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Calculus Concepts and Applications
Video Course | FREE

This video course begins with an overview of basic calculus operations and takes you on an exploration of Wolfram Language functions, including those used for computing integrals and solving differential equations. Learn from one of our symbolic computing experts about applications of calculus to real-world problems, gain insight into the technology underlying our built-in calculus functions, and find some interesting historical mathematical references as well as resources for further study. Allow the Wolfram Language to introduce you to—or help you to rediscover—some of the beauty and utility of calculus.

Course Overview
  • Video 130 minutes
  • Video 223 minutes
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Daily Study Group: Introduction to Elementary Algebra
Special Event | FREE

Certification Levels: CompletionLevel 1

Prepare for further mathematics and statistics courses by learning elementary algebra, also known as Algebra I. This Study Group follows the Wolfram U course Introduction to Elementary Algebra with lessons on how to solve linear equations, systems of linear equations, linear inequalities and quadratic equations, as well as how to perform polynomial operations.

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Introduction to Calculus
Interactive Course | FREE

Requirements: This course requires no prior knowledge of Mathematica or the Wolfram Language. Prerequisites for calculus include Algebra I (elementary algebra), Algebra II (intermediate algebra), elementary geometry and trigonometry or precalculus.

Certification Levels: CompletionLevel 1

A comprehensive introduction to fundamental concepts in calculus, including video lessons and interactive notebooks. Follow along with the examples in the Wolfram Cloud and use the material to prepare for the AP Calculus AB exam. The course starts with functions and limits, followed by differential calculus and its applications, and then moves on to integral calculus and its applications. Problem sessions, exercises, quizzes and a sample exam are provided for self-paced assessment. Earn a certificate by watching all lesson and problem session videos and completing the quizzes with a passing grade.

Course Overview
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Introduction to Cryptography
Interactive Course | FREE

Requirements: This course requires a basic understanding of number theory, algorithms, discrete mathematics and modular arithmetic and basic-level skills in any programming language.

Certification Levels: Completion

This course gives an introduction to the concepts, underlying math, principles and techniques of historic and modern cryptography; ties cryptographic protocols to real-world scenarios; and gives a necessary understanding of issues related to information security in general.

Course Overview
  • Section 122 minutes
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Introduction to Differential Equations
Interactive Course | FREE

Requirements: This course requires no prior knowledge of Mathematica or the Wolfram Language. Prerequisites for differential equations include calculus and linear algebra.

Certification Levels: CompletionLevel 1

A comprehensive introduction to fundamental concepts and solution methods for differential equations, including video lessons and interactive notebooks. Follow along with the examples in the Wolfram Cloud and use the material to prepare for courses in natural science, engineering, economics and other fields. The course starts with a discussion of direction fields and methods for solving first-order differential equations, followed by the study of second-order equations and their applications, and then moves on to solving systems of differential equations. Problem sessions, exercises and quizzes are provided for self-paced assessment. Earn a certificate by watching all lesson and problem session videos and completing the quizzes with a passing grade. Level I certification in Differential Equations is awarded to those who meet the completion requirements and also pass the course final exam.

Course Overview
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Introduction to Fractional Calculus
Video Course | FREE

Learn about computing fractional derivatives and using the popular Laplace transform technique to solve systems of linear fractional differential equations using the Wolfram Language. The first video describes the basics of fractional calculus, defines some of the common differintegrals and introduces the built-in FractionalD and CaputoD functions. The second video focuses on using LaplaceTransform and InverseLaplaceTransform to convert from time domain to frequency domain and back again. It also demonstrates how you can combine the Laplace transform with MittagLefflerE functions and CaputoD derivatives. The final video provides more background on fractional calculus and its uses and showcases demonstrative examples of both single fractional differential equations and systems of linear fractional differential equations.

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Introduction to Linear Algebra
Interactive Course | FREE

Requirements: This course requires no prior knowledge of Mathematica or the Wolfram Language. Prerequisites for linear algebra include algebra, elementary geometry and trigonometry.

Certification Levels: CompletionLevel 1

A comprehensive introduction to fundamental concepts in linear algebra, including video lessons and interactive notebooks. Follow along with the examples in the Wolfram Cloud and use the material to prepare for courses in data science, engineering and other fields. The course starts with linear equations and matrices, followed by determinants and eigenvalues, and then moves on to inner products and the singular value decomposition. Application sessions are included to show uses of linear algebra in the real world. Exercises and quizzes are provided for self-paced assessment.

