MATHEMATICS AND STATISTICS CURRICULUM - 1995/96


The following includes York University Undergraduate Programmes
Calendar copy updated for 1995/96. Additional changes for
implementation in 1995/96 will be added as they are approved. 

For requirements for BA programmes in Mathematics and Statistics,
consult the 1993/94 York University Undergraduate Programmes
Calendar and the 1994/95 Supplement to that Calendar.

updated 1995 02 14

FACULTY OF PURE AND APPLIED SCIENCE
...

V. PROGRAMME OF STUDY REQUIREMENTS OF HONOURS AND ORDINARY
PROGRAMMES 

APPLIED MATHEMATICS

See Mathematics and Statistics.
...

MATHEMATICS AND STATISTICS

The Department of Mathematics and Statistics offers BSc degree
programmes in three major subjects:

I.   Applied Mathematics
II.  Mathematics
III. Statistics

The degree programmes in each major are listed separately below.
A student should choose one of these majors based on interest and
employment goals, but it is possible to change majors provided
the requirements of the desired major can be met.

i) All BSc degree candidates must complete a programme core (see
programme specifications below).

ii) All candidates must comply with general regulation 4 (section
IV, page ##) by completing the following (in addition to 1000-
level COSC and MATH requirements):

o    12 credits from SC/BIOL1010.06, SC/CHEM1010.06,
     SC/EATS1010.06, SC/PHYS1410.06 or SC/PHYS1010.06;

o    6 credits in each of Humanities and Social Science (no
     substitutions permitted).

iii) All degree candidates, in accordance with their declared
programmes, must comply with general regulation 5 or 6 (section
IV, page ##) and, in so doing, must satisfy the course, credit
and standing requirements specified below.
To declare Honours requires successful completion of at least 24
credits and a minimum cumulative credit-weighted grade-point
average of 5.0 over all Science (SC) courses completed.

To proceed in each year of an Honours BSc programme requires a
minimum cumulative credit-weighted grade-point average of 5.0
over all Science (SC) courses completed.

To graduate in an Honours BSc programme requires successful
completion of all Faculty requirements and departmental required
courses and a minimum cumulative credit-weighted grade-point
average of 5.0 over all Science (SC) courses completed.

Notes:

1. All candidates beyond the 1000 level must obtain written
approval of their study lists from an authorized member of the
Department of Mathematics and Statistics.

2. For the purpose of satisfying departmental degree
requirements, the following minimum numbers of credits must be
completed within the Department of Mathematics and Statistics: 18
for the Ordinary Programme, 21 for the Combined Honours
Programme, 30 for the Specialized Honours Programme.

3. For BA degree programmes in Mathematics and Statistics, see
the Faculty of Arts section in this Calendar.

I. APPLIED MATHEMATICS BSc PROGRAMMES

All degree candidates must complete the programme core:
SC/COSC1540.03; SC/MATH1013.03 or SC/MATH1000.03; SC/MATH1014.03
or SC/MATH1010.03; SC/MATH1025.03; SC/MATH2015.03;
SC/MATH2030.03; SC/MATH2041.03; SC/MATH2042.03; SC/MATH2222.03;
SC/MATH2270.03; SC/MATH3241.03; SC/MATH3242.03.

In addition, all degree candidates must select, from the Group A
and Group B lists below, the number of credits required for their
chosen programme.

Group A: SC/MATH1090.03, SC/MATH2090.03, SC/MATH2280.03,
SC/MATH2320.03, SC/MATH3110.03, SC/MATH3170.06, SC/MATH3260.03,
SC/MATH3270.03, SC/MATH3271.03, SC/MATH3272.03, SC/MATH3280.06,
SC/MATH3410.03, SC/MATH3440.03, SC/MATH4000.06 (4000.03)
(projects in Applied Mathematics only), SC/MATH4141.03,
SC/MATH4142.03, SC/MATH4160.03, SC/MATH4170.06, SC/MATH4210.03,
SC/MATH4240.03, SC/MATH4241.03, SC/MATH4270.03, SC/MATH4280.03,
SC/MATH4430.03, SC/MATH4470.03, SC/MATH4830.03

Group B: SC/MATH1131.03, SC/MATH1132.03, SC/MATH3030.03,
SC/MATH3131.03, SC/MATH3132.03, SC/MATH3230.03 or SC/MATH3034.03,
SC/MATH3330.03 or SC/MATH3033.03

Note: Some sections of SC/MATH4200.06 (4200.03) may be included
in Group A or Group B at the discretion of the department.

ORDINARY PROGRAMME

o    the programme core;

o    at least 9 additional credits at the 3000 level or higher
     from groups A and B (above), including no more than 6
     credits from Group B, for an overall total of at least 42
     credits from major SC/MATH courses;

o    additional elective credits as required for an overall total
     of at least 90 credits, including at least 66 credits from
     Science courses and at least 18 credits at the 3000 or
     higher level.

SPECIALIZED HONOURS PROGRAMME

o    the programme core;

o    SC/MATH3110.03 (not required if SC/MATH1010.03 has been
     completed); SC/MATH3260.03; SC/MATH3410.03;

o    at least 24 additional credits from groups A and B (above),
     including no more than 9 credits from Group B and at least
     12 credits at the 4000 level;

o    additional elective credits as required for an overall total
     of at least 120 credits, including at least 90 credits from
     Science courses and at least 42 credits at the 3000 or
     higher level.

COMBINED HONOURS PROGRAMME

o    the programme core;

o    at least 9 additional credits at the 3000 level or higher
     from groups A and B (above), including no more than 6
     credits from Group B, for an overall total of at least 42
     credits from major SC/MATH courses;

o    additional credits (including those required for the second
     major) as required for an overall total of at least 120
     credits, including at least 90 credits from Science courses
     and at least 42 credits at the 3000 or higher level.

II. MATHEMATICS BSc PROGRAMMES

ORDINARY PROGRAMME

o    SC/COSC1520.03 and SC/COSC1530.03, or equivalents;

o    SC/MATH1300.03 and SC/MATH1310.03, or equivalents;

o    SC/MATH1090.03 or SC/MATH2090.03 or SC/MATH2320.03;

o    SC/MATH2221.03; SC/MATH2222.03; SC/MATH2310.03;

o    at least 12 credits in major (i.e., without second digit 5)
     SC/MATH courses, or approved or equivalent courses, at the
     3000 level or higher, for a total of at least 30 credits in
     major SC/MATH courses;

o    additional elective credits as required for an overall total
     of at least 90 credits, including at least 66 credits from
     Science courses and at least 18 credits at the 3000 or
     higher level.

Note: Mathematics Honours Core courses SC/MATH1000.03,
SC/MATH1010.03, SC/MATH2010.03, SC/MATH2021.03, and
SC/MATH2022.03 may replace SC/MATH1300.03, SC/MATH1310.03,
SC/MATH2310.03, SC/MATH2221.03, and SC/MATH2222.03, respectively.

HONOURS PROGRAMMES

MATHEMATICS HONOURS CORE

The core courses below are required in all Honours Mathematics
programmes.

o    SC/COSC1520.03 and SC/COSC1530.03, or equivalents;

o    SC/MATH1000.03; SC/MATH1010.03;

o    SC/MATH1090.03 or SC/MATH2090.03 or SC/MATH2320.03;

o    SC/MATH2010.03; SC/MATH3010.03;

o    SC/MATH2021.03; SC/MATH2022.03.

o    SC/MATH3020.06, or both SC/MATH3131.03 and SC/MATH3132.03;

o    SC/MATH3210.03;

o    6 credits from SC/MATH4000.06 (4000.03) (projects in pure
     mathematics), SC/MATH4010.06, SC/MATH4020.06,
     SC/MATH4030.03, SC/MATH4080.06, SC/MATH4110.03,
     SC/MATH4120.03, SC/MATH4130.03, SC/MATH4140.03,
     SC/MATH4150.03, SC/MATH4160.03, SC/MATH4170.06,
     SC/MATH4210.03, SC/MATH4230.03, SC/MATH4250.06,
     SC/MATH4280.03, SC/MATH4290.03, SC/MATH4430.03,
     SC/MATH4630.03, SC/MATH4730.03.

Note: Students may substitute non-Honours versions of the
sequence SC/MATH1000/1010/2010, but any student who does not
complete SC/MATH1010.03 must take SC/MATH3110.03 above and beyond
the normal Honours requirements. If one or more of SC/MATH2021.03
or SC/MATH2022.03 is replaced by other linear algebra courses and
if the grades obtained were less than A, then SC/MATH2090.03 or
SC/MATH2320.03 must be taken above and beyond the normal Honours
requirements.

