This course has already ended.

Luet oppimateriaalin englanninkielistä versiota. Mainitsit kuitenkin taustakyselyssä osaavasi suomea. Siksi suosittelemme, että käytät suomenkielistä versiota, joka on testatumpi ja hieman laajempi ja muutenkin mukava.

Suomenkielinen materiaali kyllä esittelee englanninkielisetkin termit. Myös suomenkielisessä materiaalissa käytetään ohjelmien koodissa englanninkielisiä nimiä kurssin alkupään johdantoesimerkkejä lukuunottamatta.

Voit vaihtaa kieltä A+:n valikon yläreunassa olevasta painikkeesta. Tai tästä: Vaihda suomeksi.

Chapter 3.4: Decisions

About This Page

Questions Answered: How can I make my program select between alternatives? How can I execute a piece of code only if a specific condition is met?

Topics: Expressions that select a value. if and else. Conditional effects on program state. Sequencing and nesting ifs.

What Will I Do? Read and work on small assignments.

Rough Estimate of Workload:? A couple of hours.

Points Available: A75.

Related Modules: GoodStuff, FlappyBug, Odds Miscellaneous (new) features in one optional assignment.


The Need to Select

Nearly all programs select between alternatives. For example: to determine the new favorite experience, we need to select between the old favorite experience and a newly added experience. Or: given a user input or “yes” or “no”, we want to select whether or not the program performs an operation of some sort.

One of the things we need, then, is a way to formulate a condition: Did the user select “yes”; is this experience better than that one? You already know what we can use for this part: the Boolean type.

The other thing we need is a way to mark commands as conditional so that the computer executes them only if a particular condition is met. It would be nice if we could also provide an alternative command to be executed in case the condition is not met.

Scala offers several tools for executing a command conditionally. In this chapter, we’ll look at the most straighforward of these tools: the if command.

Selecting Between Two Alternatives: if

you can use the words if and else to form an expression whose value depends on a particular condition — that is, the value depends on whether a particular Boolean expression evaluates to true or false.

Here’s the basic idea as pseudocode:

if (condition) value in case condition is met else value otherwise

It’s easy to experiment with this in the REPL:

if (10 > 100) "is bigger" else "is not bigger"res0: String = is not bigger
if (100 > 10) "is bigger" else "is not bigger"res1: String = is bigger
Notice the keywords if and else. Also notice the round brackets around the conditional expression, which are mandatory.
The conditional expression must be of type Boolean so that it evaluates to either true or false. In this example, the condition has been formed with a relational operator. When the computer runs the if command, it first evaluates the conditional expression, which determines what happens next.
In case the condition evaluates to false, the code that follows else is executed. The entire if expression evaluates to the value produced by evaluating the “else branch”.
In case the condition evaluates to true, the code that immediately follows the condition is executed. The entire if expression evaluates to the value of this “then branch”. (In Scala, we don’t actually spell out the word “then”, but you can read an if expression as “if X then A else B”.)


Any expression of type Boolean is a valid condition. It can be the name of a Boolean variable, for example:

val theDeathStarIsFlat = falsetheDeathStarIsFlat: Boolean = false
if (theDeathStarIsFlat) "Yeah right" else "No kidding"res2: String = No kidding

Or a Boolean literal, namely true or false (although this isn’t too useful):

if (true) "big" else "small"res3: String = big

In all the above examples, the “then” and “else” branches were expressions of type String, but an if certainly admits other subexpressions, too. Numbers work, for instance:

val number = 100number: Int = 100
if (number > 0) number * 2 else 0res4: Int = 200
if (number < 0) number * 2 else 0res5: Int = 0
The type of the entire if expression is determined by what you write in the conditional branches.

Using an if as an Expression

An if expression has a type, and you can use an if expression in any context that calls for an expression of that type. For example, you can use an if in a function’s parameter expression, you can assign an if’s value to a variable, or you can use an if as part of an arithmetic expression. Here are some more examples of valid if commands:

println(if (number > 100) 10 else 20)20
val chosenAlternative = if (number > 100) 10 else 20chosenAlternative: Int = 20
(if (number > 100) 10 else 20) * (if (number <= 100) -number else number) + 1res6: Int = -1999

That being said, the last of those commands is branchy enough that you’d do better to store the intermediate values in a temporary variables before multiplying them.

