*The Institute of Education *

### 189

Staff: Allan Thomas.

Prerequisite: Completion of. or concurrent enrolment in, Education C or D. This link study subject is not offered to students enrolled in the Library and Information Studies stream.

Contact. A 2-hour seminar/workshop each week for
eight weeks. *(Second semester.) *

Content A study of the roles of the post-primary teacher-librarian as a curriculum and information skills specialist, the post-primary teacher as a subject specialist, and possible interactions in planning and teaching together. Particular reference will be made to enquiry and resource-based learning as exemplified by the developments in the Frameworks documents and the VCE.

Assessment: Written work and practical work equivalent to up to 3000 words (100 percent). Results will be graded.

**481-418 LIBRARY AND LNFORMATION **
**STUDIES D: RESOURCE CENTRE **
**ADMLNISTRATION **

**Credit points: 25.0 **
**Staff: **Barbara Bugg.

**Prerequisites: **Successful completion of Library and
Information Studies B1**1, B12, **B13, Cll, C12, C13,
C14 and C15.

**Contact. **A 1-hour lecture and a 2-hour seminar
each week. ( *Two semesters.) *

**Content: **Aspects of the management of a school
resource centre including: organisation theory;

finance; human resources; physical resources;

management processes: and techniques and teacher- librarianship as a profession.

Assessment Assignments to a maximum of 7500 words (70 per cent); a 2-hour test (30 per cent).

Minimum 80 per cent attendance. Results will be graded.

**Prescribed texts: **Bridgland A et al *Management for *
*information Agencies - Booklets *Library and
Information Studies Division Institute of Education
University of Melbourne Melbourne 1991. *Style *
*Manual: Notes on the Presentation of Essays, Class *
*Papers, Bibliographies *9th edition Library and
Information Studies Division Institute of Education
University of Melbourne Melbourne 1991.

190 *The University of Melbourne Prospectus and Handbook 1992 — Volume Four *

Table of Prerequisites

Subject Prerequisite Special Conditions A92 VCE Maths 3 and 4:

Change and Approximation
*or *Extensions (Change
and Approximation)
*or *Reasoning and Data
*or *Extensions (Reasoning

and Data)
*or *equivalent

Al0 VCE Maths 3 and 4: Must be
Change and Approximation concurrently
*or *Extensions (Change enrolled in,
and Approximation) or have
*or *Reasoning and Data previously
*or *Extensions (Reasoning passed,

and Data) Mathematics

*or *equivalent A9 or A8 or
A92
Subject selection

Students wish to study mathematics for a variety of reasons, including enjoyment of, and interest in, mathematics, the relationship of mathematics to other subject areas, and the need for mathematics in future careers. In particular, mathematics students at the Institute may be classified as having a desire to:

• become a specialist teacher in mathematics;

• be qualified to teach mathematics at junior and middle levels of secondary school but not necessarily at senior levels; and

• study mathematics as an adjunct to studies in other disciplines, but not be qualified to teach mathematics.

Regardless of their goals, students can take both Mathematics A92 and A10, or Mathematics A92 alone, in first year. Mathematics A10 is not a prerequisite for second-year Mathematics subjects.

However, students who are strongly committed to becoming specialist Mathematics teachers are advised to choose Mathematics A10 in first year.

**Table of subjects offered in 1992 **

**Semester Points **

*B-Level *

Mathematics B12

Mathematics B84

Mathematics B87

Mathematics

Computer Studies B10 Computer Studies B7 Mathematics and

Computing 2 (see note 2) B19 B51 B11 B86 B33 B10 B8 B19

11.1,11.1 11.1,11.1 16.7,11.1

11.1 22.2 11.1,11.1

33.3
*C-Level *

Mathematics (see note 3) C32 C41 11.1,11.1 Mathematics C23 C34 11.1,11.1 Mathematics (see note 4) C2 C11 11.1,11.1 Mathematics (see note 3) C81 8.3,8.3 Mathematics: Link

Studies (see note 5) C81 8.3 C92 C93 8.3,8.3

C91 8.3 Computer Studies C5 C6 11.1,11.1

(see note 7) C7 11.1

C2 C3 11.1,13.9 Notes:

1. Mathematics X91 is only available to students enrolled in the Associate Diploma in Science.

2. Mathematics A19 and Mathematics B19 are only(

available to *BEd (Primary) *students.

