This course focuses on the language of mathematical arguments. Rather than attacking advanced topics, we will use simple mathematics to develop an understanding of how results are established. We begin with clearly stated and plausible assumptions or axioms and then develop a more and more complex theory from them. The course, and the lecturer, will have succeeded if you finish the course able to construct valid arguments of your own and to criticise those that are presented to you.
Learning Outcomes
Upon successful completion, students will have the knowledge and skills to:
On satisfying the requirements of this course, students will have the knowledge and skills to:1. Understand the role of rigorous proof in mathematics.
2. Be able to construct written arguments using induction, proof by contradiction, counting arguments, and countability.
3. Develop problem-solving skills in elementary number theory, graph theory, and probability theory.
4. Present rigorous mathematical proofs orally and in writing.
Indicative Assessment
Weekly problem sets (30%, LO 1,2,3)Mid-semester and final exams (20% and 30%, respectively, LO 1,2,3)
Mid-semester and final exams (20%, LO 1,2,3,4)
In addition,
1. in consultation with the course lecturer, students will select a topic related to this course, and through reading of the relevant literature, acquire a fundamental knowledge of that topic.
2. Write a report on the selected topic and highlight key questions currently researched in the field.
(20%, LO 1,2,3,4)
In response to COVID-19: Please note that Semester 2 Class Summary information (available under the classes tab) is as up to date as possible. Changes to Class Summaries not captured by this publication will be available to enrolled students via Wattle.
The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.
Workload
Three lectures per week and regular workshops.Requisite and Incompatibility
You will need to contact the Mathematical Sciences Institute to request a permission code to enrol in this course.
Prescribed Texts
Number, Symmetry and Shape by Diane Herrmann and Paul J. Sally Jr.Introduction to Mathematical Thinking: Problem-Solving and Proof by John D'Angelo and Douglas West
Preliminary Reading
Godel, Escher, Bach by Douglas HofstadterProofs and Refutations: The Logic of Mathematical Discovery by Imre Lakatos
Fees
Tuition fees are for the academic year indicated at the top of the page.
If you are a domestic graduate coursework or international student you will be required to pay tuition fees. Tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.
- Student Contribution Band:
- 2
- Unit value:
- 6 units
If you are an undergraduate student and have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). You can find your student contribution amount for each course at Fees. Where there is a unit range displayed for this course, not all unit options below may be available.
| Units | EFTSL |
|---|---|
| 6.00 | 0.12500 |
Course fees
- Domestic fee paying students
| Year | Fee |
|---|---|
| 2020 | $4050 |
- International fee paying students
| Year | Fee |
|---|---|
| 2020 | $5760 |
Offerings, Dates and Class Summary Links
ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage.
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.
First Semester
| Class number | Class start date | Last day to enrol | Census date | Class end date | Mode Of Delivery | Class Summary |
|---|---|---|---|---|---|---|
| 3588 | 24 Feb 2020 | 02 Mar 2020 | 08 May 2020 | 05 Jun 2020 | In Person | View |