SPECIALIZED HONOURS PROGRAMME

o    the Mathematics Honours Core;

o    at least 6 additional credits in major SC/MATH courses at
     the 4000 level (these must include either SC/MATH4010.06 or
     SC/MATH4020.06 if neither was taken as part of the
     Mathematics Honours Core);

o    at least 24 additional credits in major (i.e., without
     second digit 5) SC/MATH courses, or approved or equivalent
     courses, for a total of at least 66 credits in major SC/MATH
     courses;

o    additional elective credits as required for an overall total
     of at least 120 credits, including at least 90 credits from
     Science courses and at least 42 credits at the 3000 or
     higher level.

COMBINED HONOURS PROGRAMME

o    the Mathematics Honours Core, for a total of at least 36
     credits in major SC/MATH courses.

o    additional credits (including those required for the second
     major) as required for an overall total of at least 120
     credits, including at least 90 credits from Science courses
     and at least 42 credits at the 3000 or higher level.

III. STATISTICS BSc PROGRAMMES

ORDINARY PROGRAMME

o    SC/COSC1520.03 and SC/COSC1530.03, or SC/COSC1540.03, or
     SC/COSC1020.03 and SC/COSC1030.03, or equivalents;

o    6 credits from 1000-level major (i.e., without second digit
     5) SC/MATH courses in calculus;

o    SC/MATH1131.03; SC/MATH1132.03; SC/MATH2030.03;

o    SC/MATH2221.03 or SC/MATH1025.03 or SC/MATH2021.03;
     SC/MATH2222.03 or SC/MATH2022.03;

o    SC/MATH2310.03, or SC/MATH2015.03, or SC/MATH2010.03 and
     SC/MATH3010.03;

o    SC/MATH3033.03; SC/MATH3131.03;

o    at least 3 credits from SC/MATH3034.03, SC/MATH3132.03,
     SC/MATH3430.03, SC/MATH4130.03, SC/MATH4230.03,
     SC/MATH4630.03, SC/MATH4730.03, SC/MATH4830.03,
     SC/MATH4930.03, for a total of at least 33 credits in major
     SC/MATH courses;

o    additional elective credits as required for an overall total
     of at least 90 credits, including at least 66 credits from
     Science courses and at least 18 credits at the 3000 or
     higher level.

Note: A student may substitute SC/MATH2560.03 and SC/MATH2570.03
with an average of B+ or higher for SC/MATH1131.03 and
SC/MATH1132.03.

SPECIALIZED HONOURS PROGRAMME

o    SC/COSC1520.03 and SC/COSC1530.03, or SC/COSC1540.03, or
     SC/COSC1020.03 and SC/COSC1030.03, or equivalents;

o    SC/MATH1000.03; SC/MATH1010.03;

o    SC/MATH1131.03; SC/MATH1132.03;

o    SC/MATH2010.03;

o    SC/MATH2021.03; SC/MATH2022.03;

o    SC/MATH2030.03;

o    SC/MATH3010.03; SC/MATH3210.03;

o    SC/MATH3033.03; SC/MATH3034.03; SC/MATH3131.03;
     SC/MATH3132.03; SC/MATH3430.03;

o    6 credits from SC/MATH4130.03 (more than one version may be
     taken for credit), SC/MATH4230.03, SC/MATH4630.03,
     SC/MATH4730.03, SC/MATH4830.03, SC/MATH4930.03 (more than
     one version may be taken for credit);

o    6 additional credits from the above or from SC/MATH4030.03,
     SC/MATH4170.06, SC/MATH4280.03, SC/MATH4430.03;

o    9 additional credits from any major (second digit not 5)
     SC/MATH courses, for a total of at least 66 credits in major
     SC/MATH courses;

o    additional elective credits as required for an overall total
     of at least 120 credits, including at least 90 credits from
     Science courses and at least 42 credits at the 3000 or
     higher level.

COMBINED HONOURS PROGRAMME

o    SC/COSC1520.03 and SC/COSC1530.03, or SC/COSC1540.03, or
     SC/COSC1020.03 and SC/COSC1030.03, or equivalents;

o    6 credits from 1000-level major (i.e., without second digit
     5) SC/MATH courses in calculus;

o    SC/MATH1131.03; SC/MATH1132.03; SC/MATH2030.03;

o    SC/MATH2010.03 and SC/MATH3010.03, or SC/MATH2015.03, or
     SC/MATH2310.03;

o    SC/MATH2021.03 or SC/MATH2221.03 or SC/MATH1025.03;
     SC/MATH2022.03 or SC/MATH2222.03;

o    SC/MATH3131.03;

o    12 credits from SC/MATH3033.03, SC/MATH3034.03,
     SC/MATH3132.03, SC/MATH3430.03, SC/MATH4130.03 (more than
     one version may be taken for credit), SC/MATH4230.03,
     SC/MATH4630.03, SC/MATH4730.03, SC/MATH4830.03,
     SC/MATH4930.03 (more than one version may be taken for
     credit), for a total of at least 39 credits in major SC/MATH
     courses.

o    additional credits (including those required for the second
     major) as required for an overall total of at least 120
     credits, including at least 90 credits from Science courses
     and at least 42 credits at the 3000 or higher level.
...

STATISTICS

See Mathematics and Statistics.
...

COURSES OF INSTRUCTION
YORK CAMPUS
...

APPLIED MATHEMATICS - PURE AND APPLIED SCIENCE, ARTS

See Mathematics and Statistics.
...

MATHEMATICS AND STATISTICS - ARTS, PURE AND APPLIED SCIENCE,
ATKINSON COLLEGE

Department Office:
N520 Ross, 736-5250
Associate Professor and Chair of the Department:
G.A. Monette
Professors Emeriti:
L. Lorch, D.C. Russell, A. Shenitzer
Professors:
M. Abramson, R.G. Burns, A. Dow, J. Fox, D.A.S. Fraser, S.
Guiasu, C. Hruska, A. Karrass, I. Kleiner, S. Kochman, J.
Laframboise, J. Liu, R.P. McEachran, M.E. Muldoon, G.L. O'Brien,
P. Olin, J. Wick Pelletier, S.D. Promislow, T. Salisbury, D.
Solitar, A.D. Stauffer, J. Steprans, P.A. Taylor, W. Tholen, S.
Watson, W.J. Whiteley, M.W. Wong
Associate Professor Emeritus:
J.H. Grant
Associate Professors:
D.W.T. Bean, J.-C. Bouhenic, J.M.N. Brown, R.L.W. Brown, K.
Bugajska, C. Czado, G.E. Denzel, R.A. Ganong, S.W. Lee, T.
MacHenry, N.N. Madras, K.R. Maltman, H. Massam, D.H. Pelletier,
P.H. Peskun, A. Pietrowski, N. Purzitsky, P. Rogers, R.A.
Schaufele, A.M.K. Szeto, D. Tanny, A. Weiss, J. Wu
Assistant Professors:
N. Bergeron, S.R. Chamberlin, E.J. Janse van Rensburg, Y. Wu
NSERC University Research Fellows:
N.N. Madras, K.R. Maltman
NSERC Women's Faculty Awardee:
F. Vinette

The Department of Mathematics and Statistics offers a wide range
of courses in both pure and applied mathematics and statistics.
These meet the needs of students who wish to major in mathematics
or statistics as well as those who require some knowledge of
mathematics or statistics in other disciplines. In addition,
there are courses for those who have a general interest in these
subjects.

Actuarial Profession. Students interested in the actuarial
profession should consult the Department of Mathematics and
Statistics for guidance. The department will be glad to suggest a
programme of courses which will be helpful in preparing for
examinations of the Society of Actuaries.

Operations Research. The Canadian Operational Research Society
(CORS) has recognized that graduation from a programme in Applied
Mathematics, Mathematics, or Statistics with a prescribed set of
courses will qualify a student for the Diploma in Operations
Research awarded by CORS. Interested students should consult the
Department of Mathematics and Statistics for guidance.

For specific requirements of programmes offered by this
department, see page ## for BA programmes and page ## of section
V for BSc programmes.

COURSES IN MATHEMATICS AND STATISTICS

When selecting courses, please note the following:

1. A student taking lower-level mathematics courses may wish to
make use of the services provided by the Department's Mathematics
Laboratory.

2. AS/SC/MATH1510.06 is intended for students who, despite having
one or more OACs in mathematics (or equivalents), have a weak
mathematical background. AS/MATH1520.06 is designed for students
who do not have credit in any OACs in mathematics. Both
AS/SC/MATH1510.06 and AS/MATH1520.06 can serve as preparation for
AS/SC/MATH1500.03 and from there entrance to further calculus
courses.

3. Note on calculus courses for first-year students.

a) BBA students who wish to take only a minimum amount of
mathematics should take both AS/MATH1530.03 and AS/MATH1540.03,
or AS/MATH1550.06. The prerequisite for these courses is
AS/SC/MATH1500.03 or OAC Calculus or equivalent.

b) Science students (particularly those majoring in Biology,
Geography, Physical Education or Psychology) who do not require
other specific calculus courses to satisfy degree requirements or
as prerequisites for higher-level courses, may take
SC/MATH1505.06 to satisfy the Faculty of Pure and Applied Science
1000-level mathematics requirement.

