October 29, 2020 — Paige Bremner, Publishing Assistant, Document & Media Systems

The pandemic has postponed or canceled a lot of things this year, but luckily learning isn’t one of them. Check out these picks for new Wolfram Language books that will help you explore new software, calculus, engineering and more from the comfort of home.

August 14, 2020 — Devendra Kapadia, Manager of Calculus & Algebra, Algorithms R&D

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?”

July 2, 2020 — Amy Simpson, Blog and Information Systems Coordinator, Document and Media Systems

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.

June 23, 2020 — Christopher Carlson, Senior User Interface Developer, User Interfaces

In his blog post announcing the launch of Mathematica Version 12.1, Stephen Wolfram mentioned the extensive updates to `Dataset` that we undertook to make it easier to explore, understand and present your data. Here is how the updated `Dataset` works and how you can use it to gain deeper insight into your data.

June 2, 2020 — Paritosh Mokhasi, Kernel Developer, Algorithms R&D

Sudoku is a popular game that pushes the player’s analytical, mathematical and mental abilities. Solving sudoku problems has long been discussed on Wolfram Community, and there has been some fantastic code presented to solve sudoku problems. To add to that discussion, I will demonstrate several features that are new to Mathematica Version 12.1, including how this game can be solved as an integer optimization problem using the function `LinearOptimization`, as well as how you can generate new sudoku games.

May 6, 2020 — Tigran Ishkhanyan, Algorithms R&D

Mathematica was initially built to be a universal solver of different mathematical tasks for everything from school-level algebraic equations to complicated problems in real scientific projects. During the past 30 years of development, over 250 mathematical functions have been implemented in the system, and in the recent release of Version 12.1 of the Wolfram Language, we’ve added many more, ranging from the elementary `Sin` function to the advanced Heun functions.

April 29, 2020 — Koji Maruyama, Sales Engineer

*Mathematica 12 has powerful functionality for solving partial differential equations (PDEs) both symbolically and numerically. This article focuses on, among other things, the finite element method (FEM)–based solver for nonlinear PDEs that has been newly implemented in Version 12. After briefly reviewing basic syntax of the Wolfram Language for PDEs, including how to designate Dirichlet and Neumann boundary conditions, we will delineate how Mathematica 12 finds the solution of a given nonlinear problem with FEM. We then show some examples in physics and chemistry, such as the Gray–Scott model and the time-dependent Navier–Stokes equation. More information can be found in the Wolfram Language tutorial “Finite Element Programming,” on which most of this article is based.*

## 1. はじめに

Wolfram Research社の旗艦製品であるMathematicaは，5,000 を超える組み込み関数を有するWolfram Languageを駆動する．数理モデリング，解析の基本となる常・偏微分方程式の分野においては，これらをシンボリックに，あるいは数値的に解くための強力なソルバを搭載している．最近は有限要素法(FEM) を利用した数値的求解機能が大幅に強化され，偏微分方程式(PDE)を任意の領域上で解いたり，固有値・固有関数を求めたりすることが可能となった．ここでは，最新のバージョン12における非線形偏微分方程式のFEMによる求解を中心に，現実的な問題に応用する上での流れを例とともに紹介する．なお，有限要素法を用いて非線形PDEを解くワークフローの詳細，コードはすべて公開されている．MathematicaのWolframドキュメント内で，チュートリアル“FiniteElementProgramming”を参照いただきたい．

April 14, 2020 — Stephen Wolfram

## I Never Expected This

It’s unexpected, surprising—and for me incredibly exciting. To be fair, at some level I’ve been working towards this for nearly 50 years. But it’s just in the last few months that it’s finally come together. And it’s much more wonderful, and beautiful, than I’d ever imagined.

In many ways it’s the ultimate question in natural science: How does our universe work? Is there a fundamental theory? An incredible amount has been figured out about physics over the past few hundred years. But even with everything that’s been done—and it’s very impressive—we still, after all this time, don’t have a truly fundamental theory of physics.

Back when I used do theoretical physics for a living, I must admit I didn’t think much about trying to find a fundamental theory; I was more concerned about what we could figure out based on the theories we had. And somehow I think I imagined that if there was a fundamental theory, it would inevitably be very complicated.

February 12, 2020 — Ed Pegg Jr, Editor, Wolfram Demonstrations Project

The sparse ruler problem has been famously worked on by Paul Erdős, Marcel J. E. Golay, John Leech, Alfréd Rényi, László Rédei and Solomon W. Golomb, among many others. The problem is this: what is the smallest subset of so that the unsigned pairwise differences of give all values from 1 to ? One way to look at this is to imagine a blank yardstick. At what positions on the yardstick would you add 10 marks, so that you can measure any number of inches up to 36?

Another simple example is of size 3, which has differences , and . The sets of size 2 have only one difference. The minimal subset is not unique; the differences of also give .

Part of what makes the sparse ruler problem so compelling is its embodiment in an object inside every schoolchild’s desk—and its enduring appeal lies in its deceptive simplicity. Read on to see precisely just how complicated rulers, marks and recipes can be.

January 9, 2020 — George Beck, Document & Media Systems

Number theory is a very old subject that in modern times has branched into various large areas. One of these is additive number theory, with problems like this: when is a prime the sum of two squares? Primes are part of the more classical area now called multiplicative number theory, so as this problem of Fermat’s indicates, the two areas are intimately connected. The problem I discuss in this blog is a mix of additive and multiplicative number theory, with a dash of linear algebra.