Online courses directory (391)

This course is designed for high school students preparing to take the AP* Statistics Exam. * AP Statistics is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, this product.

Principles of Applied Mathematics is a study of illustrative topics in discrete applied mathematics including sorting algorithms, information theory, coding theory, secret codes, generating functions, linear programming, game theory. There is an emphasis on topics that have direct application in the real world.

This course was recently revised to meet the MIT Undergraduate Communication Requirement (CR). It covers the same content as 18.310, but assignments are structured with an additional focus on writing.

18.311 Principles of Continuum Applied Mathematics covers fundamental concepts in continuous applied mathematics, including applications from traffic flow, fluids, elasticity, granular flows, etc. The class also covers continuum limit; conservation laws, quasi-equilibrium; kinematic waves; characteristics, simple waves, shocks; diffusion (linear and nonlinear); numerical solution of wave equations; finite differences, consistency, stability; discrete and fast Fourier transforms; spectral methods; transforms and series (Fourier, Laplace). Additional topics may include sonic booms, Mach cone, caustics, lattices, dispersion, and group velocity.

Basic probability. Should have a reasonable grounding in basic algebra before watching. Basic Probability. Example: Marbles from a bag. Example: Picking a non-blue marble. Example: Picking a yellow marble. Term Life Insurance and Death Probability. Probability with Playing Cards and Venn Diagrams. Addition Rule for Probability. Compound Probability of Independent Events. Getting At Least One Heads. Example: Probability of rolling doubles. LeBron Asks: What are the chances of making 10 free throws in a row?. LeBron Asks: What are the chances of three free throws versus one three pointer?. Frequency Probability and Unfair Coins. Example: Getting two questions right on an exam. Example: Rolling even three times. Introduction to dependent probability. Example: Dependent probability. Example: Is an event independent or dependent?. Example: Bag of unfair coins. Monty Hall Problem. Example: All the ways you can flip a coin. Example: Probability through counting outcomes. Permutations. Combinations. Example: Ways to arrange colors. Example: 9 card hands. Example: Ways to pick officers. Getting Exactly Two Heads (Combinatorics). Probability and Combinations (part 2). Probability using Combinations. Exactly Three Heads in Five Flips. Generalizing with Binomial Coefficients (bit advanced). Example: Different ways to pick officers. Example: Combinatorics and probability. Example: Lottery probability. Mega Millions Jackpot Probability. Conditional Probability and Combinations. Birthday Probability Problem. Random Variables. Discrete and continuous random variables. Probability Density Functions. Expected Value: E(X). Binomial Distribution 1. Binomial Distribution 2. Binomial Distribution 3. Binomial Distribution 4. Expected Value of Binomial Distribution. Poisson Process 1. Poisson Process 2. Law of Large Numbers. Introduction to Random Variables. Probability (part 1). Probability (part 2). Probability (part 3). Probability (part 4). Probability (part 5). Probability (part 6). Probability (part 7). Probability (part 8).

This course introduces students to the basic concepts and logic of statistical reasoning and gives the students introductory-level practical ability to choose, generate, and properly interpret appropriate descriptive and inferential methods. In addition, the course helps students gain an appreciation for the diverse applications of statistics and its relevance to their lives and fields of study. The course does not assume any prior knowledge in statistics and its only prerequisite is basic algebra. We offer two versions of statistics, each with a different emphasis: Probability and Statistics and Statistical Reasoning. Each course includes all expository text, simulations, case studies, comprehension tests, interactive learning exercises, and the StatTutor labs. Each course contains all of the instructions for the four statistics packages options we support. To do the activities, you will need your own copy of Microsoft Excel, Minitab, the open source R software, TI calculator, or StatCrunch. One of the main differences between the courses is the path through probability. Probability and Statistics includes the classical treatment of probability as it is in the earlier versions of the OLI Statistics course.

This free online course introduces you to the mathematics of probability, chance and the analysis of data. The course begins by introducing data collection and analysis, graphs and frequency distribution. The course examines chance in the context of gambling, odds and probability. The course is of interest to anybody who needs to analyse mathematical data and is particularly valuable to students studying for exams.

This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.