Other students should be guided by paragraphs (c) and (d) below.

c) A student with at least one OAC in mathematics or equivalent,
but without previous calculus, must begin the study of calculus
with AS/SC/MATH1500.03.

d) A student with OAC Calculus or equivalent can begin with
AS/SC/MATH1000.03 or AS/SC/MATH1013.03 or AS/SC/MATH1300.03 and
then take AS/SC/MATH1010.03 or AS/SC/MATH1014.03 or
AS/SC/MATH1310.03.

4. Course numbering. Courses with second digit 5 cannot be used
to satisfy departmental degree requirements except (i) by
students in the Ordinary Mathematics for Commerce Programme; and
(ii) by students in other programmes in a few cases as noted in
programme descriptions.

Unless otherwise specified, courses whose numbers end in ".06"
(i.e., 6-credit courses) have three lecture hours per week for
two terms, while those whose numbers end in ".03" (i.e., 3-credit
courses) have three lecture hours per week for one term. In
addition, problem sessions or tutorials are scheduled for many
courses.

5. Arts students should note that some Atkinson College courses
are out-of-Faculty and there are restrictions on the number of
out-of-Faculty courses that may be taken. Science students should
note that some Atkinson College courses are out-of-department -
see the restrictions in note 2. on page ## of section V.

Atkinson College MATH courses which are cross-listed with MATH
courses offered by the Faculties of Arts and Pure and Applied
Science are identified in the course outlines below. For a list
of other Atkinson College courses which are equivalent to and/or
degree credit exclusions for MATH courses in this Calendar, Arts
students should consult the "Faculty of Arts Degree Credit
Exclusion List for Atkinson College Courses," published annually
by the Registrar's Office. Science students should consult the
"Atkinson Equivalence Table for Science Students" available in
the Science Office of Student Programmes beginning in March each
year.

AS/SC/MATH1000.03 Differential Calculus (Honours Version). Axioms
for real numbers, limits, continuity and differentiability. This
course covers slightly fewer topics than AS/SC/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.
Prerequisite: AS/SC/MATH1500.03 or OAC Calculus or equivalent.
Degree credit exclusions: AS/SC/MATH1013.03, AS/SC/MATH1300.03,
SC/MATH1505.06, AS/MATH1530.03, AS/MATH1550.06, SC/ACMS1030.06,
SC/ACMS1050.06, AS/ECON1530.03.

AS/SC/MATH1010.03 Integral Calculus (Honours Version). Riemann
integral, fundamental theorems of calculus, transcendental
functions, integration techniques, sequences, series. This course
covers fewer topics than AS/SC/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.
Prerequisite: AS/SC/MATH1000.03 or permission of the department.
Degree credit exclusions: AS/SC/MATH1014.03, AS/SC/MATH1310.03,
SC/MATH1505.06, AS/SC/AK/MATH3110.03, SC/ACMS1030.06,
SC/ACMS1050.06.

AS/SC/MATH1013.03 Applied Calculus I. 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.
Prerequisite: AS/SC/MATH1500.03 or OAC Calculus.
Degree credit exclusions: AS/SC/MATH1000.03, AS/SC/MATH1300.03,
SC/MATH1505.06, AS/MATH1530.03, AS/MATH1550.06, SC/ACMS1030.06,
SC/ACMS1050.06, AS/ECON1530.03.

AS/SC/MATH1014.03 Applied Calculus II. 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.
Prerequisite(s): One of AS/SC/MATH1000.03, AS/SC/MATH1013.03,
AS/SC/MATH1300.03, or, for non-Science students only, one of
AS/MATH1530.03 and AS/MATH1540.03, AS/MATH1550.06, AS/ECON1530.03
and AS/ECON1540.03.
Degree credit exclusions: AS/SC/MATH1010.03, AS/SC/MATH1310.03,
SC/MATH1505.06, SC/ACMS1030.06, SC/ACMS1050.06.

AS/SC/MATH1025.03 Applied Linear Algebra. 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.
Prerequisite: AS/SC/MATH1525.03 or OAC Algebra and Geometry.
Degree credit exclusions: AS/SC/MATH2000.06, AS/SC/MATH2021.03,
AS/SC/AK/MATH2221.03, SC/ACMS1020.06, SC/ACMS1050.06.

AS/SC/AK/MATH1090.03 Introduction to Sets and Logic (formerly
AS/SC/MATH1120.03 - before 1994/95). Sets, functions, relations,
induction, proof techniques, logic and logic circuits, basic
combinatorics and some basic graph theory.
Prerequisite: One OAC in mathematics or equivalent.
Degree credit exclusions: AS/SC/MATH1120.03. This course is not
open to any student who has taken or is taking any 3000- or
higher-level MATH course.

AS/SC/MATH1131.03 Introduction to Statistics I. 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.
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/PHED2050.03, AS/SC/PSYC2020.06, AS/SC/PSYC2021.03,
AS/SOCI3030.06. Not open to any student who has successfully
completed AS/SC/MATH2030.06.

AS/SC/MATH1132.03 Introduction to Statistics II. 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.
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/PHED2050.03, AS/SC/PSYC2020.06,
AS/SC/PSYC2022.03, AS/SOCI3030.06. Not open to any student who
has successfully completed AS/SC/MATH2030.06.

AS/SC/MATH1300.03 Differential Calculus with Applications.
Limits, derivatives with applications, antiderivatives,
fundamental theorem of calculus, beginnings of integral calculus.
Prerequisite: AS/SC/MATH1500.03 or OAC Calculus or equivalent.
Degree credit exclusions: AS/SC/MATH1000.03, AS/SC/MATH1013.03,
SC/MATH1505.06, AS/MATH1530.03, AS/MATH1550.06, SC/ACMS1030.06,
SC/ACMS1050.06, AS/ECON1530.03.

AS/SC/MATH1310.03 Integral Calculus with Applications.
Transcendental functions, differential equations, techniques of
integration, improper integrals, infinite series. Offered in both
terms.
Prerequisite(s): One of AS/SC/MATH1000.03, AS/SC/MATH1013.03,
AS/SC/MATH1300.03, or, for non-Science students only, one of
AS/MATH1530.03 and AS/MATH1540.03, AS/MATH1550.06, AS/ECON1530.03
and AS/ECON1540.03.
Degree credit exclusions: AS/SC/MATH1010.03, AS/SC/MATH1014.03,
SC/MATH1505.06, SC/ACMS1030.06, SC/ACMS1050.06.

AS/SC/MATH1500.03 Introduction to Calculus. Elements of
differential calculus, anti-derivatives and integrals, with
applications. Designed for students who have not taken (or have
performed inadequately in) OAC Calculus.
Prerequisite: AS/SC/MATH1510.06 or AS/MATH1520.06 or equivalent.
This course may be taken at the same time as the second half of
AS/SC/MATH1510.06 or AS/MATH1520.06.
Degree credit exclusion: May not be taken by any student who has
taken or is currently taking another university course in
calculus.

SC/MATH1505.06 Mathematics for the Life and Social Sciences. 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/MATH1300.03,
AS/SC/MATH1310.03, AS/MATH1530.03, AS/MATH1540.03,
AS/MATH1550.06, SC/ACMS1020.06, SC/ACMS1030.06, SC/ACMS1050.06,
AS/ECON1530.03, AS/ECON1540.03.

AS/SC/MATH1510.06 Fundamentals of Mathematics. 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.
Degree credit exclusions: AS/MATH1520.06, SC/ACMS1530.06. 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 and AS/SC/MATH1525.03.

AS/MATH1520.06 Fundamentals of Mathematics. Designed for the
student whose mathematical background is weak and who wishes to
gain some familiarity with mathematical techniques. Topics
include algebraic equations and inequalities, simple sequences
and series, analytic geometry, sets and functions, the binomial
theorem. This course is given on a modularized, self-paced basis
through the Department's Mathematics Laboratory.
Degree credit exclusions: AS/SC/MATH1510.06, SC/ACMS1530.06. 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 and AS/SC/MATH1525.03.

AS/SC/MATH1525.03 Elementary Linear Algebra. This course is
designed for students who have not taken OAC Algebra and
Geometry. Topics include complex numbers, mathematical induction,
rudiments of linear algebra in the context of Euclidean 2-space
and 3-space; e.g., vectors, equations of lines and planes,
matrices and linear transformations.
Degree credit exclusion: May not be taken by any student who has
taken or is taking another university course involving linear
algebra.

