring in neither mathematics
nor computer science will probably want to enrol in Section C.

4. MATH2090 (*q.v.*),
beginning in 1998/99, will be a course intended
exclusively for Computer Science majors.
The experimental character of MATH1090 this year will
be shared by one section of MATH2090 in Winter term. Success in the
experiment may mean that MATH1090 as offered before 1998/99
will not be accepted as a prerequisite to MATH2090 starting in
1999/2000.
*Computer Science version, Fall-Winter:*

The emphasis in all sections of the course except Section C will be on the syntax and semantics of propositional and predicate logic. Applications may be given to program specification and verification. To the extent that time permits, set theory and induction will be covered using the formal logical style introduced early in the course.

The final grade will be based on assignments (and possibly quizzes),
one or two class tests and a final examination.*``Non-computer science'' version (Section C), Fall only:*

Topics will be drawn from among those listed in the Main Calendar description above. The purpose of the course will be to give students (math majors and others) a gentle introduction to, and an honest appreciation for, mathematical reasoning, problem solving, and what it means to prove statements in mathematics. A student who has been ``turned off'' mathematics by rote high school treatments may find this course to be eye-opening.

*Prerequisite: *One OAC in mathematics or equivalent,

or AK/MATH1710 6.0.

*Degree credit exclusions: *AS/SC/MATH1120 3.0,

AK/MATH2400 6.0,
AK/MATH2440 6.0, AK/MATH2441 3.0.

This course is not open to any student
who has taken

or is taking any MATH course (with second digit
different

from 5) at the 3000-level or higher.

**Coordinators:** The only coordinator in either term known as we go to
press is for Section C, Fall term: A. Pietrowski.

**AS/SC/MATH1131 3.0 F
Introduction to Statistics I**

1998/99 CALENDAR COPY:*Displaying
and describing distributions, basic concepts of time series and
growth, relationships between variables, Simpson's paradox and the need for
design. Experimental design and sampling design, randomization. Probability
models and random variables, mean and variance. Basic laws of probability.*

Testing a new drug, pricing a derivative asset, evaluating the effects of free trade, making sound investment decisions, and predicting who will win the World Series are all activities that have in common the need to make sense out of ambiguous data. The modern discipline of statistics serves as a guide to scientists, policy makers and business managers who must draw inferences or make decisions on the basis of uncertain information.

MATH1131 provides an introduction to the concepts of statistics with an emphasis on developing an appreciation for variability and a critical attitude towards the use and misuse of statistics in science and business. Statistical techniques will include confidence intervals for means and tests of significance.

It is recommended that students have at least one OAC in
mathematics, but the mathematical level of the course will be
quite elementary. Although students will be making use of
the computer to calculate statistics, to create statistical
plots, and to obtain a better appreciation of statistical
concepts, *no previous experience in computing is required.*
Students will receive all the necessary instruction
about how to use the statistical computer package Minitab.

Although this course is recommended for students who wish to major in statistics, the concepts are broadly applicable and it should be interesting to students who do not plan to specialize in statistics.

The final grade may be based (in each term) on assignments and/or quizzes, class tests and a final examination. The text has not been chosen as we go to press.

*Prerequisite: *At least one OAC in mathematics is

recommended.

*Degree credit exclusions: *AS/SC/AK/MATH2560 3.0,

SC/BIOL3080 3.0, SC/BIOL3090 3.0, AS/ECON2500 3.0,

AS/SC/GEOG2420 3.0, AS/SC/KINE2050 3.0,

AS/SC/PHED2050 3.0, AS/SC/PSYC2020 6.0,

AS/SC/PSYC2021 3.0, AS/SOCI3030 6.0,

AK/MATH1720 6.0, AK/MATH2430 6.0, AK/BIOL3080 6.0,

AK/BIOL3080 3.0, AK/BIOL3090 3.0, AK/PSYC2510 3.0.

Not open to any student who has successfully completed

AS/SC/MATH2030 6.0.

**Coordinator: ** S. Chamberlin

**AS/SC/MATH1132 3.0
Introduction to Statistics II**

This course was offered for the last time in Winter of 1997/98. As a
sequel to MATH1131, it will be replaced in 1999/2000 by MATH2131 3.0.

**AS/SC/AK/MATH1300 3.0 FW
Differential Calculus with Applications**

1998/99 CALENDAR COPY:*Limits,
derivatives with applications, antiderivatives, fundamental
theorem of calculus, beginnings of integral calculus.*

Other topics include continuity, the Mean Value Theorem, curve sketching, maxima and minima, and (time permitting) applications of integration theory.

