| Semester 1, 2022 Toowoomba On-campus | |
| Units : | 1 |
| Faculty or Section : | Faculty of Health, Engineering and Sciences |
| School or Department : | School of Mathematics, Physics & Computing |
| Grading basis : | Graded |
| Course fee schedule : | /current-students/administration/fees/fee-schedules |
Staffing
Examiner:
Overview
Discrete methods underlie the areas of data structures, computational complexity and the analysis of algorithms. Continuing advances in technology - particularly in applications of computing - have enhanced the importance of discrete (or finite) mathematics for understanding not only the foundations of computer science but also the basis on which computational solutions to a wide variety of applications problems rests.
This course introduces the basic elements of discrete mathematics which provide a foundation for an understanding of algorithms and data structures used in computing. Topics covered include number systems, logic, relations, functions, induction, recursion, Boolean algebra and graph theory.
Course learning outcomes
On successful completion of this course students will be able to:
- recognise and understand how numeric and character data is stored in a computer
- interpret and write simple algorithms in pseudo-code
- recognise and analyse basic graphs and trees
- effectively use symbolic logic, to implement mathematical reasoning and construct proofs
- effectively communicate discrete mathematical concepts and arguments using appropriate mathematical notation
Topics
| Description | Weighting(%) | |
|---|---|---|
| 1. | Computer representation of character and numeric data. Binary and hexadecimal system. ASCII code. Integer and floating-point representations. | 25.00 |
| 2. | Functions and algorithms. Pseudo-code for binary/decimal and other conversions. Control structures for iteration and branching. Recursive functions. Proof by induction. | 25.00 |
| 3. | Truth tables and the laws of logic. Venn diagrams. Ordering and equivalence relationships. Digital circuits and Boolean algebra. Logical reduction and Karnaugh maps. | 25.00 |
| 4. | Graphs and trees. Eulerian and Hamiltonian graphs. Spanning trees. Dijkstra's and Prim's algorithms. Expression trees. Huffman codes. | 25.00 |
Text and materials required to be purchased or accessed
Student workload expectations
To do well in this subject, students are expected to commit approximately 10 hours per week including class contact hours, independent study, and all assessment tasks. If you are undertaking additional activities, which may include placements and residential schools, the weekly workload hours may vary.
Assessment details
| Description | Group Assessment |
Weighting (%) | Course learning outcomes |
|---|---|---|---|
| Problem Solving 1 | No | 30 | 1,2,5 |
| Problem Solving 2 | No | 30 | 4,5 |
| Problem Solving 3 | No | 40 | 1,2,3,4,5 |