AS/MATH1530.03 Introductory Mathematics for Economists I. 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 Ordinary
Mathematics for Commerce and for a minor in Statistics, but
should not be taken by those who intend to major in any other
Mathematics or Statistics programme or in Computer Science. (Same
as AS/ECON1530.03.) Offered in both terms.
Prerequisite: AS/SC/MATH1500.03 or OAC Calculus or equivalent.
Prerequisite or corequisite: AS/ECON1000.03 or AS/ECON1010.03.
Degree credit exclusions: AS/SC/MATH1000.03, AS/SC/MATH1013.03,
AS/SC/MATH1300.03, SC/MATH1505.06, AS/MATH1550.06,
SC/ACMS1030.06, SC/ACMS1050.06, AS/ECON1530.03.

AS/MATH1540.03 Introductory Mathematics for Economists II. 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.
Prerequisite: One of AS/MATH1530.03, AS/SC/MATH1000.03,
AS/SC/MATH1013.03, AS/SC/MATH1300.03, AS/ECON1530.03.
Prerequisite or corequisite: AS/ECON1000.03 or AS/ECON1010.03.
Degree credit exclusions: SC/MATH1505.06, AS/MATH1550.06,
SC/ACMS1020.06, SC/ACMS1050.06, 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, or
equivalent.

AS/MATH1550.06 Mathematics with Management Applications. 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 Mathematics or Statistics or in
Computer Science. It includes calculus, matrix algebra and
elements of optimization with applications to management.
Prerequisite: AS/SC/MATH1500.03 (may also by taken as a
first-term corequisite) or OAC Calculus or equivalent.
Degree credit exclusions: AS/SC/MATH1000.03, AS/SC/MATH1013.03,
AS/SC/MATH1300.03, SC/MATH1505.06, AS/MATH1530.03,
AS/MATH1540.03, SC/ACMS1030.06, SC/ACMS1050.06, 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 equivalent.

AS/SC/MATH1580.03 The Nature of Mathematics I. 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.
Degree credit exclusion: Not open to any student who has taken or
is taking another university mathematics course unless permission
of the course coordinator is obtained.

AS/SC/MATH1590.03 The Nature of Mathematics II. A continuation of
some of the themes explored in AS/SC/MATH1580.03. Further topics
include elements of probability and statistics, the nature of
computers, elementary set theory and logic.
Prerequisite: AS/SC/MATH1580.03 or permission of the course
coordinator.

AS/SC/MATH2010.03 Vector Differential Calculus. Power series,
partial derivatives, linear maps, differentiability of maps from
n-space to m-space, chain rule, gradients, tangent lines to
curves, tangent planes to surfaces, cross product, implicit
function theorem, multidimensional Taylor's theorem with
remainder, extrema, quadratic forms, Hessian, Lagrange
multipliers.
Prerequisite: AS/SC/MATH1010.03 or permission of the department.
Degree credit exclusions: AS/SC/MATH2015.03,
AS/SC/AK/MATH2310.03.

AS/SC/MATH2015.03 Applied Multivariate and Vector Calculus.
Topics covered include grad, div, curl and Laplacian in polar
coordinates; line and surface integrals; theorems of Gauss and
Stokes; double and triple integrals in various coordinate
systems; extrema and Taylor series for multivariate functions;
differential geometry in Euclidean 3-space.
Prerequisite: One of AS/SC/MATH1010.03, AS/SC/MATH1014.03,
AS/SC/MATH1310.03, or SC/MATH1505.06 plus permission of the
course coordinator.
Degree credit exclusions: AS/SC/MATH2010.03,
AS/SC/AK/MATH2310.03, AS/SC/MATH3310.03.

AS/SC/MATH2021.03 Linear Algebra I (Honours Version). Linear
equations, matrices, determinants, vector spaces and inner
product spaces. This course covers material similar to that in
AS/SC/AK/MATH2221.03 but at a more advanced level. It is required
in Honours Mathematics degrees.
Prerequisite or corequisite: As prerequisite, one of
SC/MATH1505.06, AS/MATH1540.03, AS/MATH1550.06, AS/ECON1540.03;
or, as prerequisite or corequisite, one of AS/SC/MATH1000.03,
AS/SC/MATH1013.03, AS/SC/MATH1300.03, or permission of the course
coordinator.
Degree credit exclusions: AS/SC/MATH1025.03, AS/SC/MATH2000.06,
AS/SC/AK/MATH2221.03, SC/ACMS1020.06.

AS/SC/MATH2022.03 Linear Algebra II (Honours Version). Linear
transformations, eigenvalues, diagonalization, quadratic forms,
Markov chains and isometries. This course covers material
similiar to that in AS/SC/AK/MATH2222.03 but at a more advanced
level. It is required in Honours degrees in Mathematics and in
Specialized Honours degrees in Statistics.
Prerequisite: AS/SC/MATH2021.03 or permission of the course
coordinator.
Degree credit exclusions: AS/SC/MATH2000.06,
AS/SC/AK/MATH2222.03.

AS/SC/AK/MATH2030.03 Elementary Probability (formerly part of
AS/SC/MATH2030.06 - before 1993/94). Introduction to the theory
of probability as preparation for further study in either
mathematical or applied probability and statistics. Topics
include probability spaces, conditional probability,
independence, random variables, distribution functions,
expectation, Chebyshev's inequality, common distributions,
moment-generating functions and limit theorems.
Prerequisite: One of AS/SC/MATH2015.03, AS/SC/AK/MATH2310.03,
AS/SC/MATH2010.03. If a student uses AS/SC/MATH2010.03 as a
prerequisite, AS/SC/AK/MATH3010.03 must be taken as a
corequisite.
Degree credit exclusion: AS/SC/MATH2030.06.

AS/SC/MATH2041.03 Symbolic Computation Laboratory I (formerly
part of AS/SC/MATH2040.06 - before 1995/96). An introduction to
symbolic computing in the Maple environment. Topics from single-
variable differential and integral calculus, including simple
ordinary differential equations, are covered. Both mathematical
understanding and applications are emphasized. Enrolment is
limited to 25.
Prerequisites: SC/AS/COSC1540.03 or equivalent computing
experience; one of AS/SC/MATH1010.03, AS/SC/MATH1014.03,
AS/SC/MATH1310.03.
Degree credit exclusion: AS/SC/MATH2040.06.

AS/SC/MATH2042.03 Symbolic Computation Laboratory II (formerly
part of AS/SC/MATH2040.06 - before 1995/96). Advanced symbolic
computing with Maple. Topics from linear algebra, differential
equations, multivariate calculus, integral theorems, are covered.
Both mathematical understanding and applications are emphasized.
Enrolment is limited to 25.
Prerequisites: AS/SC/MATH2041.03; AS/SC/MATH2010.03 or
AS/SC/MATH2015.03 or AS/SC/AK/MATH2310.03; AS/SC/MATH1025.03 or
AS/SC/MATH2021.03 or AS/SC/AK/MATH2221.03.
Prerequisites or corequisites: AS/SC/AK/MATH2270.03;
AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03.
Degree credit exclusion: AS/SC/MATH2040.06.

AS/SC/MATH2090.03 Introduction to Mathematical Logic. An
introduction to propositional logic; predicate logic, with an
emphasis on semantics; elements of axiomatic number theory. This
course is intended for Computer Science students and for
Mathematics students who plan to do further study in logic.
Prerequisite: AS/SC/AK/MATH1090.03 or AS/SC/MATH1120.03 or any
2000-level MATH course (without second digit 5) or permission of
the course coordinator.

AS/SC/AK/MATH2221.03 Linear Algebra with Applications I. Systems
of linear equations, linear and affine subspaces of Euclidean n-
space, the Gauss-Jordan algorithm, matrices and matrix algebra,
determinants, vector space concepts for Euclidean n-space (linear
dependence and independence, basis, dimension, etc.), various
applications.
Prerequisite or corequisite: As prerequisite, one of
SC/MATH1505.06, AS/MATH1540.03, AS/MATH1550.06, AS/ECON1540.03;
or, as prerequisite or corequisite, one of AS/SC/MATH1000.03,
AS/SC/MATH1013.03, AS/SC/MATH1300.03.
Degree credit exclusions: AS/SC/MATH1025.03, AS/SC/MATH2000.06,
AS/SC/MATH2021.03, SC/ACMS1020.06.

AS/SC/AK/MATH2222.03 Linear Algebra with Applications II. Linear
transformations and their representation by matrices, change of
basis and similarity, eigenvalues and eigenvectors,
diagonalization, inner product spaces, orthogonality, the Gram-
Schmidt algorithm, least squares approximations, abstract vector
spaces, various applications.
Prerequisite: AS/SC/MATH1025.03 or AS/SC/AK/MATH2221.03.
Degree credit exclusions: AS/SC/MATH2000.06, AS/SC/MATH2022.03.

AS/SC/MATH2260.06 An Introduction to Combinatorics. Basic graph
theory, permutations, combinations, inclusion-exclusion
principle, recurrence relations, generating functions, occupancy
problems, application to probability theory, geometry of the
plane, maps on the sphere, colouring problems, finite structures,
systems of distinct representatives, existence problems, magic
squares, Latin squares.
Prerequisite: One OAC in mathematics or equivalent.