The text will be announced later.

The final grade may be based on assignments, quizzes, class tests and a final examination worth at least 30%.

*Prerequisite: *AS/SC/MATH1500 3.0 or

AS/SC/MATH1515 3.0 or AK/MATH1710 6.0

or OAC Calculus or equivalent.

*Degree credit exclusions: *AS/SC/MATH1000 3.0,

AS/SC/MATH1013 3.0, AS/SC/MATH1505 6.0,

AS/MATH1530 3.0, AS/AK/MATH1550 6.0,

AS/ECON1530 3.0, AK/MATH1410 6.0.

**Coordinator: ** Fall: A. Ivić Weiss. Winter: T.B.A.

**AS/SC/AK/MATH1310 3.0 FW
Integral Calculus with
Applications**

1998/99 CALENDAR COPY:*Transcendental
functions, differential equations, techniques of integration,
improper integrals, infinite series. Offered in both terms.*

This is the second in a series of introductory calculus courses. It is designed to follow MATH1300 3.0.

Other topics include l'Hôpital's rule and infinite sequences; differential equations will be discussed only as time allows.

The final grade may be based on assignments, quizzes, class tests, and a final examination worth at least 30%.

*Prerequisites: *One of AS/SC/MATH1000 3.0,

AS/SC/MATH1013 3.0, AS/SC/AK/MATH1300 3.0.

Or, for non-Science students only, six credits:

AS/MATH1530 3.0 and AS/MATH1540 3.0,

or AS/AK/MATH1550 6.0, or

AS/ECON1530 3.0 and AS/ECON1540 3.0.

*Degree credit exclusions: *AS/SC/MATH1010 3.0, AS/SC/

MATH1014 3.0,
AS/SC/MATH1505 6.0,
AK/MATH1410 6.0.

**Coordinators:** Fall: K. Bugajska. Winter: A. Ivic Weiss

[Note: The "c" in "Ivic" should have an acute accent here,

but the editor's command of HTML is insufficient to produce it.]

**AS/SC/MATH1505 6.0
Mathematics for the Life and
Social Sciences**

1998/99 CALENDAR COPY:*A
presentation of the elements of single-variable differential and integral
calculus, elementary linear algebra and introductory probability and
statistics. This course is designed to provide a comprehensive mathematical
background for students of the biological and social sciences.
Emphasis is placed on basic mathematical skills and their applications.*

*Prerequisite: *At least one OAC in mathematics

or AS/SC/MATH1510 6.0.

*Degree credit exclusions: *AS/SC/MATH1000 3.0,

AS/SC/MATH1010 3.0, AS/SC/MATH1013 3.0,

AS/SC/MATH1014 3.0, AS/SC/AK/MATH1300 3.0,

AS/SC/AK/MATH1310 3.0, AS/MATH1530 3.0,

AS/MATH1540 3.0, AS/AK/MATH1550 6.0,

AS/ECON1530 3.0, AS/ECON1540 3.0,

AK/MATH1410 6.0.

**Coordinator: ** N. Purzitsky

**AS/SC/MATH1510 6.0
Fundamentals of Mathematics**

1998/99 CALENDAR COPY:*Designed for the student whose mathematical background is weak and who
wishes to take further courses in mathematics. Topics include algebraic
equations and inequalities; simple sequences and series; analytic geometry;
trigonometry; functions, including algebraic, exponential, logarithmic and
trigonometric functions.*

It should be noted that while the acquisition of skills needed for taking (e.g.) a calculus course will be emphasized, an understanding of the underlying concepts will also be required.

The text will probably be L. I. Holder, *A Primer for Calculus*
(this text was used in 1996-97).

The final grade will probably be based on four or five class tests and a final exam.

*Degree credit exclusions: *AS/MATH1520 6.0, AK/MATH

1710 6.0. May not
be taken by any student who has taken or is currently taking
another university course in mathematics or statistics, except for
AS/SC/MATH1500 3.0 or

AS/SC/MATH1515 3.0 or
AS/SC/MATH1525 3.0.

**Coordinator: ** J.M.N. Brown

**AS/SC/MATH1515 3.0 FW
Introduction to Calculus**

(formerly AS/SC/MATH1500 3.0) 1998/99 CALENDAR COPY:*Elements
of differential calculus, anti-derivatives and integrals, with
applications. Designed for students who have not taken (or have performed
inadequately in) OAC Calculus.*

This course is intended to prepare the above students for courses which have "OAC Calculus or equivalent" as a prerequisite.

