Problem-Solving Curriculum

Mathematics

A structured, level-by-level path through Problem-Solving. Start with Foundations of Framing the problem and Core methods in Heuristics & strategies at the Intermediate level, then build toward advanced practice and expert-level mastery — with hands-on projects and quizzes at every stage.

3 levels 9 modules 27 topics 6 weeks · about 24 hours · 8 weeks · about 32 hours · 10 weeks · about 40 hours
Intermediate

Intermediate Problem-Solving

6 weeks · about 24 hours

3 modules

Advanced

Advanced Problem-Solving

8 weeks · about 32 hours

3 modules

Expert

Expert Problem-Solving

10 weeks · about 40 hours

3 modules

Problem-Solving Course Curriculum

9 modules across 3 levels.

Intermediate

Intermediate Problem-Solving

Start with Framing the problem, Heuristics & strategies and Working backwards. Each module explains the idea, shows a worked example and ends with a short project, so Problem-Solving becomes something you can do rather than something you have only read about.

6 weeks · about 24 hours 3 modules

Topics

Project

Write a one-page explanation of Framing the problem in your own words, with an example you chose yourself, and test it against the module checklist.

Learning Path

1

Foundations of Framing the problem

Work through the three topics in this module, complete the project, then answer the self-check questions before moving on.

2

Core methods in Heuristics & strategies

Work through the three topics in this module, complete the project, then answer the self-check questions before moving on.

Prerequisites: Foundations of Framing the problem

3

Applying Working backwards

Work through the three topics in this module, complete the project, then answer the self-check questions before moving on.

Prerequisites: Core methods in Heuristics & strategies

Practice Problems

EasyExplain Framing the problem to someone who has never studied the subject, using one worked example.
Solution: A strong answer defines framing the problem precisely, gives one concrete example, and names the limitation it runs into.
MediumExplain Heuristics & strategies to someone who has never studied the subject, using one worked example.
Solution: A strong answer defines heuristics & strategies precisely, gives one concrete example, and names the limitation it runs into.
HardExplain Working backwards to someone who has never studied the subject, using one worked example.
Solution: A strong answer defines working backwards precisely, gives one concrete example, and names the limitation it runs into.

Glossary

Framing the problem

A central idea in the intermediate Problem-Solving path, covered in the module of the same name.

Example: apply Framing the problem to a small, familiar case step by step, then check your reasoning against the walkthrough.

Heuristics & strategies

A central idea in the intermediate Problem-Solving path, covered in the module of the same name.

Example: apply Heuristics & strategies to a small, familiar case step by step, then check your reasoning against the walkthrough.

Working backwards

A central idea in the intermediate Problem-Solving path, covered in the module of the same name.

Example: apply Working backwards to a small, familiar case step by step, then check your reasoning against the walkthrough.

About the Problem-Solving curriculum

The Problem-Solving curriculum is a complete, self-paced course in mathematics, organised into 3 progressive levels and 9 modules. It opens with Foundations of Framing the problem and Core methods in Heuristics & strategies, moves through Applying Working backwards and finishes with expert-level work on Leading practice in Debugging your reasoning and Mastering Explaining a solution.

Across the whole path you work through 27 individual topics — from Framing the problem and Putting framing the problem to work at the start to Putting explaining a solution to work and Checking your understanding of explaining a solution by the end. The levels are estimated at 6 weeks · about 24 hours, 8 weeks · about 32 hours and 10 weeks · about 40 hours. Each level assumes the one before it, so you can work straight through from Intermediate to Expert, or start at the level that matches what you already know.

It suits analysts, researchers and students who need to reason with numbers and defend a conclusion, not just run a tool. The emphasis is on interpretation: every technique is introduced with the question it answers, the assumption it needs and the way it fails, so you can apply it to unfamiliar data.

Every module pairs a written summary with a worked example, a short quiz to check the idea landed, and a project brief drawn from real practice. You are never asked to take a concept on trust: the reasoning, the common mistakes and the situations where the approach stops working are all laid out, so you finish a module able to explain the idea rather than only recognise it.

What you’ll be able to do

By the end of the Problem-Solving path you should be able to work confidently with:

Framing the problem

Putting framing the problem to work

Common pitfalls in framing the problem

Heuristics & strategies

Hands-on: heuristics & strategies

Common pitfalls in heuristics & strategies

Working backwards

Putting working backwards to work

How the Problem-Solving curriculum is structured

Intermediate 6 weeks · about 24 hours 3 modules 9 topics

Intermediate Problem-Solving

Start with Framing the problem, Heuristics & strategies and Working backwards. Each module explains the idea, shows a worked example and ends with a short project, so Problem-Solving becomes something you can do rather than something you have only read about.

Modules: Foundations of Framing the problem · Core methods in Heuristics & strategies · Applying Working backwards

  • Framing the problem: Framing the problem is introduced from first principles, with the few terms you actually need and an example that shows how the idea behaves in practice.
  • Putting framing the problem to work: Framing the problem is where many Problem-Solving learners first get stuck, so the module slows down, isolates the difficult step and rebuilds it with you.
  • Common pitfalls in framing the problem: Framing the problem is introduced from first principles, with the few terms you actually need and an example that shows how the idea behaves in practice.