3. Mathematics C32, C41, C23 and C34 are only available to Year 3 students.

4. Mathematics C2 and C11 are available to both Year 3 and Year 4 students.

5. Mathematics C81 is only available to Year 3 *BEd *
*(Secondary) *students. Mathematics C81 is in the
link study category.

6. Mathematics C91, C92 and C93 are only available
to Year 4 *BEd (Secondary) *students. These
subjects are in the link study category.

7. Computer Studies C2, C5, C6 and C7 are only
available to Year 3 students. Computer Studies
C7 is available as a link study only. Computer
Studies C3 is a link study and is only available o
Year 4 students in the *BEd (Secondary) *and
*BScEd *courses.

**1 **
*A-Level *

Associate Diploma in

Science (see note 1) X91 Basic Core Mathematics A92 Additional Mathematics A10 Discrete Mathematics

Computer Studies A10 Mathematics and

Computing 1 (see note 2) A19
**2 **

X91 A92 A10 A42 A10 A19

25.0 25.0 25.0 11.1 25.0 25.0

**486-146 MATHEMATICS A10: **

**ADDITIONAL MATHEMATICS **
**Credit points: 25.0 **

**Staff: **John Dowsey.

**Pre or corequisite: **Concurrent enrolment or a pass
in Mathematics A92. Credit will not be granted for
both this subject and Mathematics A42.

**Contact:. **Three 1-hour lectures, a 1-hour tutorial
and a 1-hour practical class each week, with weekly

191
problem sheets associated with the tutorials. *(Two *

*semesters.) *

Content: Discrete mathematics, including sets, graphs, groups, recurrence relations; logic and proof;

algorithms and programming; numerical methods;

problem-solving and modelling; applications.

Assessment: Two 3-hour examinations; tests during the year of up to 6 hours in total; six computer projects equivalent to a total of 1500 words; weekly tutorial exercises. Results will be graded.

**486-184 MATHEMATICS: A19 **

**MATHEMATICS AND COMPUTING 1 **
**Credit points: 25.0 **

**Staff: **Ron Welsh.

**Contact:. Two **2-hour lecture/workshops each week.

*(Two semesters.) *

**Content: **Elementary mathematical ideas explored
and developed through investigative approaches.

Appropriate computer applications and technology.

**Assessment: **Written assignments, exercises and
practical work equivalent to 1500 words; seminar
presentation of an individually negotiated topic
equivalent to 2000 words; group project, modelling
assignment, individual contribution equivalent to
2000 words; application of computers relevant to the
subject equivalent to 2250 words. Results will be
graded.

**486-159 MATHEMATICS A42: DISCRETE **
**MATHEMATICS AND NUMERICAL **
**METHODS **

**Credit points: 11.1 **
**Staff: **Barry McCrae.

**Pre orcorequisite: **Concurrent enrolment, or a pass,
in Mathematics A8 or Mathematics A9, or
Mathematics A92. Credit will not be granted for
both this subject and Mathematics A10.

Contact:. A 3-hour lecture and a 2-hour tutorial/

laboratory class each week. *(Second semester.) *
**Content: **Programming: modelling, algorithms,
representation of algorithms, structured
programming. Discrete Mathematics:set theory, logic
and propositions, graphs and digraphs as relations,
recurrence relations,combinations, Boolean algebra,
groups. Numerical Methods: errors, simple numerical
methods for integration and for the solution of non-
linear equations.

**Assessment A **2-hourexamination; up to three hours
of tests during the semester, three computer projects
equivalent to a total of 1000 words; weekly tutorial
exercises. Results will be graded.

**486-185 MATHEMATICS A92: CORE **
**MATHEMATICS **

**Credit points: 25.0 **
**Staff: **Helen Hutchens.

**Prerequisite: **VCE Units 3 and 4: Change and
Approximation or Extensions (Change and
Approximation) or Reasoning and Data, or
Extensions (Reasoning and Data). Credit will not be
granted for both this subject and Mathematics A8 or
Mathematics A9.

**Contact:. **Three 1-hour lectures, a 1-hour tutorial
and a 1-hour practical class; weekly problem sheets
associated with tutorials. *(Two semesters.) *

**Content: **Four of the following topics, depending on
student's mathematical background. Algebra;

functions and graphs; elementary probability and data analysis; probability and statistics; space and number; additional mathematics.

Assessment: Two 3-hour examinations; two assignments, one each semester, totalling approximately 30 hours/1500 words; weekly tutorial exercises. Results will be graded.

