Annotated article by Gordon Donaldson to London England\u27s Sunday Express, 17 September 1962

Article discusses religion and politics in Canada, particulary Alberta.https://egrove.olemiss.edu/west_union_med/1000/thumbnail.jp

Making of the Scottish Prayer Book of 1637

THE history of the worship of the Scottish reformed church' begins in the 155os, at a time when the liturgical position among English -speaking reformers was quite unstable. In England the first inroads on the unreformed, Latin service had been made only a very few years earlier, with the introduction, towards the end of Henry VIII's reign, of English lessons and an English litany. Under Edward VI there came in 1548 the English Order of Communion (to be inserted in the Latin mass) and in 1549 the first Book of Common Prayer, followed in little more than three years by a second. Edward's second book was the most protestant of Anglican liturgies, but even so it was not wholly satisfactory to the growing body of puritan opinion and there were already rumours of a third instalment of reform before the king died in 1553 During Mary Tudor's reign the leftward trend continued in the congregations of English- speaking exiles on the continent. Even the more conservative among them, who -if only out of loyalty to their brethren who were being martyred in England- wished to adhere in general to the second Prayer Book of Edward VI, were not disposed to insist on the book in its entirety. A more radical faction, after some of their number had been worsted in a conflict with the `conservatives' at Frankfort, concentrated in Geneva. This party deliberately rejected the Prayer Book, and their service -book, originally composed at Frankfort and in 1556 printed for their use at Geneva, was on distinctly reformed lines

Knot Floer homology and the four-ball genus

We use the knot filtration on the Heegaard Floer complex to define an integer invariant tau(K) for knots. Like the classical signature, this invariant gives a homomorphism from the knot concordance group to Z. As such, it gives lower bounds for the slice genus (and hence also the unknotting number) of a knot; but unlike the signature, tau gives sharp bounds on the four-ball genera of torus knots. As another illustration, we calculate the invariant for several ten-crossing knots.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper17.abs.htm

High School Achievement in Maine: Where You Come From Matters More Than School Size and Expenditures

Fern Desjardins and Gordon Donaldson report on their research examining the relationship between academic achievement in Maine’s public high schools and school size, per-pupil operating costs, and socioeconomic status. Using aggregated Maine Educational Assessment (MEA) scores, their study confirmed previous research that socioeconomic status (using both family and community measures) is the most important factor associated with achievement, while school size is not a critical factor. Additionally, the authors found that per-pupil operating costs are higher in the state’s largest and smallest high schools. The authors suggest that the creation of larger districts and larger schools, as supported by recent state policies, will not necessarily mitigate inequities in student achievement resulting from family and community socioeconomic status, and may not yield the desired cost savings

Fusing Educational Reform Policy and Action: Assuring the Development of Local Leaders

School change does not happen in a vacuum. It requires initiative and leadership. Because Maine\u27s educational system features a strong local control component, successful educational change requires development of local leadership. George Marnik and Gordon Donaldson report on the Maine Academyfor School Leaders, an educational leadership development project in which they were involved. Among other things, the researchers learned that successful educational change is not likely to result from a one-size-fits-all state policy. Rather, successful reform occurs one individual at a time, one school at a time

Filtering smooth concordance classes of topologically slice knots

We propose and analyze a structure with which to organize the difference between a knot in the 3-sphere bounding a topologically embedded 2-disk in the 4-ball and it bounding a smoothly embedded disk. The n-solvable filtration of the topological knot concordance group, due to Cochran-Orr-Teichner, may be complete in the sense that any knot in the intersection of its terms may well be topologically slice. However, the natural extension of this filtration to what is called the n-solvable filtration of the smooth knot concordance group, is unsatisfactory because any topologically slice knot lies in every term of the filtration. To ameliorate this we investigate a new filtration, {B_n}, that is simultaneously a refinement of the n-solvable filtration and a generalization of notions of positivity studied by Gompf and Cochran. We show that each B_n/B_{n+1} has infinite rank. But our primary interest is in the induced filtration, {T_n}, on the subgroup, T, of knots that are topologically slice. We prove that T/T_0 is large, detected by gauge-theoretic invariants and the tau, s, and epsilon-invariants; while the non-triviliality of T_0/T_1 can be detected by certain d-invariants. All of these concordance obstructions vanish for knots in T_1. Nonetheless, going beyond this, our main result is that T_1/T_2 has positive rank. Moreover under a "weak homotopy-ribbon" condition, we show that each T_n/T_{n+1} has positive rank. These results suggest that, even among topologically slice knots, the fundamental group is responsible for a wide range of complexity.Comment: 41 pages, slightly revised introduction, minor corrections and up-dated references, this is the final version to appear in Geometry and Topolog

The concordance genus of knots

In knot concordance three genera arise naturally, g(K), g_4(K), and g_c(K): these are the classical genus, the 4-ball genus, and the concordance genus, defined to be the minimum genus among all knots concordant to K. Clearly 0 <= g_4(K) <= g_c(K) <= g(K). Casson and Nakanishi gave examples to show that g_4(K) need not equal g_c(K). We begin by reviewing and extending their results. For knots representing elements in A, the concordance group of algebraically slice knots, the relationships between these genera are less clear. Casson and Gordon's result that A is nontrivial implies that g_4(K) can be nonzero for knots in A. Gilmer proved that g_4(K) can be arbitrarily large for knots in A. We will prove that there are knots K in A with g_4(K) = 1 and g_c(K) arbitrarily large. Finally, we tabulate g_c for all prime knots with 10 crossings and, with two exceptions, all prime knots with fewer than 10 crossings. This requires the description of previously unnoticed concordances.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-1.abs.htm

Three Dimensional Gauge Theories and Monopoles

The coulomb branch of $N=4$ supersymmetric Yang-Mills gauge theories in $d=2+1$ is studied. A direct connection between gauge theories and monopole moduli spaces is presented. It is proposed that the hyper-K\"ahler metric of supersymmetric $N=4$ $SU(N)$ Yang-Mills theory is given by the charge $N$ centered moduli space of BPS monopoles in $SU(2)$. The theory is compared to $N=2$ supersymmetric Yang-Mills theory in four dimensions through compactification on a circle of the latter. It is found that rational maps are appropriate to this comparison. A BPS mass formula is also written for particles in three dimensions and strings in four dimensions.Comment: 25 page