Project: Write a one-page explanation of Framing the problem in your own words, with an example you chose yourself, and test it against the module checklist.

Advanced 8 weeks · about 32 hours 3 modules 9 topics

Advanced Problem-Solving

Build on the intermediate level through Pattern recognition, Estimation & reasonableness and Modelling with equations. The emphasis shifts from knowing the ideas to choosing between them — trade-offs, failure modes and the reasoning behind each decision.

Modules: In depth Pattern recognition · Patterns and trade-offs in Estimation & reasonableness · Scaling Modelling with equations

  • Pattern recognition: Here Pattern recognition becomes a design decision. You compare alternatives, justify a choice and test it against a harder problem.
  • Hands-on: pattern recognition: Pattern recognition is pushed past the textbook case: competing approaches, their trade-offs and the situations where each one breaks down.
  • Checking your understanding of pattern recognition: Here Pattern recognition becomes a design decision. You compare alternatives, justify a choice and test it against a harder problem.

Project: Produce a short case analysis in which Pattern recognition drives the recommendation, including the alternatives you rejected and why.

Expert 10 weeks · about 40 hours 3 modules 9 topics

Expert Problem-Solving

Work at the edge of Problem-Solving through Logic puzzles, Debugging your reasoning and Explaining a solution. The modules assume fluency and ask for judgement: designing, critiquing and defending work at a professional standard.

Modules: Frontiers of Logic puzzles · Leading practice in Debugging your reasoning · Mastering Explaining a solution

  • Logic puzzles: This module asks you to critique and extend Logic puzzles rather than simply apply it, producing work another expert could review.
  • Putting logic puzzles to work: At expert level Logic puzzles is treated as a field of judgement: current practice, contested positions and the evidence behind each.
  • Checking your understanding of logic puzzles: This module asks you to critique and extend Logic puzzles rather than simply apply it, producing work another expert could review.

Project: Write a professional-standard brief on Logic puzzles — argument, evidence, limitations — plus a plan for taking the work further.

How to study Problem-Solving, phase by phase

  1. 1

    Phase 1 — Intermediate

    Set aside around 6 weeks · about 24 hours. Work through 3 modules, starting with Foundations of Framing the problem and Core methods in Heuristics & strategies. Finish the phase by completing the project brief: Write a one-page explanation of Framing the problem in your own words, with an example you chose yourself, and test it against the module checklist.

  2. 2

    Phase 2 — Advanced

    Set aside around 8 weeks · about 32 hours. Work through 3 modules, starting with In depth Pattern recognition and Patterns and trade-offs in Estimation & reasonableness. Finish the phase by completing the project brief: Produce a short case analysis in which Pattern recognition drives the recommendation, including the alternatives you rejected and why.

  3. 3

    Phase 3 — Expert

    Set aside around 10 weeks · about 40 hours. Work through 3 modules, starting with Frontiers of Logic puzzles and Leading practice in Debugging your reasoning. Finish the phase by completing the project brief: Write a professional-standard brief on Logic puzzles — argument, evidence, limitations — plus a plan for taking the work further.

  4. 4

    Phase 4 — Consolidate

    Return to the sections that felt weakest, redo their quizzes from memory, and rebuild the Write a one-page explanation of Framing the problem in your own words, with an example you chose yourself, and test it against the module checklist. without following along. Explaining Problem-Solving to someone else in plain language is the clearest signal that the Expert level has landed.

Once you have finished, the Problem-Solving path is a reasonable foundation for analytics, data science, research and quantitative roles. Because the curriculum is generated and kept as a structured outline rather than fixed videos, you can revisit any module, regenerate the outline at a different depth, or save it to your library and work through it over weeks rather than in one sitting.

Problem-Solving — Frequently Asked Questions

Common questions about studying Problem-Solving on LearnAnyCourse.

What does the Problem-Solving curriculum cover?

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The Problem-Solving curriculum is organised into 3 levels (Intermediate, Advanced and Expert) and 9 modules, including Foundations of Framing the problem, Core methods in Heuristics & strategies, Applying Working backwards, In depth Pattern recognition, Patterns and trade-offs in Estimation & reasonableness and Scaling Modelling with equations.

How long does it take to learn Problem-Solving?

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Each level is designed to take about 6 weeks · about 24 hours, 8 weeks · about 32 hours and 10 weeks · about 40 hours. Most learners work through one level at a time at their own pace.

Is the Problem-Solving curriculum free?

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Yes. Every Problem-Solving curriculum on LearnAnyCourse is free to read and study — create an account only if you want to save curricula to your personal library.

Do I need prior experience to study Problem-Solving?

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The curriculum starts at the intermediate level and builds upward, so you can begin with the fundamentals and progress to expert-level Problem-Solving topics without jumping ahead.

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