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" Joseph 's will was slow , like his mind ; he hesitated , but at length replied , " The offer is kind . There are 8-13 members of the Board who serve for periods of varying length . At the default setting , the length of each clone is previously selected , which is the largest number for the clone . Assignment 1 is at least 2000 word in length and is based solely on materials in the course package , assignment 2 is at least 2500 words in length and is based solely on materials in the course package , and assignment 3 is at least 4000 words in length and is based on materials in the course package and extra materials beyond the course package . In this course , we will follow the historical development and first study conformal maps of the disc ( distortion theorems , continuity up to the boundary ) , then discuss conformal invariants ( hyperbolic metric , harmonic measure , extremal length ) and finally develop the theory of quasiconformal maps .