126 – Mathematica
In this episode we discuss Mathematica, Wolfram Research’s technical computing system. With our guest, kernel developer Daniel Lichtblau, we discuss Mathematica’s capabilities for symbolic, numeric and other forms of computation, and we can do and how it works internally.
Here are a few links that Daniel suggested:
- My view, in 2006, of the creation of the Mathematica kernel.
- The pitfalls in symbolic integration.
- Some research needed to support Mathematica functionality.
- Some “research” that lead to Mathematica functionality.
- Here is a case where Mathematica was a primary tool in support of some research questions.
Here are the general links:
- Daniel Lichtblau (LinkedIn)
- Wolfram Research
- Wolfram Mathematica
- Wolfram|Alpha: Computational Knowledge Engine
- Siri (WP)
- Computer algebra system (WP)
- Stephen Wolfram: Official Website
- Stephen Wolfram (WP)
- Integral (WP)
- The Mathematica Book
- A New Kind Of Science
- Symbolic Math Toolbox – MATLAB – MathWorks
- Symbolic Computation (WP)
- Numerical Analysis (WP)
- Symbolic-Numeric Computation (WP)
- Graph theory (WP)
- Calculus (WP)
- Derivative (WP)
- Automatic Differentiation (WP)
- Probability (WP)
- Statistics (WP)
- Normal distribution (WP)
- Signal processing (WP)
- Polynomial greatest common divisor (WP), the free …
- Heuristic (WP)
- Differentiation (WP)
- Integration (WP)
- Risch algorithm (WP)
- Elementary function (WP)
- Abramowitz and Stegun: Handbook of Mathematical Functions
- Elliptic function (WP)
- Differential equation (WP)
- Meijer G-function (WP)
- Cylindrical algebraic decomposition (WP)
- Integer programming (WP)
- Special functions (WP)
- Laplace transform (WP)
- Fourier transform (WP)
- Root-finding algorithm (WP)
- Karatsuba algorithm (WP)
- Linear programming (WP)
- Lenstra–Lenstra–Lovász lattice basis reduction algorithm (WP)
- Knapsack problem (WP)
- Wolfram Workbench: State-of-the-Art IDE
- The Wolfram Functions Site
- Computable Document Format (CDF) for Interactive Content
- Wolfram gridMathematica
- Microkernel Pattern (WP)
- Spanning Tree Protocol (WP)
- Convex hull (WP)
- Wolfram Technology Conference 2013
- MathGroup Archive – Wolfram Research
- Math Forum Discussions – comp.soft-sys.math.mathematica
- Mathematica Stack Exchange
- Integral Calculator: Wolfram Mathematica Online Integrator
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Excellent moderation of a knowledgeable but potential challenging guest to lead into the right level of difficulty to keep the audience entertained. Enjoyed especially the question and answer for industrial application.
One question in this context comes to my mind. Why should pupils at School still be punished by math if software to solve the problem is available for years.
;-) think for themselfes!
This is a good question. Obviously, you still need math — this was exemplified nicely by my not understanding many of the things Daniel talked about :-) But I think math education should change, from the mechanics of doing calculations to more understanding and concepts. However, this is true generally for most topics in education, since computers can help with many of them. As I see it, education is too slow to pick up these trends.
Thanks Markus for the great introduction to Mathematica. I’ve been meaning to check it for awhile and will likely be brushing up against it in the near future.
In regards to your June 26 comment, I recently heard a story of a high school student who programmed their calculator using BASIC to solve algebra and trigonometric problems. He wrote out the source code on his tests and just computed the results. He failed the tests because, without ‘showing work’, the teacher could not be sure he understood the problems, haha. Hopefully things have changed since then. But I concur, there’s some backwards thinking in mathematics primary education. Maybe that will change as millennials become teachers.
Right. Like everything, education seems to be a generation problem, where the old guys have to die to make the space for new ideas :-)
There is an iniative, computer based math, to fix the math education by Conrad Wolfram (brother of Stephen Wolfram) https://www.computerbasedmath.org/
The Flatter button for this episode is not working.
It is red, labeled with ‘error ‘, and not klickable.
Thank you Matthias. The issue is fixed now.
I can’t wait for Wolfram Language being relased! Could you make an interview on Wolfram Language?
I am not planning on it. It looks too much like “Mathematica in the cloud” to me for an additional episode.
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Thanks a lot, Markus and Daniel. That was more interesting for me than you might have imagined. But I must admit that I studied math in the 1980s and even remember the L3 algorithm from my university study. But I didn’t know about the newer developments that Daniel mentioned.
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