A comprehensive, self-paced curriculum for applied mathematics. Get job-ready in 13-14 months with courses from MIT, Stanford, and Harvard. 100% free.
Version 1.0 | Last Updated: December 2025
This curriculum provides comprehensive training in applied mathematics for quantitative careers:
- 💼 Finance: Quantitative Analyst, Financial Engineer, Risk Analyst
- 💻 Technology: Machine Learning Engineer, Data Scientist
- 📊 Consulting: Operations Research Analyst
- 📈 Economics: Computational Economist
- 🎲 Insurance: Actuarial Analyst, Risk Modeler
Time Commitment: 20-25 hours/week for 13-14 months
Cost: $0 (all resources are free)
Prerequisites: Calculus I, Statistics I, high school algebra
Start today: Jump to Phase 0
- Philosophy
- Timeline
- Prerequisites
- Curriculum Structure
- Phase 0: Learning Foundations
- Phase 1: Core Mathematics
- Phase 2: Applied Core
- Phase 3: Computational Mastery
- Capstone Projects
- Complete Timeline
- Career Outcomes
- Study Strategy
- Tools & Resources
- Completion Checklist
- Getting Started TODAY
- Contributing
This curriculum focuses on core applied mathematics that provides a foundation for quantitative careers:
- Financial Engineering / Quantitative Finance
- Machine Learning / Data Science / AI
- Operations Research
- Computational Economics
- Scientific Computing / Engineering
- Risk Analysis / Actuarial Science
Our approach:
- ✅ Essentials-focused - Core topics needed for applied work
- ✅ Practical - Projects and implementation throughout
- ✅ Rigorous - Deep understanding of fundamentals
- ✅ Accessible - All resources are free and self-paced
- ✅ Balanced - Prepares for multiple career paths
Topics covered:
- Multivariable Calculus and vector calculus
- Linear Algebra (deep foundations)
- Probability & Statistics (rigorous, applied focus)
- Differential Equations (ODEs + intro to PDEs)
- Optimization (critical for all quantitative work)
- Stochastic Processes (finance, risk, modeling)
- Numerical Methods and Scientific Computing
- Programming (Python for scientific computing)
Total: 57 weeks (13-14 months with realistic pacing)
- 20-25 hrs/week: 13-14 months
- 15-20 hrs/week: 16-18 months
- 30+ hrs/week: 10-11 months
With 20% buffer for review/projects: 14-16 months realistic
Required:
- High school algebra and trigonometry
- Basic computer literacy
- Calculus I (derivatives, basic integration, fundamental theorem)
- Statistics I (descriptive statistics, intro to inference)
Don't have these prerequisites?
- For Calculus I: Start with 3Blue1Brown - Essence of Calculus (3-5 hours) + Khan Academy Calculus I
- For Statistics I: Start with Khan Academy Statistics or take MIT 18.05 from the beginning
Want to refresh before starting?
- 3Blue1Brown - Essence of Calculus (excellent visual review)
Phase 0: Learning Foundations (1 week)
↓
Phase 1: Core Mathematics (26 weeks)
├── Calculus II & Multivariable
├── Linear Algebra (DEEP)
└── Probability & Statistics
↓
Phase 2: Applied Core (24 weeks)
├── Optimization
├── Differential Equations (ODEs + intro PDEs)
├── Stochastic Processes
└── Scientific Computing
↓
Phase 3: Computational Mastery (6 weeks)
└── Numerical Linear Algebra + Projects
Total: 57 weeks (~13-14 months)
Goal: Learn how to learn efficiently
- Learning How to Learn - Watch at 1.5x speed, skip to key insights
- Key takeaways only:
- Focused vs diffuse thinking
- Pomodoro technique
- Spaced repetition
- Active recall
- Install Anaconda Python
- Set up Jupyter notebooks
- Create GitHub account
- Basic LaTeX (learn as you go)
Skip the deep dive - just get started.
