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Note: This page dates from 2005, and is kept for historical purposes.
The University of Queensland
Department of Mathematics
Semester 1, 2003
MATH1061 – Discrete Mathematics
Phone 3365 1354
Phone 3365 3255
Diane: Monday 10 am, Thursday 11am in room 67-549
Barry: Tuesday 9 am, Wednesday 10 am in room 67-243
PURPOSE OR GOAL: The broad aim of this course is to provide students with a solid basis for mathematical reasoning and the opportunity to apply this reasoning to problems in mathematics. It is expected that when students complete this course they will be able to construct logically correct and mathematically sound proofs. They will also have met the concepts of logic, set theory, relations, induction, principles of counting, probability, algebraic structures and elementary number theory, all of which play an important role in computer science and mathematics.
ASSUMED BACKGROUND: A sound background in High School Mathematics
DETAILED SYLLABUS: The following is intended as a rough guide only.
- Propositional logic, valid arguments, predicate logic
- Elementary number theory
- Elementary set theory
- Elementary graph theory
- Algebraic Structures and their applications.
- Counting methods and probability
TEACHING MODE: Five hours of class contact are scheduled each week:
Students must attend THREE one hour lectures per week and a one hour tutorial and one contact hour per week. You must sign up for a tutorial, but may just turn up to any one of the contact hours.
LECTURE TIMES: Monday 9 am, Wednesday 8 am, Thursday 12 noon.
DISABILITIES STATEMENT: Any student with a disability who may require alternative academic arrangements in the course is encouraged to seek advice at the commencement of the semester from a Disability Adviser at Student Support Services.
|1||3rd March||Logic (Ch 1)|
|2||10th March||Logic (Ch 2)||Ass 1|
|3||17th March||Number Theory (Ch 3)||Ass 2|
|4||24th March||Number Theory/Induction (Ch 3 & 4)||Ass 3|
|5||31st March||Set Theory (Ch 5)||Ass 4 (Counts 5% towards assessment)|
|6||7th April||Graphs (Ch 11)||Ass 5|
|7||14th April||Relations (Ch 10)||Possible week for Midsemester exam|
|21st April||Midsemester break|
|8||28th April||Relations (Ch 10)||Ass 6|
|9||5th May||Functions (Ch 7)||Ass. 7 (Counts 5% towards assessment)|
|10||12th May||Algebraic Structures (See Chapter headed Last)||Ass 8|
|11||19th May||Counting and Probability (Ch 6)||Ass 9|
|12||26th May||Counting and Probability (Ch 6)||Ass 10(Counts 5% towards assessment)|
|13||2nd June||Recursion (Ch 8)|
- A Course Profile
- A Textbook: Discrete Mathematics with Applications, by Susanna Epp.
- A Study Guide
- A Workbook
- A Reader
- Assignment Questions
- Practice Midsemester and Practice End of Semester Exams
- Solutions to Assignments and Practice Midsemester and End of Semester Exams
- Course Web Page: http://www.maths.uq.edu.au/~dmd/teaching/MATH1061/MATH1061.html
STUDY GUIDE: Use the Study Guide, which contains a detailed description of the material to be covered in this course, to plan a study program.
WORKBOOK: This is a companion workbook to the set text, containing learning activities, problems and additional information. Students may buy a copy from Union Copying Services (UQ Union complex) or down load a copy of from the Course Web Page.
READER: At times it desirable to include extra reading material to supplement the textbook. When this is the case we direct the student to the appropriate sections of this Reader. The reader is at the back of the workbook..
ASSIGNMENT QUESTIONS: Assignments will be handed out or they are available on the course webpage. Student must hand their assignment to their tutor in their tutorial. It is not possible for lecturers to collect assignments. The assignements will be marked and returned to you at your tutorial. Solutions to assignment questions will be available on the web.
RESOURCE MATERIALS: The following are also available in The University of Queensland, PSE Library or the Undergraduate Library:
E Billington, D Donovan, B Jones, S Oates-Williams, A Street, Discrete Mathematics: Logic and Structures, 2nd edition, QA39.2.D58.1993
R Garnier, J Taylor, Discrete Mathematics for New Technology. QA76.9.M35.G38.1992
K Rosen, Discrete Mathematics and its Application,,QA39.2.R654.1991
N. Biggs, Discrete Mathematics, QA76.9.M35.B54.1989
METHOD OF ASSESSMENT: There will be both formative and summative assessment in this course. The Final Grade in this course will be the aggregate of three components, as set out in the table below. The final mark will be taken to be the higher out of Options 1 and 2.
Students who fail to submit one of assignment 4, 7 or 10 will receive a grade of 0% for that assignment and students who fail to sit the midsemester exam will also receive 0% for this component. In these cases it is envisaged that the final grade will be taken completely from the end of semester examination.
||Assignments 4, 7 and 10 will be marked for assignment and may each contributing 5% towards your final grade.||Option 1: 15 %
Option 2: 0 %
||Option 1: 25 %
Option 2: 0 %
||Option 1: 60%
Option 2: 100 %
For the END OF SEMESTER EXAM ONLY students will be able to take one A4 sheet of paper with anything HAND WRITTEN on it. It must be in the students own handwritting.
