This is a one semester, 2 point paper, taught at the City Campus.
This paper aims to give a broad introduction to mathemetical thinking and communication, rather than technique. The main thrust is not so much finding the right answer to a problem as convincing someone else (or yourself) that the answer must be right.
By the end of this paper, you will be familiar with the basics of how to go about proving something, you will be used to seeing a new definition and deriving simple consequences of that definition, and you will have met widely used mathematical objects like groups and equivalence relations. You will also have learned more about some familiar structures: the natural numbers and the real numbers. All this will prepare you well for Stage 3 papers in Pure Mathematics. It should also prepare you to tackle new real-life problems instead of limiting yourself to problems someone else has already solved for you!
Because the nature of the course is quite different from what you have seen before, the teaching and assessment methods will also be new. An important part of what you are learning is the ability to communicate mathematics. Some time during lectures will be given over to group discussions, where you will be expected to decide and to convince your fellow students of how to prove the propositions on the blackboard. You will also be expected to participate in ``Collaborative Tutorials'': see below for details.
One of 445.130, 445.152, 445.109, 445.208 or equivalent.
Calculators will be permitted in the Test and the Examination.
The text is Chapter Zero Fundamental Notions of Abstract Mathematics by C. Schumacher (Addison-Wesley). The course will follow this book closely, so we strongly recommend that you purchase your own copy. It will be available on short loan in the Science Library.
This will be based on assignments (30%), the semester test (10%) and the final exam (60%), OR on assignments (10%), the semester test (10%) and the final exam (80%), whichever is higher.
Note that the test and coursework count at least 20% towards your final mark.
Work will be marked for its clarity and precision as well as its content. For example, a proof poorly expressed with symbols undefined might be failed even if the ``idea'' of the proof is correct. Conversely, if a proof is well set up it might gain a pass mark even if the method is completely wrong. We encourage students to work together on the assignments, but remember that what you hand in must be your own work!
The time and date of the Semester Test will be announced in class. No makeup test will be given.
STOP PRESS: the test will be on Wednesday 20 September in MLT1 from 6:30pm to 8:00pm.
The ten assignments are to be handed in by 4pm on the following Wednesdays: 26 July, 2 August, 9 August, 16 August, 23 August, 13 September, 20 September, 27 September, 4 October, 11 October.
The Student Resource Centre will not accept late assignments under any circumstances. Assignments placed in the wrong box will not be marked, so be careful where you put your work. The overall assignment mark will be based on these assignments and on marks in the collaborative tutorials (see below). Each assignment will be worth 30 marks and each collaborative tutorial will be worth 10 marks, to give a total out of 360 marks.
There are two streams, at 9am each weekday and at 3pm each weekday. The Tuesday-Friday sessions will be lectures.
Tutorial sessions will be held every Monday (except the first day of the semester). There will be five `regular' tutorials with an emphasis on review and working through problems and six `collaborative' tutorials where students work in groups of three on a problem to be handed in at the end of the session for marking.
The collaborative tutorials are run as follows: a tutorial assignment is completed during the tutorial working in groups of 3 (although we may accept groups 2 or 4 people if necessary). You don't have to be in the same group each time.
There will be a few short questions designed to be able to be answered in about 40-45 minutes. 10 minutes before the end you will be required to put your answers onto provided sheets which are handed in. A brief rundown of the answers is then given on an overhead.
R is a `regular' tutorial, C is a `collaborative' tutorial, A is an assignment due date. The date of the test is to be advised.
| Week | Dates | Mon | Tues | Wed | Thurs | Fri |
| 1 | 17-21 July | |||||
| 2 | 24-28 July | C1 | A1 | |||
| 3 | 31 July-4 August | R1 | A2 | |||
| 4 | 7-11 August | C2 | A3 | |||
| 5 | 14-18 August | R2 | A4 | |||
| 6 | 21-25 August | C3 | A5 | |||
| 28 August-8 September | BREAK | |||||
| 7 | 11-15 September | R3 | A6 | |||
| 8 | 18-22 September | C4 | A7 | |||
| 9 | 25-29 September | R4 | A8 | |||
| 10 | 2-6 October | C5 | A9 | |||
| 11 | 9-13 October | R5 | A10 | |||
| 12 | 16-20 October | C6 | ||||
You are encouraged to approach your lecturers with any questions or suggestions you have about the paper. Specific office hours will be announced in class.
| David McIntyre (Paper Coordinator) | mcintyre@math.auckland.ac.nz |
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|---|---|---|
| WWW Homepage | http://www.math.auckland.ac.nz/~mcintyre |
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| Office | Maths/Physics Building, Room 306 | |
| Phone | 373 7599 ext 8763 | |
| David Smith | smith@math.auckland.ac.nz |
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| Office | Maths/Physics Building, Room 312 | |
| Phone | 373 7599 ext 8778 | |
| Majid Ali | majid@math.auckland.ac.nz |
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| Office | Maths/Physics Building, Room 407 | |
| Phone | 373 7599 ext 5865 | |
| David Alcorn | alcorn@math.auckland.ac.nz |
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| Office | Maths/Physics Building, Room | |
| Phone | 373 7599 ext 8777 |
The WWW homepage for this paper is
http://www.math.auckland.ac.nz/~class255.
From here you will be able to download copies of the assignments and other handouts, and obtain information about your coursework marks.
This document was generated using the LaTeX2HTML translator Version 97.1 (release) (July 13th, 1997)
Copyright © 1993, 1994, 1995, 1996, 1997, Nikos Drakos, Computer Based Learning Unit, University of Leeds.
The translation was initiated by David McIntyre on 7/12/2000