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Units 1-4  \nJessica Mount MAV  \nIntroduction  \nJessica Mount  \nTaught VCE Maths since 2011  \nHead of Mathematics 2015  \nFurther Mathematics Assessor 2011 – current  \nMAV SAC writer & VCE revision lecturer  \nCurrently working at MAV as a secondary education consultant  \n[jmount@mav.vic.edu.au](jmount@mav.vic.edu.au)  \nGeneral Mathematics Study Design   \nGraphs and networks – Unit 2.  \nThis topic includes: (Undirected Networks)  \n• introduction to the notations, conventions and representations of types and properties of graphs, including edge, loop, vertex, the degree of a vertex, isomorphic and connected graphsand the adjacency matrix  \n• description of graphs in terms of faces (regions), vertices and edges and the application of Euler’s formula for planar graphs  \n• connected graphs: walks, trails, paths, cycles and circuits with practical applications  \n• weighted graphs and networks, and an introduction to the shortest path problem (solution by inspection only) and its practical application  \n• trees and minimum spanning trees, greedy algorithms and their use to solve practical problems.  \nGeneral Mathematics Study Design  \nNetworks and decision mathematics – Unit 4  \nThis topic includes Undirected Networks (some overlap from Unit 2 )  \n• the concepts, conventions and terminology of graphs including planar graphs and Euler’s rule, and directed (digraphs) and networks  \n• use of matrices to represent graphs, digraphs and networks and their application.  \n• the concepts, conventions and notations of walks, trails, paths, cycles and circuits  \n• Eulerian trails and Eulerian circuits: the conditions for a graph to have an Eulerian trail or an Eulerian circuit, properties and applications  \n• Hamiltonian paths and cycles: properties and applications.  \n• trees and spanning trees, minimum spanning trees & Prim’s algorithm  \n• use of minimal spanning trees to solve minimal connector problems.  \n• determination of the shortest path between two specified vertices in a graph, digraph or network by inspection  \n• Dijkstra’s algorithm and its use to determine the shortest path between a given vertex and each of the other vertices in a weighted graph or network.  \nGeneral Mathematics Study Design   \nThis topic includes: (Directed Graphs – not covered at all in Unit 2)  \n• use of networks to model flow problems: capacity, sinks and sources  \n• solution of small-scale network flow problems by inspection and the use of the‘maximum-flow minimum-cut’ theorem to aid the solution of larger scale problems.  \n• use of a bipartite graph and its tabular or matrix form to represent a matching problem  \n• determination of the optimum assignment/s of people or machines to tasks by inspection or by use of the Hungarian algorithm for larger scale problems.  \n• construction of an activity network from a precedence table (or equivalent) including the use of dummy activities where necessary  \n• use of forward and backward scanning to determine the earliest starting times (EST) and latest starting times (LST) for each activity  \n• use of earliest starting times and latest starting times to identify the critical path in the network and determine the float times for non-critical activities  \n• use of crashing to reduce the completion time of the project or task being modelled.  \nNETWORKS  \nNew to networks?   \n• Take the time to read and learn the theory. For many staff it will be entirely new! A few different textbooks can help.  \n• It’s a unit that will require a bit of work if you haven’t studied it before .  \n• There are many new terms in the module (path, trail, circuit, connected network, complete graph, spanning tree etc) . Without knowing the content the VCAA exam questions will seem foreign.  \n• It is not a topic I would recommend learning by doing exam questions and trying to fill in the blanks by using the answers .  \nNew to Networks   \n• Make glossary lists of all the different terms .  \n• It is a great topi","cbCainmS0PAEzO4U","https://ap.wps.com/l/cbCainmS0PAEzO4U","pdf",2906145,49,"English","# Introduction\n# General Mathematics Study Design\n## Graphs and networks - Unit 2\n## Networks and decision mathematics - Unit 4\n# Networks\n## New to networks?","[{\"question\":\"What does the Unit 2 graphs and networks topic include?\",\"answer\":\"It includes notations and representations of graphs, adjacency matrix, planar graphs and Euler’s formula, connected graphs (walks, trails, paths, cycles, circuits), weighted graphs and networks, shortest path by inspection, and trees and minimum spanning trees using greedy algorithms.\"},{\"question\":\"What additional network concepts are covered in Unit 4?\",\"answer\":\"Unit 4 covers directed graphs and networks, matrix representation, Eulerian and Hamiltonian paths and cycles, spanning trees and Prim’s algorithm, connector problems, shortest paths by inspection, Dijkstra’s algorithm, and network flow modeling including maximum-flow minimum-cut.\"},{\"question\":\"How does the activity network scheduling part determine critical path and float?\",\"answer\":\"It uses forward and backward scanning to compute earliest starting times (EST) and latest starting times (LST) for each activity. The critical path is identified using EST and LST, and float times are determined for non-critical activities, with crashing used to reduce project completion time.\"}]","Teaching Networks in General Mathematics Units 1-4 - Study Design | PDF",1789903565,123]