AS/SC/AK/MATH2270.03 Differential Equations. Introduction to
differential equations, including a discussion of the formation
of mathematical models for real phenomena; solution by special
techniques; applications; linear equations; solutions in series;
other topics if time permits.
Prerequisites: AS/SC/MATH2010.03 or AS/SC/MATH2015.03 or
AS/SC/AK/MATH2310.03; AS/SC/MATH1025.03 or AS/SC/MATH2021.03 or
AS/SC/AK/MATH2221.03.
AS/SC/MATH2280.03 The Mathematical Theory of Interest. Topics
include measurement of interest, annuities, amortization of
loans, bonds, sinking funds and depreciation. The course is at a
level which will prepare students for the interest theory portion
of the Society of Actuaries examinations.
Prerequisite: One of AS/SC/MATH1010.03, AS/SC/MATH1014.03,
AS/SC/MATH1310.03.
Degree credit exclusion: AS/AK/MATH2580.06.

AS/SC/AK/MATH2310.03 Calculus of Several Variables with
Applications. Vector functions, partial derivatives, gradient,
multiple integrals, line integrals, optimization, applications.
Offered in both terms.
Prerequisite: One of AS/SC/MATH1010.03, AS/SC/MATH1014.03,
AS/SC/MATH1310.03.
Degree credit exclusions: AS/SC/MATH2010.03, AS/SC/MATH2015.03.

AS/SC/MATH2320.03 Discrete Mathematical Structures. This course
covers the algebraic and combinatorial structures that are needed
in computer science. Topics include set theory, functions,
relations, combinatorics, elements of graph theory, posets,
lattices, Boolean algebras, moniods, groups, morphisms,
congruence relations. Intended primarily, but not exclusively,
for students in Computer Science.
Prerequisite: AS/SC/AK/MATH1090.03 or AS/SC/MATH1120.03 or any
2000-level MATH course (without second digit 5) or permission of
the course coordinator.

AS/SC/AK/MATH2560.03 Elementary Statistics I. Displaying and
describing distributions, normal distibution. Relationships
between variables, regression and correlation. The need for
design, experimental design and sampling design. Sampling
distributions, bias, variability. Probability models, random
variables, probability laws.
Prerequisite: Ontario Grade 12 Advanced Mathematics.
Degree credit exclusions: AS/SC/MATH1131.03, SC/BIOL3080.03,
SC/BIOL3090.03, AS/ECON2500.03, AS/SC/GEOG2420.03,
AS/SC/PHED2050.03, AS/SC/PSYC2020.06, AS/SC/PSYC2021.03,
AS/SOCI3030.06. Not open to any student who has successfully
completed AS/SC/MATH2030.06.

AS/SC/AK/MATH2570.03 Elementary Statistics II. Binomial
distribution, sampling distribution of sample proportions and
means, central limit theorem. Confidence intervals, tests and
decisions, abuse of tests. Inference for a single mean, comparing
two means, and for spread. Contingency tables. Simple regression
and basic analysis of variance.
Prerequisite: AS/SC/AK/MATH2560.03.
Degree credit exclusions: AS/SC/MATH1132.03, SC/BIOL3080.03,
SC/BIOL3090.03, AS/ECON3210.03, AS/ECON3500.03,
AS/SC/GEOG2420.03, AS/SC/PSYC2020.06, AS/SC/PSYC2022.03,
AS/SOCI3030.06. Not open to any student who has successfully
completed AS/SC/MATH2030.06.

AS/AK/MATH2580.06 Mathematics of Investment and Actuarial
Science. Theory of interest; annuities certain; amortization and
sinking funds; evaluation of bonds and other investments;
depreciation, depletion and capital cost; insurance, including
mortality tables, principles of life annuities, premiums and
reserves.
Prerequisite: One full university mathematics course.
Degree credit exclusion: AS/SC/MATH2280.03.

AS/SC/MATH3000.06 Problem Seminar. Heuristics (e.g., symmetry,
subcases, parity, reformulation, recursion); pigeon hole
principle; modular arithmetic; algebraic identities; summation of
series; analytic methods; inequalities; vector and complex
geometry.
Prerequisites: One of AS/SC/AK/MATH1090.03, AS/SC/MATH1120.03,
AS/SC/MATH2090.03, AS/SC/MATH2320.03; AS/SC/MATH2022.03 or
AS/SC/AK/MATH2222.03; AS/SC/MATH2010.03 or AS/SC/MATH2015.03 or
AS/SC/AK/MATH2310.03.

AS/SC/AK/MATH3010.03 Vector Integral Calculus. Integrability of
continuous functions over suitable domains, iterated integrals
and Fubini's theorem, counterexamples, change of variables,
Jacobian determinants, polar and spherical coordinates, volumes,
vector fields, divergence, curl, line and surface integrals,
Green's and Stokes' theorems, differential forms, general Stokes'
theorem.
Prerequisite: AS/SC/MATH2010.03, or AS/SC/AK/MATH2310.03, or
AS/SC/MATH2015.03 and written permission of the Mathematics
Undergraduate Director (normally granted only to students
proceeding in Honours programmes in Mathematics or in the
Specialized Honours Programme in Statistics).
Prerequisite or corequisite: AS/SC/MATH2022.03 or
AS/SC/AK/MATH2222.03.
Degree credit exclusion: AS/SC/MATH3310.03.

AS/SC/AK/MATH3020.06 Algebra I. Introduction to the basic
concepts of abstract algebra, with applications: groups (cyclic,
symmetric, Lagrange's theorem, quotients, homomorphism theorems);
rings (congruences, quotients, polynomials, integral domains,
principal-ideal and unique-factorization domains); fields (field
extensions, constructions with ruler and compasses, coding
theory).
Prerequisite: AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03.

AS/SC/AK/MATH3030.03 Stochastic Processes I. Discrete parameter
stochastic processes, including sums of independent random
variables: limit theorems (weak law of large numbers, central
limit theorem), Markov chains, recurrence and transience, birth
and death processes, branching processes.
Prerequisite: AS/SC/AK/MATH2030.03.
Degree credit exclusion: Not open to students who have completed
or are taking AS/SC/MATH4430.03.

AS/SC/MATH3033.03 Classical Regression Analysis.  General linear
model. Properties and geometry of least-squares estimation.
General linear hypothesis, confidence regions and intervals.
Multicollinearity. Relationship between ANOVA models and linear
models. Residual analysis, outliers, partial and added variable
plots.
Prerequisite: AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03.
Corequisite: AS/SC/AK/MATH3131.03 or permission of the course
coordinator.
Degree credit exclusions: AS/SC/AK/MATH3330.03,
AS/SC/GEOG3421.03, AS/SC/PSYC3030.06.

AS/SC/MATH3034.03 Modern Regression Analysis. Selecting best
model, cross-validation. Influence diagnostics. Weighted least
squares, correlated errors, transformations, Box-Cox
transformations. Logistic and Poisson regression. Generalized
linear models. Multicollinearity, ridge regression. Topics
selected from non-linear regression, scatterplot smoothing, non-
parametric regression, additive non-linear regression, projection
pursuit, robust regression.
Prerequisite: AS/SC/MATH3033.03.
Degree credit exclusions: AS/SC/AK/MATH3230.03,
AS/SC/GEOG3421.03, AS/SC/PSYC3030.06.

AS/SC/AK/MATH3050.06 Introduction to Geometries. Analytic
geometry over a field with vector and barycentric coordinate
methods, affine and projective transformations, inversive
geometry, foundations of Euclidean and non-Euclidean geometry,
applications throughout to Euclidean geometry.
Prerequisite: AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03 or
permission of the course coordinator.

AS/SC/MATH3100.03 Famous Problems in Mathematics. An attempt to
foster an appreciation of the history, the personalities and some
of the content of different areas of mathematics, by means of a
study of some specific problems which have exercised the minds of
mathematicians.
Prerequisites: At least 12 credits from 2000-level MATH courses
(without second digit 5) or permission of the course coordinator.

AS/SC/AK/MATH3110.03 Introduction to Mathematical Analysis.
Proofs in calculus and analysis. Topics include sets, functions,
axioms for R, applications of the completeness axiom,
countability, sequences and their limits, monotone sequences,
limits of functions, continuity.
Prerequisite: AS/SC/MATH1310.03 or AS/SC/MATH1014.03.
Prerequisites or corequisites: AS/SC/AK/MATH2310.03 or
AS/SC/MATH2010.03 or AS/SC/MATH2015.03; AS/SC/MATH2021.03 or
AS/SC/AK/MATH2221.03 or AS/SC/MATH1025.03.
Degree credit exclusion: AS/SC/MATH1010.03.

