Project 1: The “Homework Destroyer” (Equation Solver)

Build a solver that handles linear and quadratic equations and explains each step.

Project Overview

Attribute Value
Difficulty Level 1: Beginner
Time Estimate Weekend
Main Language Python
Alternative Languages JavaScript, C++
Knowledge Area Algebra
Tools CLI, optional plotting
Main Book “Algebra” by I.M. Gelfand

What you’ll build: A CLI tool that solves equations like 2x+3=11 and x^2-5x+6=0, showing the steps.

Why it teaches math: Solving equations is the heart of algebra. Explaining steps proves you understand the rules.

Core challenges you’ll face:

  • Parsing equation strings
  • Applying algebraic transformations consistently
  • Handling multiple solution cases

Real World Outcome

You will input an equation and get both the solution and a step-by-step explanation.

Example Output:

$ python solver.py "2x+3=11"
Step 1: subtract 3 from both sides -> 2x = 8
Step 2: divide both sides by 2 -> x = 4
Solution: x = 4

Verification steps:

  • Test with multiple equation types
  • Confirm solutions by substitution

The Core Question You’re Answering

“How can I turn algebra rules into a deterministic procedure a computer can follow?”

This project makes algebra mechanical and testable.

Concepts You Must Understand First

Stop and research these before coding:

  1. Equality transformations
    • Why must you do the same operation to both sides?
    • Book Reference: “Algebra” by I.M. Gelfand, Ch. 2
  2. Quadratic formula
    • How does the discriminant determine the number of solutions?
    • Book Reference: “Algebra” by I.M. Gelfand, Ch. 8
  3. Factoring basics
    • When can you factor instead of using the quadratic formula?
    • Book Reference: “Elementary Algebra” by Harold Jacobs, Ch. 6

Questions to Guide Your Design

  1. Parser strategy
    • Will you parse with regex or a simple tokenizer?
    • How will you handle missing multiplication symbols (like 2x)?
  2. Output clarity
    • How will you format steps so they read like a textbook?
    • How will you handle unsolvable or infinite solutions?

Thinking Exercise

Manual Solve

Solve 3x - 7 = 2x + 5 by hand and list each transformation step.

Questions while working:

  • Which step isolates the variable?
  • How do you check the result?

The Interview Questions They’ll Ask

Prepare to answer these:

  1. “Why do you apply the same operation to both sides?”
  2. “What does the discriminant tell you?”
  3. “How do you verify a solution?”
  4. “What is the difference between factoring and formula solving?”
  5. “How do you handle no-solution cases?”

Hints in Layers

Hint 1: Starting Point Handle only linear equations first.

Hint 2: Next Level Normalize equations into a standard form before solving.

Hint 3: Technical Details Implement a small tokenizer to avoid brittle string hacks.

Hint 4: Tools/Debugging Add tests that substitute the solution back into the equation.

Books That Will Help

Topic Book Chapter
Linear equations “Algebra” by I.M. Gelfand Ch. 2
Quadratics “Algebra” by I.M. Gelfand Ch. 8
Factoring “Elementary Algebra” by Harold Jacobs Ch. 6

Implementation Hints

  • Keep equation parsing simple and incremental.
  • Always reduce to a canonical form before solving.
  • Print steps in a consistent, human-friendly format.

Learning Milestones

  1. First milestone: You can solve and explain linear equations.
  2. Second milestone: You can solve quadratics reliably.
  3. Final milestone: You can handle edge cases and explain them.