Essential Math for Data Science

Discrete mathematics is the study of objects that take on distinct, separated values. The study of discrete mathematics is important in the field of Computer Science as computers can only understand discrete binary numbers. Use this course to learn more about the use and importance of discrete mathematics in the world of computer science. Examine the use of sets and perform common operations on them in Python. These operations include union, intersection, difference, and symmetric difference. When you are finished with this course, you will have the skills to use and work with sets in the real world using Python.

The graph data structure plays a significant role in modeling entities in the real world. A graph comprises nodes and edges that are used to represent entities and relationships, respectively. A graph can be used to model a social network or a professional network, roads and rail infrastructure, and telecommunication and telephone networks. Through this course, you'll explore graph data structure, graph components, and different types of graphs and their use cases. Start by discovering how to represent directed, undirected, weighted, and unweighted graphs in NetworkX. You'll then learn more about visualizing nodes and connections in graphs using Matplotlib. This course will also help you examine how to implement graph algorithms on all graph types using NetworkX. Upon completing this course, you will have the skills and knowledge to create and work with graphs using NetworkX in Python.

Mathematical optimization models allow us to represent our objectives, decision variables, and constraints in mathematical terms, and solving these models gives us the optimal solution to our problems. Linear programming is an optimization model that can be used when our objective function and constraints can be represented using linear terms. Use this course to learn how decision-making can be represented using mathematical optimization models. Begin by examining how optimization problems can be formulated using objective functions, decision variables, and constraints. You'll then recognize how to find an optimal solution to a problem from amongst feasible solutions through a case study. This course will also help you investigate the pros and cons of the assumptions made by linear programming and the steps involved in solving linear programming problems graphically as well as by using the Simplex method. When you are done with this course, you will have the skills and knowledge to apply linear programming to solve optimization problems.

Integer programming is a mathematical optimization model that helps find optimal solutions to our problems. Integer programming problems find more applications than linear programming and are an important tool in a developer's toolkit. Examine how to solve optimizations problems using integer programming through this course. Start by comparing the integer programming optimization model and linear programming. You'll then move on to the LP relaxation technique and how it can be used to obtain the starting point of an integer programming solution. You'll also explore the Pulp Python library through different case studies consisting of integer programming problems. Upon completing this course, you'll be able to apply integer programming to solve optimization problems.

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 algebra comes in handy when we need to work with a set of points represented in multi-dimensional space. Use this course to explore how systems of linear functions and equations can be represented using linear algebra. Examine how to define and compute the addition, scalar multiplication, dot product, and cross product operations on vectors, and discover how these operations are required while working with matrices. This course will also help you explore matrix multiplication, the inverse and transpose of a matrix, and computing the determinant of a matrix. By the time you finish this course, you will be able to express a system of linear functions as a matrix and perform fundamental operations on matrices, including matrix multiplication and the computation of inverses and determinants.

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.

Final Exam: Introduction to Math will test your knowledge and application of the topics presented throughout the Introduction to Math track of the Skillsoft Aspire Essential Math for Data Science Journey.

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.

Probability is a branch of mathematics that deals with uncertainty, specifically with numerical estimates of how likely an event is to occur and what might happen if that event does or does not occur. Probability has many applications in statistics, engineering, finance, machine learning, and computer science. Get acquainted with the basic constructs of probability through this course. Start by examining different types of events, outcomes, and the complement of an event. You will then simulate various probabilistic experiments in Python and note how the outcomes of these experiments tend to converge towards theoretically expected outcomes as the number of trials increases. By the time you finish this course, you will be able to define and measure probabilities of common events and simulate probabilistic experiments using Python.

Probability is all about estimating the likeliness of the occurrence of specific events. Use this course to learn more about defining and measuring joint, marginal, and conditional probabilities of events. Start by exploring the chain rule of probability and then use this rule to compute conditional probabilities of multiple events. You'll also investigate the steps involved in measuring the expected value of a random variable as the weighted sum of all outcomes, with each outcome weighted by its probability. By the time you finish this course, you will be able to compute joint, marginal, and conditional probabilities and the expected value of a random variable, as well as effectively utilize the chain rule of probability.

Bayesian models are the perfect tool for use-cases where there are multiple easily observable outcomes and hard-to-diagnose underlying causes, using a combination of graph theory and Bayesian statistics. Use this course to learn more bout stating and interpreting the Bayes theorem for conditional probabilities. Discover how to use Python to create a Bayesian network and calculate several complex conditional probabilities using a Bayesian machine learning model. You'll also examine and use naive Bayes models, which are a category of Bayesian models that assume that the explanatory variables are all independent of each other. Once you have completed this course, you will be able to identify use cases for Bayesian models and construct and effectively employ such models.

