York University

Undergraduate Minicalendar

Fall/Winter 1997/98

**AS/SC/MATH1000.03F Differential Calculus (Honours Version)**

*1995-95 York Calendar: *Axioms for real numbers, limits, continuity and differentiability. This
course covers slightly fewer topics than AS/SC/AK/MATH1300.03, 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!)

The policy of the
Mathematics Department is to be generous in the grading of
MATH1000 and MATH1010, to encourage interested students to
take these courses. 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+, A, B+) in MATH1000/MATH1010 than to get the
same mark in MATH1300/MATH1310.

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

The final grade may be based on homework/quizzes (15%), and class tests and a final examination, weighted so as to favour each student's best results.

*Prerequisite: * AS/SC/MATH1500.03 or
AS/SC/MATH1515.03 or OAC Calculus or equivalent.

*Degree credit exclusions:* AS/SC/MATH1013.03,
AS/SC/AK/MATH1300.03, AS/SC/MATH1505.06, AS/MATH1530.03,
AS/AK/MATH1550.06, AS/ECON1530.03, AK/MATH1410.06.

**Coordinator: ** Richard Ganong

**AS/SC/MATH1010.03W Integral Calculus (Honours Version)**

*1995-95 York Calendar: *Riemann integral, fundamental theorems of calculus, transcendental
functions, integration techniques, sequences, series. This course covers
fewer topics than AS/SC/AK/MATH1310.03,
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: * MATH1000.03 or permission of the department.

*Degree credit exclusion:* AS/SC/MATH1014.03, AS/SC/AK/MATH1310.03, AS/SC/MATH1505.06, AS/SC/AK/MATH3110.03, AK/MATH1410.06.

**Coordinator: ** Richard Ganong

**AS/SC/MATH1013.03FW Applied Calculus I**

*1995-95 York Calendar: *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. Tutorials and/or Mathlab help will be available.

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

The text will be
Varberg, D. and Purcell, E.J., *Calculus*. (Both the 6th and the
7th edition are acceptable.)

*Prerequisite: * AS/SC/MATH1500.03 or AS/SC/MATH1515.03 or OAC Calculus.

*Degree credit exclusions:* AS/SC/MATH1000.03, AS/SC/AK/MATH1300.03,
AS/SC/MATH1505.06, AS/MATH1530.03, AS/AK/MATH1550.06,
AS/ECON1530.03, AK/MATH1410.06.

**Coordinator:** Fall: Peter A. Taylor Winter: M.W. Wong

**AS/SC/MATH1014.03W Applied Calculus II**

*1995-95 York Calendar: *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. Three lecture hours. Tutorials and/or Mathlab help will be available.

The text will be the same as for MATH1013.03F.

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

*Prerequisites:*
One of AS/SC/MATH1000.03, AS/SC/ MATH1013.03, AS/SC/AK/MATH1300.03,
or, for non-Science students only, six credits in the form of:
AS/MATH1530.03 and AS/MATH1540.03, or AS/MATH1550.06,
or AS/ECON1530.03 and AS/ECON1540.03.

*Degree credit exclusions:* AS/SC/MATH1010.03, AS/SC/AK/MATH1310.03, AS/SC/MATH1505.06, AK/MATH1410.06.

**Coordinator: ** Peter A. Taylor

**SC/MATH1016.01F Applied Mathematics Module I**

*1995-95 York Calendar: *Designed for
students in Applied Mathematics to complement and enrich the
material in AS/SC/
MATH1013.03. 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/MATH1500.03 or AS/SC/MATH1515.03.

*Corequisite:* AS/SC/MATH1013.03 (not acceptable as a prerequisite).

**Coordinator: ** Buks van Rensburg

**SC/MATH1017.01W Applied Mathematics Module II**

*1995-95 York Calendar: *Designed for
students in Applied Mathematics to complement and enrich the
material in AS/SC/ MATH1014.03. The module treats the theory in
greater depth, and explores extended applications and modelling.

One lecture hour per week.

*Prerequisites:* AS/SC/MATH1013.03 and MATH1016.01.

*Corequisite:* AS/SC/MATH1014.03 (not acceptable as a prerequisite).

**Coordinator: ** Buks van Rensburg

**AS/SC/MATH1025.03W Applied Linear Algebra**

*1995-95 York Calendar: *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).
*Prerequisite:* AS/SC/MATH1525.03 or OAC Algebra and Geometry.

*Degree credit exclusion:* AS/SC/MATH2021.03, AS/SC/AK/MATH2221.03, AK/MATH2220.06.

**Coordinator: ** Kim Maltman

**AS/SC/AK/MATH1090.03 Introduction to Sets and Logic**

(formerly MATH1120.03)

*1995-95 York Calendar: *Sets,
functions, relations, induction, proof techniques, logic and logic
circuits, basic combinatorics and some basic graph theory.

This course should be of value to mathematics or computer science majors, and may also appeal to students wanting to apply mathematics to the social and management sciences.

The text has not yet been chosen.

The final grade will be based on class tests and a final examination (and possibly assignments).