Topics to be discussed include: limits, derivatives, tangents, rate of change, maxima and minima, curve sketching, trigonometric functions, logarithmic and exponential functions, fundamental theorem of calculus, and areas.

The text will be announced later.

The final grade may be based on assignments, quizzes, class tests, and a final examination.

*Prerequisite: *AS/SC/MATH1510 6.0
or one OAC course in mathematics.

*Degree credit exclusion: *AS/SC/MATH1500 3.0.
May not be taken by any student who has taken or is currently
taking another university course in calculus.

**Coordinator: ** J. Wick Pelletier

**AS/MATH1530 3.0 FW
Introductory Mathematics for Economists I**

1998/99 CALENDAR COPY:*This
course introduces and develops topics in differential calculus,
integral calculus, and their applications in economics. This course or
equivalent is required for all Economics majors or minors; it also satisfies
the mathematics requirement for the Schulich School of Business. It is
suitable for the Ordinary Stream of the
Mathematics for Commerce Programme,
but should not be taken by those who intend to major in any
other COSC or MATH or Statistics programme. (Same as
AS/ECON1530 3.0.) Offered in both terms.*

The pair MATH1530 3.0 and MATH1540 3.0 is designed to give the student an introduction to mathematics sufficient for a thorough understanding of modern textbooks in economic theory. The emphasis is on the acquisition of tools for later use and on an understanding of both concepts and techniques for applications, rather than on theoretical proofs or a rigorous development of the mathematics involved. The pair is similar to MATH1550 6.0.

Topics will include single-variable differentiation, limits, continuity, series, exponential and logarithmic functions, single-variable optimization, and integration. Applications to problems in economics involving supply and demand functions, maximization of profits, elasticity of demand and consumers' surplus will be considered.

The text last year was Sydsaeter and Hammond, *Mathematics for
Economic Analysis*, together with selected exercises from Haeussler
and Paul, *Introductory Mathematical Analysis*. Both of these
texts are published by Prentice Hall. Last year a
``package'' consisting of the first text together with the selected
exercises from the second text was available from the York bookstore.
It is anticipated that the same texts will be used this year, although
students should check with their section instructor at the start of
classes.

The final grade may be based on term tests and/or assignments and a final examination. Instructors will announce details in class.

*Prerequisite: *AS/SC/MATH1500 3.0 or AS/SC/

MATH1515 3.0
or OAC Calculus or equivalent.

*Corequisite: *AS/ECON1000 3.0 or AS/ECON1010 3.0.

*Degree credit exclusions: *AS/SC/MATH1000 3.0, AS/SC/

MATH1013 3.0,
AS/SC/AK/MATH1300 3.0, AS/SC/

MATH1505 6.0,
AS/AK/MATH1550 6.0, AS/ECON1530 3.0,

AK/MATH1410 6.0.

**Coordinators:** Fall: M. Abramson. Winter: T.B.A.

**AS/MATH1540 3.0 FW
Introductory Mathematics for
Economists II**

1998/99 CALENDAR COPY:*This course introduces and develops topics, including matrix algebra,
optimization, comparative statics of general function models, and their
applications in economics. This course or equivalent is required for all
Economics majors or minors; it also satisfies the mathematics requirement
for the Faculty of Administrative Studies. (Same as
AS/ECON1540 3.0.) Offered in both terms.*

This course is normally taken by students who have completed MATH1530 3.0 and are in the Ordinary Mathematics for Commerce Programme.

The material that is covered in the course is mainly matrix algebra and functions of many variables. The material will be covered in a way that will be of interest to students in economics and business. The emphasis will be on the acquisition and use of tools rather than on a rigorous development of the tools. Applications will include the solution of linear equations, and maxima and minima of functions of several variables with and without constraints.

The text and grading scheme are anticipated to be the same as those for MATH1530 3.0.

*Prerequisite: *One of AS/MATH1530 3.0,

AS/SC/MATH1000 3.0, AS/SC/MATH1013 3.0,

AS/SC/AK/MATH1300 3.0, AS/ECON1530 3.0.

*Corequisite: *AS/ECON1000 3.0 or AS/ECON1010 3.0.

*Degree credit exclusions: *AS/SC/MATH1505 6.0,

AS/AK/MATH1550 6.0, AS/ECON1540 3.0.