Probability distributions are statistical models that show the possible outcomes and statistical likelihood of any given event and are often useful for making business decisions. Get familiar with the theoretical concepts around statistics and probability distributions through this course and delve into applying statistical concepts to analyze your data using Python. Start by exploring statistical concepts and terminology that will help you understand the data you want to use for estimations on a population. You'll then examine probability distributions - the different forms of distributions, the types of events they model, and the various functions available to analyze distributions. Finally, you'll learn how to use Python to calculate and visualize confidence intervals, as well as the skewness and kurtosis of a distribution. After completing this course, you'll have a foundational understanding of statistical analysis and probability distributions.

Python libraries, such as NumPy and SciPy, are used for mathematical and numerical analysis. Through this course, learn how to generate uniform, binomial, and Poisson distributions using these libraries. Begin by exploring uniform distributions and delve into continuous and discrete distributions. You will then explore binomial distributions in-depth, including real-life situations where they can be applied. This course will also help you learn more about Poisson distributions and recognize their use cases. While examining these distributions, you will use functions, such as the probability density or probability mass functions and cumulative distributions functions, among others, to make estimations from your data. Upon completion of this course, you'll have the skills and knowledge to implement and visualize uniform, binomial, and Poisson distributions in Python.

This course dives deep into normal distributions, also known as Gaussian distributions, while also introducing you to the law of large numbers and the Central Limit Theorem. You will begin by using Python's SciPy library to generate a normal distribution and examine the use of several available functions that allow you to make estimations on normally distributed data. This course will also help you understand and visualize the law of large numbers and explore the Central Limit theorem by generating multiple samples and analyzing them. After you are done with this course, you'll have the skills and knowledge to analyze data and build your own models.

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.

One-sample T-tests are probably the single most commonly used type of hypothesis test. Through this course, learn to manually implement the one-sample T-test to know exactly how the p-value and test statistic are calculated. You'll examine various library implementations of the one-sample T-test and apply the test on data drawn from several different distributions. This course will also help you explore the non-parametric Wilcoxon signed-rank test, which is conceptually very similar to the one-sample T-test and helps estimate the median rather than the mean of that population without making assumptions about the population distribution. Upon completion of this course, you will be able to use the one-sample T-test as well as its non-parametric equivalent to evaluate both one-sided and two-sided hypotheses about the population mean or median.

In situations where two independent samples are drawn from different populations or where paired samples are available, such as in a before-after scenario, two-sample and paired T-tests are needed, respectively. Use this course to explore how two-sample T-tests can be used to test the null hypothesis that two independent samples have drawn from populations with equal means. You'll examine type I and type II errors and the use of paired samples T-tests. By the time you finish this course, you will be able to test whether two samples - either drawn independently or explicitly linked - are drawn from populations with equal means.

Two-sample T-tests are great for comparing population means given two samples. However, if the number of samples increases beyond two, we need a much more versatile and powerful technique - analysis of variance (ANOVA). Use this course to learn more about non-parametric tests and the ANOVA analysis. In this course, you'll explore the different use cases for Mann-Whitney U-tests, the use of the non-parametric paired Wilcoxon signed-rank test, and perform pairwise T-tests and ANOVA. You'll also get a chance to try your hand at the non-parametric variant of ANOVA - Kruskal Wallis test and post hoc tests, such as Tukey's honestly significant difference test (HSD). After completing this course, you will be able to account for the effect of one or two independent categorical variables, each having an arbitrary number of levels, on a dependent variable using ANOVA.

Final Exam: Statistics and Probability will test your knowledge and application of the topics presented throughout the Statistics and Probability track of the Skillsoft Aspire Essential Math for Data Science Journey.

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.

Decision trees are an effective supervised learning technique for predicting the class or value of a target variable. Unlike other supervised learning methods, they're well-suited to classification and regression tasks. Use this course to learn how to work with decision trees and classification, distinguishing between rule-based and ML-based approaches. As you progress through the course, investigate how to work with entropy, Gini impurity, and information gain. Practice implementing both rule-based and ML-based decision trees and leveraging powerful Python visualization libraries to construct intuitive graphical representations of decision trees. Upon completion, you'll be able to create, use, and share rule-based and ML-based decision trees.

Machine learning (ML) is widely used across all industries, meaning engineers need to be confident in using it. Pre-built libraries are available to start using ML with little knowledge. However, to get the most out of ML, it's worth taking the time to learn the math behind it. Use this course to learn how distances are measured in ML. Investigate the types of ML problems distance-based models can solve. Examine different distance measures, such as Euclidean, Manhattan, and Cosine. Learn how the distance-based ML algorithms K Nearest Neighbors (KNN) and K-means work. Lastly, use Python libraries and various metrics to compute the distance between a pair of points. Upon completion, you'll have a solid foundational knowledge of the mechanisms behind distance-based machine learning algorithms.

