Wolfram Computation Meets Knowledge

Date Archive: 2022 August

Education & Academic

Wolfram|Alpha Pro Teaches Step-by-Step Arithmetic for All Grade Levels

In grade school, long arithmetic is considered a foundational math skill. In the past several decades in the United States, long arithmetic has traditionally been introduced between first and fifth grade, and remains crucial for students of all ages. The Common Core State Standards for mathematics indicate that first-grade students should learn how to add “a two-digit number and a one-digit number.” By second grade, students “add and subtract within 1000” and, in particular, “relate the strategy to a written method.” In third grade, multiplication by powers of 10 is introduced, and by fourth grade students are tasked to “use place value understanding and properties of operations to perform multi-digit arithmetic,” including multiplication and division. A fifth grader will not only be expected to “fluently multiply multi-digit whole numbers using the standard algorithm,” but also “add, subtract, multiply, and divide decimals.”
Education & Academic

Splitting a Point with Mathematica and MathTensor: A Mathematica Memoir

In the past few years, there have been many significant anniversaries in the Mathematica world. This has made me think about my long personal history working with all things Mathematica. Here I present an account of how I got involved with this world, developed my part of it and continue to use it. I show what I think is a unique application that differs from the other thousands of applications in Mathematica or the Wolfram Language presented on the various Wolfram Research websites, Wolfram Community and elsewhere. Finally, I attempt to describe the physics of what I do. The beginning historical part with much name-dropping can be skipped for those who want to read only about technical or physics issues.
Education & Academic

Fractional Calculus in Wolfram Language 13.1

What is the half-derivative of x?

Fractional calculus studies the extension of derivatives and integrals to such fractional orders, along with methods of solving differential equations involving these fractional-order derivatives and integrals. This branch is becoming more and more popular in fluid dynamics, control theory, signal processing and other areas. Realizing the importance and potential of this topic, we have added support for fractional derivatives and integrals in the recent release of Version 13.1 of the Wolfram Language.
Education & Academic

Discrete-Time Systems to FIR Filter Design: Explore Signal Processing in the New MOOC from Wolfram U

Recognizing the importance of the topics and the powerful capabilities in the Wolfram Language for signal processing, we set out to develop a fully interactive course about signal and system processing to make the subject accessible to a wide audience. After sharing and reviewing the course materials, notes and experiences we’ve collected from university undergraduate-level courses over many years, this resulting Wolfram U course represents the collaborative efforts of two principal authors, Mariusz Jankowski and Leila Fuladi, and a team of knowledgeable staff. It is our great pleasure to introduce to you the new, free, interactive course Signals, Systems and Signal Processing, which we hope will help you understand and master this difficult but tremendously important and exciting subject.