May not be taken by any student who has taken or is taking

AS/SC/MATH1025 3.0, AS/SC/MATH2000 6.0,

AS/SC/MATH2021 3.0, AS/SC/AK/MATH2221 3.0,

AK/MATH2220 6.0, or equivalent.

**Coordinators:** Fall: T.B.A. Winter: M. Abramson

**AS/AK/MATH1550 6.0
Mathematics with Management Applications**

1998/99 CALENDAR COPY:*This
course is designed to provide a mathematical background for students in
the BBA programme. It is also suitable for the Ordinary Programme in
Mathematics for Commerce, but should not be
taken by those who intend to major in any other programme in COSC or MATH
or Statistics. It includes calculus, matrix algebra and
elements of optimization with applications to management.*

This course is designed primarily for students interested in business programmes. It satisfies a requirement for entry to the BBA programme in the Schulich School of Business.

One theme of the course is optimization - how to maximize or minimize a function subject to certain constraints. Most of the course is a discussion of calculus and its applications; matrix theory and its applications are also discussed. The emphasis will be on techniques and on applications to business and management problems. The content of this course is very similar to that of the two courses MATH1530 3.0 and MATH1540 3.0. These courses will also satisfy the requirements for the programmes mentioned above, and they are suitable for those who plan to major in economics.

Those who wish a stronger foundation in calculus, or who wish to major in any Mathematics programme other than those mentioned above, should avoid calculus courses with second digit 5.

The text will be Haeussler and Paul, *Introductory
Mathematical Analysis ...* (latest ed.), Prentice-Hall.

The method for determining the final grade has not yet been decided.

*Prerequisite: *AS/SC/MATH1515 3.0 (may also be taken

as a first-term corequisite) or AS/SC/MATH1500 3.0 or

OAC Calculus or equivalent.

*Degree credit exclusions: *AS/SC/MATH1000 3.0,

AS/SC/MATH1013 3.0, AS/SC/AK/MATH1300 3.0,

AS/SC/MATH1505 6.0, AS/MATH1530 3.0,

AS/MATH1540 3.0, AS/ECON1530 3.0, AS/ECON1540 3.0.

This course may not be taken by any student who has

taken or is taking AS/SC/MATH1025 3.0 or AS/SC/

MATH2000 6.0 or AS/SC/MATH2021 3.0 or AS/SC/AK/

MATH2221 3.0 or AK/MATH2220 6.0 or equivalent.

**Coordinator: ** M. W. Wong

**AS/SC/MATH1580 3.0 F
The Nature of Mathematics I**

1998/99 CALENDAR COPY:*Designed
to create a positive attitude towards mathematics through an
examination of topics relevant to the study of mathematics at the elementary
school level. Topics include numeral systems, number theory, nature of
algebra and geometry. Intended primarily, but not exclusively, for Education
students in the P/J stream.*

The main objective of this course is to provide opportunities for students to develop a positive attitude towards mathematics and to achieve success in thinking mathematically. The course has been designed with prospective elementary and middle school teachers as the principal intended audience. All students who feel that their background in mathematics is incomplete or whose past experiences have caused them to avoid mathematics, are particularly encouraged to take this course.

Topics (for example, numbers and number systems, graphs and networks, symmetry and patterns, growth and form, change, statistics, and the role of mathematics in society) will be chosen on the basis of their relevance to the formative and transition years' curriculum. An exploratory approach will be used in which students will work in small groups on selected problems and projects. Throughout, the focus will be on developing students' reading, writing and speaking skills in communicating mathematics to each other and to an audience.

The final grade will be based on a combination of assignments, projects and participation. The specific breakdown will be discussed and decided upon in the first class.

*Degree credit exclusions: *Not open to any student who has taken or is taking another
university mathematics course unless permission of the course coordinator is
obtained.

**Coordinator: ** Pat Rogers

**AS/SC/MATH1590 3.0 WT
he Nature of Mathematics II**

1998/99 CALENDAR COPY:*A
continuation of some of the themes explored in AS/SC/MATH1580 3.0. Further
topics include elements of probability and statistics, the nature of
computers, elementary set theory and logic.*

This course will continue in the spirit of MATH1580 3.0.

*Prerequisite: *AS/SC/MATH1580 3.0 or permission of
the course coordinator.

*Degree credit exclusions: *Not open to any student who has

taken or is taking another university mathematics course

(except AS/SC/MATH1580 3.0), unless
permission of the

course coordinator is obtained.

**Coordinator: ** Pat Rogers

Contents Page, 1998/99 Minicalendar

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