MATH2302 Announcements
SECaT survey
Please complete the course SECaT survey, accessible through the email sent to you
last week or via the survey portal https://eval.uq.edu.au/.
We really appreciate your feedback!
Exam preparation
Exams prior to 2016 are not entirely relevant, as we no longer cover coding theory
or cryptography, but the questions on enumeration, graph theory and design theory
are good practice. Solutions to the 2016 final exam will be posted on blackboard.
Tutorial revision problems and practice problem sets available on blackboard.
Re-do the in-class questions, they are all available on blackboard in the weekly
summaries under Learning Resources.
MATH2302 Course Summary
Enumeration
Selections
Permutation and derangements
Combinatorial identities
Group actions
Generating functions (ordinary and exponential)
Inclusion and exclusion
Q1 – Q4 on exam
22 marks
Unordered or Ordered
With repetition or Without repetition
Orbits, Stabilizers, Fix, Counting Theorem
Partitions
Möbius formula and Möbius inversion
Posets
Solving linear recurrence relations using generating functions
MATH2302 Course Summary
Graph Theory and Graph Algorithms
Degree sequence
Eulerian graphs
Matchings
Hamiltonian graphs
Definitions
Shortest path: Dijkstra
Spanning tree: Prim / Kruskal
Algorithms
Trees
Maximum matching in bipartite graphs
Maximum matching in weighted bipartite graphs
Independence number, Clique number, Domination number
Vertex chromatic number (), edge chromatic number ′()
Q5 – Q8 on exam
21 marks
Note: Graph means
simple graph.
MATH2302 Course Summary
Classification of surfaces
Q9 – Q10 on exam
11 marks
Homeomorphic surfaces
Connected sum of surfaces #
Euler characteristic of a surface
Orientable and non-orientable surfaces
Representing a surface as a word
Rules for manipulating words
Classification Theorem
Classification of surfaces
topics are not on
the exam reference
pages
MATH2302 Course Summary
Design Theory
Symmetric
Idempotent
Half-idempotent
Quasigroups
Steiner triple systems
Q11 – Q12 on exam
11 marks
Skolem construction for STS(6 + 1)
Bose construction for STS(6 + 3)
Necessary conditions for existence
MATH2302 Course Summary
Final examination
2 hours with 10 minutes perusal
Questions are not in order of difficulty, so use perusal to plan the order in which
you will do the questions
Calculators must be Casio FX-82 or have UQ approval sticker
5:45pm on Thursday 14 November, Location sent to you by email
12 questions, worth a total of 65 marks
You must get at least 40% on the final examination to pass the course,
at least 60% on the final examination to get a grade of 5,
at least 70% on the final examination to get a grade of 6, and
at least 80% on the final examination to get a grade of 7.
Last 3 pages are reference pages, which you may detach
(available on blackboard under Assessment/Examinations)
Mobile phones turned off during exams, and not allowed to wear a watch
MATH2302 Course Summary
Where to from here?
MATH3301 – Graph Theory & Design Theory (Semester 2)
pre-requisite MATH2302
MATH3302 – Coding and Cryptography (Semester 1)
pre-requisite MATH2301
MATH4303 – Advanced Combinatorics (Semester 1, even years only)
pre-requisite MATH2302
MATH4302 – Combinatorial Designs (Semester 1, odd years only)
pre-requisite MATH2301 and MATH2302
MATH3303 – Abstract Algebra & Number Theory (Semester 1)
pre-requisite MATH2301
MATH4301 – Advanced Algebra(Semester 2, odd years only)
pre-requisite MATH3303
MATH3306 – Set Theory & Mathematical Logic (Semester 2)
recommended pre-requisite MATH1061
MATH4304 – Number Theory (Semester 2, even years only)
pre-requisite MATH3303