The Data Science Course: From Beginner to Advanced

Learn foundational mathematical concepts crucial for data science, focusing on linear algebra with vectors and matrices. Discover how these tools represent and work with data, emphasizing practical relevance over equations.

Represent vectors as lists of numbers representing features of a data point, written as column or row. Explore vector types by dimension and perform operations like addition and scalar multiplication.

Explore matrix concepts, notations, and fundamental types; view matrices as rectangular grids with rows and columns, and learn square, identity, and zero matrices used to organize data.

Master basic matrix operations and their relevance to data manipulation in data science. Learn how addition, subtraction, scalar multiplication, and matrix multiplication transform data, support models, and enable distance calculations.

Explore the geometric intuition of vectors in 2D and 3D space. Learn how scaling and rotation move data points through matrix transformations for feature engineering and machine learning models.

Explore how linear algebra underpins data representation by treating observations as vectors and datasets as matrices, enabling efficient computation and algorithm compatibility through the design matrix or feature matrix.

Learn how linear algebra underpins data science, enabling data organization with vectors and matrices, matrix operations, and data transformation such as scaling, rotating, and projecting for scalable, effective models.

Explore vectors and matrices as data representations, perform basic operations and their geometric transformations, and recognize linear algebra as the universal language for data science, with calculus and optimization next.

Explore calculus fundamentals—functions, limits, and derivatives—and learn how these ideas drive optimization in data science algorithms to find the best solutions.

Learn how a function maps input to a single output. Explore domain and range, and distinguish linear from non-linear functions used in data science models.

Explore how limits describe a function’s approaching value, identify holes, and define continuity as drawing a function without lifting the pencil, with data science optimization implications.

Understand derivatives as rates of change and the slope of a tangent, with speed as an analogy, showing how positive, negative, or zero slopes guide data science and machine learning.

Master basic rules of differentiation, including the power rule (derivative of x^2 is 2x), constant rule, and linearity, plus product and chain rules for data science.

Explains the fundamental idea of optimization, finding maximum and minimum values, and how derivatives guide gradient descent to minimize the cost function in machine learning models.

Calculus, especially derivatives and optimization, drives machine learning by guiding parameter updates along the cost function toward its lowest point, enabling neural networks and linear regression to learn from data.

Explore calculus foundations from functions to limits and continuity. Then study derivatives as rate of change and their role in optimization for machine learning, linking linear algebra and probability.

Explore the essentials of probability theory, building on linear algebra and calculus to help data science quantify uncertainty and predict outcomes. Analyze how events influence each other in data science.

Explore fundamentals of probability by defining experiments, outcomes, sample space, and events, and calculate probability as favorable outcomes over total outcomes, with coin and dice examples.

Explore conditional probability and independent events, learn how to express P(A|B), and see how independence vs dependence affects decisions in data science like recommendations and transaction risk.

Explore random variables, turning outcomes into numbers, and distinguish discrete and continuous types with coin flips and height measurements to guide data science methods.

Understand probability distributions as the likelihood map for a random variable’s possible values, using bar charts for discrete outcomes and curves for continuous ranges, including normal and uniform distributions.

Learn how the expected value, the long-term average of outcomes, guides decision making under uncertainty and risk in data science through a fair die example and practical applications.

Explore the gap between expected value and actual outcomes, clarifying theoretical long-term averages, finite observations, and the role of variability and uncertainty in data science models.

Explore the essentials of probability theory, including events, sample space, conditional versus independent events, random variables and distributions, and the role of expected value in data uncertainty.

Explore data types, structures, and quality, and learn how to assess data before analysis by examining data organization, goodness, and common data problems.

Explore fundamental data types: numerical, categorical, and ordinal, and how tabular, time series, text, image, and graph data structures are organized and used to load, store, process, and train models.

Explore fundamental data types and their properties, from numerical data (discrete and continuous) to categorical data (nominal and ordinal), and learn how counting frequencies informs preparation for analysis and modeling.

Highlight how data quality underpins reliable insights by ensuring accuracy, completeness, consistency, validity, and timeliness to prevent garbage in, garbage out.

Identify common data quality issues such as missing values, outliers, duplicates, and inconsistencies, and learn how these problems impact calculations, model performance, and data reliability.

Clean and preprocess data to unlock reliable insights and improve model performance. Tackle missing values, outliers, and duplicates; standardize formats and transform data to a 0–1 scale.

Explore the idea of big data as huge volume, velocity, and variety that transform analysis, requiring techniques to store, process, and extract value from structured, semi-structured, and unstructured data.

Explore data fundamentals, including numerical, categorical, and ordinal types. Examine tabular, time series, text, and image structures; assess data quality, missing values, and outliers, and emphasize cleaning for big data.

Explore statistical thinking and descriptive statistics to collect, analyze, interpret, and present data, using population and sample, averages, and measures of spread.

Explore the concepts of population and sample, why sampling is necessary, and how statistical inference uses representative sample data to estimate characteristics of a larger population.

Explore measures of central tendency, including mean, median, and mode, and learn their properties and uses.

Explore measures of dispersion, including range, variance, and standard deviation, to understand data spread and interpretation; learn how standard deviation reveals how much data deviates from the mean.