Measures of central tendency and dispersion. Mean, median, mode, variance, and standard deviation. Statistics intro: mean, median and mode. Example: Finding mean, median and mode. Mean median and mode. Exploring Mean and Median Module. Exploring mean and median. Average word problems. Sample mean versus population mean.. Reading Box-and-Whisker Plots. Constructing a box-and-whisker plot. Box-and-Whisker Plots. Creating box and whisker plots. Example: Range and mid-range. Range, Variance and Standard Deviation as Measures of Dispersion. Variance of a population. Sample variance. Review and intuition why we divide by n-1 for the unbiased sample variance. Simulation showing bias in sample variance. Unbiased Estimate of Population Variance. Another simulation giving evidence that (n-1) gives us an unbiased estimate of variance. Simulation providing evidence that (n-1) gives us unbiased estimate. Will it converge towards -1?. Variance. Population standard deviation. Sample standard deviation and bias. Statistics: Standard Deviation. Exploring Standard Deviation 1 Module. Exploring standard deviation 1. Standard deviation. Statistics: Alternate Variance Formulas. Statistics: The Average. Statistics: Variance of a Population. Statistics: Sample Variance. Statistics intro: mean, median and mode. Example: Finding mean, median and mode. Mean median and mode. Exploring Mean and Median Module. Exploring mean and median. Average word problems. Sample mean versus population mean.. Reading Box-and-Whisker Plots. Constructing a box-and-whisker plot. Box-and-Whisker Plots. Creating box and whisker plots. Example: Range and mid-range. Range, Variance and Standard Deviation as Measures of Dispersion. Variance of a population. Sample variance. Review and intuition why we divide by n-1 for the unbiased sample variance. Simulation showing bias in sample variance. Unbiased Estimate of Population Variance. Another simulation giving evidence that (n-1) gives us an unbiased estimate of variance. Simulation providing evidence that (n-1) gives us unbiased estimate. Will it converge towards -1?. Variance. Population standard deviation. Sample standard deviation and bias. Statistics: Standard Deviation. Exploring Standard Deviation 1 Module. Exploring standard deviation 1. Standard deviation. Statistics: Alternate Variance Formulas. Statistics: The Average. Statistics: Variance of a Population. Statistics: Sample Variance.

Introduction to probability. Independent and dependent events. Compound events. Mutual exclusive events. Addition rule for probability. Basic Probability. Probability space exercise example. Probability space. Example: Marbles from a bag. Example: Picking a non-blue marble. Example: Picking a yellow marble. Probability 1. Probability with Playing Cards and Venn Diagrams. Addition Rule for Probability. Compound Probability of Independent Events. Getting At Least One Heads. Example: Probability of rolling doubles. LeBron Asks: What are the chances of making 10 free throws in a row?. LeBron Asks: What are the chances of three free throws versus one three pointer?. Frequency Probability and Unfair Coins. Example: Getting two questions right on an exam. Example: Rolling even three times. Independent probability. Frequency Stability. Introduction to dependent probability. Example: Dependent probability. Example: Is an event independent or dependent?. Example: Bag of unfair coins. Dependent probability. Monty Hall Problem. Intersection and union of sets. Relative complement or difference between sets. Universal set and absolute complement. Subset, strict subset, and superset. Bringing the set operations together. Basic set notation. Probability (part 1). Probability (part 2). Probability (part 3). Probability (part 4). Probability (part 5). Probability (part 6). Probability (part 7). Probability (part 8). Introduction to Random Variables. Basic Probability. Probability space exercise example. Probability space. Example: Marbles from a bag. Example: Picking a non-blue marble. Example: Picking a yellow marble. Probability 1. Probability with Playing Cards and Venn Diagrams. Addition Rule for Probability. Compound Probability of Independent Events. Getting At Least One Heads. Example: Probability of rolling doubles. LeBron Asks: What are the chances of making 10 free throws in a row?. LeBron Asks: What are the chances of three free throws versus one three pointer?. Frequency Probability and Unfair Coins. Example: Getting two questions right on an exam. Example: Rolling even three times. Independent probability. Frequency Stability. Introduction to dependent probability. Example: Dependent probability. Example: Is an event independent or dependent?. Example: Bag of unfair coins. Dependent probability. Monty Hall Problem. Intersection and union of sets. Relative complement or difference between sets. Universal set and absolute complement. Subset, strict subset, and superset. Bringing the set operations together. Basic set notation. Probability (part 1). Probability (part 2). Probability (part 3). Probability (part 4). Probability (part 5). Probability (part 6). Probability (part 7). Probability (part 8). Introduction to Random Variables.

