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LearnMathora

Guided routes

Learning paths

Same destination, different doors. Pick the description that sounds like you and follow the stops in order — each is a normal page you can leave and return to anytime.

Beginner math foundations

Starting from scratch — or rebuilding shaky ground.

Unknowns, shapes, and waves: the shared language every later course speaks. Finish this and nothing on the platform is closed to you.

  1. 01Variables & expressions
  2. 02Solving equations
  3. 03Linear relationships
  4. 04Triangles & angles
  5. 05The Pythagorean theorem
  6. 06Sine, cosine & tangent
  7. 07The unit circle

Math for machine learning & data science

Here for ML/data science? This is your road — clearer than the textbooks.

The complete mathematical foundation for machine learning, in the right order: linear algebra (through SVD), the calculus of gradients, counting into probability and statistics, and the optimization that ties it all into how models learn. Each topic is rebuilt visually and intuitively. Recommended prerequisites: comfort with basic algebra and functions.

  1. 01Precalc refresh — variables & functions
  2. 02Linear algebra — vectors
  3. 03Dot product & similarity
  4. 04Norms & distance
  5. 05Matrices as transformations
  6. 06Rank & the four subspaces
  7. 07Eigenvectors
  8. 08Matrix decompositions & SVD
  9. 09Calculus — derivatives
  10. 10Partial derivatives & gradients
  11. 11Chain rule & backpropagation
  12. 12Counting — the probability bridge
  13. 13Random variables & distributions
  14. 14Conditional probability & Bayes
  15. 15Estimation, likelihood & MLE
  16. 16Correlation & regression
  17. 17Optimization — loss functions
  18. 18Gradient descent & learning rate
  19. 19Convexity & constraints
  20. 20Capstone — statistics for ML

Calculus & change

Ready for the platform's flagship course.

The full journey from functions to the fundamental theorem — derivatives, integrals, and the ideas that connect them.

  1. 01Why calculus exists
  2. 02Functions → Limits (lessons 1–4)
  3. 03Derivatives & rules (5–6)
  4. 04Antiderivatives & integrals (7–9)
  5. 05The fundamental theorem
  6. 06Optimization & related rates
  7. 07The calculus of oscillation

Linear algebra & structure

For data, graphics, ML — the mathematics of many things at once.

Vectors to eigenvectors, with the projection geometry that powers compression, least squares, and (later) Fourier analysis.

  1. 01Vectors
  2. 02The dot product
  3. 03Matrices as transformations
  4. 04Solving systems
  5. 05Orthogonality & least squares
  6. 06Eigenvectors in action

Signals & systems

The engineering track: how devices hear, filter, and respond.

From “what is a signal?” to filters and frequency response — with the trig, complex-number, and oscillation bridges built in at the right moments.

  1. 01Identities & phase (bridge)
  2. 02What is a signal?
  3. 03Systems & the LTI idea
  4. 04Convolution
  5. 05Complex numbers, rehabilitated
  6. 06Euler's formula & phasors
  7. 07Oscillation, decay & resonance
  8. 08Difference equations
  9. 09Filters & frequency response

Fourier & the frequency domain

The deep end: spectra, sampling, FFTs, and honest analysis.

Builds the frequency domain from linear-algebra geometry, makes it computable, and faces the real-world fine print of sampling and windowing.

  1. 01Orthogonality & projections (bridge)
  2. 02Why sinusoids? Signals as vectors
  3. 03Fourier series
  4. 04The Fourier transform
  5. 05DFT & FFT
  6. 06Sampling & aliasing
  7. 07Reconstruction & sinc
  8. 08Windowing, leakage & the STFT
  9. 09The z-transform & poles

Differential equations & dynamic systems

Predicting the future: growth, decay, oscillation, simulation.

Nature's laws as rate equations — read them, solve them, simulate them, and meet the resonance that connects them to signals.

  1. 01The fundamental theorem (bridge)
  2. 02Reading rate laws
  3. 03Exponential growth & decay
  4. 04Predicting step by step
  5. 05Systems in motion
  6. 06Second-order equations & oscillation
  7. 07Resonance in systems (bridge onward)

Data, probability & uncertainty

For honest reasoning with data, measurements, and noise.

From coin flips to confidence to the noise floor of real instruments — statistics as self-defense and as engineering.

  1. 01Thinking in probability
  2. 02Center, spread & honest summaries
  3. 03The bell curve
  4. 04Sampling & evidence
  5. 05Noise, averaging & SNR
  6. 06The art of counting (bridge)

Applied math for engineering & computing

The grand tour: every pillar, pointed at real systems.

A long road for serious learners: foundations → calculus → linear algebra → dynamics → signals → frequency domain. Everything connects; this is the order it connects in.

  1. 01Beginner math foundations (path)
  2. 02Calculus & change (path)
  3. 03Linear algebra & structure (path)
  4. 04Differential equations & dynamics (path)
  5. 05Signals & systems (path)
  6. 06Fourier & frequency domain (path)
  7. 07Data & uncertainty (path, anytime)

Probability & statistics for data science

Turning data into trustworthy conclusions — and ML-ready intuition.

The data scientist's core: count, then reason about chance, then infer from samples, then model relationships — ending at the statistics behind machine learning. Heavy on figures and interpretation.

  1. 01Counting — the probability bridge
  2. 02Thinking in probability
  3. 03Random variables & distributions
  4. 04Conditional probability & Bayes
  5. 05Describing data
  6. 06The bell curve & CLT
  7. 07Sampling, inference & p-values
  8. 08Estimation, likelihood & MLE
  9. 09Correlation & regression
  10. 10Statistics for machine learning

Engineering math

For engineers: the math behind systems, signals, and control.

The applied-engineering spine — linear algebra and calculus into differential equations, then signals, systems, and the frequency domain. Built around real engineering intuition.

  1. 01Linear algebra — vectors
  2. 02Matrices as transformations
  3. 03Calculus — derivatives
  4. 04Integrals & accumulation
  5. 05Differential equations
  6. 06Oscillation & resonance
  7. 07Signals & systems
  8. 08Convolution & LTI
  9. 09The Fourier transform
  10. 10Sampling & aliasing

Core university math

The standard first-year+ sequence, rebuilt for understanding.

The classic university core — single- and multivariable calculus, linear algebra, probability, and a first taste of differential equations — in a coherent, visual order.

  1. 01Functions & limits
  2. 02Derivatives
  3. 03Integrals
  4. 04The fundamental theorem
  5. 05Linear algebra — vectors
  6. 06Matrices & systems
  7. 07Eigenvalues & eigenvectors
  8. 08Partial derivatives & gradients
  9. 09Probability
  10. 10Differential equations