Genny maths Flashcards
What is an annuity?
An annuity is a form of compound interest where regular and equal payments are made periodically
OR as a single sum investment from
which regular and equal payments are received.
What is the present value formula?
PV = M((1 + i)^n − 1/r(1 + i)^n)
what is a simple network?
pairs of vertices are connected by max one edge
what is a complete network?
every vertex is joined to every other vertex
difference between connected and disconnected networks?
connected you can get to vertex by following the edges. disconnected you can’t as there disjointed
difference between directed and undirected network?
directed can only move one direction on the edge but undirected can move any direction
what is the degree of vertex?
no. of edges coming out of a vertex
how do you find no. of edges other then counting?
0.5 x the sum of the degrees
what are faces in networks?
no. of shapes in a network created by the lines +1 (for the outside)
what is a walk?
Any route, can repeat edges and vertices
what is a trail?
no edges are repeated (e.g. ABCB, OR ABCDAC
what is a path?
no vertices are repeated and end on different vertices
what is a cycle?
no vertices are repeated however the first and last one must
what is opened or closed…? which does it apply for?
open starts and stops at different vertices, closed finishes as same vertex. Applies to walks and trails
Name the 4 movements?
Walk, trail, path, cycle and closed walk/trail
what is a eulerian trail
a closed trail (no repeated edges and start/finish on same vertex) and degree of all vertices are even
what is a semi-eulerian trail
a open trail (no repeated edges and start/finish on different vertex) and degree of ONLY 2 vertices are odd
what is a hamiltonian cycle?
a closed path (includes every vertex once and start/finish on same vertex)
what is a semi-hamiltonian cycle/ hamiltonian path?
a open path (includes every vertex once and start/finish on different vertex)
what is the shortest path?
shortest path goes to all vertices ONCE
whats a tree?
simple connected network with no circuit
how to find no. of vertices on a tree?
= no. of edges + 1
whats prims algorithm 3 steps?
- draw vertices only
- start with small edges
- continue until all vertices are connected (but not complete a curcuit)
whats an immediate predecessor?
it must be complete before next activity can commence (the one before it)
whats an earliest start time?
write on left of vertex and use forward scanning of longest time.
whats critical path?
activities that cant be delayed without delaying the entire project
what is earliest completion time?
minimum time to taken to complete all activities (basically critical path time)
whats float time?
max time an activity not on critical path can be delayed
how do you find the latest start time?
backward scanning on the right side of the vertex
float time formula?
= latest finish time (LFT the rightest right) - earliest start time (EST the leftiest left) - activity time
what is a planar graph?
no edges cross over (can be drawn on a plane)
what is the hungarian algorithm steps (5)?
- subtract smallest value in row from every element in the row
- min lines to cover ‘0s’
- if column doesnt contain 0, subtract lowest value from column
- min lines to cover ‘0s’
- add smallest uncovered value to elements that covered by 2 lines. then subtract it from all uncovered elements
- continue until 4 lines drawn
