MATHS135-20B (TGA)

Discrete Structures

15 Points

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Division of Health Engineering Computing & Science
School of Computing and Mathematical Sciences
Department of Mathematics and Statistics


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Paper Description

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An introduction to a number of the structures of discrete mathematics with wide applicability in areas such as: computer logic, analysis of algorithms, telecommunications, networks 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: sets, binary relations, directed and undirected graphs; propositional and some predicate logic; permutations, combinations, and elementary probability theory; modular arithmetic.

Students have until the sixth Friday from Mon 13th July to determine if they wish to change down to a less difficult Mathematics paper (subject to lecturer’s approval) without any fees loss. It is recommended such a change be done as soon as possible.

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Paper Structure

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There will be a series of a number of online lectures to watch each week (less than 50 minutes worth) available on MOODLE, as well as 2 workshop classes on Thursday and Friday (see below) . The workshop is where students will chiefly work on example problems individually or in small groups. The workshops are on the Hamilton campus but will be recorded and I'm hoping to make online attendance possible, if practicable. Assessment is fixed but there may be some changes to paper delivery based on how many students are studying off-campus and also student feedback.

Tutor Dr Ian Hawthorn will be present on the Tauranga campus on Wednesdays, including an in-person tutorial. Students may alternatively sign-up to an online tutorial.

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Learning Outcomes

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Students who successfully complete the paper should be able to:

  • Learning Outcomes
    • 1.Demonstrate understanding of the basic notions of sets, functions, and binary relations defined on sets (especially partial orders and equivalence relations).
    • 2. Demonstrate understanding of the concepts of directed and undirected graphs and some of their applications.
    • 3. Understand and produce logical formulae, and to determine the validity of simple such formulae.
    • 4. Demonstrate understanding of basic combinatorial concepts such as permutations and combinations, and methods of counting, and ability to apply them.
    • 5. Demonstrate understanding of basic ideas of probability.
    • 6. Demonstrate understanding of basic concepts of modular arithmetic and some of their applications.
    Linked to the following assessments:
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The assessment will consist of TWO Tests and TEN Assignments as follows:

DATE: Test One: Evening online test - Date To Be Advised - not before September 7th (30%)

DATE: Test Two: Date To Be Advised: Between 27th October and 13th November during final test period) (30%).

The TOTAL assignment component is worth 40%. There will be 10 assignments of which only the best 8 marks will be counted.

There will be NO test resits.

A final overall grade of RP (Restricted pass) will not be accepted as a prerequisite for entry into any higher level Maths paper.

COPYING of other students’ Assignments/Tests will receive zero (this will include all students involved) and be reported to the Disciplinary Committee. In particular, you will be reported for any evidence of communication with other students during online tests.
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Assessment Components

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The internal assessment/exam ratio (as stated in the University Calendar) is 100:0. There is no final exam. The final exam makes up 0% of the overall mark.

The internal assessment/exam ratio (as stated in the University Calendar) is 100:0 or 0:0, whichever is more favourable for the student. The final exam makes up either 0% or 0% of the overall mark.

Component DescriptionDue Date TimePercentage of overall markSubmission MethodCompulsory
1. Assignments
2. Test One
  • Online: Submit through Moodle
3. Test Two
  • Online: Submit through Moodle
Assessment Total:     100    
Failing to complete a compulsory assessment component of a paper will result in an IC grade
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Required and Recommended Readings

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Required Readings

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There are no required readings.
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Online Support

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All information relating to this paper including assessment marks will be posted on MOODLE.
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10 hours a week, including viewing record lectures, two weekly workshops and one weekly tutorial.
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Linkages to Other Papers

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Prerequisite papers: At least one of MATHS165, MATHS166, MATH165, MATH166, or 14 credits in NCEA Level 3 Mathematics.




Restricted papers: COMP235, MATH258

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