Fundamental Math for Data Science

With data now being one of the most valuable assets to tap into, the demand for data science skills increases by the day. Statistics and sampling are at the core of data science. Use this course as a theoretical introduction to using samples to reveal various statistics. Examine what exactly is meant by statistics and samples. Explore descriptive statistics, namely measures of central tendency and of dispersion. Study probability sampling techniques, including simple random sampling and cluster sampling. Investigate how undersampling and oversampling are used to generate more balanced datasets. Upon completion, you'll know the best way to use statistics and samples for your specific goals and needs.

Data is one of the most valuable assets a business has, but it's only as valuable as the methods used to interpret it. Data science, which at its core includes statistics and sampling, is the key to data interpretation. In this course, practice using the pandas library in Python to work with statistics and sampling. Practice loading data from a CSV file into a pandas DataFrame. Compute a variety of statistics on data. While doing so, see how to visualize the relationship between data and computed statistics. Moving along, implement several sampling techniques, such as stratified sampling and cluster sampling. Then, explore how a balanced sample can be created from an imbalanced dataset using the imblearn module in Python. Upon completion, you'll be able to generate samples and compute statistics using various tools and methods.

Hypothesis testing is the bedrock of inferential statistics, allowing us to draw inferences reliably about the population as a whole. Use this course to learn more about the distinction between descriptive and inferential statistics and how the latter seek to generalize from the sample to the population as a whole. Examine the components of a typical hypothesis test, such as the null and alternative hypothesis, the test statistic, and the p-value. You'll also explore type-I and type-II errors and the use cases and conceptual underpinnings of t-tests and ANOVA. By the time you finish this course, you will be able to identify use-cases for hypothesis testing and conceptually construct the appropriate null and alternative hypotheses for such tests.

Matrix decomposition refers to the process of expressing a matrix as the product of other matrices. These factorized matrices are a lot easier to work with than the original matrix, as they usually possess specific properties desirable in the contexts of various mathematical procedures. Use this course to learn how to use matrix decomposition. Explore precisely what matrices and vectors are and how they're used. Then, study various matrix operations, such as computing the transpose and the inverse of a matrix. Moving on, identify why matrices are great for expressing linear transformations of points in a coordinate space. Work with important transformations, such as shearing, reflection, and rotation. Implement the LU, QR, and Cholesky decompositions and examine their applicability and restrictions. Upon completion, you'll know when and how to implement various matrix decompositions.

Eigenvalues, eigenvectors, and the Singular Value Decomposition (SVD) are the foundation of many important techniques, including the widely used method of Principal Components Analysis (PCA). Use this course to learn when and how to use these methods in your work. To start, investigate precisely what eigenvectors and eigenvalues are. Then, explore various examples of eigendecomposition in practice. Moving on, use eigenvalues and eigenvectors to diagonalize a matrix, noting why diagonalizing matrices is extremely efficient in computing matrix higher powers. By the end of the course, you'll be able to apply eigendecomposition and Singular Value Decomposition to diagonalize different types of matrices and efficiently compute higher powers of matrices in this manner.

Calculus is a branch of mathematics that deals with continuous change and with how the output of a function changes when the inputs into that function change by vanishingly small amounts. Calculus has wide-ranging applications - in optimization, machine learning, economics, and medicine. You will start this course by defining a derivative in terms of its mathematical formula and interpreting that derivative of a function at a point in two ways: as the slope of the tangent line to the function at that point or as the instantaneous rate of change of that function at that point. You will also apply these concepts to a constant function, verify that its derivative is zero, and understand the reason behind it. By the time you finish this course, you'll have a good foundation in the basics of differential calculus.

Linear functions change at a constant rate, and that in turn, makes the rate of change of a linear function a constant. This and other related insights into linear and other mathematical functions can be quantified using calculus. Through this course, you'll examine the steps involved in applying the differentiation operation to study a moving particle. You'll then understand how the partial derivative of a function that depends on multiple independent variables is computed with respect to one of those independent variables by holding all other independent variables constant. This course will also allow you to investigate how partial derivatives play a crucial role in the training phase of building a machine learning (ML) model. Upon completion of this course, you will be able to compute the partial derivative of a function that depends on multiple independent variables and better understand the training process of a machine learning model.

Integral calculus is a major branch of calculus that deals with integrating - i.e., aggregating - an infinite number of infinitesimal increments to a function. Integration is the inverse operation of differentiation and has wide-ranging applications across science, engineering, and social sciences. Begin this course by understanding how integration can be used to compute the area under a curve. You'll then explore the relationship between derivatives and integrals and discover how differentiation and integration are inverse operations. You'll wrap up the course by investigating the steps involved in computing the integral of several different types of functions and visualize these integrals using a combination of SymPy, Seaborn, and Matplotlib. By the time you finish this course, you'll be able to solve definite as well as indefinite integrals and visualize such integrals as the area under a curve in Python.

Linear Regression analysis is a simple yet powerful technique for quantifying cause and effect relationships. Use this course to get your head around linear regression as the process of fitting a straight line through a set of points. Learn how to define residuals and use the least square error. Define and measure the R-squared, implement regression analysis, visualize your data by computing a correlation matrix and plotting it in the form of a correlation heatmap, and use scatter plots as a prelude to performing the regression analysis. Finish by implementing the regression analysis first using functions that you write yourself and then using the scikit-learn python library. By the end of the course, you'll be able to identify the need for linear regression and implement it effectively.

Gradient descent is an extremely powerful numerical optimization technique widely used to find optimal values of model parameters during the model training phase of machine learning. Use this course as an introduction to gradient descent, examining how it can be used in a wide variety of optimization problems. Explore how it can be used to perform linear regression, carefully studying the matrix equations used to compute the gradients and updating the model parameters using the gradients as well as the learning rate hyperparameter. Finally, apply a form of gradient descent known as stochastic gradient descent to fit an S-curve, thus implementing logistic regression on a data set. By the end of the course, you'll be able to assuredly implement logistic regression using gradient descent.