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Mathematics

Current Events & History

The Singular Euler–Maclaurin Expansion A New Twist to a Centuries-Old Problem

Of all mathematical operations, addition is the most basic: It’s what we learn first in school. Historically, it is the most ancient. While the simple task of getting the sum of two numbers is simple, sums of many numbers can easily turn into a challenging numerical problem if the number of summands is very large.

Current Events & History

Is Your Function Continuous? Squaring Away the New Function Properties in the Wolfram Language

The Wolfram Language has several hundred built-in functions, ranging from sine to Heun. As a user, you can extend this collection in infinitely many ways by applying arithmetic operations and function composition. This could lead you to defining expressions of bewildering complexity, such as the following:

&#10005 f = SinhIntegral[ LogisticSigmoid[ ScorerHi[Tanh[AiryAi[HermiteH[-(1/2), x] - x + 1]]]]];
You may then ask, “Is continuous?” or “Can be written as a composition of an increasing function with another function?” The powerful new tools for studying function properties in Version 12.2 provide quick answers to such questions—opening the doors for applying a network of theorems and ideas that have been developed by mathematicians during the last few centuries.
Education & Academic

3D-Printed Jewelry Made with the Wolfram Language Showcases the Beauty of Mathematics

I enjoy turning mathematical concepts into wearable pieces of art. That’s the idea behind my business, Hanusa Design. I make unique products that feature striking designs inspired by the beauty and precision of mathematics. These pieces are created using the range of functionality in the Wolfram Language. Just in time for Valentine’s Day, we recently launched Spikey earrings in the Wolfram Store, which are available in rose gold–plated brass and red nylon. In this blog, I’ll give a look under the hood and discuss how an idea becomes a product through the Wolfram Language.

Education & Academic

Step-by-Step Math Tools in Wolfram|Alpha Help Your Chemistry Course Prep

Math is one of the main things that deters students from wanting to learn more about chemistry. Being a chemical engineering student, I understand this, especially for students who just have to get chemistry out of the way as a general education requirement. Essentially, step-by-step solutions are like your own on-demand math tutor: in addition to calculating the answer, Wolfram|Alpha shows you how it got there. Here are six important math skills that you will definitely use on a regular basis in your chemistry class and how they relate to different chemistry concepts.

Education & Academic

How We Navigated a Hybrid Remote Learning Environment Using Wolfram Technology

The past year of learning ushered in a variety of new experiences for instructors and students alike, and the United States Military Academy at West Point was no exception. In addition to masks in the classroom, reduced class sizes to allow for social distancing, rigorous testing and tracing efforts, and precautionary remote video classes, we have also needed to adjust aspects of our teaching styles. While such adjustments were voluntary, to enhance the discussion I chose to teach several lessons outside under large white tents and even in stadium bleachers to safely enable larger conversations with my cadets. Sometimes this meant carrying a large whiteboard with a tripod out to the stadium. At other times it meant putting quiz-style questions on a website so that students could submit answers via forms that were easier to grade while allowing everyone to work at a safe distance on individual devices.

Best of Blog

Learn Linear Algebra in Five Hours Today with the Wolfram Language!

Linear algebra is probably the easiest and the most useful branch of modern mathematics. Indeed, topics such as matrices and linear equations are often taught in middle or high school. On the other hand, concepts and techniques from linear algebra underlie cutting-edge disciplines such as data science and quantum computation. And in the field of numerical analysis, everything is linear algebra!

Today, I am proud to announce a free interactive course, Introduction to Linear Algebra, that will help students all over the world to master this wonderful subject. The course uses the powerful functions for matrix operations in the Wolfram Language and addresses questions such as "How long would it take to solve a system of 500 linear equations?" or "How does data compression work?"

Education & Academic

New Wolfram Books: Releases from Wolfram Media and Others Featuring the Wolfram Language

The first half of 2020 has brought with it another exciting batch of publications. Wolfram Media has released Conrad Wolfram's The Math(s) Fix. Keep an eye out for the upcoming third edition of Hands-on Start to Wolfram Mathematica later in 2020.