mathematics

MATH-MATIC

MATH-MATIC 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 MATH-MATIC rather than just read about it. In short: MATH-MATIC is the marketing name for the AT-3 (Algebraic Translator 3) compiler, an early programming language for the UNIVAC I and UNIVAC II. MATH-MATIC was written beginning around 1955 by a team led by Charles Katz under the direction of Grace Hopper.

Key takeaways

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

Reference excerpt

MATH-MATIC is the marketing name for the AT-3 (Algebraic Translator 3) compiler, an early programming language for the UNIVAC I and UNIVAC II. MATH-MATIC was written beginning around 1955 by a team led by Charles Katz under the direction of Grace Hopper. A preliminary manual was produced in 1957 and a final manual the following year. Syntactically, MATH-MATIC was similar to Univac's contemporaneous business-oriented language, FLOW-MATIC, differing in providing algebraic-style expressions and floating-point arithmetic, and arrays rather than record structures.

Notable features Expressions in MATH-MATIC could contain numeric exponents, including decimals and fractions, by way of a custom typewriter. MATH-MATIC programs could include inline assembler sections of ARITH-MATIC code and UNIVAC machine code. The UNIVAC I had only 1000 words of memory, and the successor UNIVAC II as little as 2000. MATH-MATIC allowed for larger programs, automatically generating code to read overlay segments from UNISERVO tape as required. The compiler attempted to avoid splitting loops across segments.

Influence In proposing the collaboration with the ACM that led to ALGOL 58, the Gesellschaft für Angewandte Mathematik und Mechanik wrote that it considered MATH-MATIC the closest available language to its own proposal. In contrast to Backus' FORTRAN, MATH-MATIC did not emphasise execution speed of compiled programs. The UNIVAC machines did not have floating-point hardware, and MATH-MATIC was translated via A-3 (ARITH-MATIC) pseudo-assembler code rather than directly to UNIVAC machine code, limiting its usefulness.

Sample program A sample MATH-MATIC program:

(2) TYPE-IN ALPHA . (2A) READ A B C SERVO 4 STORAGE A IF SENTINEL JUMP TO SENTENCE 8 . (3) READ D F SERVO 5 . (4) VARY Y 1 (0.1) 3 SENTENCE 5 THRU 6 . (5) X1 = (7*103*Y*A*SIN ALPHA)3 / (B POW D+C POW E) . (6) WRITE AND EDIT A Y D E X1 SERVO 6 . (7) JUMP TO SENTENCE 2A . (8) CLOSE-INPUT AND REWIND SENTENCE 3 . (9) CLOSE-OUTPUT SENTENCE 6 . (10) READ F G H N SERVO 4 STORAGE A IF SENTINEL JUMP TO SENTENCE 20 . (11) EXECUTE SENTENCE 3 . (12) X2 = (3 ROOT (E-G)+LOG (D+N)) / (F2.6*EXP H) . (13) WRITE EDIT F D F X2 SERVO 6 . (16) JUMP TO SENTENCE 10 . (20) STOP .

Notes

References Ash, R.; Broadwin, E.; Della Valle, V.; Greene, M.; Jenny, A.; Katz, C.; Yu, L. (1957-04-19). Preliminary Manual for MATH-MATIC and ARITH-MATIC Systems for Algebraic Translation and Compilation for UNIVAC I and II (PDF) (Technical report). Philadelphia: Remington Rand Univac. Archived from the original (PDF) on 2014-12-26. Retrieved 2016-03-19. Bemer, Robert W. (1969), A Politico-Social History of Algol (With a Chronology in the Form of a Log Book) (PDF), retrieved 2016-03-20 Knuth, Donald; Trabb Pardo, Luis (August 1976). The Early Development of Programming Languages (Technical report). Computer Science Department, School of Humanities and Sciences, Stanford University. Retrieved 2016-03-19. Sammet, Jean (1969). Programming Languages: History and Fundamentals. Prentice-Hall. pp. 132, 135–137. ISBN 978-0-13-729988-1. Univac MATH-MATIC Programming System (PDF) (Technical report). Remington Rand Univac. 1958. Retrieved 2016-03-19. "MATH-MATIC — Mathematically oriented autocode (Computer Language)". Online Historical Encyclopaedia of Programming Languages. Archived from the original on 2016-04-02. Retrieved 2016-03-20. "UNICODE — UNIVAC hybrid of FORTRAN and MATH-MATIC". Online Historical Encyclopaedia of Programming Languages. Archived from the original on 2016-04-03. Retrieved 2016-03-20.

Worked examples

Example 1 — a first encounter with MATH-MATIC

Start with the simplest possible case. Write down what MATH-MATIC 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 MATH-MATIC 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 MATH-MATIC 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 MATH-MATIC

In research: MATH-MATIC 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 MATH-MATIC 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: MATH-MATIC is common in secondary-school and first-year university syllabi. It links to neighbouring topics Numerical programming languages, Programming languages, Programming languages created in 1957, so understanding it makes those chapters shorter.
In everyday life: Look for MATH-MATIC 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 MATH-MATIC in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what MATH-MATIC 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 MATH-MATIC out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is MATH-MATIC in simple terms?

Why does MATH-MATIC 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 MATH-MATIC?

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 MATH-MATIC.