MATHS 1008 - Mathematics for Information Technology I
North Terrace Campus - Semester 2 - 2015
General Course Information
Course Code MATHS 1008 Course Mathematics for Information Technology I Coordinating Unit School of Mathematical Sciences Term Semester 2 Level Undergraduate Location/s North Terrace Campus Units 3 Contact Up to 5 hours per week Available for Study Abroad and Exchange Y Prerequisites SACE Stage 2 Mathematical Studies Assumed Knowledge SACE Stage 2 Mathematical Studies Course Description This course provides an introduction to a number of areas of discrete mathematics with wide applicability. Areas of application include: computer logic, analysis of algorithms, telecommunications, gambling and public key cryptography. In addition it introduces a number of fundamental concepts which are useful in Statistics, Computer Science and further studies in Mathematics.
Topics covered are: Discrete mathematics: sets, relations, logic, graphs, mathematical induction and difference equations; probability and permutations and combinations; information security and encryption: prime numbers, congruences.
Course Coordinator: Dr Adrian Koerber
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning OutcomesOn successful completion of this course students will be able to:
- Demonstrate understanding of concepts in discrete mathematics, probability and cryptography.
- Employ methods related to these concepts in a variety of applications.
- Apply logical thinking to problem solving in context.
- Use appropriate technology to aid problem solving.
- Demonstrate skills in writing mathematics.
University Graduate Attributes
This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:
University Graduate Attribute Course Learning Outcome(s) Knowledge and understanding of the content and techniques of a chosen discipline at advanced levels that are internationally recognised. all The ability to locate, analyse, evaluate and synthesise information from a wide variety of sources in a planned and timely manner. 2,3 An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. 1,2,3,4 A proficiency in the appropriate use of contemporary technologies. 4 A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. all
Required ResourcesMathematics for Information Technology I student notes.
- Ross, K. A. & Wright, C. R. B., Discrete Mathematics, Prentice Hall
- Johnsonbaugh, R., Discrete Mathematics (7th ed), Prentice Hall
- Goodman, R., An introduction to stochastic models, Benjamin-Cummings
- Ross, S., Introduction to probability models (7th ed), Academic Press
Online LearningThis course uses MyUni exclusively for providing electronic resources, such as lecture notes, assignment papers, and sample solutions. Students should make appropriate use of these resources. Link to MyUni login page: https://myuni.adelaide.edu.au/webapps/login/
Learning & Teaching Activities
Learning & Teaching ModesThis course relies on lectures to guide students through the material, tutorial classes to provide students with class/small group/individual assistance, and a sequence of written and online assignments to provide formative assessment opportunities for students to practice techniques and develop their understanding of the course.
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Quantity Workload hours Lectures 48 72 Tutorials 11 22 Assignments 11 55 Mid Semester Test 1 7 Total 156
Learning Activities SummaryThe two topics of discrete mathematics and probability detailed below are taught in parallel, with two lectures a week on each. The tutorials are a combination of the two topics, pertaining to the previous week's lectures. Note that some sections only loosely fall into the categories of discrete mathematics or probability but are so listed to indicate the stream they are taught in.
Lecture OutlineDiscrete Mathematics
- Sets and relations, equivalence relations, functions. (4 lectures)
- Logic, predicate caclulus. (2 lectures)
- Types of argument. (2 lectures)
- Switching circuits. (2 lectures)
- Graphs, trees, spanning trees, Kruskal's algorithm, binary search trees. (5 lectures)
- Mathematical induction. (3 lectures)
- Cryptosysytems, Caesar cipher, Hill cipher. (2 lectures)
- Elementary number theory. (2 lectures)
- Public key cryptography, the mathematics of the RSA algorithm. (2 lectures)
- Sample spaces, events, inclusion-exclusion. (3 lectures)
- Conditional probablility and the product rule. (1 lecture)
- Probability trees, independent events, Bayes' Formula, Law of Total Probability. (2 lectures)
- Discrete random variables and probability distributions. (6 lectures)
- Counting techniques. (6 lectures)
- Linear homogeneous recurrence relations with constant coefficients. (6 lectures)
Tutorial 1: Sets, relations, Venn diagrams, simple probability.
Tutorial 2: Functions, 1-1, onto. Conditional probability.
Tutorial 3: Propositions, truth tables. Probability tree diagrams.
Tutorial 4: Types of argument, negation. Bayes' Theorem, Law of Total Probability.
Tutorial 5: Boolean expressions, circuit diagrams. Permutation, combinations, counting arguments.
Tutorial 6: Mathematical induction, recursive definitions. Partitions. Binomial probability.
Tutorial 7: Graphs, trees, paths. Binomial proability distribution.
Tutorial 8: Kruskal's algorithm. Binary search trees. Mode, median. Normal distribution.
Tutorial 9: Binary search trees. Caesar cipher. Markov chains.
Tutorial 10: Hill cipher, elementary number theory. Recurrence relations.
Tutorial 11: Congruence, Fermat's theorem. Inhomogeneous recurrence relations.
Note: Precise tutorial content may vary due to the vagaries of public holidays.
The University's policy on Assessment for Coursework Programs is based on the following four principles:
- Assessment must encourage and reinforce learning.
- Assessment must enable robust and fair judgements about student performance.
- Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
- Assessment must maintain academic standards.
Assessment Task Task Type Weighting Learning Outcomes Assignments Formative 15% all Mid Semester Test Summative and Formative 15% 1,2,3 Exam Summative 70% 1,2,3,5
Assessment Related RequirementsAn aggregate score of 50% is required to pass the course. Furthermore students must achieve at least 45% on the final examination to pass the course.
Assessment item Distributed Due date Weighting Assignment 1 week 1 week 3 1.4% Assignment 2 week 2 week 4 1.4% Assignment 3 week 3 week 5 1.4% Assignment 4 week 4 week 6 1.4% Assignment 5 week 5 week 7 1.4% Assignment 6 week 6 week 8 1.4% Assignment 7 week 7 week 9 1.4% Assignment 8 week 8 week 10 1.4% Assignment 9 week 9 week 11 1.4% Assignment 10 week 10 week 12 1.4% Assignment 11 week 11 week 13 1.4% Mid Semester Test week 8 15%
- All written assignments are to be submitted at the designated time and place with a signed cover sheet attached.
- Late assignments will not be accepted without a medical certificate.
- Written assignments will have a one week turn-around time for feedback to students.
Grades for your performance in this course will be awarded in accordance with the following scheme:
M10 (Coursework Mark Scheme) Grade Mark Description FNS Fail No Submission F 1-49 Fail P 50-64 Pass C 65-74 Credit D 75-84 Distinction HD 85-100 High Distinction CN Continuing NFE No Formal Examination RP Result Pending
Further details of the grades/results can be obtained from Examinations.
Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.
Final results for this course will be made available through Access Adelaide.
The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.
SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.
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