# Mathematics concept required for Deep Learning

Why is Math required for Deep Learning?

1. Geometry and Linear Algebra
• Geometry of Vectors
• Angles and Dot Products with Cosine similarity
• Hyperplanes
• The geometry of Linear Transformation
• Rank of Matrix
• Linear Dependence
• Invertibility
• Determinant

Learn Linear Algebra here and basics on Geometry here

2. Matrix Decomposition
• Finding Eigenvalues and Eigenvectors
• Decomposing Matrices
• Operations on Eigendecomposition
• Single Value Decomposition
• Principle Component Analysis
• Matrix Approximation
• Eigendecomposition and Diagonalization of Symmetric Matrices
• Gershgorin circle theorem
• LU Decomposition, QR Decomposition/Factorization
• Symmetric Matrices, Orthogonalization and Orthonormalization

3. Single Variable Calculus
• Differential Calculus
• Rules of calculus

Learn calculus here

4. Probability and Distributions
• Sum Rule, Product Rule, and Bayes Theorem
• Gaussian Distribution
• Discrete and Continuous Probabilities
• Combinatorics
• Conditional and Joint Distributions
• Bernoulli Distribution
• Discrete Uniform Distribution
• Binomial Distribution
• Poisson Distribution
• Continuous Uniform Distribution
• Gaussian Distribution
• Exponential Family Distribution

Refer this for videos on Probability and for different distributions here.

5. Naive Bayes
• Optical Characters Recognition
• Probabilistic Model for Classification
• Naive Bayes Classifier

6. Multivariate Calculus
• Higher-dimensional Differentiation
• Multivariate chain rule
• Backpropagation Algorithm
• Integral Calculus, Partial Derivatives
• Vector-Values Functions
• Jacobian, Laplacian, Lagrangian Distribution

7. Integral Calculus
• Theorem of Calculus
• Sign Conventions
• Geometric interpretation
• Multiple integrals Concepts and Change of Variables

For basics of integral calculus refer here.

8. Random Variables
• The concept of Discrete to Continuous in Random Variables
• Means, Variances, Standard Deviation and its concept on a continuum
• Probability Density Function
• Cumulative Distribution Function
• Joint Density Function
• Marginal Distribution
• Covariance and Correlation

An in-depth guide to this topic here

9. Statistics
• Evaluation and Comparison of Estimators
• Conducting Hypothesis Tests
• Constructing Confidence intervals

10. Probability on Maximum Likelihood
• Principle of Maximum Likelihood with examples
• Numerical optimization and Negative Log-Likelihood
• Maximum Likelihood for Continuous Variables
• Moment Generating Function
• Prior and Posterior, Maximum a Posteriori Estimation, Sampling Methods

• Information Theory (Optional For beginners) Learn about it here

After getting good at the above mathematical topics you can go ahead and get your hands dirty with these topics.

• Hamiltonian Calculus
• Halleys Calculus
• Complex Numbers
• Quaternions
• Sedenions
• Np Problems

A one-stop guide for all the above topics here

2. Three reasons why mathematics will help in your future with a career in Deep Learning field:-
• Math help in selecting a correct algorithm considering its complexity, training time, feature and accuracy
• Approximate the right confidence interval and unpredictability.
• Help in selecting an algorithm’s acceptance plan and in choosing its parameter setting.
3. Some of the interesting application requiring Deep Learning Algorithm: –
• Suppose you have your great-great-grandfather black and while a picture may be captured in the early 20th century, well now with the help of Deep Neural Network its now possible to colourize that black and white picture and for a surprise, this is also possible with a video.

Stanford documentation about the above here

• Pixel recursive super-resolution being developed by Google Brain Researchers has come up with this deep learning neural network, and this is capable of predicting a somewhat precise image of an almost blurred image.

• Lip reading developed by Oxford University is a deep learning neural network capable of reading the lips of a person and convert that directly into the text and doesn’t even need the sound of a person speaking.

Stanford documentation on this here.

• Deep Learning neural network is now capable of detecting the location of the picture where it was clicked on and display it on a map.

Refer to PlaNet documentation here.

• Some endangered whale species are being detected with convolution neural network and this is where deep learning concepts are being implemented to save them.

• Self-driving cars, which can detect traffic and choose an optimal path is already developed.

Refer to Stanford documentation here.

• Apart from this Deep learning algorithms are being implemented everywhere, for example, earthquake prediction, music composition, entertainment, healthcare, and of course Robotics.

More here

References: –

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