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STEM Foundations Learning Path

A Supplementary Resource for Research Engineers​

This foundations path is a supplementary resource designed to support your journey through the Research Engineering Learning Path. When you encounter mathematical concepts, scientific principles, or programming techniques you need to understand better, come here for structured learning resources.

This is a Reference Library

You don't need to complete this before starting research! The Research Engineering Learning Path is your main guide. Use these foundations for just-in-time learning when you need to refresh or learn specific concepts.

Philosophy: Just-in-Time Learning​

What is Just-in-Time Learning?​

Rather than spending years studying prerequisites, we believe in:

  • Learning what you need, when you need it
  • Building foundations as you encounter them in research
  • Self-awareness about your knowledge gaps
  • Targeted study for specific research goals

How to Use This Path​

  1. Start with self-assessment - Be honest about what you know
  2. Identify gaps as they arise - Notice when you're stuck
  3. Study targeted topics - Focus on what's blocking you
  4. Apply immediately - Use new knowledge in your research
  5. Iterate and grow - Build deeper understanding over time

Self-Assessment Guide​

Ask Yourself These Questions​

Before diving into foundations, reflect on your current knowledge:

Mathematics​

  • Can I solve basic algebra problems?
  • Do I understand functions and graphs?
  • Am I comfortable with derivatives and integrals?
  • Can I work with matrices and vectors?
  • Do I understand probability and statistics?

Science​

  • Do I understand the scientific method?
  • Can I design a controlled experiment?
  • Am I familiar with basic physics concepts?
  • Do I understand chemical reactions and bonds?
  • Can I explain biological systems?

Computing​

  • Can I write basic programs?
  • Do I understand algorithms and data structures?
  • Am I comfortable with computational thinking?
  • Can I analyze algorithm complexity?
  • Do I understand computer architecture?

Finding Your Starting Point​

Based on your self-assessment:

Field-Specific Foundation Maps​

Different research fields require different foundations. Here's what you'll likely need:

Computer Science & AI Research​

Essential Stages: 2-4 (Algebra through Calculus, Programming basics)

  • Core Math: Algebra, Calculus, Linear Algebra
  • Programming: Python, Data Structures, Algorithms
  • Statistics: Probability, Distributions, Hypothesis Testing
  • Start Research: After Stage 4, learn more as needed

Biology & Life Sciences​

Essential Stages: 1-4 (Basic Math through Statistics)

  • Math: Arithmetic through Statistics
  • Science: Chemistry, Biology, Scientific Method
  • Computing: Basic Programming, Data Analysis
  • Start Research: Can begin with Stage 3, add as needed

Psychology & Social Sciences​

Essential Stages: 1-4 (Focus on Statistics)

  • Math: Basic through Statistics (heavy emphasis)
  • Science: Scientific Method, Experimental Design
  • Computing: Statistical Software, Data Analysis
  • Start Research: Strong Stage 4 statistics essential

Physics & Engineering​

Essential Stages: 1-5 (Through Advanced Math)

  • Math: Complete through Differential Equations
  • Physics: Mechanics, E&M, Thermodynamics
  • Computing: Numerical Methods, Simulations
  • Start Research: Need solid Stage 5 for most work

Data Science & Machine Learning​

Essential Stages: 2-5 (Math and Programming Heavy)

  • Math: Linear Algebra, Calculus, Statistics
  • Programming: Python, R, SQL
  • Theory: Algorithms, Optimization
  • Start Research: Can start after Stage 4, build as you go

The Learning Stages​

Our curriculum is organized into 7 progressive stages:

Stage 0: Early Foundations (Pre-K to Grade 2)​

Building blocks of mathematical thinking and scientific observation

Stage 1: Primary Foundations (Grades 3-5)​

Core arithmetic, basic science, and introduction to logical thinking

Stage 2: Middle School Foundations (Grades 6-8)​

Pre-algebra, earth science, life science, and computational thinking

Stage 3: Secondary Foundations (Grades 9-12)​

Algebra through pre-calculus, physics, chemistry, biology, and programming

Stage 4: College Core (Years 1-2)​

Calculus, linear algebra, statistics, and intermediate programming

Stage 5: Expansion (Years 2-3)​

Advanced mathematics, specialized sciences, and advanced computing

Stage 6: Advanced Topics (Years 3-4)​

Graduate-level preparation in mathematics, science, and computing

Connection to Research Engineering​

Start Research Engineering Now!​

You don't need to wait! Begin the Research Engineering Learning Path immediately. You can start research with:

  • Curiosity and willingness to learn (That's all!)
  • Basic computer literacy (Can use a computer and internet)
  • Reading comprehension (Can follow instructions)

As you progress through research engineering, return here when you need to strengthen specific foundations. Most people need:

  • Basic programming ability (Stage 2-3) - Learn as you implement
  • Understanding of the scientific method (Stage 1-2) - Learn by doing research
  • Comfort with basic statistics (Stage 3-4) - Learn when analyzing data
  • Self-directed learning skills (Any stage) - Develop through practice

How Foundations Support Research​

Each research step benefits from specific foundations:

  1. Literature Review: Reading comprehension, domain knowledge
  2. Problem Identification: Critical thinking, pattern recognition
  3. Hypothesis Formation: Scientific method, logical reasoning
  4. Experimental Design: Statistics, controlled variables
  5. Implementation: Programming, mathematics
  6. Data Analysis: Statistics, visualization
  7. Validation: Statistical testing, error analysis
  8. Documentation: Technical writing, clear communication

Learning Resources​

Free Online Platforms​

  • Khan Academy: Complete K-12 and early college curriculum
  • MIT OpenCourseWare: College-level courses
  • Coursera: University courses (audit for free)
  • edX: University courses (audit for free)
  • YouTube: 3Blue1Brown, StatQuest, Organic Chemistry Tutor

Practice Resources​

  • Project Euler: Mathematical programming challenges
  • Brilliant.org: Interactive math and science (free tier)
  • PhET Simulations: Interactive science simulations
  • Wolfram Alpha: Computational knowledge engine

See our Complete Resources Guide for more.

Community Support​

You're Not Alone​

Learning foundations can be challenging. Connect with others:

  • Discord Community: Ask questions, find study partners
  • Study Groups: Form or join foundation study groups
  • Peer Support: Share your learning journey
  • Mentorship: Connect with those who've walked this path

Tips for Success​

1. Be Patient with Yourself​

Building foundations takes time. Celebrate small victories.

2. Focus on Understanding, Not Memorization​

Conceptual understanding beats rote memorization every time.

3. Practice Actively​

Work problems, write code, run experiments - active learning sticks.

4. Connect to Your Goals​

Always link what you're learning to your research interests.

5. Use Multiple Resources​

If one explanation doesn't click, try another source.

6. Teach What You Learn​

Explaining concepts to others solidifies your understanding.

Your Next Steps​

  1. Assess your current knowledge using the questions above
  2. Identify your research field and its requirements
  3. Choose your starting stage based on your assessment
  4. Begin with one topic that interests or blocks you
  5. Apply immediately in a small project or problem

Remember: This is a reference library, not a race. Use what you need, when you need it.

Ready to start your research journey? 👉 Begin the Research Engineering Learning Path - This is your main path!

Need to strengthen specific foundations? Choose your resource:

Remember: These foundations are here to support you when needed, not to delay your research journey!

"The expert in anything was once a beginner who never gave up."