Step I

Fundamentals of Mathematics

Linear Algebra & Mathematics

• System of Linear Equation
• Matrix Operation
  • Addition, Multiplication, Division Using Python
  • Addition, Multiplication, Division Using NumPy
  • Inverse
  • Transpose
• Properties of Matrix
• Solving Linear Equation using Gaussian Elimination 
• LU Decomposition of Linear Equation
• Row Echelon Form
• Determinant
• Trace
  • With Numpy
• Eigenvalues and Eigenvectors
• Eigenspace
• Orthogonal and Orthonormal Vectors
• Cholesky Decomposition
  • With NumPy
• Eigen Decomposition
• Diagonalization
• Singular Value Decomposition — Implementation
• Matrix Approximation
• Vector Operations
• Linear Mappings
• Affine Spaces

Statistics

• Mean, Standard Deviation, and Variance — Implementation
• Sample Error and True Error
• Bias Vs Variance and Its Trade-Off
• Hypothesis Testing
  • T-test
  • Paired T-test
  • p-value
  • F-Test
  • z-test
• Confidence Intervals
• Correlation and Covariance
• Correlation Coefficient
• Covariance Matrix
• Pearson Correlation
• Normal Probability Plot
• Q-Q Plot
• Residuals Leverage Plot
• Pearson Product-Moment Correlations
• Spearman’s Rank Correlation Measure
• Kendall Rank Correlation Measure
• Robust Correlations
• Evaluation Metrics – Accuracy, Precision, Recall, F1-Score, MAE, MSE
• RMSE and R-Squared Error
• Precision-Recall Curve
• ROC-AUC curve

Geometry

• Vector Norms
• Inner, Outer, Cross Products
• Lengths and Angles
• Orthogonality and Orthonormal Vectors
• Orthogonal Projections
• Rotations
  • With NumPy
• Piecewise Functions
• Constraints and Splines
• Box-Cox Transformation using Python
• Fourier transformation
• Inverse Fast Fourier Transformation

Calculus

• Function Differentiation
• Implicit Differentiation
• Inverse Trigonometric Functions Differentiation
• Logarithmic Differentiation
• Partial Differentiation
• Advanced Differentiation
• Gradients
• Gradients of Matrices
• Useful Identities for Gradient Computation
• Backpropagation
  • Gradient Descent Algorithm
• Higher-Order Derivatives
• Multivariate Taylor Series

Probability & Distributions

• Probability
• Chance and Probability
• Discrete and Continuous Probabilities
• Addition Rule for Probability
• Law of total probability
• Sum Rule, Product Rule, and Bayes’ Theorem
• Uniform Distribution
• Normal Distribution
• Poisson Distribution
• Exponential Distribution
• Binomial Distribution
• Gaussian Distribution
• Central Limit Theorem
• Conjugacy and the Exponential Family
• Change of Variables/Inverse Transformation

Regression

• Parameter Estimation
• Bayesian Linear Regression
• Normal Equation in Linear Regression
• Maximum Likelihood as Orthogonal Projection

Dimensional Reduction

• Introduction to Dimensionality Reduction
• Projection Perspective
• Eigenvector Computation and Low-Rank Approximations
• Principal Component Analysis (PCA)
• PCA implementation in Python
• Latent Variable Perspective
• Low-Rank Approximations
• Overview of Linear Discriminant Analysis (LDA)
• Mathematical Explanation of Linear Discriminant Analysis (LDA)
• Generalized Discriminant Analysis (GDA)
• TSNE Algorithm

Vector Models

• Separating Hyperplanes
• Primal Support Vector Machine
• Dual Support Vector Machine
• Kernels 

These are the topics that you’ll be required to cover in “Mathematics” to get your roots strong. Right after, you’ll be required to choose the appropriate programming language to get started with data science. Which one to pick and how to pick? Will see about that in the next step.

Undeniably, Data science has become one of the hottest industries over the past few years from now. Being dominant in almost every sector, data science is powering up businesses (small-mid-large) and helping them in making business decisions and that’s what makes it special and demand is rising like a storm in the market for such professionals. In fact, people with no such background have also taken their way toward data science and by going through different processes many have made a career transition. 

Data Science is the study of data using tools and technologies to build predictive models and derive meaningful information. Career transition helps you in getting a “Handsome Salary” and alongside expanding your knowledge in various sectors. This is something called A Good Call. Now, the question arises, if you’re already working in some domain then “How to switch your career in Data Science?” and to make your way smooth and provide you in-depth details, we have drafted this article that will guide you through all the way so that you can start your new path towards data science.