More recurrence examples Give asymptotic upper and lower bounds for T .n/ in each of the following recurrences. Assume that T .n/ is constant for sufficiently small n. Make your bounds as tight as possible, and justify your answers. a. T .n/ D 4T .n=3/ C n lg n. b. T .n/ D 3T .n=3/ C n= lg n. c. T .n/ D 4T .n=2/ C n2pn. d. T .n/ D 3T .n=3 2/ C n=2. e. T .n/ D 2T .n=2/ C n= lg n. f. T .n/ D T .n=2/ C T .n=4/ C T .n=8/ C n. g. T .n/ D T .n 1/ C 1=n. h. T .n/ D T .n 1/ C lg n. i. T .n/ D T .n 2/ C 1= lg n. j. T .n/ D pnT .pn/ C n.
The Second Great Awakening & Visions of the Millennium Great awakening → looking sociarder in a time of dramatic change Charles Grandison Finney ● Rejects predestinations; all people are sinners, so god wants everyone ○ You are a free agent...you can reject sin. ○ You may be born a sinner, but you are not damned ● Perfectionism: perfect community ○ If everyone rejects sin, it can be achieved ○ Looking for societal order ● Ushering in an religious millennium ● Would be asked to come in and talk to workers… White Middle Class Protestants ● Don't feel comfortable; feel besieged → soooo mrish ○ Irish are seen as the reason there needs to be reform Reform Movements ● Temperance movement : anti alcohol movement ○ Drinking was used in all occasions ○ Average intake is 10.6 gallons of hard liquor (not counting cider and beer) ○ An epidemic...going to tear America apart ● Public schools movement ○ Horace Mann ○ Trying to impose order in schools ○ Also to control Irish...our idea of protestant morality is spread to them ■ Culture, religion, government ■ Similar to trump: want to take back America ■ Children will learn that parents are bad, follow false religion (Catholic is bad) ○ inner discipline: taught in schools, listen to white authority figures, self control ○ Republicanism: public good/good of all people, power rests with the people ■ Cannot be loyal to the pope (Catholic) and be a member of a republic ○ Factories of Assimilation ■ Teach what their parents don’t ■ Teaching social order ○ Begins in North and spreads to Mid West ■ NO public school in south until post civil war