Mathematics Video Study Plans & Proof Locators

Master equations, proofs, and real analysis through structured video roadmaps & course maps.

mathematics

Non-Euclidean Geometry: Models & Geodesics

01Euclid's Fifth Postulate and the Birth of New Geometries
02Hyperbolic Space and the Poincaré Disk Model
03Geodesics: Defining Straight Lines in Curved Spaces
+ 2 more learning modules
15h5 modules
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mathematics

Knot Theory — Moves, Coloring & Polynomials

01Introduction to Topology and Knots
02Reidemeister Moves & Knot Equivalence
03Knot Invariants and Tricolorability
+ 2 more learning modules
12h5 modules
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mathematics

Category Theory: Functors, Monads & FP

01Mathematical Foundations: Functions, Composition & Types
02Introduction to Category Theory: Objects & Morphisms
03Functors: Mapping Between Categories
+ 2 more learning modules
12h5 modules
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mathematics

Complex Analysis: Residues & Contour Integrals

01Foundations of Complex Numbers
02Complex Functions and Holomorphic Properties
03Complex Integration and Cauchy's Theorem
+ 2 more learning modules
18h5 modules
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mathematics

Numerical Analysis: Roots, Splines & Errors

01Computer Arithmetic and Error Analysis
02Root-Finding Methods
03Polynomial Interpolation & Runge's Phenomenon
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18h5 modules
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mathematics

TDA: Simplicial Complexes & Homology

01Foundations: Intuitive Topology & Linear Algebra
02Simplicial Complexes: Building Shapes from Data
03Homology: Measuring Holes in Data
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16h5 modules
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mathematics

Generating Functions: Recurrences & Partitions

01Foundations of Sequences and Power Series
02Combinatorics Foundations & Binomial Theorem
03Introduction to Ordinary Generating Functions (OGFs)
+ 3 more learning modules
30h6 modules
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mathematics

Analytic Number Theory: Primes & Zeta Function

01Foundations of Number Theory and Primes
02Mathematical Analysis & Complex Number Foundations
03Arithmetic Functions and Dirichlet Convolution
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30h6 modules
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mathematics

Stochastic Calculus: Brownian & Black-Scholes

01Foundations of Probability & Calculus
02From Random Walks to Brownian Motion
03The Itô Integral & Stochastic Integration
+ 3 more learning modules
18h6 modules
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mathematics

Information Theory: Entropy & Coding

01Mathematical Foundations: Probability & Logarithms
02Quantifying Data: Shannon Entropy
03Source Coding & Lossless Compression
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15h5 modules
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mathematics

Measure Theory: Lebesgue Integral & Convergence

01Mathematical Foundations: Real Analysis & Set Theory
02The Riemann Integral and Its Limitations
03Sigma-Algebras and Measure Spaces
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24h6 modules
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mathematics

Spectral Graph Theory: Matrices & Eigenvalues

01Foundations of Linear Algebra: Vectors & Matrices
02Introduction to Graph Theory and Network Representations
03The Graph Laplacian Operator
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15h5 modules
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mathematics

ML Optimization: Calculus, Hessians & Gradients

01Single-Variable Calculus Foundations
02Linear Algebra Foundations for Optimization
03Multivariable Calculus & The Gradient Vector
+ 3 more learning modules
35h6 modules
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mathematics

Bayesian Inference: Priors, Conjugacy & MCMC

01Probability Foundations & Bayes' Theorem
02Probability Distributions & Likelihood
03The Bayesian Framework: Prior to Posterior
+ 3 more learning modules
32h6 modules
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mathematics

Game Theory: Nash, Sequential & Evolutionary

01Foundations of Strategic Thinking
02Simultaneous Games & Nash Equilibrium
03Sequential Games & Backward Induction
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15h5 modules
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mathematics

Visualizing Chaos: Dynamics & Fractals

01Foundations of Differential Equations & State Space
02Introduction to Dynamical Systems & Stability
03Bifurcation Theory: When Systems Mutate
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16h5 modules
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mathematics

Abstract Algebra (Groups, Rings & Cryptography)

01Foundations of Modular Arithmetic & Number Theory
02Introduction to Group Theory
03Ring Theory and Finite Fields
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24h5 modules
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mathematics

Fourier Transform: Series, Calculus & DSP

01Mathematical Foundations: Complex Numbers & Waves
02The Fourier Series: Decomposing Periodic Signals
03The Continuous Fourier Transform
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16h5 modules
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Currently cataloging 18 Mathematics video roadmaps covering Euclid's Fifth Postulate and the Birth of New Geometries, Hyperbolic Space and the Poincaré Disk Model, Geodesics: Defining Straight Lines in Curved Spaces, Elliptic Geometry and Spherical Spaces, Curvature, Topology, and the Gauss-Bonnet Theorem. Latest path updated: "Non-Euclidean Geometry: Models & Geodesics".

Rigorous mathematical education demands step-by-step visual proof tracking. This directory organizes university-level mathematics lectures—spanning linear algebra, multivariable calculus, differential equations, real analysis, and abstract algebra—into structured learning paths, study plans, and interactive course maps. Rather than scrubbing through continuous multi-hour recordings, locate exact blackboard moments where instructors solve Fourier transforms, prove fundamental theorems, or demonstrate complex eigenvector transformations. Designed for quantitative mastery, each roadmap maps foundational single-variable prerequisites directly to advanced analytical concepts, enabling instant retrieval of specific mathematical notation and problem-solving steps.