Practice on if expressions

Suppose we execute the following commands in the REPL:

val favePet = "llama"
val animal = "cat"
val remark = if (animal == favePet) "Yes!" else "Okay"

What is now the value of the last variable, remark?

Assume the above commands have already been executed, followed by this one:

println(if (remark == "Yeah") "positive" else "neutral" + " reaction")

Which of the following is correct?

Next, we execute this command:

println(if (remark == "Okay") "neutral" else "positive" + " reaction")

Which of the following is correct?

Next, we execute this command:

println((if (remark == "Okay") "neutral" else "positive") + " reaction")

Which of the following is correct?

Next, we execute this command:

println("That was a " + if (remark == "Okay") "neutral" else "positive" + " reaction.")

Which of the following is correct?

Next, we execute this command:

println("That was a " + (if (remark == "Okay") "neutral" else "positive") + " reaction.")

Which of the following is correct?

Formatting an if expression

Where a single-line if expression would be long and hard to read, you can split it across multiple lines as shown here:

val longerRemark =
  if (animal == favePet)
    "Outstanding! The " + animal + " is my favorite animal."
    "I guess the " + animal + " is nice enough."

Notice how it’s customary to indent the two branches of an if to a deeper level than the lines that start with if and else. Once you’re used to this convention, it makes the if expression faster to read as a whole.

This style convention is worth following when you write multi-line ifs, despite the fact that, in Scala, indentations don’t affect the program’s behavior.

Mini-assignment: describing an image, part 1 of 2

In module Miscellaneous, file misc.scala, add an effect-free function that:

  • has the name describe;
  • takes a single parameter, of type Pic; and
  • returns the string "portrait" in case the given picture’s height is greater than its width, and the string "landscape" otherwise (i.e., if the image is square or wider than it’s high).

A+ presents the exercise submission form here.

Finishing class Experience

You can use if in a class, thus enabling objects to make decisions when their methods are invoked.

The chooseBetter method

From Chapter 3.3, we already have a partial implementation for class Experience. The one part still missing is the chooseBetter method that compares two experiences and returns the higher-rated one.

We’d like the method to work as follows:

val wine1 = new Experience("Il Barco 2001", "okay", 6.69, 5)wine1: o1.goodstuff.Experience = o1.goodstuff.Experience@1b101ae
val wine2 = new Experience("Tollo Rosso", "not great", 6.19, 3)wine2: o1.goodstuff.Experience = o1.goodstuff.Experience@233b80
val betterOfTheTwo = wine1.chooseBetter(wine2)betterOfTheTwo: o1.goodstuff.Experience = o1.goodstuff.Experience@1b101ae
betterOfTheTwo.nameres7: String = Il Barco 2001

In essence, chooseBetter is similar to the familiar max function (Chapter 1.6) that picks the larger of two given numbers.

Here is class Experience with a pseudocode implementation for chooseBetter:

class Experience(val name: String, val description: String, val price: Double, val rating: Int) {

  def valueForMoney = this.rating / this.price

  def isBetterThan(another: Experience) = this.rating > another.rating

  def chooseBetter(another: Experience) = {
    Determine if this experience is rated higher than the experience given as * another*.
    If so, return a reference to the this object. Otherwise, return the reference stored in * another*.


And here is the method in Scala:

def chooseBetter(another: Experience) = {
  val thisIsBetter = this.rating > another.rating
  if (thisIsBetter) this else another
The word this alone constitutes an expression whose value is a reference to the object whose method is being called.
chooseBetter’s execution ends in an if expression; the method returns the value of that expression. Depending on whether thisIsBetter stores true or false, the if expression’s value will be a reference to either the active object or the parameter object, respectively.

Improving code by calling an object’s own methods

That implementation of chooseBetter works. But class Experience is now needlessly repetitive. Both isBetterThan and chooseBetter do the same comparison this.rating > another.rating, so we have a double definition of what counts as “better” in our application.

In addition to being inelegant, this is unhelpful to anyone who wants to modify the application. For instance, if we wanted GoodStuff to compare experiences by their value for money rather than their rating, we’d need to modify the code in two places. In this small-scale program, the problem is isn’t too terrible, but redundant code can make larger programs very difficult to work with.

Let’s improve our code.