Making inferences based on sample data. Confidence intervals. Margin of error. Hypothesis testing. Introduction to the Normal Distribution. Normal Distribution Excel Exercise. ck12.org Normal Distribution Problems: Qualitative sense of normal distributions. ck12.org Normal Distribution Problems: Empirical Rule. ck12.org Normal Distribution Problems: z-score. ck12.org Exercise: Standard Normal Distribution and the Empirical Rule. Empirical rule. ck12.org: More Empirical Rule and Z-score practice. Z scores 1. Z scores 2. Z scores 3. Central Limit Theorem. Sampling Distribution of the Sample Mean. Sampling Distribution of the Sample Mean 2. Standard Error of the Mean. Sampling Distribution Example Problem. Confidence Interval 1. Confidence Interval Example. Small Sample Size Confidence Intervals. Mean and Variance of Bernoulli Distribution Example. Bernoulli Distribution Mean and Variance Formulas. Margin of Error 1. Margin of Error 2. Hypothesis Testing and P-values. One-Tailed and Two-Tailed Tests. Type 1 Errors. Z-statistics vs. T-statistics. Small Sample Hypothesis Test. T-Statistic Confidence Interval. Large Sample Proportion Hypothesis Testing. Variance of Differences of Random Variables. Difference of Sample Means Distribution. Confidence Interval of Difference of Means. Clarification of Confidence Interval of Difference of Means. Hypothesis Test for Difference of Means. Comparing Population Proportions 1. Comparing Population Proportions 2. Hypothesis Test Comparing Population Proportions. Chi-Square Distribution Introduction. Pearson's Chi Square Test (Goodness of Fit). Contingency Table Chi-Square Test. ANOVA 1 - Calculating SST (Total Sum of Squares). ANOVA 2 - Calculating SSW and SSB (Total Sum of Squares Within and Between).avi. ANOVA 3 -Hypothesis Test with F-Statistic. Introduction to the Normal Distribution. Normal Distribution Excel Exercise. ck12.org Normal Distribution Problems: Qualitative sense of normal distributions. ck12.org Normal Distribution Problems: Empirical Rule. ck12.org Normal Distribution Problems: z-score. ck12.org Exercise: Standard Normal Distribution and the Empirical Rule. Empirical rule. ck12.org: More Empirical Rule and Z-score practice. Z scores 1. Z scores 2. Z scores 3. Central Limit Theorem. Sampling Distribution of the Sample Mean. Sampling Distribution of the Sample Mean 2. Standard Error of the Mean. Sampling Distribution Example Problem. Confidence Interval 1. Confidence Interval Example. Small Sample Size Confidence Intervals. Mean and Variance of Bernoulli Distribution Example. Bernoulli Distribution Mean and Variance Formulas. Margin of Error 1. Margin of Error 2. Hypothesis Testing and P-values. One-Tailed and Two-Tailed Tests. Type 1 Errors. Z-statistics vs. T-statistics. Small Sample Hypothesis Test. T-Statistic Confidence Interval. Large Sample Proportion Hypothesis Testing. Variance of Differences of Random Variables. Difference of Sample Means Distribution. Confidence Interval of Difference of Means. Clarification of Confidence Interval of Difference of Means. Hypothesis Test for Difference of Means. Comparing Population Proportions 1. Comparing Population Proportions 2. Hypothesis Test Comparing Population Proportions. Chi-Square Distribution Introduction. Pearson's Chi Square Test (Goodness of Fit). Contingency Table Chi-Square Test. ANOVA 1 - Calculating SST (Total Sum of Squares). ANOVA 2 - Calculating SSW and SSB (Total Sum of Squares Within and Between).avi. ANOVA 3 -Hypothesis Test with F-Statistic.

