mathematics

MATHLAB

MATHLAB is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand MATHLAB rather than just read about it. In short: MATHLAB is a computer algebra system created in 1964 by Carl Engelman at MITRE and written in Lisp. "MATHLAB 68" was introduced in 1967 and became rather popular in university environments running on DECs PDP-6 and PDP-10 under TOPS-10 or TENEX. In 1969 this version was included in the DECUS user group's library (as 10-142) as royalty-free software.

Key takeaways

MATHLAB belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect MATHLAB to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of MATHLAB from memory before moving on to harder problems.

Reference excerpt

MATHLAB is a computer algebra system created in 1964 by Carl Engelman at MITRE and written in Lisp. "MATHLAB 68" was introduced in 1967 and became rather popular in university environments running on DECs PDP-6 and PDP-10 under TOPS-10 or TENEX. In 1969 this version was included in the DECUS user group's library (as 10-142) as royalty-free software. Carl Engelman left MITRE for Symbolics where he contributed his expert knowledge in the development of Macsyma.

Features Abstract from DECUS Library Catalog:

MATHLAB is an on-line system providing machine aid for the mechanical symbolic processes encountered in analysis. It is capable of performing, automatically and symbolically, such common procedures as simplification, substitution, differentiation, polynomial factorization, indefinite integration, direct and inverse Laplace transforms, the solution of linear differential equations with constant coefficients, the solution of simultaneous linear equations, and the inversion of matrices. It also supplies fairly elaborate bookkeeping facilities appropriate to its on-line operation.

Applications MATHLAB 68 has been used to solve electrical linear circuits using an acausal modeling approach for symbolic circuit analysis. This application was developed as a plug-in for MATHLAB 68 (open-source), building on MATHLAB's linear algebra facilities (Laplace transforms, inverse Laplace transforms and linear algebra manipulation).

Print publications Engelman, Carl (1971). "The legacy of MATHLAB 68". Proceedings of the second ACM symposium on Symbolic and algebraic manipulation - SYMSAC '71. New York, NY: ACM. pp. 29–41. doi:10.1145/800204.806265. ISBN 9781450377867. S2CID 14328833.

References

Worked examples

Example 1 — a first encounter with MATHLAB

Start with the simplest possible case. Write down what MATHLAB claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to MATHLAB before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about MATHLAB ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of MATHLAB

In research: MATHLAB appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses MATHLAB in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: MATHLAB is common in secondary-school and first-year university syllabi. It links to neighbouring topics Computer algebra systems, Notebook interface, so understanding it makes those chapters shorter.
In everyday life: Look for MATHLAB outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study MATHLAB in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what MATHLAB means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain MATHLAB out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is MATHLAB in simple terms?

Why does MATHLAB matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study MATHLAB?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on MATHLAB.