You’ve already seen that an object can call its own method to “send itself a message”: this.myMethod(params). Let’s use this to compose a new version of chooseBetter:

def chooseBetter(another: Experience) = {
  val thisIsBetter = this.isBetterThan(another)
  if (thisIsBetter) this else another
The Experience object asks itself: “Are you better than this other experience?”

Now chooseBetter relies on whichever kind of comparison is defined in isBetterThan. We have eliminated the redundancy.

A more compact solution: a method call as a conditional

A method call, too, can serve as an if’s conditional expression, as long as the method returns a Boolean. We can use that fact to simplify chooseBetter further. This is illustrated in the REPL session below (which assumes that wine1 and wine2 are defined as above):

if (wine1.isBetterThan(wine2)) "yes, better!" else "no, wasn’t better"res8: String = "yes, better!"
if (wine2.isBetterThan(wine1)) "yes, better!" else "no, wasn’t better"res9: String = "no, wasn’t better"
if (wine1.isBetterThan(wine1)) "yes, better!" else "no, wasn’t better"res10: String = "no, wasn’t better"

Here, evaluating the if entails calling the method; the value of the conditional is whichever Boolean the method returns. After calling the method, execution continues into one of the if’s two branches.

We’re now equipped to write a more compact implementation for chooseBetter. We don’t need to use the temporary local variable thisIsBetter as we did above.

def chooseBetter(another: Experience) = if (this.isBetterThan(another)) this else another

Our Experience class is now ready. Later, in Chapter 4.2, we’ll turn our attention to GoodStuff’s other key class, Category.

Assignment: Odds (Part 7 of 9)

Let’s return again to the Odds program and add a method that reports an event’s odds in a format called moneyline, which is popular among North American betting agencies. This slightly curious format works as follows:

(Below, P and Q refer to the numbers that make up the fractional represtentation P/Q of an Odds.)

In case the event’s estimated probability is at most 50%, its moneyline number is positive and equals 100 * P / Q. For instance, the moneyline number for 7/2 odds is 350, because 100 * 7 / 2 = 350. This positive number indicates that if you bet 100 monetary units and win, you profit 350 units in addition to getting your bet back. A fifty–fifty scenario (1/1 odds) has a moneyline number of 100.

In case the event’s estimated probability is over 50%, its moneyline number is negative and equals -100 * Q / P. For instance, the moneyline number for 1/5 Odds is -500, because -100 * 5 / 1 = -500. This negative number indicates that if you want to make a profit of 100 units, you have to place a bet of 500 units.

Task description

In class Odds, add a moneyline method that returns Odds object’s moneyline representation as an Int:

val norwayWin = new Odds(5, 2) norwayWin: Odds = o1.Odds@171c36b
norwayWin.moneylineres11: Int = 250

In OddsTest1, add a command that prints out the first Odds object’s moneyline number. The program’s output should now look like this:

Please enter the odds of an event as two integers on separate lines.
For instance, to enter the odds 5/1 (one in six chance of happening), write 5 and 1 on separate lines.
The odds you entered are:
In fractional format: 11/13
In decimal format: 1.8461538461538463
In moneyline format: -118
Event probability: 0.5416666666666666
Reverse odds: 13/11
Odds of happening twice: 407/169
Please enter the size of a bet:
If successful, the bettor would claim 369.2307692307692
Please enter the odds of a second event as two integers on separate lines.
The odds of both events happening are: 251/13
The odds of one or both happening are: 110/154
Just one new line of output.

Instructions and hints

  • Use an if expression.
  • moneyline must return an integer. Drop any decimals from the result; always round towards zero. Scala’s integer division drops the decimals for you (Chapter 1.3), so the easiest solution is simply to do the arithmetic in the right order: multiply first, divide second.
  • It’s a single word, so write moneyline not moneyLine.

A+ presents the exercise submission form here.

Apocalyptic programming

According to Finnish folklore, God punished the hazel grouse (for reasons that are disputed) and condemned it to grow smaller until the world ends. People will know that the end is nigh when the grouse is vanishingly small.


A hazel grouse.

This story has given rise to an odd Finnish idiom: a Finn may say that something “shrinks like the grouse before the apocalypse”.

Let’s model this programmatically, because why not. Here’s a class that represents grouses:

class Grouse {

  private var size = 400
  private val basePic = Pic("bird.png")

  def foretellsDoom = this.size <= 0

  def shrink() = {
    if (this.size > 0) {
      this.size = this.size - 1

  def toPic = this.basePic.scaleTo(this.size)


You can find the class and a GUI that uses it within the IntroApps module. The GUI uses techniques from Chapter 3.1 to shrink the image of a grouse against a white background until the grouse vanishes from sight.

