Here are my solutions to R Worksheet 1. These aren’t necessarily the only ways to solve these problems.

Remember that you can get R help at the R Practicals in Weeks 2 and 3.

Exercise 1.1. Type 2 + 3 into the console next to the arrow, and then press Enter. What happens?

Let’s try!

2 + 3

We see the answer [1] 5. First, the [1] just tells us that what follows is the first part of the answer – since our answer here only has one part, we can ignore this. (It is useful when the answer is a very long vector or a table of values.) Then the 5 is the answer we want.

Exercise 1.2. Calculate:
(a) \(943 - 242\),
(b) \(29 \times 31\),
(c) \(2^{8+5}\),
(d) \(\displaystyle \frac{19 + 21}{5 \times 3}\).

We calculate these as follows:

943 - 242
## [1] 701
29 * 31
## [1] 899
2^(8 + 5)
## [1] 8192
(19 + 21) / (5 * 3)
## [1] 2.666667

Exercise 1.3. Use R to find:
(a) \(\frac{1}{7}\) to 4 decimal places;
(b) \(\log(10)\) to 3 significant figures;
(c) \(\sqrt{712 + 34}\) to the nearest integer.

We can find these as follows:

round(1 / 7, digits = 4)
## [1] 0.1429
signif(log(10), digits = 3)
## [1] 2.3
round(sqrt(712 + 34))
## [1] 27

Exercise 1.4. Create an object called john, and assign it the value 7. Then create an object called paul and assign it the value \(12^2\). Then get R to tell you the value of paul multiplied by the value of john.

We do this as follows:

john <- 7
paul <- 12^2
paul * john
## [1] 1008

Exercise 1.5. This exercise continues with the objects assigned in Exercise 1.4.
(a) Assign the value of paul mutiplied by john to the new value ringo.
(b) Check the value of ringo.
(c) Double the value of ringo, keeping it still stored as ringo.
(d) Add 7 to the value of ringo.
(e) Check the new value of ringo. (It should be 2023.)

We do this as follows:

ringo <- paul * john
ringo
## [1] 1008
ringo <- 2* ringo
ringo <- ringo + 7
ringo
## [1] 2023

The answer is indeed 2023, as it should be.

Exercise 1.6. Write down the commands you used to solve Exercises 1.4 and 1.5 in a new R Script. Save your work with a explanatory filename that will allow you to find it again later.

Exercise 1.7. Continuing with your R Script from Exercise 1.6, add comments to make it clear which commands are doing what, then re-save your R Script.

My R Script R1-solutions.R looked like this:

# MATH1710: R WORKSHEET 1
# MY SOLUTIONS
# Last updated: 9 October 2023

# Exercise 1.1
2 + 3  # Gets output "[1] 5", meaning the answer is 5

# Exercise 1.2
943 - 242
29 * 31
2^(8 + 5)
(19 + 21) / (5 * 3)

# Exercise 1.3
round(1 / 7, digits = 4)
signif(log(10), digits = 3)
round(sqrt(712 + 34))

# Exercise 1.4
john <- 7
paul <- 12^2
paul * john

# Exercise 1.5
ringo <- paul * john
ringo
ringo <- 2* ringo
ringo <- ringo + 7
ringo  # Answer is 2023, as it should be

# Exercise 1.5 created this R Script

# Exercise 1.6 added comments to this R Script