Math for Intelligence

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• Statistics for Intelligence
• Finding Paul Revere
• Causation vs. Correlation
• Dot Product
• Animated Math | Grant Sanderson @ 3blue1brown.com
• Courses & Certifications
  • Free Mathematics Courses for Data Science & Machine Learning | Matthew Mayo - KDnuggets
  • Google's Crash Course
  • Bloomberg Lectures
  • Brilliant.org
• Introduction to Matrices and Matrix Arithmetic for Machine Learning | Jason Brownlee
• Essential Math for Data Science:  ‘Why’ and ‘How’ | Tirthajyoti Sarkar - KDnuggets
• Gentle Dive into Math Behind Convolutional Neural Networks | Piotr Skalski - Towards Data Science
• Varient: Limits
• Neural Networks and Deep Learning - online book | Michael A. Nielsen
• Convolution vs. Cross-Correlation (Autocorrelation)
• Quantum algorithms

• Fundamentals:
  • Linear Algebra | MIT
  • Linear Algebra | Khan Academy
  • Differential Calculus | Khan Academy
  • Multivariable Calculus | Khan Academy

Mathematics Ontology

Mathematics for Machine Learning | M. Deisenroth, A Faisal, and C. Ong .. Companion webpage ...

Scalar, Vector, Matrix & Tensor

• Scalars, Vectors, Matrices and Tensors with Tensorflow 2.0 | Mukesh Mithrakumar - Dev

Scalars

a single number. For example weight, which is denoted by just one number.

Vectors

are an array of numbers. The numbers are arranged in order and we can identify each individual number by its index in that ordering. We can think of vectors as identifying points in space, with each element giving the coordinate along a different axis. In simple terms, a vector is an arrow representing a quantity that has both magnitude and direction wherein the length of the arrow represents the magnitude and the orientation tells you the direction. For example wind, which has a direction and magnitude.

Matrices

• Eigenvalues and eigenvectors | Wikipedia
• Markov Matrix, also known as a stochastic matrix | DeepAI
• Kernels | Wikipedia
• Adjacency matrix | Wikipedia

A matrix is a 2D-array of numbers, so each element is identified by two indices instead of just one. If a real valued matrix A has a height of m and a width of n, then we say that A in Rm x n. We identify the elements of the matrix as A_(m,n) where m represents the row and n represents the column.

Tensors

In mathematics, a tensor is an algebraic object that describes a (multilinear) relationship between sets of algebraic objects related to a vector space. Objects that tensors may map between include vectors and scalars, and, recursively, even other tensors. Tensors can take several different forms – for example: scalars and vectors (which are the simplest tensors), dual vectors, multi-linear maps between vector spaces, and even some operations such as the dot product. Tensors are defined independent of any basis, although they are often referred to by their components in a basis related to a particular coordinate system. Wikipedia

3blue1brown

• Animated Math | Grant Sanderson @ 3blue1brown.com
  • Essence of linear algebra
  • Essence of calculus

Gilbert Strang (MIT) - Linear Algebra

• MIT Open Courseware - Linear Algebra
• Gilbert Strang's Books
• YouTube Playlist

Fourier Transform (FT), Fourier Series, and Fourier Analysis

• Quantum Fourier transform (QFT)
• Engineers solve 50-year-old puzzle in signal processing - Vladimir Sukhoy and Alexander Stoytchev | Mike Krapfl - TechXplore

Joseph Fourier showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. Joseph was a French mathematician and physicist born in Auxerre and best known for initiating the investigation of Fourier series, which eventually developed into Fourier analysis and harmonic analysis, and their applications to problems of heat transfer and vibrations. The Fourier transform and Fourier's law of conduction are also named in his honor. Fourier is also generally credited with the discovery of the greenhouse effect.

• Fourier Transform (FT) decomposes a function of time (a signal) into its constituent frequencies. This is similar to the way a musical chord can be expressed in terms of the volumes and frequencies of its constituent notes. Fourier Transform | Wikipedia

• Fourier Series is a periodic function composed of harmonically related sinusoids, combined by a weighted summation. The discrete-time Fourier transform is an example of Fourier series. For functions on unbounded intervals, the analysis and synthesis analogies are Fourier Transform and inverse transform. Fourier Series | Wikipedia

• Fourier Analysis the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier Analysis | Wikipedia