Your task is to read the given code and modify makePic so that it turns the entire view black at the end. The method should therefore return:

  • the bird pic against a white background (as per the given code) only if calling foretellsDoom on the grouse returns false; and
  • a fully black endOfWorldPic if the return value is true.

In practical terms, the only thing you need to add is an if expression in makePic.

A+ presents the exercise submission form here.

Affecting Program State with an if

The branches of a selection command may specify effects on program state. They may print text onscreen and assign to vars, for example. Like here:

if (number > 0) {
  println("The number is positive.")
  println("More specifically, it is: " + number)
} else {
  println("The number is not positive.")
println("I have spoken.")
You can surround a branch with curly brackets and write more than one command within them. Those commands will be executed one after the other in case that branch is chosen.
It’s customary to indent the lines between the curly brackets.
The example’s last line isn’t part of the if command but follows it. After executing one of the two branches above, that println will be executed no matter the value of the conditional.

The animations below detail how the code works, first for a positive number, then for a negative.

Note: Earlier in this chapter, we used the if command to form expressions, that is, chunks of code that evaluate to a (meaningful) value. We used ifs to select between two alternative values. On the other hand, in the code animated above, the if selects between different effects on program state. Here’s the general notion summarized as pseudocode:

if (condition) {
  commands to be executed in case the condition evaluates to true
} else {
  commands to be executed in case the condition evaluates to false

When an if affects program state, convention dictates that you use line breaks, indentations, and curly brackets as in the examples above. We’ll follow this custom in O1 (as noted in our style guide).

Some Scala programmers...

... do omit the curly brackets from branches that contain just a single command, even if the if is effectful. We’ll consistently use curly brackets in effectful if s, however.

ifs that produce Unit

The following assignment to meaninglessResult doesn’t make a lot of sense but is worth a moment of consideration:

val meaninglessResult =
  if (number > 1000) {
    println("Pretty big")
  } else {
    println("No so big")
  }Not so big
meaninglessResult: Unit = ()

Here, the if expression has no meaningful value. The code does print one of the two strings depending on the value in number, but it doesn’t assign anything useful in meaninglessResult, just the Unit value (Chapter 1.6). This is because the ifs branches end in print commands that don’t return anything beyond Unit. It makes little sense to assign the value of such an if to a variable.

Perhaps you’ll also find it instructive to compare the above code with these two:

val result = if (number > 1000) "Pretty big" else "Not so big"result: String = Not so big
println(result)Not so big
println(if (number > 1000) "Pretty big" else "Not so big")Not so big

if without else

When you use an if to affect program state, you don’t always need an else branch. You may wish to execute one or more commands if a condition is met but do nothing otherwise.

Of course, you could write something like this:

if (condition) {
  commands to be executed in case the condition was true
} else {
The empty else branch does nothing. But we don’t even have to write it; we can simply omit this part.

If there’s no else branch and the conditional evaluates to false, the computer simply disregards the rest of the if:

if (condition) {
  commands to be executed in case the condition was true and skipped otherwise

Here’s a more concrete example:

if (number != 0) {
  println("The quotient is: " + 1000 / number)
println("The end.")
The else branch has been omitted.
This if command is effectful (it prints stuff), which is why we use line breaks and curly brackets.
The second print command isn’t part of the if but follows it. This piece of code invariably finishes by printing "The end." no matter if number was zero or not. If it was zero, that’s all the code prints out.

If you wish, you can also view an animation of that example:

Practice reading ifs

Pause to reflect on the following program.

var first = 20
var second = 10

if (first < second) {
  first = first / 2

if (first < 2 * second) {
  first = first * 2
  second = second / 2
} else {
  first = first + 1
  second = second - 1

val theyAreTheSame = (first == second)

if (theyAreTheSame) {
  first = first + 1

println(s"$first $second")

Think about a single of execution of this code. What happens at each step?

How many times, in total, does the computer execute a conditional expression (of any if)?
How many times, in total, does an if command’s conditional expression evaluate to true?
The middle if has an else branch. How many times is that else branch executed?
What does the last line of code print out?

