astronomy

Qaiser Mushtaq

Qaiser Mushtaq 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 Qaiser Mushtaq rather than just read about it. In short: Qaiser Mushtaq (born 28 February 1954), (D.Phil.(Oxon), ASA, KIA), is a Pakistani mathematician and academic who has made numerous contributions in the field of Group theory and Semigroup. He has been vice-chancellor of The Islamia University Bahawalpur from December 2014 to December 2018.

Key takeaways

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

Reference excerpt

Qaiser Mushtaq (born 28 February 1954), (D.Phil.(Oxon), ASA, KIA), is a Pakistani mathematician and academic who has made numerous contributions in the field of Group theory and Semigroup. He has been vice-chancellor of The Islamia University Bahawalpur from December 2014 to December 2018. Mushtaq is one of the leading mathematicians and educationists in Pakistan. Through his research and writings, he has exercised a profound influence on mathematics in Pakistan. Mushtaq is an honorary full professor at the Mathematics Division of the Institute for Basic Research, Florida, US. His research contributions in the fields of group theory and Left Almost Semigroup (LA-semigroup) theory have won him recognition at both national and international levels. In Graham Higman's words, "he has laid the foundation of coset diagrams for the modular group", to study the actions of groups on various spaces and projective lines over Galois fields. This work has been cited in the Encyclopedia of Design Theory.

Biography Qaiser Mushtaq was born in Sheikhupura, Pakistan to Pir Mushtaq Ali and Begum Saghira Akhter, and belongs to the Qureshi family of Gujranwala. He is a descendant of Shah Jamal Nuri. Mushtaq married Aileen Qaiser, a senior journalist educated from the National University of Singapore and Wolfson College, Oxford. They have two daughters, Shayyan Qaiser and Zara Qaiser. He received primary education from the Convent of Jesus and Mary, Sialkot, and secondary education from Government Pilot Secondary School, Sialkot. Mushtaq studied for a certain period at Murray College till his family moved to Rawalpindi, where he studied at Gordon College. He did his MSc and M.Phil. from Quaid-i-Azam University, Islamabad. He then joined Bahauddin Zakariya University, Multan, as a lecturer for a period of one year before returning to Quaid-i-Azam University in 1979. Later, in 1980, he received the Royal Scholarship to do his D.Phil. at Wolfson College, Oxford. He was a doctoral student of Graham Higman and was awarded a doctorate in 1983 for a thesis entitled Coset Diagrams for the Modular Group. In 1990 he was at the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, as a visiting mathematician. He also worked as an associate professor at the Universiti Brunei Darussalam from 1993 to 1999, after which he returned to Pakistan. Mushtaq is a tenured professor at Quaid-i-Azam University, and a former syndicate member, Quaid-i-Azam University, Islamabad. He is also an honorary full professor at the Mathematics Division, Institute for Basic Research, Florida, US. He served as vice chancellor of The Islamia University of Bahawalpur from 19 December 2014 to December 2018.

Research in mathematics He has parametrised actions of the modular group on projective lines over Galois fields. This method has proven to be so effective and rewarding, that its wide uses can be seen in Combinatorial Group Theory, Algebraic Number Theory, and Theory of Group Graphs. His graphical technique helped to solve George Abram Miller's problem (1901) on alternating groups as homomorphic images of the modular group. He has also invented a new algebraic structure known as Locally Associative LA-semigroup, and has done some fundamental research on LA-semigroups producing some significant results in this theory. Consequently, a number of useful mathematical results have emerged which otherwise were applicable under restricted conditions only. Mushtaq has collaborated in research with the late Graham HigmanFRS (Oxford) and the late Gian-Carlo Rota (MIT). He has been an invited speaker at Oxford University, MSRI Berkeley, Harvard University, Massachusetts Institute of Technology and Southampton University; and an invited speaker at several international conferences. He has supervised, as a sole supervisor, the highest number of M.Phil. and PhD students in Pure Mathematics in Pakistan (see the Mathematics Genealogy Project). As a result, he has established a research group in Pakistan, the largest of its kind, which is producing high level original research in mathematics.

Research papers Mushtaq has over a hundred research papers to his credit. He has written and edited several books, some of which are, Mathematics: The Islamic Legacy (which received a prize from the National Book Council of Pakistan), published by UNESCO and other international publishers; A Course in Group Theory, and Discrete Lectures in Mathematics. He has also written books on topics other than mathematics. They are, Focus on Pakistan, and Pakistan: An Introduction. He was also an invited writer for the monumental book, comprising six volumes, entitled the History of Civilizations of Central Asia, published by UNESCO (translated into several foreign languages). He is also known for his analytical writings and research articles on history, mathematics, science, education, and philosophy. He has been an active opposer of the use of impact factors and citation counts of the Higher Education Commission. He led the movement against its use which he believed has damaged the growth of mathematics in Pakistan. One of his essays was published by the American Mathematical Society. The International Mathematical Union has included it in its report on the use of impact factors. Mushtaq also founded the mathematical quarterly, PakMS Newsletter, in Pakistan.

Journals and bulletins He is an editor of the Asian-European Journal of Mathematics (World Scientific). He is an associate editor of the Bulletin of the Southeast Asian Mathematical Society (Springer-Verlag). Additionally, he is an editor of the Quasigroups and Related Systems (Maldova Academy of Sciences) and the Bulletin of the Malaysian Mathematical Society, an advisory editor of the Journal of Interdisciplinary Mathematics, an associate editor of the journal Advances in Algebra and Analysis, a reviewer for the Mathematical Reviews of the American Mathematical Society (US) and the Zentrablatt fur Mathematik (Springer-Verlag, Germany).

Honours and awards

He was an overseas scholar of the Royal Commission for the Exhibition of 1851 in 1980 and a senior Fulbright Scholar in 1990. Mushtaq was elected an associate member of the International Centre for Theoretical Physics, Trieste, Italy in 1991. Mushtaq has been awarded several awards due to his contribution to mathematical sciences.

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Worked examples

Example 1 — a first encounter with Qaiser Mushtaq

Start with the simplest possible case. Write down what Qaiser Mushtaq 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 Qaiser Mushtaq 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 Qaiser Mushtaq 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 Qaiser Mushtaq

In research: Qaiser Mushtaq 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 Qaiser Mushtaq 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: Qaiser Mushtaq is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1954 births, Academic staff of Bahauddin Zakariya University, Academic staff of Quaid-i-Azam University, so understanding it makes those chapters shorter.
In everyday life: Look for Qaiser Mushtaq 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 Qaiser Mushtaq in 20 minutes

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

Frequently asked questions

What is Qaiser Mushtaq in simple terms?

Why does Qaiser Mushtaq 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 Qaiser Mushtaq?

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 Qaiser Mushtaq.