486-286 **MATHEMATICS B11: ANALYSIS B **
**Credit points: 11.1 **

**Staff: **Helen Hutchens.

**Prerequisite: **Mathematics B12 or B87.

Contact:. Two 1-hour lectures, a 1-hour tutorial class
each week. *(Second semester.) *

**Content: **Sequences and series: absolute and
conditional convergence, tests for convergence.

Complex functions: exponential and related functions, continuity and differentiability, Cauchy- Riemann equations, analytic functions, and mappings.

Assessment: A 2-hour examination; tutorial and project work totalling up to 20 pages. Results will be graded.

486-288 **MATHEMATICS B12: ANALYSIS A **
**Credit points: 11.1 **

**Staff: **Neal Byrne.

**Prerequisite: **Mathematics A8 or A9. Credit is not
granted for both this subject and Mathematics B87.

**Contact:. **Two 1-hour lectures and a 1-hour tutorial
class each week. *(First semester.) *

**Content: **Infinite and improper integrals. Functions
of two variables: differentiability, chain rules, Taylor
series, stationary points, Lagrange multipliers, and
multiple integrals.

Assessment: A 2-hour examination (100 per cent).

Results will be graded.

192 *The University of Melbourne Prospectus and Handbook 1992 —Volume Four *
**487-239 MATHEMATICS B19: **

**MATHEMATICS AND COMPUTING 2 **
**Credit points: 33.3 **

**Staff: **Ron Welsh.

Prerequisite: Mathematics A19 (Mathematics and Computing 1) or approved equivalent.

**Contact:. **Two 2-hour lecture/workshops and a 1-
hour tutorial each week. *(Two semesters.) *

**Content: **Continuation of Mathematics and
Computing 1. Topics include: appropriate computer
applications and technology. Students will be
expected to adopt a more analytical and independent
approach to their learning.

**Assessment: **Written assignments, exercises and
practical work equivalent to 3000 words; seminar
presentation equivalent to 2000 words; group
research project, individual contribution equivalent
to 3000 words; computer application equivalent to
2000 words. Results will be graded.

**486-294 MATHEMATICS B31: MECHANICS **
This subject is not offered in 1992.

**486-295 MATHEMATICS B32: **

**VECTOR CALCULUS **
**Credit points: 11.1 **
**Staff: **Neal Byrne.

**Prerequisites: **Mathematics A8 or A9; Mathematics
A10 or B87.

**Contact:. **Two 1-hour lectures each week; a 1-hour
tutorial and/or a 1-hour practical class each week for
a total of 16 hours. *(First semester.) *

**Content: Scalar **and vector point functions, gradient,
divergence and curl in cartesian and curvilinear
Coordinates; Cartesian tensors; Theorems of Gauss
and Stokes with applications.

Assessment: A 2-hour examination (100 per cent).

Results will be graded.

486-296 **MATHEMATICS B33: BOUNDARY **
**VALUE PROBLEMS AND DIFFERENTIAL **
**EQUATIONS **

**Credit points: 11.1 **
**Staff: **Neal Byrne.

**Prerequisite: **Mathematics B12 or B87.

**Contact:. Two 1-hour **lectures and a 1-hour tutorial
class each week. *(Second semester.) *

**Content: **Ordinary differential equations of second
order: Euler-type; series solutions; Fourier series;

Legendre functions; Partial Differential Equations:

standard types, separation of variables, application to vibrating strings, membranes and heat conduction.

Assessment: A 2-hour examination; three 1-hour tests; weekly tutorial exercises. Results will be graded.

**486-299 MATHEMATICS B51: **

**NUMERICAL METHODS **
**Credit points: 11.1 **

**Staff: **John Warner.

**Prerequisite: **Mathematics A10 or A42.

**Contact:. Two **1-hour lectures and a 1-hour tutorial
class each week. This subject may be taken as a
project in cases approved by the Lecturer-in-Charge,
particularly in years when the lecture program is not
offered. *(Second semester.) *

**Content: **Mathematical discussion (including error
analysis) and programming of selected numerical
methods from the following general fields: solution
of non-linear equations, systems of linear equations,
numerical integration, ordinary differential
equations, approximation of functions; difference
equations.

Assessment: A 2-hour examination (50 per cent);

three equally-weighted programming projects (25 per cent); equally-weighted weekly assignments (25 per cent). Results will be graded.