Prerequisites for this section:
- Calculus I (derivatives, basic integration)
If you need Calc I review: Watch 3Blue1Brown - Essence of Calculus before starting.
Primary Resource:
| Course | Duration | Link |
|---|---|---|
| MIT 18.02SC Multivariable Calculus | 8 weeks (fast-track) | OCW |
Fast-track approach:
- Week 1-2: Vectors, dot product, cross product
- Week 3-4: Partial derivatives, gradients, directional derivatives
- Week 5-6: Multiple integrals (double, triple)
- Week 7-8: Vector calculus (line integrals, Green's theorem)
What to skip:
- Detailed proofs (unless you enjoy them)
- Stokes' theorem details (know the concept)
- Triple integrals in exotic coordinates
Supplementary Resources:
- Khan Academy - Multivariable Calculus for additional practice
Projects:
- Visualize gradient descent (Python)
- Compute flux through surfaces
Total Time: 64-80 hours
Primary Resources:
| Resource | Duration | Link |
|---|---|---|
| 3Blue1Brown - Essence of Linear Algebra | 2 weeks | YouTube |
| MIT 18.06SC Linear Algebra | 8 weeks | OCW |
Study Plan:
- Week 1-2: Watch ALL 3Blue1Brown (build intuition first)
- Week 3-10: MIT 18.06SC lectures + problem sets
Focus areas (don't skip these):
- Matrix operations and systems of equations
- Vector spaces and linear independence
- Eigenvalues and eigenvectors
- Singular Value Decomposition (SVD)
- Least squares and projections
- Positive definite matrices
What you can skim:
- Abstract vector space proofs
- Determinant computation methods (know concepts, use software for computation)
Mandatory Projects:
- Implement QR decomposition from scratch
- Image compression using SVD
- PCA on real dataset (Kaggle data)
- PageRank algorithm
Why this matters:
- Foundation for ALL quantitative work (finance, ML, operations research, economics)
- Used daily in any quantitative role
- Essential for understanding optimization, statistics, and numerical methods
- Most applied mathematics builds on linear algebra
- Finance: Portfolio theory, risk models, factor models
- ML/AI: Neural networks, dimensionality reduction, recommendation systems
- Operations Research: Network flows, optimization algorithms
- Economics: Input-output models, equilibrium computation
Total Time: 100-125 hours
Prerequisites: Calculus I, basic understanding of summation notation
If you've completed an introductory statistics course: You can skip basic descriptive statistics and focus on the advanced topics listed below.
If you're new to statistics: You'll need to cover the full MIT 18.05 course including all foundational material.
Primary Resource:
| Course | Duration | Link |
|---|---|---|
| MIT 18.05 Introduction to Probability and Statistics | 8 weeks | OCW |
Or alternative (pick ONE):
| Course | Duration | Link |
|---|---|---|
| Harvard Stats 110 | 8 weeks | Website |
Focus areas:
- Random variables and distributions
- Expectation, variance, covariance
- Joint distributions
- Central Limit Theorem
- Maximum likelihood estimation
- Bayesian inference basics
- Hypothesis testing (refresh from Stats 1)
What to skip:
- Combinatorics deep-dives (know basics)
- Measure theory (way too theoretical)
Projects:
- Monte Carlo simulations
- A/B testing analysis
- Implement MLE estimator
- Bayesian inference problem
Total Time: 64-80 hours
Duration: 26 weeks
Hours: 228-285 hours (~9-11 hrs/week)
After Phase 1, you have the core foundation for any applied math work.
This is foundational for ALL quantitative fields.