Explore data distributions with histograms and box plots, highlighting shapes like normal and skewed distributions, and the five-number summary (minimum, Q1, median, Q3, maximum) for cross-group comparison.

Learn how covariance measures how two numeric variables change together and how correlation standardizes this relationship to a -1 to 1 scale, noting that correlation does not imply causation.

Understand the shape and distribution of data, including center and spread, to guide tool selection, detect outliers, and interpret results for robust, accurate modeling.

Builds statistical thinking through descriptive statistics, clarifying populations and samples and the need for inference, and uses central tendency, dispersion, histograms, box plots, correlation, and covariance to describe data.

Master descriptive statistics to summarize data with averages and measures of spread. Apply inferential statistics to make educated guesses and draw reliable conclusions about a population from a sample.

Learn how inferential statistics use samples to infer population characteristics, with examples from polling, drug trials, and spending habits across groups.

Learn how hypothesis testing uses sample data to assess a population claim by weighing evidence against the null hypothesis and considering the alternative, in inferential statistics.

Explore the p value in hypothesis testing, its role in deciding to reject or fail to reject null hypothesis, and how p value less than 0.05 indicates statistically significant result.

Learn how confidence intervals provide a range around a sample estimate to reveal reliability in population parameters. Apply 95% confidence intervals to report results and predictions in data science.

Explore type I and type II errors in hypothesis testing, including false positives and negatives, null hypotheses, and significance levels like 0.05 to interpret study results.

Unpack the difference between correlation and causation in data science, and show why correlation does not imply causation. Understand confounding variables and why controlled experiments establish true cause and effect.

Explore inferential statistics to generalize from sample to population, test hypotheses with p values, estimate with confidence intervals, and note that correlation does not imply causation.

Explore the fundamentals of machine learning, from data types and structures to math and statistics, and how algorithms transform data into predictive power.

Explore machine learning as a subset of artificial intelligence that lets computers learn from data without explicit programming. Discover supervised and unsupervised learning, with reinforcement learning as the third paradigm.

Explore supervised learning, including regression and classification, where models learn from labeled data to predict continuous values like house prices or classify items as spam or not spam.

Explore unsupervised learning, clustering, and dimensionality reduction to discover hidden patterns in unlabeled data, group similar data points, and simplify features for easier visualization and improved model performance.

Explore the simplest machine learning workflow within the data science lifecycle, from data collection and cleaning to feature engineering, model selection, training, evaluation, and deployment, with iterative refinements.

Identify features as input attributes and the target variable as the prediction in supervised learning. The lecture contrasts supervised and unsupervised learning with house price and spam classification examples.

Compare supervised learning, which learns from labeled examples, with unsupervised learning, which finds patterns in unlabeled data to uncover structure and natural groupings.

Define machine learning as teaching computers to learn from data, summarize supervised and unsupervised learning, and cover regression, classification, clustering, dimensionality reduction, features, and target variables.

Discover supervised learning through regression, predicting continuous values by fitting a line or curve to data. Define regression problems, measure error, and learn how models forecast sales and house prices.

Explore how regression problems in supervised learning predict continuous numeric targets from input features, with examples like house prices, sales revenue, hospital stay length, and tomorrow's temperature.

Explore simple linear regression, using a single feature to fit a line that predicts house prices from size, with y = mx + b and optimal m and b.

Explore how cost functions measure prediction error in regression and guide learning toward smaller loss. Learn mean squared error, error penalties, and how calculus-based optimization minimizes cost to improve accuracy.

Evaluate regression models after training using mean absolute error and root mean squared error, where mae reflects difference in original units, rmse penalizes errors, and lower values indicate better performance.

Train a linear model y = mx + b by iteratively estimating m and b with gradient descent to minimize the MSE on training data, producing the best fit line.

Explore how error arises in regression predictions, from missing information and randomness to model limitations, and learn to analyze residuals to minimize, not eliminate, error.

Explore supervised learning through classification, predicting categories or labels such as spam detection or organizing objects in an image; define the problem, explore algorithms, evaluate performance, and understand decision boundaries.

Define the classification problem in supervised learning; show how models assign unseen data to predefined categories, with binary and multi-class examples like spam detection, image recognition, medical diagnosis.

Learn logistic regression as a fundamental classifier that maps linear outputs to probabilities between 0 and 1 using the S-shaped sigmoid, with thresholding to classify emails as spam or not.

Explore basic classification with decision trees, a flow-chart like algorithm that predicts outcomes by yes-or-no questions on data features, handling numeric and category data with explainable results.

Evaluate classification models with accuracy, precision, recall, F1 score, true positives, and false positives, noting accuracy can mislead on imbalanced data, and use the metric to balance precision and recall.

Discover how a classification model uses decision boundaries, linear boundaries from logistic regression or non-linear boundaries from trees and neural networks, to separate classes and generalize to unseen data.

Explore how the decision boundary separates groups in classification, using apples and oranges as examples, from simple straight lines to complex boundaries learned from labeled data through features.

Explore supervised learning through classification, predicting categories and labels with logistic regression and decision trees. Learn about accuracy, precision, recall, F1 score, and decision boundaries that separate classes in data.