**487-206 MATHEMATICS B84: **

**LINEAR ALGEBRA **
**Credit points: 11.1 **
**Staff: **Helen Hutchens.

**Prerequisite: **Mathematics A8 or A9.

**Contact:. Two **1-hour lectures and a 1-hour tutorial
class each week. *(First semester.) *

**Content: Vector **Spaces: bases and dimension; inner
product. Linear Transformations: matrix
representation, equivalent matrices; eigenvalues and
eigenvectors; equivalent relations on matrices;

applications of linear algebra.

Assessment: A 2-hour examination; tutorial and project work totalling up to 20 pages. Results will be graded.

**487-208 MATHEMATICS B86: **

**PROBABILITY AND STATISTICS **
**Credit points: 11.1 **

**Staff: **Meei Pyng Ng.

**Prerequisites: **Mathematics A8 or A9; Mathematics
B12 or B87.

**Contact:. Two 1-hour lectures and a 1-hour **tutorial
class each week. *(Second semester.) *

**Content: **Bivariate random variables; sampling from
normal populations; analysis of variance; linear
regression and correlation; rank methods.

Assessment: A 3-hour examination; a project

*The Institute of Education *

### 193

equivalent to 1500 words; weekly tutorial exercises.

Results will be graded.

**487-209 MATHEMATICS B87: **

**CONTLNUING MATHEMATICS **
**Credit points: 16.7 **

**Staff **Meei Pyng Ng.

**Prerequisite: **Mathematics A8 or A9. Credit is not
granted for both this subject and Mathematics B12.

**Contact. **Three 1-hour lectures, a 1-hour tutorial
and a 1-hour practical class each week. *(First *
*semester.) *

**Content: **Complex numbers; polar coordinates;

mathematical induction; inverse circular and hyperbolic functions; integration by parts; functions of two variables: partial derivatives, double integration; Taylor series; vectors and application;

first and second order differential equations.

**Assessment A **3-hour examination; three 1-hour
tests during the semester, weekly tutorial exercises.

Results will be graded.

**618-262 DECISION-MAKING **
**Credit points: 12.0 **

**Staff: **Moshe Sniedovich.

**Prerequisites: **Mathematics 02 and 04.

**Contact 39 **lectures (three each week). *(Second *
*semester.) *

**Content **Topics in decision analysis including: single
and multi-stage decision models, **in **particular those
using linear programs; zero-sum games; preference
relations and optimisation; multi-criteria decision-
making: decision trees; use of computer packages for
the Macintosh.

**Assessment Written **assignments totalling up to 26
pages: up to three hours of written end-of-semester
examinations. Results will be graded.

**618-221 MATHEMATICAL LOGIC **
**Credit points: 12.0 **

**Staff: John **Groves.

**Prerequisite: **Mathematics B87 or B12.

**Contact. 39 lectures **(three each week). *(First *
*semester.) *

**Content **Topics include: first order theories and
basic model theory, including completeness and
compactness: undecidability and incompleteness.

Assessment Written assignments totalling up to 26 pages; up to three hours of written end-of-semester examination. Results will be graded.

**486-376 MATHEMATICS C2: **

**COMBINATORICS AND NUMBER THEORY **
**Credit points: 11.1 **

**Staff: **Angelina Byrne.

**Prerequisites: **Mathematics B87 or B12, plus one
other Group 2 Mathematics subject.

**Contact:. **Two 1-hour lectures and a 1-hour tutorial
class each week for one semester. *(First semester.) *
**Content: **General rules of combinatorics: samples,
permutations and combinations, distributions and
partitions, occupancy problems, recurrence relations,
generating functions. Number systems: postulates
for the positive integers, prime numbers and the
fundamental theorem of arithmetic, congruences,
diophantine equations, quadratic residues, and
primitive roots.

Assessment A 2-hour examination; up to 30 pages of written work. Results will be graded.

**486-377 MATHEMATICS C3: GEOMETRY **
This subject is not offered in 1992.

**486-379 MATHEMATICS C5: INDIVIDUAL **
**READING AND STUDY COURSE **

**Credit points: 5.6 to 13.9 **
**Staff: To be advised. **

**Prerequisites: **486-179 and 486-181 and at least 8.0
points of other mathematics study or equivalent.

This subject is normally only available to enable completion of a qualification.

Contact: As negotiated in the IEP.

