Math from Foundations to Machine Learning — Expanded Projects

Generated from MATH_FROM_FOUNDATIONS_TO_MACHINE_LEARNING.md. Each file mirrors the complete inline project body so the main guide and deep-dive pages cannot drift.

Project Index

# Project Difficulty Time
1 Scientific Calculator and Numeric Foundations Beginner 8-12 hours
2 Logic, Sets, and Proof Lab Intermediate 8-16 hours
3 Algebraic Equation Solver Beginner 6-10 hours
4 Inequality and Absolute-Value Region Analyzer Intermediate 6-12 hours
5 Function Grapher and Analysis Workbench Intermediate-Advanced 16-28 hours
6 Sequences, Series, and Recurrence Lab Intermediate 8-16 hours
7 Counting, Combinatorics, and Modeling Studio Advanced 14-28 hours
8 Sudoku Constraint Solver Beginner-Intermediate 8-14 hours (about a weekend)
9 Graph Traversal Visualizer Intermediate 8-14 hours (about a weekend)
10 RSA Cryptosystem from Scratch Intermediate 1-2 weeks
11 Monte Carlo Probability Lab Beginner-Intermediate 12-20 hours
12 Distribution and Random-Variable Visualizer Beginner-Intermediate 10-16 hours
13 Naive Bayes Spam Filter Intermediate 1-2 weeks
14 A/B Testing and Uncertainty Dashboard Intermediate 1-2 weeks
15 Conic Sections Mapper Intermediate-Advanced 10-18 hours
16 Vector Geometry and 2D Graphics Toolkit Intermediate-Advanced 12-20 hours
17 Ballistics and Trigonometry Simulator Beginner-Intermediate 8-14 hours
18 Complex Plane Explorer Intermediate-Advanced 8-16 hours
19 Chaos and Mandelbrot Explorer Intermediate 10-18 hours
20 Matrix Systems and Visualization Studio Advanced 16-26 hours
21 Matrix Transformations and 3D Rendering Engine Advanced 3-5 weeks
22 Matrix Cipher Encoder Intermediate 1-2 weeks
23 Dot-Product Recommendation Engine Intermediate 1-2 weeks
24 Eigenvalue and Eigenvector Explorer Advanced 2-3 weeks
25 PCA Image Compressor Advanced 2-3 weeks
26 Numerical Derivative and Tangent Explorer Intermediate 1-2 weeks
27 Symbolic Differentiation Engine Intermediate 2-3 weeks
28 Numerical Polynomial Root Finder Intermediate 1-2 weeks
29 Numerical Integration and Area Estimator Intermediate 1-2 weeks
30 Numerical Stability and Conditioning Lab Expert 2-3 weeks
31 Physics Engine and Numerical Dynamics Lab Advanced 2-3 weeks
32 Epidemic Growth Simulator Intermediate 1-2 weeks
33 Gradient Descent Visualizer and Optimizer Advanced 2-3 weeks
34 Linear Regression and Curve-Fitting Engine Advanced 3-4 weeks
35 PyMath Core Engine Expert 4-6 weeks
36 Logistic Regression Classifier Advanced 2-3 weeks
37 Information-Theory and Loss Engineering Lab Advanced 2-3 weeks
38 K-Means Clustering from Scratch Intermediate 1-2 weeks
39 Decision Tree Classifier from Scratch Advanced 2-3 weeks
40 Markov Chain Text Generator Intermediate 1-2 weeks
41 Complete ML Pipeline and House-Price Predictor Level 5: Master 4 weeks
42 Manual Neuron and Single-Neuron Backpropagation Level 3: Advanced 1-2 weeks
43 Matrix Calculus Backpropagation Workbench Level 4: Expert 2-3 weeks
44 Autograd Engine Level 4: Expert 2 weeks
45 MLP Classifier from First Principles Level 4: Expert 3-4 weeks
46 Backpropagation Flow Visualizer Level 3: Advanced 2 weeks
47 Convolutional Kernel Explorer Level 2: Intermediate 8-16 hours
48 CNN from Scratch Level 5: Master 3 weeks
49 Recurrent Character Generator Level 5: Master 3 weeks
50 Neural Network Framework Level 5: Master 4-8 weeks
51 Convex Optimization and KKT Solver Level 4: Expert 2-3 weeks
52 Real Analysis Foundations Lab Level 4: Expert 2 weeks
53 Sequence and Series Convergence Lab Level 2: Intermediate 1 week
54 Measure-Theoretic Probability Sandbox Level 4: Expert 2 weeks
55 Statistical Learning and Generalization-Bounds Lab Level 4: Expert 2 weeks
56 Functional Analysis and RKHS Kernel Lab Level 5: Master 3 weeks
57 Graph Message-Passing Playground Level 3: Advanced 1-2 weeks
58 Spectral Graph and Laplacian Clusterer Level 4: Expert 2 weeks
59 Random Matrix Theory for High-Dimensional ML Level 5: Master 2-3 weeks
60 Decision-Ready ML Math Workbench Level 5: Master 3-4 weeks
61 GPT from Scratch Level 5: Master 3+ months

Follow the canonical numeric order. Each project page contains its prerequisites, visible outcome, conceptual preparation, milestones, layered hints, debugging guidance, and Definition of Done.