FOR ALL QUIZZES: WRITE ALL ANSWERS ON PAPER FIRST. WHEN WE RE-QUIZ, TYPE ANSWERS TO CODE QUESTIONS INTO THE APPROPRIATE CONSOLE.

Keywords, Reserved Words and Tokens, and Operators

Quiz

1. List five reserved words in R.
2. List five reserved words in Python.
3. List five reserved words in Octave.

In all programming languages, there are certain characters, words, and symbols that have a fixed meaning and must be used in certain ways. This is the same as notation conventions in various mathematical fields. When we talk about arithmetic, + and = have fixed definitions. If instead we are talking about algebra, operators can take on different meaning, but saying something is a group (or field, ring, etc.) has a fixed meaning.

In the programming context, these syntactical elements are referred to by many different labels (keywords, reserved words, operators, etc.). Some minor language specific distinctions aside, they share the same practical definition: these are the (sequences of) characters that have particular uses in your code, and you cannot redefine their meaning.

Keep these in mind as we move through the following sections - they show up in almost all of them.

Re-Quiz

Variable Declaration

Quiz: Variable Declaration

1. Declare an integer in R, Python, and Octave
2. Declare a sequential data structure (i.e., a collection with items in ordinal positions) in R, Python, and Octave
3. Declare a key-value data structure (i.e., a collection with keys mapping to values) in R, Python, and Octave
4. Declare a variable derived from other variables.
5. Contrast immutable and mutable variables and collections.

“Variable” has a similar (but not identical!) meaning in programming and mathematics.

They are similar in the sense that we can express relationships between variables, and transformations of them, and so on, in both perspectives without having to know particular values. Of course, to get particular results in either, we need to know the particular variable value.

“Variable” in programming tends to be bit more expansive than typical use in mathematics, but in both realms we think of variables as being constrained to a certain domain - e.g., something might be a “natural” or “complex” scalar (or vector, matrix, etc). The same is true in programming, and these domains are called types. When a variable is actually several items of some type gathered together, this is generally called a collection, with specific names for different types of collections that either have items in particular ordinal positions (e.g., array(...) in R) or associated with particular keys (e.g., dicts in Python).

Re-Quiz: Variable Declaration

Function Declaration

Quiz: Function Declaration

1. Declare a function in R, Python, and Octave
2. What does “signature” mean relative to functions?
3. Write a function in R, Python, and Octave that returns multiple values.
4. Write a function in R, Python, and Octave that has no inputs or outputs, but has a side-effect.

Like in mathematics, a function is a special kind of variable in programming. In mathematics, functions represent a transformation from domain to range; the same is true in programming, though functions (or approximate synonyms like methods, definitions, procedures) can often also produce side-effects (e.g., writing a file or drawing a plot), and we call the domain arguments and range returns.

In programming, we typically use functions as a way to organize a related series of instructions to the computer. This is similar to how we use functions to represent mechanisms in applied mathematics (modeling).

Like other variables, functions have a type defined by the type of the arguments it accepts and the type of its returns. This type is sometimes called the signature.

There are some functions that are built-in - these can behave differently from functions you define in your code.

Like other variables, functions may be arguments to other functions. In mathematics, this notion appears in composition and with operators (e.g., operators in physics, summation or product operators). In programming, this is often called a functional approach, and functions which are supplied as arguments are often called lambda functions.

Re-Quiz: Function Declaration

Scope

Quiz: Scope

1. Running the following Python, what is print out?

a = 4

def afun(a):
  print(a)

afun(a)
afun(2)

1. Running the following blocks of R, what is print out?

a <- 4

afun <- function(a) {
  print(a)
  a <- 7
}

afun(a)
afun(2)

1. Running the following blocks of Octave, what is print out?

global a = 4

function afun (a)
  printf ("%d\n", a)
  global a;
  a = 5;
endfunction

afun (2)
afun (a)

In programming, scope is how the computer determines the value of a variable. If we only ever use unique variable names, then scope is simply a question of how does the computer find the variable. Is it a function argument? Defined within the function? Defined outside the function at the same level? Globally defined? Your code will need to ensure that the computer can find the appropriate variable. This happens differently in different languages, so you will need to understand at the general way it happens in one you choose.

This is akin to understanding the definition of variables in applied mathematics problems based on the context of the problem. Are we talking about physics? Then c probably refers to the speed of light, and we can use the mass-energy equivalence in whatever specific problem we are addressing. Are we solving quadratics? Then c is probably the constant coefficient of a quadratic polynomial, and we can use the quadratic formula.

The overlap in names in that mathematics example (i.e., c is both the speed of light and a particular coefficient in a quadratic) highlights another important aspect of scope: when your code re-uses names, how does the computer know which c to use? Like finding the variables, different languages resolve these questions differently, so make sure you know what’s happening with yours.

Re-Quiz

Logical Operators & Conditionals

Quiz: Logical Operators & Conditionals

1. What are the operators, keywords, or built-in functions for and, or, not, and xor in R, Python, and Octave?
2. In the following code blocks, what is print out?

def testfun(a):
  if (a == 5):
    print("five alive!")
  elif ((a % 2 != 0) & (a % 3 == 0)):
    print("that's triply odd!")
  else:
    print("even odds are boring!")

testfun(5)
testfun(15)
testfun(2)

a <- 1:10
ifelse(a < 5, "need at least 5", "woohoo!")

a = 4

if (mod(a,2) != 0)
  printf("that's odd\n")
elseif (length(unique(factor(a))) != 1)
  printf("it has multiple prime factors\n")
else
  printf("boring power!\n")
endif

Programming and mathematical logic share a very deep connection. At a fundamental level, computers are constructed of components called logic gates and programming languages ultimately translate to manipulation of the arrangements of these gates.

Beyond all the logical operations under the hood, however, logical operations are a common part of a programmer’s toolkit. Often we want to take different actions depending on how one value compares to another (e.g., is a < 5?), and often we want to combine multiple comparisons (e.g., is a > 0 and a < 5).

Once we have evaluated a condition as true or false, we can direct the flow of the program through different branches of action via if and else keywords. The details of how to do so varies by language, so make sure you understand how these work for your language of choice.

A final note, though not specific to actual code syntax: a useful way to think about how to direct flow with conditionals is to use truth tables. Truth tables are an enumeration of the possible condition combinations and what you want to happen in response to them. They also have a side benefit: if your conditionals are too complex, then you will have trouble writing out the tables and know you need to consider a different approach.

Re-Quiz