Course Overview
  • Section 138 minutes
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Introduction to Mathematica for Students and Teachers
Video Course | FREE

This video course provides an introduction to Mathematica for students, teachers and beginners of all kinds. It quickly covers a wide range of topics from algebra to calculus using examples, all delivered from the viewpoint of a highly skilled and experienced classroom teacher. It starts with the concept of a computational notebook and builds step by step to more advanced topics such as plotting, graphics and solving equations. The course includes techniques for entering mathematical notation using your keyboard and palette buttons and finding help using the Wolfram Documentation Center. The course is recorded by Ruth Dover, a math instructor and Wolfram Innovator who has taught thousands of students how to use Mathematica and the Wolfram Language over the course of her career.

Course Overview
  • Video 116 minutes
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Signals, Systems and Signal Processing
Interactive Course | FREE

Requirements: This course requires basic working knowledge of the Wolfram Language.

Certification Levels: Completion

This course gives an introduction to the concepts, mathematics, principles and techniques of signal processing in linear, time-invariant (LTI) systems. The course covers methods of analysis for both continuous-time and discrete-time signals and systems, presents sampling and gives an elementary introduction to filter design. Many everyday signal processing examples are included. The concepts and methods of signals and systems presented here play an important role in many areas of science and engineering, and therefore the course should be of interest to a broad range of students.

Course Overview
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A Guide to Mathematics with the Wolfram Language

A Guide to Mathematics with the Wolfram Language
Video Course | FREE

Learn about using the Wolfram Language for a broad range of mathematics. You can do symbolic, numeric and algebraic calculations, as well as geometry and calculus. These videos will introduce tools for solving and manipulating equations and calculations, including logical, Boolean and geometric expressions. Various built-in functions to help you solve polynomial and linear equations as well as number precision and order of interpolation are discussed. The videos cover common applied mathematics topics, such as matrices, linear algebra, optimization and numerical calculus. More advanced applications like time series calculations, image processing functionality and some data management are featured in later videos.

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Asymptotics: The Art of Approximation

Asymptotics: The Art of Approximation
Video Lesson | FREE

This video class introduces asymptotics as an alternative to exact and numerical methods. The class opens with some historical notes and explains how asymptotic methods can be useful. Examples shown include applications for the solution of differential equations, integrals, difference and algebraic equations and the computation of sums of infinite series. Learn how to use the built-in asymptotic functions in the Wolfram Language to solve hard problems that cannot be solved exactly.

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Bringing Math to Life through Visual Learning

Bringing Math to Life through Visual Learning
Video Lesson | FREE

This video class demonstrates how to encourage critical thinking in the classroom with the use of Wolfram|Alpha and the Wolfram Demonstrations Project. No previous experience with Mathematica or the Wolfram Language is required.

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Calculus Applications and Algorithms

Calculus Applications and Algorithms
Video Lesson | FREE

This class provides applications of calculus functions in the Wolfram Language and a discussion of the internal methods used for solving problems.

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Calculus Fundamentals

Calculus Fundamentals
Video Lesson | FREE

This class gives a broad overview of calculus operations in the Wolfram Language. Learn details about the functionality for computing integrals and solving differential equations, and become familiar with the Wolfram Language built-in functions Integrate and DSolve. See how animations and interactive graphics are useful for understanding concepts. This class is suitable for beginners wanting to use Mathematica and the Wolfram Language to solve calculus problems.

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Discrete Calculus Concepts and Applications

Discrete Calculus Concepts and Applications
Video Lesson | FREE

This video gives a broad overview of discrete calculus functions in the Wolfram Language, along with applications to fractals, sequence recognition and the study of algorithms. This class requires no previous Wolfram Language experience.

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Graphs and Networks: Concepts and Applications

Graphs and Networks: Concepts and Applications
Video Lesson | FREE

Graph theory and network analysis are used to model and analyze connections between entities in the real world—the World Wide Web, social networks and airline routes, just to name a few. The Wolfram Language provides a unified computational perspective from across multiple disciplines in the application of graphs and networks. This video class covers the fundamental properties of graphs and explores workflows available for network modeling and analysis.

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