astronomy

Ted Hurley

Ted Hurley is a astronomy 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 Ted Hurley rather than just read about it. In short: Ted Hurley (born Thaddeus C. Hurley on 22 September 1944) is an Irish mathematician and retired university professor specialising in algebra, specifically in group theory, group rings, cryptography, coding theory and computer algebra.

Key takeaways

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

Reference excerpt

Ted Hurley (born Thaddeus C. Hurley on 22 September 1944) is an Irish mathematician and retired university professor specialising in algebra, specifically in group theory, group rings, cryptography, coding theory and computer algebra. In 1976, Hurley was a founding member of the Irish Mathematical Society, and he served as its inaugural secretary (1977-1979).

Early life and education Hurley was born and grew up in Tuam, Co. Galway, Ireland, to James Hurley and Bridget Walsh. He earned his BSc (1965) and MSc (1966) in mathematical science from University College Galway (UCG, now known at the University of Galway). There he won the Peel Prize in Geometry and the Sir Joseph Larmor Prize. He earned his PhD (1970) from the University of London for the thesis Representations of Some Relatively Free Groups in Power Series Rings done under Karl W. Gruenberg.

Career After positions at Imperial College London, the University of Sheffield and University College Dublin (UCD), in 1980 Hurley took up a senior position at University College Galway (later known as the National University of Ireland Galway, and now as University of Galway. He was Statutory (Senior) Lecturer in Mathematics at UCG from 1980 to 1988, Associate Professor from 1988 to 1996, and Professor of Mathematics from 1996 on. He was Head of the Department of Mathematics from 1996 to 2001 and Head of Discipline from 2001 to 2010 within the School of Mathematics. He has also been a vocal public commentator on mathematics' education, including the importance of numeracy and mathematics to our lives, in the Irish print media and has also discussed these issues on popular national radio shows. In 1976, Hurley was a founding member of the Irish Mathematical Society, and he served as its inaugural secretary (1977-1979). Over the years, he has been a vocal public commentator on mathematics’ education—including the importance of numeracy and mathematics to our lives—in the Irish print media and radio. Hurley’s work was originally mostly in group theory, specifically on structural features of infinite groups (relatively free groups, commutators and powers in groups), and also group rings. Later, his interests expanded to include algebraic coding theory and cryptography. His main early works looked at existing problems and include: (i) critically improving Philip Hall’s famous work on Stability Groups, (ii) providing the general solution to Fox’s problem on the identification of ideals in a group ring, (iii) constructing counterexamples, to the Lie Dimension subgroup conjecture which had been open for many years. Work on group rings led, to new results and structures in coding theory and in cryptography. He showed that codes, including convolutional and quantum codes, could be constructed from known algebraic structures giving unique methods for constructing these to desired type, length, rate and distance. Cryptographic algebraic schemes (quantum safe) are described in [1],[2], and methods for constructing non-separable matrices for use in information and quantum theory are described in [3].

Selected papers 2021 "Unique builders for classes of matrices Special Matrices", Hurley, Ted. Special Matrices, vol. 9, no. 1, 2021, pp. 52–65. 2018 "Coding theory: the unit-derived methodology". Hurley T., Hurley D., International Journal of Information and Coding Theory, 5 (1):55-80 2018 "Quantum error-correcting codes: the unit design strategy". Hurley T., Hurley D., Hurley B. International Journal of Information and Coding Theory, 5 (2):169-182 2017 "Solving underdetermined systems with error-correcting codes". Hurley, T. International Journal of Information and Coding Theory, 4 (4) 2014 "Cryptographic schemes, key exchange, public key". Hurley, Ted. International Journal Of Pure And Applied Mathematics, 6 (93):897-927 2014 "Algebraic Structures for Communications". Hurley, Ted (2014). Contemporary Mathematics, (611):59-78 2014 "Systems of MDS codes from units and idempotents". Hurley, Barry and Hurley, Ted (2014). Discrete Mathematics, (335):81-91 2011 "Group ring cryptography". Hurley, B., Hurley, T. (2011). Int. J. Pure Appl. Math, 69 (1):67-86 2009 "Convolutional codes from units in matrix and group rings". Hurley, T. (2009). Int. J. Pure Appl. Math, 50 (3):431-463] 2006 "Group Rings And Rings Of Matrices". Hurley T., Hurley D., International Journal of Information and Coding Theory, Vol 31 No. 3 2006, 319-335 2000 "Groups related to Fox subgroups". Hurley, T, Sehgal, S (2000). Communications In Algebra, 28 :1051-1059 1996 "The modular Fox subgroups". Hurley, T.C., Sehgal, S.K. (1996). Commun. Algebra, 24 (14):4563-4580 1991 "The Lie Dimension Subgroup Conjecture*", Thaddeus C. Hurley and Sudarshan K. Sehgal, Journal Of Algebra 143, 46-56 1990 "On the Class of the Stability Group of a Series of Subgroups", Ted Hurley. Journal of the London Mathematical Society s2-41(1) 1986 "On commutators and powers in groups II". Hurley, T.C. (1986). Arch. Math, 46 (5):385-386

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Ted Hurley

Start with the simplest possible case. Write down what Ted Hurley claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, 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 Ted Hurley 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 Ted Hurley 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 Ted Hurley

In research: Ted Hurley appears in astronomy 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 Ted Hurley 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: Ted Hurley is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1944 births, 20th-century Irish mathematicians, 21st-century Irish mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Ted Hurley 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 Ted Hurley in 20 minutes

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

Frequently asked questions

What is Ted Hurley in simple terms?

Why does Ted Hurley matter?

Because it connects several astronomy 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 Ted Hurley?

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 Ted Hurley.