AS/SC/AK/MATH3131.03 Mathematical Statistics I (formerly
AS/SC/MATH3030.03 - before 1993/94). Topics include common
density functions, probability functions, principle of
likelihood, the likelihood function, the method of maximum
likelihood, likelihood regions, tests of hypotheses, likelihood
ratio tests, goodness of fit tests, conditional tests, and
confidence sets with a view towards applications.
Prerequisite: AS/SC/AK/MATH2030.03 or permission of the course
coordinator.
Degree credit exclusion: AS/SC/MATH3030.03 (taken before
1993/94).

AS/SC/AK/MATH3132.03 Mathematical Statistics II (formerly
AS/SC/MATH3031.03 - before 1993/94). Important examples and
methods of statistical estimation and hypothesis testing are
discussed in terms of their mathematical and statistical
properties. Topics include sufficiency, Bayesian statistics,
decision theory, most powerful tests, likelihood ratio tests.
Prerequisite: AS/SC/MATH3030.03 (taken before 1993/94) or
AS/SC/AK/MATH3131.03.
Degree credit exclusions: AS/SC/MATH3031.03, AS/SC/MATH3130.03.

AS/SC/MATH3140.06 Number Theory and Theory of Equations. A study
of topics in number theory and theory of equations using relevant
methods and concepts from modern algebra, such as Abelian groups,
unique factorization domains and field extensions.
Prerequisite: AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03 or
permission of the course coordinator.

AS/SC/AK/MATH3170.06 Operations Research I. A study of linear
programming; transportation problems, including network flows,
assignment problems and critical path analysis; integer
programming; dynamic programming and an introduction to
stochastic models. Application to a set of problems
representative of the field of operations research.
Prerequisites: AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03;
SC/AS/COSC1530.03 or SC/AS/COSC1540.03 or equivalent.

AS/SC/MATH3190.03 Set Theory and Foundations of Mathematics. The
following topics are covered: paradoxes in native set theory;
functions and relations, transfinite numbers, their ordering and
their arithmetic; well-ordered sets and ordinal numbers; Zorn's
lemma; an introduction to axiomatic set theory.
Prerequisite(s): AS/SC/MATH2022.03, or AS/SC/AK/MATH2222.03, or
both AS/SC/MATH2090.03 and AS/SC/MATH2320.03.

AS/SC/AK/MATH3210.03 Principles of Mathematical Analysis.
Rigorous presentation, with proofs, of fundamental concepts of
analysis: limits, continuity, differentiation, integration,
fundamental theorem.
Prerequisite: AS/SC/MATH2010.03 or AS/SC/AK/MATH3110.03.

AS/SC/AK/MATH3230.03 Analysis of Variance. Categorical variables;
one factor and two factor analysis; fixed, random and mixed
models; nested designs; an introduction to randomized block and
Latin square designs. Second term.
Prerequisite: AS/SC/AK/MATH3330.03.
Degree credit exclusions: AS/SC/MATH3034.03, AS/SC/GEOG3421.03,
AS/SC/PSYC3030.06.

AS/SC/MATH3241.03 Numerical Methods I. An introductory course in
computational linear algebra. Topics include simple error
analysis, linear systems of equations, linear least squares and
interpolation. (Same as SC/AS/COSC3121.03.)
Prerequisites: SC/AS/COSC1030.03 or SC/AS/COSC1530.03 or
SC/AS/COSC1540.03; AS/SC/MATH1025.03 or AS/SC/AK/MATH2221.03 or
AS/SC/MATH2021.03.
Degree credit exclusion: SC/AS/COSC3121.03.

AS/SC/MATH3242.03 Numerical Methods II. Algorithms and computer
methods for solving problems of differentiation, integration,
differential equations, non-linear equations and unconstrained
optimization. (Same as SC/AS/COSC3122.03.)
Prerequisites: AS/SC/AK/MATH2270.03; AS/SC/MATH3241.03 or
SC/AS/COSC3121.03.
Degree credit exclusion: SC/AS/COSC3122.03.

AS/SC/AK/MATH3260.03 Introduction to Graph Theory. Introductory
graph theory with applications. Graphs, digraphs. Eulerian and
Hamiltonian graphs. The travelling salesman. Path algorithms;
connectivity; trees; planarity; colourings; scheduling; minimal
cost networks. Tree searchs and sortings, minimal connectors and
applications from physical and biological sciences.
Prerequisite: At least 6 credits from 2000-level MATH courses
(without second digit 5).

AS/SC/AK/MATH3270.03 Dynamical Systems. Properties of vector
fields and flows. Equilibrium and periodic solutions. Stability
and energy function method. Invariant manifolds, Poincare-
Bendixson theorem. Hopf-bifurcation, chaotic behaviours.
Applications to interacting populations, reaction kinetics and
damped sinusoidally driven pendulum.
Prerequisites: AS/SC/MATH2021.03 or AS/SC/AK/MATH2221.03 or
AS/SC/MATH1025.03; AS/SC/AK/MATH2270.03.

AS/SC/MATH3271.03 Partial Differential Equations. Partial
differential equations of mathematical physics and their
solutions in various coordinates, separation of variables in
Cartesian coordinates, application of boundary conditions;
Fourier series and eigenfunction expansions; generalized
curvilinear coordinates; separation of variables in spherical and
polar coordinates.
Prerequisites:  AS/SC/AK/MATH2270.03; one of AS/SC/MATH2010.03,
AS/SC/MATH2015.03, AS/SC/AK/MATH2310.03; AS/SC/AK/MATH3010.03 is
also desirable, though not essential, as prerequisite for
students presenting AS/SC/MATH2010.03 or AS/SC/AK/MATH2310.03.
Degree credit exclusion: AS/MATH4200A.06.

AS/SC/MATH3272.03 Special Functions. The special functions of
mathematical physics: Bessel functions, Legendre functions, Gamma
function, Hermite functions, Laguerre functions, Chebyshev
polynomials, hypergeometric and confluent hypergeometric
functions; boundary value problems, heat flow, wave motion in
Cartesian and polar coordinates; Laplace and Fourier transforms.
Prerequisite: AS/SC/MATH3271.03 or permission of the course
coordinator.
Degree credit exclusion: AS/MATH4200A.06.

AS/SC/MATH3280.06 Actuarial Mathematics. Actuarial mathematics at
a level appropriate for examination 150 of the Society of
Actuaries. Topics include survival distributions and life tables,
premiums and reserves for life insurance and annuities, multiple
life functions, multiple decrement models, valuation theory of
pension plans.
Prerequisite: AS/SC/MATH2280.03.
Prerequisite or corequisite: AS/SC/AK/MATH2030.03, or
AS/SC/MATH3030.03 (taken before 1993/94).

AS/SC/AK/MATH3330.03 Regression Analysis. Simple regression
analysis, multiple regression analysis, matrix form of the
multiple regression model, estimation, tests (t- and F-tests),
multicollinearity and other problems encountered in regression,
diagnostics, model building and variable selection, remedies for
violations of regression assumptions. First term.
Prerequisites: One of AS/SC/MATH1132.03, AS/SC/MATH2030.06,
AS/SC/AK/MATH2570.03, AS/SC/PSYC2020.06, or equivalent; some
acquaintance with matrix algebra (such as is provided in
AS/SC/MATH1025.03, SC/MATH1505.06, AS/MATH1550.06,
AS/SC/MATH2021.03, or AS/SC/AK/MATH2221.03).
Degree credit exclusions: AS/SC/MATH3033.03, AS/ECON4210.03,
AS/SC/GEOG3421.03, AS/SC/PSYC3030.06.

AS/SC/AK/MATH3410.03 Complex Variables. An introduction to the
theory of functions of a complex variable with applications to
the evaluation of definite integrals, solution of two-dimensional
potential problems, conformal mapping and analytic continuation.
Prerequisite: AS/SC/MATH2015.03 or AS/SC/AK/MATH3010.03 or
permission of the course coordinator.

AS/SC/MATH3430.03 Sample Survey Design. Principal steps in
planning and conducting a sample survey. Sampling techniques
including simple random sampling, stratified random sampling,
cluster sampling, and sampling with probabilities proportional to
size. Estimation techniques including difference, ratio, and
regression estimation.
Prerequisite: AS/SC/AK/MATH2030.03, or AS/SC/MATH3030.03 (taken
before 1993/94), or AS/SC/AK/MATH3330.03.

AS/SC/MATH3440.03 The Mathematics of Physics. Various topics in
physics which require mathematical analysis are discussed. The
emphasis is on showing how such mathematical techniques as
multivariable calculus, ordinary and partial differential
equations, probability and calculus of variations arise in the
study of these topics. Normally offered in alternate years.
Prerequisite: AS/SC/AK/MATH2270.03.
Prerequisite or corequisite: AS/SC/MATH2015.03 or
AS/SC/AK/MATH3010.03.
Degree credit exclusion: Not open to Physics majors.