*Prerequisite:* One OAC in mathematics or equivalent, or AK/MATH1710.06.

*Degree credit exclusions:*
AS/SC/MATH1120.03, AK/MATH2400.06, AK/MATH2440.06, AK/MATH2441.03. 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.

**Coordinator: ** Fall: T.B.A. Winter: W. Tholen

**AS/SC/MATH1131.03F Introduction to Statistics I**

*1995-95 York Calendar: *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, 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 and 1132 provide an introduction to the concepts of statistics with an emphasis on developing a critical attitude towards the use and misuse of statistics in science and business. Statistical techniques will include confidence intervals for means or comparing two means, contingency tables, simple regression and basic analysis of variance.

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 some 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 in class 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 text will be D.S. Moore and G.P. McCabe,
*Introduction to the Practice of Statistics* (2nd ed.), W.H. Freeman.

The final grade may be based (in each term) on assignments and/or quizzes, class tests and a final examination.

*Prerequisite:* At least one OAC in mathematics is recommended.

*Degree credit exclusions:*
AS/SC/AK/MATH2560.03, SC/BIOL3080.03, SC/BIOL3090.03,
AS/ECON2500.03, AS/SC/GEOG2420.03, AS/SC/KINE2050.03,
AS/SC/PHED2050.03, AS/SC/PSYC2020.06, AS/SC/PSYC2021.03,
AS/SOCI3030.06, AK/MATH1720.06, AK/MATH2430.06, AK/BIOL3080.06,
AK/BIOL3080.03, AK/BIOL3090.03, AK/GEOG3520.03, AK/PSYC2510.03.
Not open to any student who has successfully completed AS/SC/MATH2030.06.

**Coordinator: ** T.B.A.

**AS/SC/MATH1132.03W Introduction to Statistics II**

*1995-95 York Calendar: *Inference
for the binomial, sample mean, central limit theorem, control
charts. Confidence intervals, tests and decisions. Abuses of tests.
Comparing two means, inference for spread. Contingency tables. Simple
regression and basic analysis of variance.

See the description of MATH1131 for further comments.

*Prerequisite: * AS/SC/MATH1131.03.

*Degree credit exclusions:*
AS/SC/AK/MATH2570.03, SC/BIOL3080.03, SC/BIOL3090.03, AS/ECON3210.03, AS/ECON3500.03, AS/SC/GEOG2420.03, AS/SC/KINE2050.03, AS/SC/PHED2050.03, AS/SC/PSYC2020.06, AS/SC/PSYC2022.03, AS/SOCI3030.06, AK/MATH2430.06, AK/BIOL3080.06 and .03, AK/BIOL3090.03, AK/GEOG3520.03, AK/PSYC3010.03, AK/PSYC3110.03. Not open to any student who has successfully completed AS/SC/MATH2030.06.

**Coordinator: ** T.B.A.

**AS/SC/AK/MATH1300.03FW Differential Calculus with Applications**

*1995-95 York Calendar: *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/MATH1500.03 or AS/SC/MATH1515.03 or AK/MATH1710.06 or OAC Calculus or equivalent.

*Degree credit exclusions:*
AS/SC/MATH1000.03, AS/SC/MATH1013.03, AS/SC/MATH1505.06,
AS/MATH1530.03, AS/AK/MATH1550.06, AS/ECON1530.03, AK/MATH1410.06.

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

**AS/SC/AK/MATH1310.03FW Integral Calculus with Applications**

*1995-95 York Calendar: *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 MATH1300.03.

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/MATH1000.03, AS/SC/MATH1013.03,
AS/SC/AK/MATH1300.03. Or, for non-Science students only, six credits:
AS/MATH1530.03 and AS/MATH1540.03, or AS/AK/MATH1550.06,
or AS/ECON1530.03 and AS/ECON1540.03.

*Degree credit exclusion:* AS/SC/MATH1010.03, AS/SC/ MATH1014.03, AS/SC/MATH1505.06, AK/MATH1410.06.

**Coordinator:** Fall: S.O. Kochman. Winter: A. I. Weiss

**AS/SC/MATH1505.06 Mathematics for the Life and Social Sciences**

*1995-95 York Calendar: *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 (Science) 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/MATH1510.06.

*Degree credit exclusions:*
AS/SC/MATH1000.03, AS/SC/MATH1010.03, AS/SC/MATH1013.03,
AS/SC/MATH1014.03, AS/SC/AK/MATH1300.03, AS/SC/AK/MATH1310.03,
AS/MATH1530.03, AS/MATH1540.03, AS/AK/MATH1550.06, AS/ECON1530.03,
AS/ECON1540.03, AK/MATH1410.06.

**Coordinator: ** N. Purzitsky

**AS/SC/MATH1510.06 Fundamentals of Mathematics**

*1995-95 York Calendar: *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 class tests (10% or 15% each) and a final exam (60% or 40%).

*Degree credit exclusions:*
AS/MATH1520.06, AK/MATH1710.06. 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/MATH1500.03 or
AS/SC/MATH1515.03 or AS/SC/MATH1525.03.

