- Class Number 4467
- Term Code 2930
- Class Info
- Unit Value 6 units
- Mode of Delivery In Person
- Dr Malcolm Brooks
- Dr Malcolm Brooks
- Class Dates
- Class Start Date 25/02/2019
- Class End Date 31/05/2019
- Census Date 31/03/2019
- Last Date to Enrol 04/03/2019
Introduction to discrete mathematics and its use in mathematical modelling. Emphasis will be placed on developing facility, technique and use in applications. Modelling of processes and phenomena which occur in economics and the physical, environmental and life sciences will be used as a vehicle throughout. Topics to be covered include: combinatorics and counting, induction and recurrence relations, graph theory and networks, matrix arithmetic and Markov chains, logic and finite set theory.
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. Recall, invent or interpret examples of motivation for mathematical constructs introduced in the course and used in discrete mathematics as models of processes in the world
2. Be sufficiently familiar with terminology from discrete mathematics used in the course as to be able to interpret, use and attempt to answer questions involving these words
3. Translate representations of mathematical information between the different formats presented in the course
4. Competently perform mathematical calculations in discrete mathematics using methods presented in the course
5. To an extent determined by each student's needs, interests and input, develop maturity of mathematical reasoning as well as general academic skills such as information literacy, tenacity, communication and collaboration. (This learning outcome may not necessarily be achieved by all students who pass the course, but all students will have the opportunity to develop these attributes by participating in course activities such as lectures, tutorials, consultation, assessment and use of the course website.)
Where appropriate, indication will be given of current research areas related to topics in the course.
Examination Material or equipment
In both the mid-semester exam and the final exam the permitted materials will be:
- One A4 sheet (both sides) of notes, hand-written by the student and in original form (not printed or photographed).
- A simple (non-programmable) scientific calculator.
- A non-annotated translation dictionary (for ESL students).
Course Notes: PDF copies of all lecture slides will be made available on the course website, in addition to the ECHO lecture recordings.
Worked Examples: For each of the twelve course topics A1 - D3, sets of practice questions will be made available on the course website. Worked solutions to these questions will be provided in time to help with the writing up of solutions to corresponding assignment questions.
Optional Text: Susanna Epp: Discrete Mathematics with Applications; 3rd or 4th ed. Cengage.
References to this text will be provided for all course topics except the last (Random Walks).
The text does not cover every single subtopic in the course, and does cover some subtopics not required for the course, but is nonetheless a good match to course in both level and content.
Students will be given feedback in the following forms in this course:
- Workshops: Demonstrators will give individual guidance and correction to student work on, and presentation of, worksheet problems.
- Homework Assignments: Demonstrators will grade, but not correct, assignment work. Brief indications of where and how errors have been made will be provided with each student’s work. Common errors will be briefly discussed with the whole class after homework is returned. Students will then have an opportunity to ask the demonstrator about other errors.
- Mid-semester exam: Students will be given an opportunity to view their exam scripts in a workshop following the exam, to view official solutions, and to ask the demonstrator about any grading issues.
Student FeedbackANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.
Please note, that where there are multiple assessment tasks of the same type, e.g weekly quizzes, a date range is used in the Assessment Summary. The first date is the approximate due date of the first task, the return date is the approximate return date for the final task. Further information is provided in the assessment section of the class summary, and details are provided on the course wattle site
|Week/Session||Summary of Activities||Assessment|
|1||A1 Logic: Statements and Predicates. Valid Arguments.||Weekly assignments and online quizzes will reinforce the content. Practice problems related to each section will be available on Wattle.|
|2||A2 Sets: Set Operations and identities. Russell's Paradox.||Weekly assignments and online quizzes will reinforce the content. Practice problems related to each section will be available on Wattle.|
|3||A3 Relations and Functions: Definition & Properties of Relations and Functions.||Weekly assignments and online quizzes will reinforce the content. Practice problems related to each section will be available on Wattle.|
|4||B1 Numbers: N,Z,Q,R. Base n. Computer & Modular Arithmetic.|
|5||B2 Sequences and Induction: Implicit to Explicit Seq Def by Induction. Sorting.|
|6||B3 Matrices: Matrix & Vector Operations. Linear Functions.|
|7||C1 Counting: Cardinality. Permutations & Combinations. Stars & Bars. Pigeonhole Principle.|
|8||C2 Probability: Probability Properties. Distributions. Random Variables.|
|9||C3 Markov Processes: Markov States &Transition Matrices. Steady State.|
|10||D1 Graph Theory: Graphs & Digraphs. Degree. Euler & Hamilton Graphs. Trees.|
|11||D2 Weighted Graphs: Minimum Span. Travelling Sales Person Problem. Shortest Path. Max Flow. Matching.|
|12||D3 Random Walks: Graph 'Walking'. Webgraphs & PageRank Algorithm.|
Workshop registration via Wattle, starting in Week 0.
