Introduction to Programming
Middle School= is assignment, not equality — count = count + 1 is fine.A program is a precise sequence of instructions that transforms input into output. Programming languages give us abstractions above raw bits: a variable is a named box holding a value; a type classifies what a value is and what may be done to it; an expression computes a value; and a statement performs an action, often changing the program's state (the current contents of all variables).
Core primitive types include integers, floats (reals), booleans (True/False), and strings (text). Assignment x = 5 binds a name to a value. Operators combine values: arithmetic (+ - * / % **), comparison (== != < >), and logical (and or not). Evaluation follows precedence rules, just like mathematics.
The single most important mental model for a beginner is that a program has state that changes over time. Reading code is not like reading a static equation; it is like watching a machine step forward, mutating its memory at each line. The value of x depends on when you look.
A subtle but vital point: = in programming is assignment, not mathematical equality. The line count = count + 1 is nonsense as an equation but perfectly sensible as an instruction: "take the current value of count, add one, store it back." Confusing these two meanings is the root of many beginner bugs.
Discipline. Computers are ruthlessly literal. They do exactly what you wrote, not what you meant. Debugging is the art of finding the gap between the two — and that gap is always your own instruction, never the machine's whim.
A classic first real program: convert a temperature from Celsius to Fahrenheit, then classify it. We trace state as it evolves.
# A program is input -> transformation -> output.
def celsius_to_fahrenheit(c):
return c * 9 / 5 + 32 # arithmetic expression, precedence: * / before +
def describe(celsius):
f = celsius_to_fahrenheit(celsius) # state: f now holds a float
# Booleans and comparison produce True/False:
freezing = celsius <= 0
boiling = celsius >= 100
if freezing:
label = "freezing"
elif boiling:
label = "boiling"
else:
label = "liquid"
return f, label
for c in [-10, 25, 100]:
fahrenheit, state = describe(c)
print(str(c) + "C = " + str(fahrenheit) + "F (" + state + ")")
# Output:
# -10C = 14.0F (freezing)
# 25C = 77.0F (liquid)
# 100C = 212.0F (boiling)Trace it: describe(25) sets f = 77.0, evaluates freezing = False and boiling = False, so the else branch sets label = "liquid". Each line reads the current state and may update it — the essence of imperative programming.
Q1 What is the difference between a statement and an expression?
An expression evaluates to a value (3 + 4 becomes 7). A statement performs an action and may not produce a value (x = 7 stores something; if ...: directs flow). Expressions are the nouns of a language; statements are the verbs. Many statements contain expressions.
Q2 Why does 5 / 2 give 2.5 but 5 // 2 give 2?
/ is true division and yields a float. // is floor (integer) division, discarding the fractional part. The companion operator % (modulo) gives the remainder, so 5 // 2 == 2 and 5 % 2 == 1, and together they satisfy 2*2 + 1 == 5.
Q3 What is a "type error" and why do types exist at all?
A type error occurs when you apply an operation to a value it does not support — e.g. adding a number to a list. Types exist to catch nonsense early and to tell operators how to behave: "3" + "4" concatenates to "34", while 3 + 4 adds to 7. The same symbol means different things depending on the operands' types.
Q4 Why is count = count + 1 valid if it is false as an equation?
Because = is assignment, evaluated right-to-left: first compute the right side using the old value of count, then rebind the name to the result. It is a command ("increment count"), not an assertion of equality. This is why languages like it exist alongside pure mathematics — they describe processes, not timeless truths.
How the ideas connect
Every key idea in this chapter, branching from the core concept — use it to see the whole picture at a glance.
The key facts, visualised
Worked problems, step by step
Follow each solution line by line, then try to reproduce it on paper before moving on.
Example 1Trace: x = 5; x = x + 3; x = x * 2. Final x?
- x becomes 5.
- x = 5 + 3 = 8.
- x = 8 * 2 = 16.
Example 2Swap two variables a=1, b=2 using a temp t.
- t = a (t=1).
- a = b (a=2).
- b = t (b=1).
Now you try
Work each one out first, then tap to reveal the worked answer.