Assignment: FlappyBug (Part 12 of 17: Minor Adjustments)

Task description

Add two if commands to the FlappyBug game so that:

  • the bug darts upwards only in case the key pressed by the user is the space bar (rather than any old key, as in the current version); and
  • the bug accelerates (i.e., the value of its instance variable yVelocity increases) only if the bug is in the air (i.e., located above the ground level).

Instructions and hints

  • You need to modify the onKeyDown method in FlappyBugApp and the fall method in class Bug. Both are described in Chapter 3.1.
  • The parameter of the event handler onKeyDown indicates which key was pressed. You can use the equality operator == to compare the parameter value with Key.Space, a constant that corresponds to the Space key.
  • You won’t need any else branches.

A+ presents the exercise submission form here.

Combining ifs

else if chains

If you want to select among more than two alternatives, you can write an if command within the else branch of another if:

val description = if (number < 0) "negative" else if (number > 0) "positive" else "zero"

Brackets may clarify the structure of the code:

val description = if (number < 0) "negative" else (if (number > 0) "positive" else "zero")

Perhaps the best way to highlight the multiple branches is to split the code across multiple lines and indent it:

val description =
  if (number < 0)
  else if (number > 0)

A similar chain of “else ifs” also works for selecting among multiple effectful commands:

if (number < 0) {
  println("The number is negative.")
} else if (number > 0) {
  println("The number is positive.")
} else {
  println("The number is zero.")

Mini-assignment: describing an image, part 2 of 2

Edit the describe function you wrote in misc.scala earlier so that it returns:

  • the string "portrait" if the picture’s height is greater than its width;
  • the string "landscape" if the picture’s width is greater than its height; and
  • the string "square" if the picture’s height and width are exactly equal.

A+ presents the exercise submission form here.

Nesting ifs

You’re free to nest if commands within each other. When you do, you need to be especially careful about which else goes with which if. Take a look at this REPL session:

val number = 100number: Int = 100
if (number > 0) {
  if (number > 1000) {
    println("More than a thousand.")
  } else {
     println("Positive but no more than a thousand.")
}  Positive.
Positive but no more than a thousand.
In case the number is 100, the outer if’s contents are executed. This includes the first println.
Within that if is another if. Since the inner if’s condition isn’t met, the program jumps to the else branch.
Note: the inner if’s branches are indented to a still deeper level.
Since we indented the code as convention dictates, the word if is vertically aligned with the curly brackets that delimit the corresponding branches. In our example, this applies both to the inner...
... and the outer if. Do keep in mind, however, that whereas the curly brackets actually affect how the commands nest within one another, the indentations are there only for readability.
In this example, the outer if has no else branch.

In the above example, the else matches the “closer” of the two ifs. The else branch was executed because the outer if’s condition was met but the inner one’s wasn’t. By adjusting the curly brackets, we can attach the else to the outer if instead:

if (number > 0) {
  if (number > 1000) {
    println("More than a thousand.")
} else {
  println("Zero or negative.")
Now the outer if has two branches and its else branch would have been executed only if the number hadn’t been positive.
The else branch connects with the nearest complete “then branch” that precedes it. In this case, the outer ifs “then branch” is the latest one to close.
In this example, the inner if has no else branch. As a result, the program produces just the single line of output.

Practice on nested ifs

As you read the following program, pay particular attention to curly brackets and indentation.

The program uses the modulo operator to determine whether a number is even or odd.

if (number > 0) {
  if (number % 2 == 0) {
  } else {

if (number > 0) {
  if (number % 2 == 0) {
} else {
Enter all the letters that get printed when the above code is run and number has the value 5. (Just the letters, please; e.g., ACFG.)
Enter the letters that get printed when the above code is run and number has the value 6.
Enter the letters that get printed when the above code is run and number has the value -5.
Enter the letters that get printed when the above code is run and number has the value -6.

Assignment: Odds (Part 8 of 9)

Task description

The app object OddsTest2 from Chapter 3.3 creates a couple of Odds objects and reports selected facts about them. Edit it:

  1. Remove the println commands that print the return values of isLikely and isLikelierThan (the ones whose output begins with the word “The”). This is because you’re about to replace these lines with new ones that produce a different printout than before.
  2. The revised OddsTest2 should check whether the event represented by the first Odds object is more likely than the second. Based on this check, the program should print either "The first event is likelier than the second." or "The first event is not likelier than the second." as appropriate.
  3. Next, the program should print the line "Each of the events is odds-on to happen." in case both of the events are likely. If neither event is likely, or only one is, the program should print nothing at this point.
    • As per our earlier definition, an event counts as likely in case the chances of it occurring are greater than those of it not occurring, that is, in case isLikely returns true.
  4. The final line of output, which thanks the user, should appear no matter which odds the user entered.

