Programming
Problem solving, readable code, and the building blocks of software.
03Teaching
Make complex ideas approachable.
Two complementary paths: programming turns ideas into executable steps; mathematics develops the reasoning that makes those steps understandable.
Core interests
Mathematics
Logical thinking, mathematical language, and structured problem solving.
Learn by doing
Move from an explanation to a worked example, then independent practice.
Illustrative learning paths
Programming
- For
- Learners building programming foundations
- Starting point
- Basic computer literacy
- Goal
- Break down a problem and express a solution in code.
Suggested sequence
- Variables & expressions
- Control flow & functions
- Data structures
- Problem solving & debugging
Mathematics
- For
- Learners strengthening mathematical reasoning
- Starting point
- Basic arithmetic and algebra
- Goal
- Explain each step of a solution and justify the reasoning.
Suggested sequence
- Mathematical language & logic
- Functions & relationships
- Discrete structures
- Proof & problem solving
∴LEARNING CORNER
One idea. Two ways to see it.
A small example of how I like to teach: start with an executable idea, then reveal the structure behind it.
Sum the integers from 1 to n
Start with an accumulator. Each iteration adds the current number to the running total.
def sum_to(n):
total = 0
for value in range(1, n + 1):
total += value
return total
sum_to(5) # 15For a nonnegative integer n, the loop performs n additions: O(n) time and O(1) auxiliary space.
See the structure in the sum
Write the same sum forwards and backwards. Each column adds to n + 1, and there are n columns.
S = 1 + 2 + ⋯ + n
S = n + (n − 1) + ⋯ + 1
2S = n(n + 1)
S = n(n + 1) / 2The formula gives a direct calculation and explains why the solution works.
Try it yourself
Find the sum of even numbers from 2 to 2n. Can you write both a loop and a direct formula?
Show a hint and solution
2 + 4 + ⋯ + 2n = 2(1 + 2 + ⋯ + n) = n(n + 1).
sum(range(2, 2 * n + 1, 2))The two perspectives complement each other: code expresses the steps; mathematics reveals the structure.