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 B11, 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.