**Content: Each student **must negotiate an Individual
Educational Program (IEP) of between 2.0 and 5.0
points with the Head of the School of Science and
Mathematics Education. The IEP will be supervised
by a member of the Division of Mathematics and
Computer Science. Each IEP must give details of the
content to be covered, the books to be read/studied,
the length of time to be committed and number of
points for the program, as well as assessment details
and the number of hours of regular contact to be
made between the supervisor and the student.

Assessment: As specified in the IEP.

**486-381 MATHEMATICS C11: **

**COMPLEX FUNCTIONS **
**Credit points: 11.1 **
**Staff: Angelina Byrne. **

**Prerequisites: Mathematics B11 and either **
**Mathematics B12 or B87. **

**Contact:. Two 1-hour lectures and a 1-hour tutorial **
**each week for one semester. ***(Second semester.) *

194 *The University of Melbourne Prospectus and Handbook 1992 — Volume Four *
**Content: **Integration: definition, Cauchy's integral

formulae, Taylor and Laurent series, singularities, residues, contour integration; conformal mapping.

Assessment: A 2-hour written examination; up to 10 pages of written assignments. Results will be graded.

**486-383 MATHEMATICS C21: **

**STATISTICAL ANALYSIS **
This subject is not offered in 1992.

**486-384 MATHEMATICS C23: PROBABILITY **
**AND STOCHASTIC PROCESSES **

**Credit points: 11.1 **
**Staff: **John Dowsey.

**Prerequisites: **Mathematics B84 and B86.

**Contact:. **Two 1-hour lectures and a 1-hour tutorial
class each week, with a directed reading assignment.

*(First semester.) *

**Content: **Probability Theory: generating functions
and their applications. Introduction to stochastic
processes; Queuing Theory: simulation.

Assessment: A 3-hour examination or equivalent; a project equivalent to 2500 words; weekly tutorial exercises. Results will be graded.

486-385 **MATHEMATICS C31: **

**MATHEMATICAL METHODS **
This subject is not offered in 1992.

**486-386 MATHEMATICS C32: **

**LINEAR PROGRAMMING **
**Credit points: 11.1 **

**Staff: **Angelina Byrne.

**Prerequisites: **Mathematics B84 and B87, or
Mathematics B12.

**Contact:. **Two 1-hour lectures each week for 10
weeks; a 1-hour tutorial and/or a 1-hour practical
class each week for a total of 12 hours; a project in
lieu of lectures for two weeks. *(First semester.) *
**Content: **The linear programming problem; the
simplex method and related algorithms; duality;

parametric linear programming; sensitivity analysis;

integer linear programming; the transportation problem; game theory.

Assessment: A 2-hour written examination; an assignment of up to 25 pages. Results will be graded.

**486-387 MATHEMATICS C33: **

**GRAPH THEORY **

This subject is not offered in 1992.

486-388 **MATHEMATICS C34: NETWORKS: **

**FLOW THEORY AND APPLICATIONS **
**Credit points: 11.1 **

**Staff: **John Dowsey.

**Prerequisites: **Mathematics B87 or B12, plus one
other Group 2 Mathematics subject.

**Contact:. **Three 1-hour lectures each week for eight
weeks, a 1-hour tutorial and/or a 1-hour practice
class each week for a total of 12 hours; two directed
reading assignments. *(Second semester.) *

**Content: The place of **network concepts in the
solution of practical problems; shortest (longest)
path algorithms; critical path analysis and associated
problems; maximum flow algorithms; applications.

Assessment: A 2-hour examination; two projects equivalent to 1500 words each; weekly tutorial exercises. Results will be graded.

**486-391 MATHEMATICS C41: **

**ALGEBRAIC STRUCTURES **
**Credit points: 11.1 **

**Staff: **Helen Hutchens.

**Prerequisites: **Mathematics B87 or B12, plus one
other Group 2 Mathematics subject.

**Contact:. **Two 1-hour lectures and a 1-hour tutorial
class each week. *(Second semester.) *

**Content:Introduction **to algebraic structures: groups,
rings, fields, vector spaces and modules; basic
structural results and applications.

Assessment: A 2-hour examination; tutorial and project work of up to 20 pages. Results will be graded.

486-395 **MATHEMATICS C81: COMPUTERS **
**IN MATHEMATICS EDUCATION **

**Credit points: 83 **
**Staff: **John Warner.

**Special requirements: This **subject qualifies as a link
study within the requirements of the *BScEd *course.

**Pre or corequisites: A **pass in Mathematics B87 or
B12, plus one other Group 2 Mathematics subject.

Students should have passed or be currently enrolled in Education C or C00.