Primary Resource:
| Course | Duration | Link |
|---|---|---|
| Stanford EE364a - Convex Optimization | 10 weeks | Website |
Use the free textbook:
- Convex Optimization by Boyd & Vandenberghe (PDF free)
Focus areas:
- Convex sets and functions
- Linear and quadratic programming
- Gradient descent and Newton's method
- Duality theory
- Interior-point methods
- Applications: portfolio optimization, resource allocation, regression, engineering design
Why this matters for each field:
- Finance: Portfolio optimization, risk management, derivative pricing
- ML/AI: Training algorithms, neural networks, SVM
- Operations Research: Supply chain, scheduling, resource allocation
- Economics: Equilibrium computation, mechanism design
Projects:
- Portfolio optimization (Markowitz model)
- Resource allocation problem
- Regression via optimization (implement from scratch)
- Engineering design optimization
Total Time: 100-120 hours
Essential for modeling dynamic systems in finance, economics, physics, and engineering.
Primary Resource:
| Course | Duration | Link |
|---|---|---|
| MIT 18.03 - Differential Equations | 8 weeks | OCW |
Study Plan:
- Weeks 1-3: First and second-order ODEs
- Weeks 4-5: Systems of ODEs and phase planes
- Weeks 6-7: Laplace transforms (important for engineering/control theory)
- Week 8: Introduction to PDEs (heat equation, wave equation concepts)
Why each topic matters:
- ODEs: Growth models, decay, population dynamics, interest rate models
- Systems of ODEs: Multi-asset pricing, predator-prey, economic equilibrium
- Laplace transforms: Engineering, control systems, circuit analysis
- PDEs: Option pricing (Black-Scholes), heat diffusion, wave propagation
Projects:
- Population dynamics model (continuous time)
- SIR epidemic model
- Compound interest and continuous growth models
- Simple option pricing via heat equation analogy
Total Time: 64-80 hours
CRITICAL for finance, risk analysis, and probabilistic modeling.
Self-Study Options (choose ONE):
Option 1: MIT OCW Approach
| Resource | Duration | Link |
|---|---|---|
| MIT 6.041 Probabilistic Systems Analysis - Lectures 18-24 | 4 weeks | OCW |
| Supplement with textbook: Introduction to Stochastic Processes by Lawler | Reference | Library/online |
Option 2: Textbook Self-Study
- Use Introduction to Probability Models by Sheldon Ross (Chapters 4-6)
- Work through examples and exercises
- Implement simulations in Python
Focus areas:
- Markov chains (discrete time)
- Random walks and Brownian motion
- Poisson processes
- Introduction to continuous-time processes
- Applications to finance and queueing
Why this matters:
- Finance: Stock price models, interest rate models, risk analysis
- Operations Research: Queueing theory, inventory models
- Economics: Dynamic programming, search models
- Insurance/Actuarial: Claim processes, ruin theory
Projects:
- Monte Carlo simulation of stock prices (geometric Brownian motion)
- Queueing system analysis
- Random walk simulations
- Markov chain modeling (credit ratings, customer behavior)
Total Time: 32-40 hours
Condensed - learn to implement everything efficiently.
Primary Resources:
| Resource | Duration | Link |
|---|---|---|
| SciPy Lecture Notes | 2 weeks | Website |
Focus:
- NumPy for arrays and numerical computation
- SciPy for optimization, integration, ODEs
- Matplotlib for visualization
- Performance considerations
Projects:
- Implement numerical ODE solvers (Euler, RK4)
- Matrix operations and decompositions
- Optimization algorithms from scratch
- Data visualization for time series
Total Time: 16-20 hours
Duration: 24 weeks
Hours: 212-260 hours (~9-11 hrs/week)
After Phase 2, you can apply mathematics to real-world problems in any quantitative field.
Bridge theory to practice - learn how computers actually do linear algebra.
