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Course: MATH 3012, Fall 2011
School: Georgia Tech
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Word Count: 466

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Hamilton 1 Denitions cycle - a simple cycle that includes every vertex with out repetition. graph isomorphism - a dierent representation of a graph that is the exact same. simple graph - no loops, no more than one edge between 2 vertices. isomorphic graphs bipartite graph - 2-colorable graph, can be split into two disjoint sets so every vertex in set 1 connects to a vertex in set 2. vertex coloring...

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Hamilton 1 Denitions cycle - a simple cycle that includes every vertex with out repetition. graph isomorphism - a dierent representation of a graph that is the exact same. simple graph - no loops, no more than one edge between 2 vertices. isomorphic graphs bipartite graph - 2-colorable graph, can be split into two disjoint sets so every vertex in set 1 connects to a vertex in set 2. vertex coloring - coloring of vertices of a graph such that no 2 adjacent vertices are the same color (4 is the largest minimum) plane graph chromatic number - number of colors you need. planar graph - 2-D graph no overlaps. chromatic polynomial - the number of ways a graph can be colored using no more than a given number of colors. (t is the number of colors). subdivision of a graph - when you subdivide edges in the graph. complete graph - every edge that can be drawn is. Kn = (t)(t 1)(t (n 1)) complete bipartite graph - 2 disjoint sets of vertices where every vertex in set 1 is connected to every vertex in the second set. Tree with n vertices: (t)(t 1)(n1) Cycle Cn = (t 1)n + (1)n (t 1) vertex - The dot. edge - the line tree - an undirected graph with any 2 vertices connected by EXACTLY 1 simple path. A connected graph with out cycles. multiple edge - more than 1 edge between the 2 same vertices. forest - disjoint union of trees. loop - edge that starts and ends at the same vertex. shortest path - shortest path... degree - The number of edges drawn to a vertex. degree sequence - the non-increasing sequence of vertex degrees in a graph path - in a sequence of vertices such that from each vertex there is an edge to the next vertex in the sequence. trail - A walk in which all the edges are distinct. walk - alternating sequence of vertices and edges, starting and ending with a vertex. cycle - a path that starts and ends at the same vertex. circuit - a closed trail. closed walk - same really as a cycle. Eulerian circuit - an Euler trail that starts and ends on the same vertex. Eulerian trail - a trail that visits each edge once. minimum spanning tree -tree of smallest weight. 2 Theorem Handshaking lemma - deg (v ) = 2 E . Prims algorithm. Pick a vertex. Pick the least weight vertex. Keep picking the least weight vertex until done. (vertex focused) Kruskals algorithm. Pick the least weighted edges. keep doing so until you have all the vertices connected. Eulers Formula. V E + F = 2. Kuratowskis theorem: A graph is planar IFF it doesnt contain a subgraph of K5 or K3,3 . Dijkstras shortest path algorithm: Uh, just look at all the paths and nd the smallest one.
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Georgia Tech - MATH - 3012
Chapter 1Fundamental Principles of Counting1.1Rules of Sum and Product1. If the possible outcomes of a procedure can be divided into two disjoint categoriesand if the 1st category has m1 outcomes and the 2nd has m2 outcomes then the totalnumber of o
Georgia Tech - MATH - 3012
1Russells ParadoxIf S is a set, there are two possibilities. S S or S S .Let G = cfw_S S is a set &amp; S S . Let B = cfw_S S is a set &amp; S S C1: If G G then G is a set &amp; G GC2: If G G, then G G2FunctionsA function f A B x A f (x) B . f maps to f (x).
Georgia Tech - MATH - 3012
Vector Space Axioms The kernel of T is cfw_c Rn T (c) = 0(a) Vector Addition(e) Additive Identity(b) Scalar Multiplication(f) Multiplicative Assoc.(c) Additivetivity(g) MultiplicativetityCommuta-(d) Additive AssociativityIden-ba Bases and
Purdue - CIVIL ENGI - CE 297
MechanicsPhysical science on the behavior of bodies under the action of forces.I. Rigid Bodies1. Statics (bodies at rest)2. Dynamics (bodies in motion)II. Deformable Bodies - Strength of materialsIII. Fluids1. Hydraulics (incompressible uids)2. Co
Purdue - CIVIL ENGI - CE 297
Scalars and VectorsscalarA physical quantity having only magnitude, not direction.For example, time, distance between two points, mass,speed, kinetic energy, temperature, density and volume.vectorA physical quantity having magnitude and direction.F
Purdue - CIVIL ENGI - CE 297
External and internal forcesExternal forcesThe action of other bodies on the rigid body under consideration.Internal forcesThe forces which hold together the particles formingthe rigid body.CE 2972Principle of transmissibilityA force may be consi
Purdue - CIVIL ENGI - CE 297
Equilibrium of a rigid bodyA body is said to be in equilibrium when the external forces acting on itform a system of forces equivalent to zero.R = F = 0M R = M = (r F) = 0Awhere A is an arbitrary point.In component form, Fx = 0 Fy = 0 Fz = 0 M
Purdue - CIVIL ENGI - CE 297
Center of gravity of a two-dimensional bodyGravitational attraction of the earth on a rigid body, a distributedforce, can be represented by a single equivalent force W applied atthe center of gravity.CE 2972Center of gravity of a two-dimensional bod
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Analysis of structures Structures are made of several interconnected parts. The total structure and any part of the structure is in equilibrium. Determine reactions Determine internal forces From Newtons third law, the internal forces between two par
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Purdue - CIVIL ENGI - CE 297
Moment of inertia of an areaFor linearly-varying distributed loads,Resultant forceR= ky dA = k Ay dA = k Q xAThe first moment of the area about the x -axisQx =y dAAThe first moment of the area about the y -axisQy =Ax dACE 2972Moment of i
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
Purdue - CIVIL ENGI - CE 297
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Purdue - STAT - 511
79. Let A1 = older pump fails, A2 = newer pump fails, and x = P(A1 A2). Then P(A1)= .10 + x, P(A2) = .05 + x, and x = P(A1 A2) = P(A1) P(A2) = (.10 + x)( .05 + x) . Theresulting quadratic equation, x2 - .85x + .005 = 0, has roots x = .0059 and x = .8441
Purdue - STAT - 511
Purdue - STAT - 511
Purdue - STAT - 511
The question about |X| : note that |X| is always non-negative and cannot be symmetric; thisautomatically means that it cannot be normally distributed.
Purdue - STAT - 511
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Purdue - STAT - 511
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Purdue - STAT - 511
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PIPE IDAVFLOWMNTCEGRADEMATRLACIDITYDURBLTYP 1591611.0312.250.070014.55P 160913.4830.060152.58P 160993.1440.06014.68P 1656315.172.630.0501P 1000110.9432.50.07019.35P 100188.32.50.020115.6530.060013.75.9
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Random number from a normal distributionRandom Number between 0 and 1Random Number between 0 and 10Random Number between 5 and 10with mean 100 and std dev 100.268489844.5609751955.60972944481.601403770.0397747135.9956192558.69709545388.7233436
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