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Aspects of the life and legacy of American D.E. Smith are discussed. Literature attests to the high regard in which he was held by those who came into contact with him, and to the mark he made--both in his native country and beyond--as a consummate mathematical educator who began reforms in teaching during the early 1900s and as an avid historian whose monumental collection of artefacts was donated (to Columbia University) to inform students and professionals of the time, and those of future generations, about the heritage of the discipline. [ABSTRACT FROM AUTHOR]

Loathe or love them, reviews and reviewers are considered a necessary evil by some and happily embraced by others, tolerated as an intrusion en route to publication or seen as providing a valuable academic standards safety net. Almost everyone has an opinion on them. [ABSTRACT FROM AUTHOR]

Words of Frank F. Bonsall (1920-2011) on what ownership of work should mean for mathematicians--taken from a thought provoking essay published over forty years ago--are still pertinent in 21st century academia where important aspects of intellectual probity lie at the heart of research endeavours. [ABSTRACT FROM AUTHOR]

American intellectual Cassius Jackson Keyser (1862-1947) set down a personal philosophy of ideals that underpins the essential elements of aspiration and motivation all of us need for a fulfilled existence--as mathematician, as citizen, sapientia ianua vitae never ceases to apply. Here we have an intriguing dose of percipience from a notable mathematical writer and once regular commentator on the benefits available from mathematics to the human condition. [ABSTRACT FROM AUTHOR]

Is genuine individuality for staff throughout U.K. academia in general, and mathematics by association, becoming eroded? This opinion piece suggests that it is most certainly on the decline, arguing for the accommodation of a wide variety of character types to enhance a workplace now dominated by frenetic busyness and inextricably tangled up with an overbearing compliance threatening to run riot in H.E. [ABSTRACT FROM AUTHOR]

Some little-known words by David Eugene Smith--American mathematician, educator, and historian of mathematics--appeared well over a century ago. The passages presented provide an appealing general description of mathematical engagement and give a sense of the community in which it takes place, both of which resonate in our modern day tertiary sector. [ABSTRACT FROM AUTHOR]

Musings of British mathematician and logician Augustus de Morgan (1806-1871) provide a light-hearted look at particular types of character that inhabit the world of mathematics and places around it. [ABSTRACT FROM AUTHOR]

In this short Note we discuss the main context in which the constant 1/e arises (that is, in certain types of probability problems), and offer derivations of it from a pedagogic point of view. [ABSTRACT FROM AUTHOR]

This short essay marks the centenary of a paper authored by C.J. Keyser who, in pondering the various strands of a career in mathematics in 1923, raised themes that are still very much relevant to our tertiary sector--in particular, his intuitions underscore something of the ageless nature of mathematical study. [ABSTRACT FROM AUTHOR]

We state and prove a new result which involves the diagonal entries of any nth root of a general 2×2 matrix belonging to a particular class, and offer supporting examples. [ABSTRACT FROM AUTHOR]

We derive, using matrices, new classes of linear recurrence identities linking the general term of a degree three linear recurrence sequence with those of an associated ‘cohort’ sequence that differs only in its initial values. The class description is seen to recover that previously established for the so called Horadam sequence and its cohort sequence set. [ABSTRACT FROM AUTHOR]

Two outstanding thinkers and writers about mathematics each had very interesting things to say about the subject. Their words—although from bygone eras—still carry resonance today, as do those of some other mathematicians which are also included in context. [ABSTRACT FROM AUTHOR]

You aren’t the first, and you won’t be the last, so don’t fight it—accept and embrace the inexorable march of time. Praemonitus praemunitus? [ABSTRACT FROM AUTHOR]

We state and prove a condition for an identity which involves the diagonal entries of any nth root of a general 2 × 2 matrix, and develop a method for obtaining all roots through a so called generator pair of parameters defined by its eigenvalues. [ABSTRACT FROM AUTHOR]

We state, and prove by a succinct matrix method deployed previously, a result for terms of a sequence generated by a fully general (linear) fourth order recurrence equation which--being characterised by four additional independent parameters--describes a new class of highly non-linear identities. [ABSTRACT FROM AUTHOR]

While for many it is a timeless norm with no hope of resolution, not everyone accepts that mathematics and writing appear to have an unbridgeable gulf between them. [ABSTRACT FROM AUTHOR]

We derive, using matrices, new classes of linear recurrence identities linking the general term of the so called Horadam sequence with those of an associated 'cohort' sequence that differs only in its initial values. [ABSTRACT FROM AUTHOR]

Writing/speaking well--with real intent, focus and clarity--has always been an issue of the utmost importance to some of those working in academia generally, within which mathematicians are no exception. We give consideration to the conventional literature survey and other expository pieces as useful centres of an initial discussion, and develop the broader theme as referenced to two of our very best past communicators and popularisers of mathematics across both facets of dissemination--P.R. Halmos and G.-C. Rota, de facto grand seigneurs of the early modern day period. [ABSTRACT FROM AUTHOR]

