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