Primary Resource:
| Course | Duration | Link |
|---|---|---|
| MIT 18.065 - Matrix Methods | 6 weeks (selected lectures) | OCW |
Focus on:
- QR decomposition and Gram-Schmidt
- SVD computation
- Eigenvalue algorithms
- Iterative methods for large systems
- Randomized linear algebra
Projects:
- Large-scale PCA
- Recommender system (collaborative filtering)
- Image processing with matrix methods
- Capstone: Choose one substantial project (see below)
Total Time: 60-75 hours
Choose ONE substantial project that aligns with your career interests:
Black-Scholes Option Pricing Implementation
- Derive and implement Black-Scholes PDE
- Monte Carlo simulation for option pricing
- Greeks computation (delta, gamma, vega)
- Compare analytical vs numerical solutions
- Uses: PDEs, stochastic processes, numerical methods
Supply Chain Optimization System
- Multi-objective optimization problem
- Network flow algorithms
- Stochastic demand modeling
- Sensitivity analysis
- Uses: Optimization, probability, algorithms
Neural Network from Scratch
- Implement backpropagation (no libraries)
- Gradient descent variants
- Train on real dataset
- Compare to scikit-learn/PyTorch
- Uses: Linear algebra, calculus, optimization
Dynamic Optimization Model
- Optimal control or dynamic programming
- Economic equilibrium computation
- Agent-based simulation
- Policy analysis
- Uses: Optimization, ODEs, stochastic processes
Risk Model for Insurance/Finance
- Value at Risk (VaR) computation
- Monte Carlo risk simulation
- Loss distribution estimation
- Stress testing framework
- Uses: Probability, stochastic processes, statistics
Kaggle Competition (End-to-End)
- Feature engineering with linear algebra
- Custom loss functions and optimization
- Statistical validation
- Full pipeline from data to deployment
- Uses: Statistics, optimization, linear algebra
Deliverables (for any option):
- GitHub repository with clean, documented code
- 10-15 page technical report (LaTeX)
- Presentation or blog post explaining your work
- Jupyter notebooks with analysis
Timeline: Integrated into Phase 3 (6 weeks)
| Phase | Duration | Hours | What You Learn |
|---|---|---|---|
| Phase 0 | 1 week | 8-10 | Meta-learning, environment setup |
| Phase 1 | 26 weeks | 228-285 | Core mathematical foundations |
| Phase 2 | 24 weeks | 212-260 | Applied techniques & modeling |
| Phase 3 | 6 weeks | 60-75 | Computational mastery + capstone |
| Total | 57 weeks | 508-630 hours | Complete applied mathematics |
Time commitments:
- At 20-25 hrs/week: 13-14 months
- At 15-20 hrs/week: 16-18 months
- At 30+ hrs/week: 10-11 months
Realistic timeline with buffer (20% extra for review/projects): 14-16 months
This curriculum provides the mathematical foundation for various quantitative careers:
Finance & Risk:
- Quantitative Analyst
- Financial Engineer
- Risk Analyst
Technology:
- Machine Learning Engineer
- Data Scientist
- Research Engineer
Consulting & Operations:
- Operations Research Analyst
- Management Science Consultant
Economics & Policy:
- Computational Economist
- Economic Modeler
- Policy Analyst
Other Quantitative Roles:
- Actuarial Analyst
- Algorithm Developer
- Quantitative Researcher
Graduate Programs: This curriculum prepares you for Master's programs in:
- Financial Engineering / Mathematical Finance
- Operations Research
- Data Science / Machine Learning
- Computational Science / Applied Mathematics
- Statistics / Econometrics
- Industrial Engineering
Monday: 3 hours (new material)
Tuesday: 2 hours (problem sets)
Wednesday: 3 hours (new material)
Thursday: 2 hours (problem sets)
Friday: 3 hours (projects)
Saturday: 4 hours (review + harder problems)
Sunday: 3 hours (projects/catch-up)
Total: 20 hours/week
- If completing problem sets with >90% accuracy → skip ahead
- If concepts feel intuitive → move faster
- If you have prior programming experience → accelerate computational sections
- If struggling with >50% of problems → review prerequisites
- If concepts feel abstract → add more YouTube resources
- If debugging takes forever → improve programming skills first
- End of each month: Can you explain the main concepts to someone else?