**Coordinator: ** I. Kleiner

**AS/SC/MATH1515.03FW Introduction to Calculus**

(formerly AS/SC/MATH1500.03)

*1995-95 York Calendar: *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 breakdown of the final grade has not been determined.

*Prerequisite:* AS/SC/MATH1510.06
or equivalent, or permission of the Department.

*Degree credit exclusions:*
AS/SC/MATH1500.03.
May not be taken by any student who has taken or is currently
taking another university course in calculus.

**Coordinator:** Fall: J. Wick Pelletier. Winter: A. Pietrowski

**AS/MATH1530.03FW Introductory Mathematics for Economists I**

*1995-95 York Calendar: *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 Faculty of Administrative Studies. It is
suitable for the Ordinary and Honours General 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/ECON1530.03.) Offered in both terms.

The pair MATH1530.03 and MATH1540.03 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.

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/MATH1500.03 or AS/SC/ MATH1515.03 or OAC Calculus or equivalent.

*Corequisite:* AS/ECON1000.03 or AS/ECON1010.03.

*Degree credit exclusions:*
AS/SC/MATH1000.03, AS/SC/MATH1013.03, AS/SC/AK/MATH1300.03, AS/SC/MATH1505.06, AS/AK/MATH1550.06, AS/ECON1530.03, AK/MATH1410.06.

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

**AS/MATH1540.03FW Introductory Mathematics for Economists II**

*1995-95 York Calendar: *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/ECON1540.03.) Offered in both terms.

This course is normally taken by students who have completed MATH1530.03 and are in the Ordinary or Honours General Stream of the 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 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 MATH1530.03.

*Prerequisite:* One of AS/MATH1530.03, AS/SC/MATH1000.03, AS/SC/MATH1013.03, AS/SC/AK/MATH1300.03, AS/ECON1530.03.

*Corequisite:* AS/ECON1000.03 or AS/ECON1010.03.

*Degree credit exclusions:*
AS/SC/MATH1505.06, AS/AK/MATH1550.06, AS/ECON1540.03.
May not be taken by any student who has taken or is taking
AS/SC/MATH1025.03, AS/SC/MATH2000.06, AS/SC/MATH2021.03,
AS/SC/AK/MATH2221.03, AK/MATH2220.06, or equivalent.

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

**AS/AK/MATH1550.06 Mathematics with Management Applications**

*1995-95 York Calendar: *(*Note*: Some of the following, while official as we go to press,
is outdated, and is corrected below.) 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 and the minor in Statistics, 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.

*Correction:*
This course is **not** suitable for the Honours Minor in Statistics,
and **is** suitable also for the Honours General Stream in
Mathematics for Commerce.

This course is designed primarily for students interested in business programmes. It satisfies a requirement for entry to the BBA programme in the Faculty of Administrative Studies.

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 MATH1530.03 and MATH1540.03. 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 probably be Haeussler and Paul, *Introductory
Mathematical Analysis ...* (8th ed.), Prentice Hall. (It is not
really analysis ....)

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

*Prerequisites:*
AS/SC/MATH1515.03 (may also be taken as a first-term
corequisite) or AS/SC/MATH1500.03 or OAC Calculus or equivalent.

*Degree credit exclusions:*
AS/SC/MATH1000.03, AS/SC/MATH1013.03, AS/SC/AK/MATH1300.03,
AS/SC/MATH1505.06, AS/MATH1530.03, AS/MATH1540.03, AS/ECON1530.03,
AS/ECON1540.03. This course may not be taken by any student who has
taken or is taking AS/SC/MATH1025.03 or AS/SC/ MATH2000.06 or
AS/SC/MATH2021.03 or AS/SC/AK/ MATH2221.03 or AK/MATH2220.06 or equivalent.

**Coordinator: ** Richard Ganong

**AS/SC/MATH1580.03F The Nature of Mathematics I**

*1995-95 York Calendar: *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.

Another main objective of this course is to provide opportunities for students to achieve success in thinking mathematically. The course is intended primarily for students concurrently enrolled in the Primary/Junior or Junior/Intermediate programmes in the Faculty of Education. Prospective students should not be discouraged from taking this course either because their backgrounds in mathematics are incomplete or because past experiences have caused them to fear mathematics.

The course will examine some of the areas of mathematics which are relevant to the Primary, Junior and Intermediate curriculum and will focus on the role of language and critical thinking in the construction of mathematical ideas and concepts. An investigative, exploratory approach will be encouraged. Students will work in small groups on selected problems and attention will be given to developing students' reading, writing and speaking skills in communicating mathematics.

The final grade will be based on a combination of specific assignments and projects. The specific breakdown will be decided upon at the start of the course.

*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: ** Martin Muldoon

**AS/SC/MATH1590.03W The Nature of Mathematics II**

(pending approval)

*1995-95 York Calendar: *A
continuation of some of the themes explored in AS/SC/MATH 1580.03. 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 MATH1580.03.

*Prerequisite:* AS/SC/MATH1580.03 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/1580.03), unless
permission of the course coordinator is obtained.

**Coordinator: ** Martin Muldoon