AS/SC/MATH3450.03 Introduction to Differential Geometry. Curves
and surfaces in 3-space, tangent vectors, normal vectors,
curvature, introduction to topology and to manifolds.
Prerequisites: AS/SC/AK/MATH3010.03; AS/SC/MATH2022.03 or
AS/SC/AK/MATH2222.03; or permission of the course coordinator.
Degree credit exclusion: AS/SC/AK/MATH4250.06.

AS/SC/MATH3480.03 Introductory Topology. Elementary concepts of
the topology of the plane. Neighbourhoods, continuity, open and
closed sets, compactness, connectedness. Fixed point theorems.
Homotopies of curves. Combinatorial classification of surfaces.
Some three-dimensional topology. Metric spaces.
Prerequisite: AS/SC/MATH2010.03 or AS/SC/MATH2015.03 or
AS/SC/AK/MATH2310.03 or permission of the course coordinator.

AS/MATH3500.06 Mathematics in the History of Culture. An
introduction to the history of mathematical ideas from antiquity
to the present, with emphasis on the role of these ideas in other
areas of culture such as philosophy, science and the arts. (Same
as AS/HUMA3990A.06.)
Prerequisite: 6 credits in university-level mathematics (other
than AS/SC/MATH1500.03, AS/SC/MATH1510.06, AS/MATH1520.06,
AS/SC/MATH1525.03, or SC/ACMS1530.06) is strongly recommended.
Degree credit exclusion: AS/HUMA3990A.06.

AS/SC/MATH4000.06 (4000.03) Individual Project. A project of a
pure or applied nature in mathematics or statistics under the
supervision of a faculty member. The project allows the student
to apply mathematical or statistical knowledge to problems of
current interest. A report is required at the conclusion of the
project.
Prerequisites: Open to students in Honours programmes in Applied
Mathematics, Mathematics, and Statistics. Permission of the
course coordinator is required.

AS/SC/AK/MATH4010.06 Real Analysis. Survey of the real and
complex number systems, and inequalities. Metric space topology.
The Riemann-Stieltjes integral. Some topics of advanced calculus,
including more advanced theory of series and interchange of limit
processes. Lebesgue measure and integration. Fourier series and
Fourier integrals.
Prerequisite: AS/SC/AK/MATH3210.03 or permission of the course
coordinator.

AS/SC/AK/MATH4020.06 Algebra II. Continuation of Algebra I, with
applications: groups (finitely generated Abelian groups, solvable
groups, simplicity of alternating groups, group actions, Sylow's
theorems, generators and relations); fields (splitting fields,
finite fields, Galois theory, solvability of equations);
additional topics (lattices, Boolean algebras, modules).
Prerequisite: AS/SC/AK/MATH3020.06 or permission of the course
coordinator.

AS/SC/AK/MATH4030.03 Probability Theory. Elementary measure
theory, convergence of random variables, strong law of large
numbers, convergence in distribution, stable laws, conditional
expectation, martingales.
Prerequisite: AS/SC/MATH3030.03 (taken after 1993/94) or
AK/MATH3030.03.

AS/SC/AK/MATH4080.06 Topology. Topological spaces, continuity,
connectedness, compactness, nets, filters, metrization theorems,
complete metric spaces, function spaces, fundamental group,
covering spaces.
Prerequisite: AS/SC/MATH3480.03 or AS/SC/AK/MATH3210.03 or
permission of the course coordinator.

AS/SC/MATH4100.03 Topics in Mathematical Education. This course
consists of a series of presentations, by the students, of
mathematical topics chosen in consultation with the instructor. 
Suitability of the material for presentation in high schools is
discussed.
Prerequisite: Permission of the course coordinator.

for 1995/96
AS/SC/MATH4100A.03 Topics in Mathematical Education: Theory and
Practice.
...
(condensed course description of approximately 40 words)
...
A two-hour seminar every two weeks, practical hours. Two terms.
Three credits.
Prerequisites: All 1000- and 2000-level core requirements for an
Honours degree programme in Applied Mathematics, Mathematics,
Mathematics for Commerce, or Statistics; permission of the course
coordinator.
Note: This course is open to students enrolled in the
Intermediate/Senior concurrent Education programme, but may not
be used to satisfy any of the requirements for a first or second
teaching subject.

AS/SC/MATH4110.03 Topics in Analysis. One or two topics which may
be chosen from the following: special functions, integral
transforms, Fourier series, divergent series, asymptotic
expansions, theory of approximation, partial differential
equations, calculus of variations, calculus of manifolds,
introduction to functional analysis, difference equations.
Prerequisite: Permission of the course coordinator.

AS/SC/MATH4120.03 Topics in Algebra. One or two topics which may
be chosen from the following: category theory, commutative
algebra, infinite Abelian groups, non-associative algebras,
presentation theory, representations of finite groups, universal
algebra.
Prerequisite: Permission of the course coordinator.
AS/SC/MATH4130.03 Topics in Probability and Statistics. One or
two topics which may be chosen from the following: statistical
decision theory, statistical inference, sequential analysis,
information theory, large sample theory, design of experiments,
stochastic processes, time series.
Prerequisite: Permission of the course coordinator.

AS/SC/MATH4140.03 Topics in Number Theory. Topics chosen from
quadratic diophantine equations and infinite continued fractions,
elements of algebraic number theory, p-adic numbers, other topics
selected according to student interest.
Prerequisite: Permission of the course coordinator.

AS/SC/MATH4141.03 Advanced Numerical Methods. Systems of non-
linear equations: Newton-Raphson, quasi Newton methods;
optimization problems: steepest descents, conjugate gradient
methods; approximation theory: least squares, singular value
decomposition, orthogonal polynomials, Chebyshev and Fourier
approximation, Pade approximation; matrix eigenvalues: power
method, householder, QL and QR algorithms.
Prerequisite: AS/SC/MATH3242.03 or SC/AS/COSC3122.03.

AS/SC/MATH4142.03 Numerical Solutions to Partial Differential
Equations. Review of partial differential equations, elements of
variational calculus; finite difference methods for elliptic
problems, error analysis, boundary conditions, non-Cartesian
variables, PDE-eigenvalue problems; hyperbolic and parabolic
problems, explicit and implicit methods, stability analysis;
Rayleigh-Ritz and Galerkin method for ODEs, finite element
methods.
Prerequisites: AS/SC/AK/MATH2270.03; AS/SC/MATH3242.03 or
SC/AS/COSC3122.03; AS/SC/MATH3272.03 is strongly recommended.

AS/SC/MATH4150.03 Topics in Geometry. One or two topics which may
be chosen from the following: projective geometry, algebraic
geometry, geometrical algebra, finite geometries, differential
geometry, Riemannian geometry, discrete applied geometry.
Prerequisites: AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03; 6
credits from 3000-level MATH courses (without second digit 5); or
permission of the course coordinator.

for 1995/96
AS/SC/MATH4150C.03 Topics in Geometry: Geometries from a
Transformation Point of View. 
...
(condensed course description of approximately 40 words)
...
Prerequisites: AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03; 6
credits from 3000-level MATH courses (without second digit 5); or
permission of the course coordinator.

AS/SC/MATH4160.03 Combinatorial Mathematics. Topics from algebra
of sets, permutations, combinations, occupancy problems,
partitions of integers, generating functions, combinatorial
identities, recurrence relations, inclusion-exclusion principle,
Polya's theory of counting, permanents, systems of distinct
representatives, Latin rectangles, block designs, finite
projective planes, Steiner triple systems.
Prerequisites: AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03; 6
credits from 3000-level MATH courses (without second digit 5); or
permission of the course coordinator.

AS/SC/MATH4170.06 Operations Research II. Selected topics from
game theory, decision theory, simulation, reliability theory,
queuing theory, non-linear programming, classification,
pattern-recognition and prediction. Each chapter contains an
optimization problem and methods and algorithms for solving it.
The course is rich in examples.
Prerequisites: AS/SC/MATH2010.03 or AS/SC/MATH2015.03 or
AS/SC/AK/MATH2310.03; AS/SC/MATH1132.03 or AS/SC/MATH2030.06 or
AS/SC/AK/MATH2030.03; AS/SC/AK/MATH3170.06; or permission of the
course coordinator.
Degree credit exclusion: AS/MATH4570.06.

AS/SC/MATH4200.06 (4200.03) Special Topics. The department may
offer courses or seminars on particular topics not ordinarily
available. Some Special Topics courses may not be eligible for
Science (SC) credit. Two terms. Six credits. One term. Three
credits.
Prerequisite: Permission of the course coordinator.

AS/SC/AK/MATH4210.03 Complex Analysis. Development of the
principal results in complex variable theory, including Taylor
and Laurent series, the calculus of residues, the maximum modulus
theorem and some special functions. Introduction to some more
advanced topics.
Prerequisite: AS/SC/AK/MATH3410.03 or permission of the course
coordinator.

