# Exercise 1.

x <- c(-4, 1, 0, 0, 5, -3, 2)
y <- c(1, 1, -5, 4, 3, -2, 0) 
x[c(1, 2, 6)]
y[1:4]
x[x<0]
x[-3]
x[x<0 & y!=1]
y[y<0 | x<=0]
y[rep(1:2,2)]

# Exercise 2.
x <- 5
y <- 7
s1 <- (x+y) / 2
s1
s1 <- mean(c(x,y))
s1

s2 <- 4 * (x<7) + y * (x>=7) + 1 * (x>8)
s2
s3 <- min(c(x,y))
s3
s4 <- (x+y)/2 * (x>=5) + y * (x<5)
s4

# Exercise 3.

A <- matrix(c(1,2,6,5,2,5,6,1,3), byrow=T, nrow=3)
B <- matrix(c(1,1,1,2,1,3), byrow=T, nrow=3)
C <- diag(diag(A))
5*solve(A)+3*solve(A%*%t(A))-2*B%*%t(B)+diag(3)+diag(c(5,6,3))

# Exercise 4.

#a

chem<-c(93,71,77,78,77,81,88,74,67,78,77,67,63,83,73,70,78,95,88,75)
phys<-c(42,67,59,70,59,50,50,51,45,64,49,49,48,51,56,47,53,56,49,71)
math<-c(98,68,36,92,44,45,58,31,70,46,41,46,65,62,20,22,92,56,28,94)
arch<-c(34,33,24,24,31,22,23,32,31,26,75,81,87,100,81,100,77,89,100,77)
sex <- factor(c(rep("Male",6),rep("Female",4),rep("Male",2),
rep("Female",4),rep("Male",4)))
year<-c(1,1,1,1,1,2,2,2,2,2,1,1,1,1,1,2,2,2,2,2)

grades <-data.frame(chem,phys,math,arch,sex,year)

#b

sgr <- split(grades, grades$sex)
mycolmeans <-function(x, index) { 
	colMeans(x[, index]) 
}
lapply(sgr, mycolmeans, index=1:4)

#c

sapply(grades[,1:4],max)

#d

max(grades[,1:4])

#e
#overall
avgr <- apply(grades[,1:4],1,mean)
cbind(sort(avgr),grades[order(avgr),])

# by year
sgr2 <- split(grades,grades$year)
myrowmeans <- function(x, index){
	rowMeans(x[, index])
}
avgr2 <- lapply(sgr2, myrowmeans, index=1:4)

cbind(sort(avgr2[[1]]), sgr2[[1]][order(avgr2[[1]]),])
cbind(sort(avgr2[[2]]), sgr2[[2]][order(avgr2[[2]]),])

#f

grades2 <- grades
grades2[,1:4] <- sapply(grades[,1:4],scale)
avgr.st <- apply(grades2[,1:4],1,mean)
which.max(avgr.st)
grades[which.max(avgr.st),]

#g
res1 <- sapply(grades[,1:4], function(x) x>=50)
res2 <- apply(res1,1,function(x) all(x))
sum(res2)/length(res2)

#e

suc <- grades[res2,1:4]
sapply(suc[,1:4],mean)
sapply(suc[,1:4],var)