|Assessment task||Value||Due Date||Return of assessment||Learning Outcomes|
|Weekly Written Assignments (Ten)||10 %||17/03/2019||14/06/2019||1,2,3,4,5|
|Weekly Online Multiple Choice Quizzes (Ten)||5 %||18/03/2019||03/06/2019||2,3,4|
|Participation in Workshops (Ten)||5 %||11/03/2019||31/05/2019||1,2,3,4,5|
|Mid-Semester Examination||30 %||01/04/2019||10/05/2019||1,2,3,4,5|
|Final Examination||50 %||06/06/2019||04/07/2019||1,2,3,4,5|
PoliciesANU has educational policies, procedures and guidelines, which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Misconduct Rule before the commencement of their course. Other key policies and guidelines include:
Assessment RequirementsThe ANU is using 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. For additional information regarding Turnitin please visit the ANU Online website Students may choose not to submit assessment items through Turnitin. In this instance you will be required to submit, alongside the assessment item itself, hard copies of all references included in the assessment item.
Moderation of AssessmentMarks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.
Although there are no participation requirements (hurdles) for this course please note that:
Workshop Participation contributes 10% to your final grade. Details of how this is assessed are given in the details of this assessment item stated earlier in this document.
Assessable material for the course is specified by lecture content (rather than any text). So it is important to keep up regular monitoring of lectures, preferably by attending but otherwise by accessing the lecture recordings and/or PDF notes on Wattle.
Attendance has the advantage that I (your lecturer, Malcolm) will be available for up to half an hour after each lecture to answer questions.
A mid-semester and a final examination will be scheduled by the central ANU Examinations Department.
Please note, that where a date range is used in the Assessment Summary in relation to exams, the due date and return date indicate the approximate timeframe in which the exam will be held and results returned to the student (official end of Semester results released on ISIS). Students should consult the course wattle site and the ANU final examination timetable to confirm the date, time and venue of the exam.
Assessment Task 1
Learning Outcomes: 1,2,3,4,5
Weekly Written Assignments (Ten)
Each assignment has questions relating to current Workshop material. Answer types range over requiring examples (LO1), selecting correct terminology (LO2), interpreting and creating diagrams and expressions (LO3), calculating various values and expressions from given data (LO4), correcting or completing simple given proofs (LO5) and, occasionally, creating justifications or proofs of given statements (LO5).
Assignments will be made available on the course website (Wattle) on the evening of your Workshop day for the relevant material. Answers are to be hand written in the spaces provided on the assignment. You will be allowed six days to do this.The completed assignment must be scanned and uploaded to Wattle before the deadline stated on the assignment. Late assignments will not be accepted. Your Workshop demonstrator will grade your assignment and you will normally be able to view your grade and possible brief comments online within a week of the submission deadline.
All ten assignments count towards your final course grade.
The date range for these tasks indicates the approximate due date for the first assignment and the approximate return date for the last assignment. There are 10 assignments due over the semester. It is intended that the marked assignments will be returned within 1 week after submission.
Assessment Task 2
Learning Outcomes: 2,3,4
Weekly Online Multiple Choice Quizzes (Ten)
Each quiz has randomly generated questions relating to current Workshop material. Question types include: selecting correct terminology (LO2), interpreting and creating diagrams and expressions (LO3), and calculating various values and expressions from given data (LO4).
Quizzes will become available on Monday evening of each teaching week, starting in Week 3. (This includes the three Monday public holidays this semester, in particular Canberra Day in Week 3.) Quizzes will remain open for exactly one week. Once started, you will have a fixed time limit to finish, usually 15 or 20 minutes. Quiz closing times will not be extended.
All ten quizzes count towards your final course grade.
The date range for these tasks indicates the approximate due date for the first quiz and the approximate return date for the last quiz. There are 10 quizzes due over the semester.
Assessment Task 3
Learning Outcomes: 1,2,3,4,5
Participation in Workshops (Ten)
You are strongly encouraged to attend the weekly 2-hour workshops, starting in week 3. You can select from available workshop times when the workshop registration link opens on Wattle.