Late ASSIGNMENTS will only be accepted with a medical certificate and within a week of the due date.
MIDSEMESTER EXAM: Arrangements for the midsemester exam are still being finalised. Final details will be announced in lectures and on the webpage. Therefore if students do not attend all lectures they should regularly check the webpage for the time and date of the exam. To give students an indication of the standard of the midsemester exam, a copy of a practice midsemester exam has been included in the course material.
END OF SEMESTER EXAM: For the END OF SEMESTER EXAM ONLY students will be able to take one A4 sheet of paper with anything HAND WRITTEN on it. It must be in the students own handwritting. The end of semester exam will be timetabled by the University administration later in the semester. Copies of the exam timetable are available on the University of Queensland website http://www.uq.edu.au and will also be posted in the various libraries around campus. This exam will be 2 hours duration and will be based on the entire semester’s work. To give students an indication of the standard of the end of semester exam, a copy of the past end of semester exam has been included in the course material. The student may also look at any past MATH1061/7861 (see also MT161/861) exam paper. Copies of these are available in the PSE library.
ASSESSMENT CRITERIA: Solutions submitted for each piece of submitted work will be marked for accuracy, appropriateness of mathematical techniques and clarity of presentation, as will be demonstrated by exemplars presented in lectures. Sample marking schemes will be discussed in lectures.
To earn a Grade of 7, a student must demonstrate an excellent understanding of concepts presented in this course. This includes clear expression of nearly all deductions and explanations, the use of appropriate and efficient mathematical techniques and accurate answers to nearly all questions and tasks with appropriate justification.
To earn a Grade of 6, a student must demonstrate a comprehensive understanding of concepts presented in this course. This includes clear expression of most of their deductions and explanations, the general use of appropriate and efficient mathematical techniques and accurate answers to most questions and tasks with appropriate justification.
To earn a Grade of 5, a student must demonstrate an adequate understanding of the concepts presented in this course. This includes clear expression of some of their deductions and explanations, the use of appropriate and efficient mathematical techniques in some situations and accurate answers to some questions and tasks with appropriate justification.
To earn a Grade of 4, a student must demonstrate an understanding of the basic concepts presented in this course. This includes occasionally expressing their deductions and explanations clearly, the occasional use of appropriate and efficient mathematical techniques and accurate answers to a few questions and tasks with appropriate justification. They will have demonstrated knowledge of techniques used to solve problems and applied this knowledge in some cases.
To earn a Grade of 3, a student must demonstrate some knowledge of the basic concepts presented in this course. This includes occasional expression of their deductions and explanations, the use of a few appropriate and efficient mathematical techniques and attempts to answer a few questions and tasks accurately and with appropriate justification. They will have demonstrated knowledge of techniques used to solve problems.
To earn a Grade of 2, a student must demonstrate some knowledge of the concepts presented in this course. This includes attempts at expressing their deductions and explanations and attempts to answer a few questions accurately.
A student will earn a Grade of 1 if they show a poor knowledge of the basic concepts presented in this course. This includes attempts at answering some questions but showing an extremely poor understanding of the key concepts.
LATENESS: Assignments should be submitted by the specified date, late assignments will not be accepted without a medical certificate.
SUPPLEMENTARY MIDSEMESTER EXAM Students who have a compelling reason and are unable to attend the midsemester exam may request in writing an alternate time. The request should be addressed to the Head of the Mathematics Department, The University of Queensland, stating the reason for the absence. If the request is granted the student will be advised, in lectures and on the Course Web Page, of the alternate date, closer to the time.
On completion of the course, the graduate will have
IN-DEPTH KNOWLEDGE OF THE FIELD OF STUDY
- An in-depth understanding and well-founded knowledge of the mathematics presented in this course.
- An understanding of the breadth of mathematics.
- An understanding of the applications of mathematics to relevant fields.
- An enhanced ability to present a logical sequence of reasoning using appropriate mathematical notation and language.
- An enhanced ability to interact effectively with others in order to work towards a common goal.
- An enhanced ability to select and use the appropriate level, style and means of written communication, using the symbolic, graphical, and diagrammatic forms relevant to the context.
INDEPENDENCE AND CREATIVITY
- An enhanced ability to work and learn independently.
- An enhanced ability to generate and synthesise ideas.
- An enhanced ability to formulate problems mathematically.
- An enhanced ability to generate approaches for the mathematical solution of problems including the identification and adaptation of existing methods.
ETHICAL AND SOCIAL UNDERSTANDING
- A knowledge and respect of ethical standards in relation to working in the area of mathematics.
- An appreciation of the history of mathematics as an ongoing human endeavour.
- An appreciation of the power of mathematics to affect our culture and technology.
Sourced From http://www.maths.uq.edu.au/~dmd/teaching/MATH1061/prof-1061.html