AS/SC/MATH4230.03 Non-Parametric Methods in Statistics. Order
statistics; general rank statistics; one-sample, two-sample, and
k-sample problems; Kolmogorov-Smirnov statistics; tests of
independence and relative efficiencies.
Prerequisite: AS/SC/MATH3030.03 (taken before 1993/94) or
AS/SC/AK/MATH3131.03; AS/SC/MATH3031.03 or AS/SC/AK/MATH3132.03
is recommended but not required.

AS/SC/MATH4240.03 Topics in Applied Mathematics. One or two
topics which may be chosen from the following:
A    numerical analysis
B    discrete applied mathematics
C    operations research
D    mathematical physics
E    mathematical biology
G    mathematical modelling
Normally offered in alternate years.
Prerequisite: Permission of the course coordinator.

AS/SC/MATH4241.03 Applied Group Theory (formerly
AS/SC/MATH4120M.03 - before 1995/96). Introduction to group
theory and its applications in the physical sciences. Finite
groups. Compact Lie groups. Representation theory, tensor
representations of classical Lie groups, classification of semi-
simple Lie groups.
Prerequisite: AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03.
Degree credit exclusion: AS/SC/MATH4120M.03.

AS/SC/AK/MATH4250.06 Differential Geometry. Curves and surfaces
in 3-space, tangent vectors, normal vectors, curvature,
introduction to topology, manifolds, tangent spaces, multilinear
algebra and tensors. Normally offered in alternate years.
Prerequisites: AS/SC/AK/MATH3010.03; AS/SC/MATH2022.03 or
AS/SC/AK/MATH2222.03; or permission of the course coordinator.
Degree credit exclusion: AS/SC/MATH3450.03.

AS/SC/MATH4270.03 Integral Transforms and Equations. This course
studies the Laplace, Fourier, Hankel and Mellin transforms; the
solution of integral equations; and the treatment of asymptotic
expansions. The applications are to problems in circuit theory,
heat flow, elasticity, transport theory and scattering theory.
Prerequisites: AS/SC/AK/MATH2270.03; AS/SC/AK/MATH3410.03.
Prerequisite(s) or corequisite: AS/SC/MATH3271.03;
AS/SC/MATH3272.03.

AS/SC/MATH4280.03 Risk Theory. A study of the stochastic aspects
of risk with emphasis on insurance applications. Topics include
an introduction to utility theory, individual and collective risk
theory, compound Poisson processes, ruin theory, non-proportional
reinsurance.
Prerequisite: AS/SC/AK/MATH2030.03, or AS/SC/MATH3030.03 (taken
before 1993/94); AS/SC/MATH3280.06 is recommended but not
required.

AS/SC/MATH4290.03 Mathematical Logic. Predicate logic, rules of
inference, elimination of quantifiers, semantics and model
theory, the completeness and compactness theorems, ultrapowers
and non-standard analysis.
Prerequisite: AS/SC/MATH2090.03 or permission of the course
coordinator.

AS/SC/MATH4300.06 (4300.03) Directed Readings. A student may
arrange to do independent study with a member of the Mathematics
and Statistics Department. Such an arrangement must have prior
approval of the department Chair. Faculty of Arts students should
see page ## for regulations governing independent reading
courses. Some Directed Readings topics may not be eligible for
Science (SC) credit. Two terms. Six credits. One term. Three
credits.

AS/SC/MATH4400.06 The History of Mathematics. Selected topics in
the history of mathematics, discussed in full technical detail
but with stress on the underlying ideas, their evolution and
their context.
Prerequisites: 36 credits from MATH courses (without second digit
5), including at least 12 credits at or above the 3000 level. (12
of the 36 credits may be taken as corequisites.)

AS/SC/MATH4430.03 Stochastic Processes II. Continuous parameter
stochastic processes: Markov jump processes, Poisson processes,
renewal theory. Topics from queuing theory, Brownian motion,
stationary processes.
Prerequisite: AS/SC/MATH3030.03 (taken after 1993/94) or
AK/MATH3030.03.

AS/SC/MATH4470.03 Gas and Fluid Dynamics. Fundamental laws;
conservation of mass, momentum and energy; vortex motion;
incompressible, compressible and viscous flows; turbulent flow;
surface waves. (Same as SC/PHYS4120.03.)
Prerequisites: AS/SC/MATH2015.03; AS/SC/AK/MATH2270.03;
SC/PHYS2010.03 or SC/EATS2470.04.
Degree credit exclusions: SC/PHYS3180.03, SC/PHYS4120.03.

AS/MATH4501.03 Financial Accounting. This introduction to
financial accounting takes a conceptual approach with heavy
emphasis on concepts and on case analysis. It examines the
concepts, principles, and practices of financial accounting from
the perspective of the users of financial statements. (Same as
AS/CC4501.03.)
Degree credit exclusions: AS/CC4501.03, AS/ECON3580.03,
AD/ACTG2010.03, AD/ACTG2011.03, AD/ACTG3000.03, AD/ACTG5010.03,
AD/ACTG5100.03.

AS/MATH4502.03 Managerial Accounting. This course focuses on the
basic accounting concepts that form the foundation for management
decisions. Performance appraisal, pricing, financing, output,
investment, and other similar managerial decisions are examined
and applied in case situations. Technical aspects of management
accounting are not emphasized. (Same as AS/CC4502.03.)
Prerequisite: AS/MATH4501.03 or AS/CC4501.03.
Degree credit exclusions: AS/CC4502.03, AS/ECON3590.03,
AD/ACTG3020.03, AD/ACTG5020.03, AD/ACTG5210.015.

AS/MATH4570.06 Applied Optimization. Topics chosen from decision
theory, game theory, inventory control, Markov chains, dynamic
programming, queuing theory, reliability theory, simulation, non-
linear programming. This course is designed primarily for
students in the General Stream of Honours Mathematics for
Commerce.
Prerequisites: AS/SC/AK/MATH3170.06; AS/SC/AK/MATH3330.03;
AS/SC/AK/MATH3230.03 or AS/SC/MATH3430.03.
Degree credit exclusion: AS/SC/MATH4170.06.

AS/SC/MATH4630.03 Applied Multivariate Statistical Analysis. The
course covers the basic theory of the multivariate normal
distribution and its application to multivariate inference about
a single mean, comparison of several means and multivariate
linear regression. As time and interest permit, further related
topics may also be covered.
Prerequisites: AS/SC/MATH3030.03 (taken before 1993/94) or
AS/SC/AK/MATH3131.03; AS/SC/MATH3034.03 or AS/SC/AK/MATH3230.03;
AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03.

AS/SC/MATH4730.03 Experimental Design. An examination of the
statistical issues involved in ensuring that an experiment yields
relevant information. Topics include randomized block, factorial,
fractional factorial, nested, Latin square and related designs.
Further topics as time permits. The emphasis is on applications.
Prerequisites: A second 6 credits in statistics; including either
AS/SC/MATH3033.03, or both AS/SC/AK/MATH3230.03 and
AS/SC/AK/MATH3330.03, or permission of the course coordinator.

AS/SC/MATH4830.03 Time Series and Spectral Analysis. Treatment of
discrete sampled data by linear optimum Wiener filtering, minimum
error energy deconvolution, autocorrelation and spectral density
estimation, discrete Fourier transforms and frequency domain
filtering and the Fast Fourier Transform algorithm. (Same as
SC/EATS4020.03 and SC/PHYS4060.03.)
Prerequisites: SC/AS/COSC1540.03 or equivalent FORTRAN
programming experience; AS/SC/AK/MATH2270.03; one of
AS/SC/MATH2010.03 (before FW92), AS/SC/MATH2015.03,
AS/SC/MATH2310.03 (before FW92), AS/SC/AK/MATH3010.03.
Degree credit exclusions: SC/AS/COSC4010B.03, SC/AS/COSC4242.03,
SC/EATS4020.03, SC/PHYS4060.03.

AS/SC/MATH4930.03 Topics in Applied Statistics. Each time this
course is given, it is on a topic chosen from the following:
A    statistical quality control
B    simulation and the Monte Carlo method
C    forecasting and applied time series
D    applied decision theory.
Prerequisites: AS/SC/AK/MATH3330.03; AS/SC/AK/MATH3230.03 or
AS/SC/MATH3430.03.
Corerequisite (for AS/MATH4930A.03 only): AS/SC/MATH4730.03.
Degree credit exclusion (for AS/MATH4930B.03 only):
SC/AS/COSC3408.03.

for 1995/96
AS/SC/MATH4930B.03 Topics in Applied Statistics: Simulation - a
Statistical Perspective. 
...
(condensed course description of approximately 40 words)
...
Prerequisites: AS/SC/AK/MATH3330.03; AS/SC/AK/MATH3230.03 or
AS/SC/MATH3430.03.
Degree credit exclusion: SC/AS/COSC3408.03.

...

STATISTICS - ARTS, PURE AND APPLIED SCIENCE

See Mathematics and Statistics.