**Contact:. A **2-hour lecture/workshop each week.

*(Second semester.) *

**Content: **Topics include: software for mathematics
classrooms; the computer as an adjunct to
mathematical tasks and investigations; review and

**195 **
evaluation of mathematics software; the design of

simple software tools; the use of spreadsheets in modelling; algebraic and numerical solvers; the computer as an electronic blackboard.

Assessment Equally-weighted tutorial exercises (50 per cent); two major assignments, each equivalent to an essay of 1500 words. Minimum 80 per cent attendance; all exercises and assignments must be submitted. Results will be graded.

**486-398 MATHEMATICS C91: **

**MATHEMATICAL MODELLING **
**Credit points: 8.3 **

**Staff: **Angelina Byrne.

**Special requirements:This **subject qualifies as a link
study within the requirements of the *BScEd *course.

**Pre or corequisites: **Passes in any two 11.1-point
Group 3 Mathematics subjects. Students should have
passed or be currently enrolled in Education C10 or
Education **D. **

**Contact:. **Three hours of lecture/seminar/video
presentations and a 1-hour tutorial each week for
eight weeks. *(Second semester.) *

**Content: **Students prepare seminar papers and
assignments on selected topics in mathematical
modelling under the supervision of a staff member.

Assessment Up to 100 pages of written assignments;

class participation and a seminar presentation of up to one hour. Minimum 80 per cent attendance; all assignments must be submitted. Results will be graded.

**486-399 MATHEMATICS C92: **

**HISTORY OF MATHEMATICS **
**Credit points: 8.3 **

**Staff: **William Pye.

**Special requirements:This **subject qualifies as a link
study within the requirements of the *BScEd *course.

**Prerequisite: Any two **11.1-point Group 2
Mathematics subjects.

**Contact. **Four 1-hour seminar/discussions each week
for seven weeks of the semester. *(Second semester.) *
**Content: **Early first mathematics; expansion of
mathematical truth in the Middle Ages; geometry
and the truth about nature; arithmetic, algebra, nature
and the mind; The Infinite: large and small;

strengthening of foundations. Seminars will be based on projects prepared and presented by students.

Assessment: Preparation and presentation of at least one class project; a paper of approximately 1500 to 2000 words and two papers of approximately 1000 to 1500 words each. Students must present at least one topic in class and complete all written work. Minimum 80 per cent attendance. Results will be graded.

**487-300 MATHEMATICS C93: **

**DEVELOPMENTS IN MATHEMATICS **
**EDUCATION **

**Credit points: 8.3 **
**Staff: **Gary Asp.

**Special requirements: This **subject qualifies as a link
study within the requirements of the *BScEd *course.

**Prerequisite: **Any two 11.1-point Group 3
Mathematics subjects.

**Contact. **Four 1-hour sessions each week for six
weeks, including lecture/seminar/discussion sessions,
student presentations, workshop/laboratory sessions
and excursions. *(To be advised.) *

**Content: **General issues affecting the present
direction of mathematics education, with particular
emphasis on Victoria, including major themes
developed by current school mathematics curriculum
projects.

Assessment: Up to six assignments equivalent to 600 words each; a major assignment equivalent to 2500 words requiring independent exploration of one issue affecting mathematics education. Students must satisfactorily complete all assignments; minimum 80 per cent attendance. Results will be graded.

**618-311 MATHEMATICAL MODELLING **
**Credit points: 15.0 **

**Staff: **Frank Barrington.

**Prerequisites: **Mathematics B87, B84 and B11.

**Contact:. **Thirteen 2 to 3-hour hour lecture/tutorials.

*(First semester.) *

**Content: **Topics include: the theory and practice of
mathematical modelling applied to areas such as
economics, social sciences, ecology and population
dynamics, traffic flow and mechanics.

Assessment: Project reports and written assignments totalling up to 40 pages; up to two hours of end-of- semester written examinations. Results will be graded.

**618-301 METRIC SPACES **
**Credit points: 15.0 **

**Staff: **Klaus Ecker.

**Prerequisites: **Mathematics 618-101 and 618-102, or
equivalent.

**Contact:. **39 lectures. *(First semester.) *

**Content: **Metric spaces: properties of the real line;

metrics and norms, open and closed sets.

Convergence: convergence, completeness, continuity, compactness, connectedness; contraction mappings; applications.

Assessment: Written assignments of up to 26 pages in total; up to three hours of end-of-semester written examinations. Results will be graded.