Permutations and combinations. Using combinatorics to solve questions in probability. Permutations. Combinations. Counting 2. Example: Ways to arrange colors. Example: 9 card hands. Example: Ways to pick officers. Permutations. Combinations. Permutations and combinations. Example: Probability through counting outcomes. Example: All the ways you can flip a coin. Getting Exactly Two Heads (Combinatorics). Probability and Combinations (part 2). Probability using Combinations. Exactly Three Heads in Five Flips. Example: Different ways to pick officers. Example: Combinatorics and probability. Example: Lottery probability. Mega Millions Jackpot Probability. Generalizing with Binomial Coefficients (bit advanced). Conditional Probability and Combinations. Conditional Probability (Bayes Theorem) Visualized. Birthday Probability Problem. Probability with permutations and combinations. Permutations. Combinations. Counting 2. Example: Ways to arrange colors. Example: 9 card hands. Example: Ways to pick officers. Permutations. Combinations. Permutations and combinations. Example: Probability through counting outcomes. Example: All the ways you can flip a coin. Getting Exactly Two Heads (Combinatorics). Probability and Combinations (part 2). Probability using Combinations. Exactly Three Heads in Five Flips. Example: Different ways to pick officers. Example: Combinatorics and probability. Example: Lottery probability. Mega Millions Jackpot Probability. Generalizing with Binomial Coefficients (bit advanced). Conditional Probability and Combinations. Conditional Probability (Bayes Theorem) Visualized. Birthday Probability Problem. Probability with permutations and combinations.

Random variables. Expected value. Probability distributions (both discrete and continuous). Binomial distribution. Poisson processes. Random Variables. Discrete and continuous random variables. Probability Density Functions. Expected Value: E(X). Expected value. Law of Large Numbers. Term Life Insurance and Death Probability. Binomial Distribution 1. Binomial Distribution 2. Binomial Distribution 3. Binomial Distribution 4. Expected Value of Binomial Distribution. Galton Board Exploration. Poisson Process 1. Poisson Process 2. Random Variables. Discrete and continuous random variables. Probability Density Functions. Expected Value: E(X). Expected value. Law of Large Numbers. Term Life Insurance and Death Probability. Binomial Distribution 1. Binomial Distribution 2. Binomial Distribution 3. Binomial Distribution 4. Expected Value of Binomial Distribution. Galton Board Exploration. Poisson Process 1. Poisson Process 2.

Fitting a line to points. Linear regression. R-squared. Correlation and Causality. Fitting a Line to Data. Estimating the line of best fit exercise. Estimating the line of best fit. Squared Error of Regression Line. Proof (Part 1) Minimizing Squared Error to Regression Line. Proof Part 2 Minimizing Squared Error to Line. Proof (Part 3) Minimizing Squared Error to Regression Line. Proof (Part 4) Minimizing Squared Error to Regression Line. Regression Line Example. Second Regression Example. R-Squared or Coefficient of Determination. Calculating R-Squared. Covariance and the Regression Line. Correlation and Causality. Fitting a Line to Data. Estimating the line of best fit exercise. Estimating the line of best fit. Squared Error of Regression Line. Proof (Part 1) Minimizing Squared Error to Regression Line. Proof Part 2 Minimizing Squared Error to Line. Proof (Part 3) Minimizing Squared Error to Regression Line. Proof (Part 4) Minimizing Squared Error to Regression Line. Regression Line Example. Second Regression Example. R-Squared or Coefficient of Determination. Calculating R-Squared. Covariance and the Regression Line.

This course, which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates.

This course provides an introduction to the theory and practice of quantum computation. Topics covered include: physics of information processing, quantum logic, quantum algorithms including Shor's factoring algorithm and Grover's search algorithm, quantum error correction, quantum communication, and cryptography.

This course is an introduction to the basics of random matrix theory, motivated by engineering and scientific applications.

This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.

This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts and teaches an understanding and construction of proofs. MIT students may choose to take one of three versions of Real Analysis; this version offers three additional units of credit for instruction and practice in written and oral presentation.

The three options for 18.100:

• Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible.
• Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology.
• Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication. This fulfills the MIT CI requirement.

Learn how to use regression models, the most important statistical analysis tool in the data scientist's toolkit. This is the seventh course in the Johns Hopkins Data Science Specialization.

“Why is math important?  Why do I have to learn math?”  These are typical questions that you have most likely asked at one time or another in your education.  While you may learn things in math class that you will not use again, the study of mathematics is still an important one for human development.  Math is widely-used in daily activities (e.g. shopping, cooking, etc.) and in most careers (e.g. medicine, teaching, engineering, construction, business, statistics in psychology, etc.).  Math is also considered a “universal language.”  One of the fundamental reasons why you learn math is to help you tackle problems, both mathematical and non-mathematical, with clear, concise, and logical steps.  In this course, you will study important fundamental math concepts. This course begins your journey into the “Real World Math” series.  These courses are intended not just to help you learn basic algebra and geometry topics, but also to show you how these topics are used in everyday life.  In thi…