The example runs below detail the expected output:

Please enter the odds of the first event as two integers on separate lines.
Please enter the odds of the second event as two integers on separate lines.
The first event is not likelier than the second.
Thank you for using OddsTest2. Please come back often. Have a nice day!
Please enter the odds of the first event as two integers on separate lines.
Please enter the odds of the second event as two integers on separate lines.
The first event is likelier than the second.
Thank you for using OddsTest2. Please come back often. Have a nice day!
Please enter the odds of the first event as two integers on separate lines.
Please enter the odds of the second event as two integers on separate lines.
The first event is likelier than the second.
Each of the events is odds-on to happen.
Thank you for using OddsTest2. Please come back often. Have a nice day!

Instructions and hints

  • Use multiple if commands.
  • To check whether two different events are likely, you can nest one if inside another. Or, if you want, you can take an advance peek at Chapter 5.1 and pick out another means of combining two conditions into one.

A+ presents the exercise submission form here.

Summary of Key Points

  • You can use an if command to select which of two commands or sequences of commands is executed.
  • You can also use an if to indicate that the execution of a piece of code is conditional: the code is executed only if specific circumstances apply.
  • When you write an if, you need to specify the selection condition you want. Any expression of type Boolean is valid for that purpose.
  • You can combine if commands by sequencing them one after the other or by nesting them within each other.
  • Links to the glossary: if; Boolean; expression; DRY.

Optional assignment: a game of precision

Write a new program where the user is supposed to click the exact center of the window with a mouse click. This simple game is over when the user manages to click, say, within three pixels of the center. At that point, the program should display an image of your choosing to signal victory.

To model the problem domain, you may wish to create a simple object that keeps track of whether the game is over in a Boolean variable. Also write a GUI that displays the game’s state.

No automatic feedback is available for this optional assignment.


Please note that this section must be completed individually. Even if you worked on this chapter with a pair, each of you should submit the form separately.


Thousands of students have given feedback that has contributed to this ebook’s design. Thank you!

The ebook’s chapters, programming assignments, and weekly bulletins have been written in Finnish and translated into English by Juha Sorva.

The appendices (glossary, Scala reference, FAQ, etc.) are by Juha Sorva unless otherwise specified on the page.

The automatic assessment of the assignments has been developed by: (in alphabetical order) Riku Autio, Nikolas Drosdek, Joonatan Honkamaa, Jaakko Kantojärvi, Niklas Kröger, Teemu Lehtinen, Strasdosky Otewa, Timi Seppälä, Teemu Sirkiä, and Aleksi Vartiainen.

The illustrations at the top of each chapter, and the similar drawings elsewhere in the ebook, are the work of Christina Lassheikki.

The animations that detail the execution Scala programs have been designed by Juha Sorva and Teemu Sirkiä. Teemu Sirkiä and Riku Autio did the technical implementation, relying on Teemu’s Jsvee and Kelmu toolkits.

The other diagrams and interactive presentations in the ebook are by Juha Sorva.

The O1Library software has been developed by Aleksi Lukkarinen and Juha Sorva. Several of its key components are built upon Aleksi’s SMCL library.

The pedagogy of using O1Library for simple graphical programming (such as Pic) is inspired by the textbooks How to Design Programs by Flatt, Felleisen, Findler, and Krishnamurthi and Picturing Programs by Stephen Bloch.

The course platform A+ was originally created at Aalto’s LeTech research group as a student project. The open-source project is now shepherded by the Computer Science department’s edu-tech team and hosted by the department’s IT services. Markku Riekkinen is the current lead developer; dozens of Aalto students and others have also contributed.

The A+ Courses plugin, which supports A+ and O1 in IntelliJ IDEA, is another open-source project. It was created by Nikolai Denissov, Olli Kiljunen, and Nikolas Drosdek with input from Juha Sorva, Otto Seppälä, Arto Hellas, and others.

For O1’s current teaching staff, please see Chapter 1.1.

Additional credits appear at the ends of some chapters.

a drop of ink
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