A worksheet will be made available on Wattle for each workshop. You are not expected to start on this before your workshop; a separate set of pre-workshop questions will be provided to help you prepare, with brief answers provided on-line before the workshop.
In the first 55 minutes of the workshop you will be encouraged to work collaboratively on the worksheet questions, asking for help from the demonstrator as needed. You may also ask the demonstrator about any of the answers to the preparation questions that you did not understand. In the next 55 minutes your demonstrator will select students to present solutions to the class. The aim here is to give you an opportunity to practice and improve your skill in verbal communication of
mathematics, and to give the demonstrator an opportunity to correct any misconceptions that you or other class members may have about underlying theory.
At each workshop a mark will be recorded for you as follows:
0: Did not attend or attended but did not participate.
1: Participated in group work but made no contribution to discussion or presentation.
2: Participated in group work and contributed to discussion or presentation.
To allow for occasional absences, your workshop participation score will be calculated from your best eight (out of ten) workshop marks.
Assessment Task 4
Learning Outcomes: 1,2,3,4,5
90 mins + reading time. Covers sections A1,A2,A3,B1,B2 of the course. A sample, plus solutions, will be available on Wattle.
This exam is redeemable via the final exam: if the percentage score on the mid-semester exam is less than the percentage score on the final exam, only the final exam will count and will be weighted at 80% instead of 50%.
The date range is a general indication of when the mid-semester exam will be held. Please check the course Wattle site and the ANU Examination Timetable to confirm the date, time and location of the mid-semester exam.
Assessment Task 5
Learning Outcomes: 1,2,3,4,5
180 mins + reading time. Covers the entire course, but with a very strong emphasis on material not tested in the mid-semester exam. A sample, plus solutions, will be available on Wattle.
Some scaling of marks on the final exam may occur if the distribution of marks leads to results significantly out of line with previous years.
Regardless of performance on other assessment items, a minimum scaled score of 40% on the final exam is required to pass the course. (This is known as a 'course hurdle'.)
The date range in the Assessment Summary indicates the start of the end of semester exam period and the date official end of semester results are released on ISIS. Please check the ANU final Examination Timetable http://www.anu.edu.au/students/program-administration/assessments-exams/examination-timetable to confirm the date, time and location of the exam.
Academic IntegrityAcademic integrity is a core part of our culture as a community of scholars. At its heart, academic integrity is about behaving ethically. This means that all members of the community commit to honest and responsible scholarly practice and to upholding these values with respect and fairness. The Australian National University commits to embedding the values of academic integrity in our teaching and learning. We ensure that all members of our community understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with. The University has policies and procedures in place to promote academic integrity and manage academic misconduct. Visit the following Academic honesty & plagiarism website for more information about academic integrity and what the ANU considers academic misconduct. The ANU offers a number of services to assist students with their assignments, examinations, and other learning activities. The Academic Skills and Learning Centre offers a number of workshops and seminars that you may find useful for your studies.
Online SubmissionThe 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.
Hardcopy SubmissionFor some forms of assessment (hand written assignments, art works, laboratory notes, etc.) hard copy submission is appropriate when approved by the Associate Dean (Education). Hard copy submissions must utilise the Assignment Cover Sheet. Please keep a copy of tasks completed for your records.
No submission of assessment tasks without an extension after the due date will be permitted. If an assessment task is not submitted by the due date, a mark of 0 will be awarded. OR Late submission of assessment tasks without an extension are penalised at the rate of 5% of the possible marks available per working day or part thereof. Late submission of assessment tasks is not accepted after 10 working days after the due date, or on or after the date specified in the course outline for the return of the assessment item. Late submission is not accepted for take-home examinations.
Please check individual tasks for details.
Referencing RequirementsAccepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.
Except in exceptional circumstances marked assignments will be returned by the second workshop after the due date. Exceptions include unexpected unavailability of the demonstrator, disruptions to the timetable resulting from public holidays, and weeks 6 and 12 prior to breaks.
Extensions and PenaltiesExtensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure The Course Convener may grant extensions for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.
Resubmission of Assignments
Assignments cannot be resubmitted.
Distribution of grades policyAcademic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes. Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.
Support for studentsThe University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).
- ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
- ANU Diversity and inclusion for students with a disability or ongoing or chronic illness
- ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
- ANU Academic Skills and Learning Centre supports you make your own decisions about how you learn and manage your workload.
- ANU Counselling Centre promotes, supports and enhances mental health and wellbeing within the University student community.
- ANUSA supports and represents undergraduate and ANU College students
- PARSA supports and represents postgraduate and research students