Typical Comic-book `bang’ mark [Image from vectorstock ].
which is approximately 
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Posts Tagged 'Algebra'
Bang! Bang! Bang! Explosively Large Numbers
Published March 26, 2020 Occasional Leave a CommentTags: Algebra, Number Theory
The Rambling Roots of Wilkinson’s Polynomial
Published January 30, 2020 Occasional Leave a CommentTags: Algebra, Numerical Analysis
Finding the roots of polynomials has occupied mathematicians for many centuries. For equations up to fourth order, there are algebraic expressions for the roots. For higher order equations, many excellent numerical methods are available, but the results are not always reliable.
A 10th-order polynomial (blue) and a slightly perturbed version, with the coefficient of 
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Adjoints of Vector Operators
Published January 23, 2020 Occasional Leave a CommentTags: Algebra, Analysis
We take a fresh look at the vector differential operators grad, div and curl. There are many vector identities relating these. In particular, there are two combinations that always yield zero results:
Question: Is there a connection between these identities?
Some Fundamental Theorems of Maths
Published October 24, 2019 Occasional Leave a CommentTags: Algebra, Analysis, Geometry
Every branch of mathematics has key results that are so
important that they are dubbed fundamental theorems.
The customary view of mathematical research is that of establishing the truth of propositions or theorems by rigorous deduction from axioms and definitions. Mathematics is founded upon axioms, basic assumptions that are taken as true. Logical reasoning is then used to deduce the consequences of those axioms with each major result designated as a theorem.
As each new theorem is proved, it provides a basis for the establishment of further results. The most important and fruitful theorem in each area of maths is often named as the fundamental theorem of that area. Thus, we have the fundamental theorems of arithmetic, algebra and so on. For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus.
The Brief and Tragic Life of Évariste Galois
Published August 15, 2019 Irish Times Leave a CommentTags: Algebra, Group Theory, History
On the morning of 30 May 1832 a young man stood twenty-five paces from his friend. Both men fired, but only one pistol was loaded. Évariste Galois, a twenty year old mathematical genius, fell to the ground. The cause of Galois’s death is veiled in mystery and speculation. Whether both men loved the same woman or had irreconcilable political differences is unclear. But Galois was abandoned, mortally wounded, on the duelling ground at Gentilly, just south of Paris. By noon the next day he was dead [TM169 or search for “Galois” at irishtimes.com].
French postage stamp issued in 1984.
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The Many Modern Uses of Quaternions
Published October 4, 2018 Irish Times 1 CommentTags: Algebra, Hamilton
The story of William Rowan Hamilton’s discovery of new four-dimensional numbers called quaternions is familiar. The solution of a problem that had bothered him for years occurred to him in a flash of insight as he walked along the Royal Canal in Dublin. But this Eureka moment did not arise spontaneously: it was the result of years of intense effort. The great French mathematician Henri Poincaré also described how sudden inspiration occurs unexpectedly, but always following a period of concentrated research [TM148, or search for “thatsmaths” at irishtimes.com].
The Flight of the Bumble Bee
Published August 23, 2018 Occasional Leave a CommentTags: Algebra, Puzzles
Alice and Bob, initially a distance l apart, walk towards each other, each at a speed w. A bumble bee flies from the nose of one to the nose of the other and back again, repeating this zig-zag flight at speed f until Alice and Bob meet. How far does the bumble bee fly?