The concept of iterated generating functions has existed for some time now—these are polynomials that, subject to a recursive process, continuously retain (preserve) and develop more and more lead terms whose coefficients correspond to elements of an infinite sequence. In this paper we focus on the formulation of conditions governing the preserving nature of schemes producing such polynomials, with examples provided that reveal a variety of iterated generating function behaviours. [ABSTRACT FROM AUTHOR]

We develop some recent work on interesting periodicity properties of a second order linear recurrences equence known as the Horadam sequence. Sufficient conditions for cyclicity are stated and proved, using a new generating function approach, which address both non-degenerate and degenerate characteristic root cases—through these we consolidate our knowledge of, and recover, some previously observed periodics equence behaviours which include the phenomenon of so called ‘masked’ cyclicity. [ABSTRACT FROM AUTHOR]

This essay discusses those austere aspects of Orwell’s cultivated and profound literary classic that have taken root in U.K. higher education, where the boundaries separating his fictional world from ours have already started to fall away. [ABSTRACT FROM AUTHOR]

Time spent surveying work on the so called Horadam sequence {wn}n=0∞ = {wn}0∞ = {wn(a, b; p, q)}0∞--defined by the linear recurrence wn = pwn-1 - qwn-2 in its most general form (n ≥ 2; arbitrary initial values w0 = a, w1 = b)--has identified considerable variation in the nature of results generated but also, more importantly, in the quality of papers containing them. It urges the following short opinion piece which discusses this observation and touches on some wider issues relating to research. [ABSTRACT FROM AUTHOR]

We present--as an alternative to the standard technique deployed historically--a matrix based method that delivers both of the characteristic root dependent closed forms for the general term of the celebrated Horadam sequence. [ABSTRACT FROM AUTHOR]

Using an existing matrix method developed by the authors, a non-linear recurrence identity class is formulated for terms of a quasi Fibonacci sequence which--in addition to fundamental sequence variables--is characterised by four arbitrary parameters. The possibility for further systematic re-application of the technique is also discussed and illustrated. [ABSTRACT FROM AUTHOR]

We state, and prove using matrices, two (related) linear recurrence identities for terms of the so called Horadam sequence; each result expresses the general term of the sequence as a linear combination of terms with particular initial values. First offered by A.F. Horadam himself in the 1960s, our approach to their formulation is quite different and, we believe, new. [ABSTRACT FROM AUTHOR]

We state and prove a non-linear recurrence identity for terms of the so called Ho- radam sequence, and then offer its generalisation which is available from the same methodology. We illustrate how the overarching idea may be used to sequentially produce extended versions, each in turn with an extra level of non-linearity and term index complexity. These identities can all be captured in matrix determinant form. [ABSTRACT FROM AUTHOR]

The existential hypothesis of mathematical 'genius' rests irrefutably with the af- firmative. We can't all be one of course-that sublime solopreneur in creativity--but we may still contribute to research as lesser mortals. This short essay attempts to explore what the notion means to both us and non-mathematicians. [ABSTRACT FROM AUTHOR]

We offer a formalised proof argument to establish the invariance, with respect to matrix power, of the n − 1 anti-diagonal ratios within a fixed n-dimensional tri-diagonal matrix. [ABSTRACT FROM AUTHOR]

We state and prove (first by construction, and then by induction) the invariance, with respect to matrix power, of the anti-diagonals ratio of a general 2 × 2 matrix, adding these proofs to others found previously. [ABSTRACT FROM AUTHOR]

The so called geometric mean sequence recurrence, with additional scaling variable, produces a sequence for which the general term has a known closed form. Two types of derivative sequence--comprising products of such sequence terms--are examined. In particular, the general term closed forms formulated are shown to depend strongly on a mix of three existing sequences, from which sequence growth rates are deduced and other results given. [ABSTRACT FROM AUTHOR]

We state and prove the invariance, with respect to matrix power, of both the diagonals and anti-diagonals ratio of a special case 2 × 2 matrix. The proof methodology is new, contrasting with those deployed previously in establishing anti-diagonals matrix invariants. [ABSTRACT FROM AUTHOR]

We state, and prove by a succinct matrix method, a non-linear recurrence identity class for terms of the so called Horadam sequence. A particular instance was established (in equivalent form) over half a century ago by A.F. Horadam, which provides a starting point for the discussion and an introduction to our formulation technique. [ABSTRACT FROM AUTHOR]

Mathematical aesthetic, having a variety of forms, is commonly experienced by mathematicians as a genuine reality and is available at every level of study. This short essay in hopefully moving beyond standardised hermeneutic critique attests to its authenticity through the words of some mathematical proponents, and reminds us that it should be promoted to children and students as a phenomenon that is as accessible as it is incontestable. [ABSTRACT FROM AUTHOR]

We state and prove an invariance property, with respect to matrix power, for those n - 1 immediate off-diagonal ratios of a tri-diagonal n-square matrix. Illustrative examples are given. [ABSTRACT FROM AUTHOR]

We state and prove the invariance, with respect to matrix power, of the antidiagonals ratio of a general 2 x 2 matrix. The proof methodology--utilising basic properties of a so called (two vertex) quiver--is new, and adds to others found recently. [ABSTRACT FROM AUTHOR]