Knowing the math behind machine learning (ML) opens up many exciting avenues. There are vast amounts of ML algorithms you could learn. However, the distance-based algorithms K Nearest Neighbors and K-means clustering are arguably the most popular due to their simplicity and efficacy. In this course, practice building a classification model using the K Nearest Neighbors algorithm. Build upon this algorithm to perform regression. Then, perform a clustering operation by implementing the K-means algorithm. And in doing so, explore the techniques involved in converging the centroids towards their optimal positions. Upon completion, you'll be able to perform classification, regression, and clustering using the KNN and K-means algorithms.

Simple to use yet efficient and reliable, support vector machines (SVMs) are supervised learning methods popularly used for classification tasks. This course uncovers the math behind SVMs, focusing on how an optimum SVM hyperplane for classification is computed. Explore the representation of data in a feature space, finding a hyperplane to separate the data linearly. Then, learn how to separate non-linear data. Investigate the optimization problem for SVM classifiers, looking at how the weights of the model can be adjusted during training to get the best hyperplane separating the data points. Furthermore, apply gradient descent to solve the optimization problem for SVMs. When you're done, you'll have the foundational knowledge you need to start building and applying SVMs for machine learning.

Support vector machines (SVMs) are a popular tool for machine learning enthusiasts at any level. They offer speed and accuracy, are computationally uncomplicated, and work well with small datasets. In this course, learn how to implement a soft-margin SVM classifier using gradient descent in the Python programming language and the LIBSVM library to build a support vector classifier and regressor. For your first task, generate synthetic data that can be linearly separated by an SVM binary classifier, implement the classifier by applying gradient descent, and train and evaluate the model. Moving on, learn how to use a pre-built SVM classifier supplied by the LIBSVM module. Then use LIBSVM to train a support vector regressor, evaluate it, and use it for predictions. Upon completion, you'll know how to work with custom SVM classifiers and pre-built SVM classification and regression models.

First conceived in the 1940s, it wasn't until the early 2010s that artificial neurons showed their true potential as layered entities in the form of neural networks. When big data processing using distributed computing became mainstream, the computational capacity was now available to train these neural networks on huge datasets. Knowing this is one thing, but understanding how it all works is where the true potential lies. Use this course to gain an intuitive understanding of how neural networks work. Explore the mathematical operations performed by a single neuron. Recognize the potential of thousands of neurons connected together in a well-architected design. Finally, implement code to mathematically perform the operations in a single layer of neurons working on batch input. When you're finished, you'll have a solid grasp of the mechanisms behind neural networks and the math behind neurons.

Because neural networks comprise thousands of neurons and interconnections, one can assume training a neural network involves millions of computations. This is where a general-purpose optimization algorithm called gradient descent comes in. Use this course to gain an intuitive and visual understanding of how gradient descent and the gradient vector work. As you advance, examine three neural network activation functions, ReLU, sigmoid, and hyperbolic tangent functions, and two variants of the ReLU function, Leaky ReLU and ELU. In examining variants of the ReLU activation function, learn how to use them to deal with deep neural network training issues. Finally, implement a neural network from scratch using TensorFlow and basic Python. When you're done, you'll be able to illustrate the mathematical intuition behind neural networks and be prepared to tackle more complex machine learning problems.

Final Exam: Math Behind ML Algorithms will test your knowledge and application of the topics presented throughout the Math Behind ML Algorithms track of the Skillsoft Aspire Essential Math for Data Science Journey.

Principal component analysis (PCA) is a must-know pre-processing technique for anyone working with machine learning (ML). Used to process data fed into ML models, PCA is useful in many scenarios, such as exploratory data analysis, dimensionality reduction, and latent feature extraction. Use this course to learn the basic intuition behind principal component analysis along with how to use PCA. Start by visualizing how principal components work. Then, examine how they can be computed mathematically using the eigenvectors and eigenvalues of the covariance matrix of the data. As you advance, manually compute principal components, view the re-oriented data, and compare this result with the principal components computed. Lastly, use PCA for dimensionality reduction to train a classification model. When you're done, you'll have the skills and knowledge to use PCA to build more robust machine learning models.

Users marvel at a system's ability to recommend items they're likely to appreciate. As someone working with machine learning, implementing these recommendation systems (also called recommender systems) can dramatically increase user engagement and goodwill towards your products or brand. Use this course to comprehend the math behind recommendation systems and how to apply latent factor analysis to make recommendations to users. Examine the intuition behind recommender systems before investigating two of the main techniques used to build them: content-based filtering and collaborative filtering. Moving on, explore latent factor analysis by decomposing a ratings matrix into its latent factors using the gradient descent algorithm and implementing this technique to decompose a ratings matrix using the Python programming language. By the end of this course, you'll be able to build a recommendation system model that best suits your products and users.

Final Exam: Advanced Math will test your knowledge and application of the topics presented throughout the Advanced Math track of the Skillsoft Aspire Essential Math for Data Science Journey.