Maxima (Computer Algebra)

If you haven’t done so already, you may want to start by reading the Preface to the Computing Series: Software as a Force Multiplier, Sections 1-3.

Maxima: a Computer Algebra System (CAS) for symbolic computation

Last updated: Feb 19, 2023 (fixed links). Nov 11, 2022 (added omega-math’s excellent web interface, and generating function calculation of the partition of integers problem).

Maxima is a computer algebra system (CAS) for symbolic computation that is free, open source, runs on multiple operating systems (Win,Mac,Linux), and covers a wide range of mathematical capabilities and graphical capabilities. These include algebraic simplification, polynomials, methods from calculus, matrix equations, differential equations, number theory, combinatorics, hypergeometric functions, tensors, gravitational physics, PDEs, nonlinear systems, plus including 2-D/3-D plotting and animation.  With a large and responsive user community, there is plenty of help to get up the learning curve, and with its active developer base, Maxima and its ecosystem continue to gain capability, including a fantastic web interface by Omega-Math/Vroom-Labs (see the screenshot below, r0*0). The result is a free, versatile, powerful mathematical computing package for engineers, scientists, mathematicians, programmers, and students. This article will help you get started with Maxima and set you up with resources to flatten the learning curve.

Omega-Math’s web interface to Maxima. Used here to calculate the first 10 elements of p(n), the number of ways to partition integer n, using a generating function comprising a truncated series of polynomials up to degree n=10


Continue reading this article…

Bare Bones Programming: The C Language

…for Embedded and Low-Level Systems Development

C provides the convenience of learning one language while retaining the ability to target a variety of platforms including modern operating systems (Linux, Windows, Mac), real-time operating systems, systems-on-a-chip, and a host of microcontrollers for embedded development. And if you have to “mov” the bits around yourself (device drivers, DMA controllers), you can do that too. This is a significant efficiency over assembly languages which are essentially chip-specific control codes and therefore require understanding the architecture of the target chip.

Continue reading this article…

Stats: 1,089,379 article views since 2010 (Aug '24 update)

Dear Readers:

Welcome to the conversation!  We publish long-form pieces as well as a curated collection of spotlighted articles covering a broader range of topics.   Notifications for new long-form articles are through the feeds (you can join below).  We love hearing from you.  Feel free to leave your thoughts in comments, or use the contact information to reach us!

Reading List…

Looking for the best long-form articles on this site? Below is a curated list by the main topics covered.

Mathematics History & Philosophy

  1. What is Mathematics?
  2. Prehistoric Origins of Mathematics
  3. The Mathematics of Uruk & Susa (3500-3000 BCE)
  4. How Algebra Became Abstract: George Peacock & the Birth of Modern Algebra (England, 1830)
  5. The Rise of Mathematical Logic: from Laws of Thoughts to Foundations for Mathematics
  6. Mathematical Finance and The Rise of the Modern Financial Marketplace
  7. A Course in the Philosophy and Foundations of Mathematics
  8. The Development of Mathematics
  9. Catalysts in the Development of Mathematics
  10. Characteristics of Modern Mathematics

Topics in Mathematics: Pure & Applied Mathematics

  1. Fuzzy Classifiers & Quantile Statistics Techniques in Continuous Data Monitoring
  2. LOGIC in a Nutshell: Theory & Applications (including a FORTH simulator and digital circuit design)
  3. Finite Summation of Integer Powers: (Part 1 | Part 2 | Part 3)
  4. The Mathematics of Duelling
  5. A Radar Tracking Approach to Data Mining
  6. Analysis of Visitor Statistics: Data Mining in-the-Small
  7. Why Zero Raised to the Zero Power IS One

Technology: Electronics & Embedded Computing

  1. Electronics in the Junior School - Gateway to Technology
  2. Coding for Pre-Schoolers - A Turtle Logo in Forth
  3. Experimenting with Microcontrollers - an Arduino development kit for under £12
  4. Making Sensors Talk for under £5, and Voice Controlled Hardware
  5. Computer Programming: A brief survey from the 1940s to the present
  6. Forth, Lisp, & Ruby: languages that make it easy to write your own domain specific language (DSL)
  7. Programming Microcontrollers: Low Power, Small Footprints & Fast Prototypes
  8. Building a 13-key pure analog electronic piano.
  9. TinyPhoto: Embedded Graphics and Low-Fat Computing
  10. Computing / Software Toolkits
  11. Assembly Language programming (Part 1 | Part 2 | Part 3)
  12. Bare Bones Programming: The C Language

Technology: Sensors & Intelligent Systems

  1. Knowledge Engineering & the Emerging Technologies of the Next Decade
  2. Sensors and Systems
  3. Unmanned Autonomous Systems & Networks of Sensors
  4. The Advance of Marine Micro-ROVs

Maths Education

  1. Maxima: A Computer Algebra System for Advanced Mathematics & Physics
  2. Teaching Enriched Mathematics, Part 1
  3. Teaching Enriched Mathematics, Part 2: Levelling Student Success Factors
  4. A Course in the Philosophy and Foundations of Mathematics
  5. Logic, Proof, and Professional Communication: five reflections
  6. Good mathematical technique and the case for mathematical insight

Explore…

Timeline