- Every 3 months: Take a week off to review and consolidate
- Python: Anaconda distribution
- IDE: VS Code or PyCharm Community
- Notebooks: Jupyter
- LaTeX: Overleaf (online)
- Version Control: Git + GitHub
- YouTube: 3Blue1Brown, StatQuest, MIT OCW
- Practice: LeetCode (algorithms), Kaggle (ML projects)
- Books: Use OCW free textbooks
- Community: OSSU Discord, r/learnmath, r/MachineLearning
- Struggle for 30 min (build problem-solving)
- Search Math Stack Exchange
- Ask in OSSU Discord
- Review prerequisites
Phase 0:
- ☐ Watched Learning How to Learn key concepts
- ☐ Environment set up (Python, GitHub, LaTeX)
Phase 1:
- ☐ Multivariable Calculus (MIT 18.02SC - 8 weeks)
- ☐ Linear Algebra (3Blue1Brown + MIT 18.06SC - 10 weeks)
- ☐ Probability & Statistics (MIT 18.05 or Harvard Stats 110 - 8 weeks)
Phase 2:
- ☐ Optimization (Stanford EE364a - 10 weeks)
- ☐ Differential Equations (MIT 18.03 - 8 weeks)
- ☐ Stochastic Processes (self-study - 4 weeks)
- ☐ Scientific Computing with Python (2 weeks)
Phase 3:
- ☐ Numerical Linear Algebra (MIT 18.065 - 6 weeks)
- ☐ Capstone project completed
- Day 1: Read this entire curriculum (30 min)
- Day 2: Watch 3Blue1Brown Essence of Calculus (3 hours) - refresh Calc 1
- Day 3: Set up Python environment (1 hour) + start MIT 18.02SC
- Day 4-7: MIT 18.02SC lectures 1-3 + problem sets
- Complete first 4 weeks of Multivariable Calculus
- Start watching 3Blue1Brown Linear Algebra (prep for next phase)
- Join OSSU Discord
- Create GitHub repo to track your progress
- Finished Multivariable Calculus
- Halfway through Linear Algebra
- Built first project (gradient visualization)
Found a broken link? Have a suggestion? Want to improve the curriculum?
We welcome contributions! See CONTRIBUTING.md for guidelines.
Quick ways to contribute:
- 🐛 Report broken links or errors
- 💡 Suggest better resources
- ✏️ Fix typos or improve clarity
- 📚 Share your experience completing sections
- ⭐ Star this repo to show support!
Questions? Open an issue or join discussions:
- GitHub Discussions
- OSSU Discord - #mathematics channel
- r/learnmath on Reddit
Share your progress:
- Use hashtag
#StreamlinedAppliedMathon social media - Tag us when you complete a phase
- Share projects in discussions
Stay updated:
- ⭐ Star this repo
- 👀 Watch for updates
- 📬 Subscribe to releases
This curriculum is licensed under CC BY-SA 4.0.
You are free to:
- Share and redistribute
- Adapt and build upon
- Use commercially
Under these terms:
- Give appropriate credit
- Share adaptations under the same license
This curriculum requires dedication and consistency.
The journey ahead:
- Strong mathematical foundations
- Practical computational skills
- Portfolio-worthy projects across multiple domains
- Deep understanding of applied mathematics
In 13-14 months of consistent work, you'll have:
- ✅ Comprehensive knowledge of applied mathematics
- ✅ Programming and computational proficiency
- ✅ Portfolio of completed projects
- ✅ Strong foundation for quantitative work
- ✅ Preparation for advanced study or professional work
The key: Consistency. Show up 20 hours every week.
Your path forward: After completing the core curriculum, you'll have the mathematical foundation to:
- Pursue specialized areas (financial engineering, machine learning, operations research, computational economics)
- Continue with advanced study
- Apply mathematics to real-world problems
- Build on these foundations throughout your career
All paths start with solid fundamentals. That's what this curriculum provides.
Version 1.0 | Created December 2025
License: CC BY-SA 4.0
Author: Streamlined Applied Math Curriculum
Last Updated: December 19, 2025
Ready to start? Download this curriculum, set up your environment, and begin MIT 18.02SC next Monday! 🚀