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Mathematical knowledge
ADVANCE3
26, 97 (1977)
IN MATHEMATlCS
Book Reviews M. G. KARPO~, Finite Orthogonal 5’erie.s in the 1976, 250 pp. The analysis and synthesis of Boolean Walsh-Fourier series is an idea whose time has come. V. S. Huzu~e~w~, of Sir Harold Jeffreys’
Su&icient Statistics, Dekker, invariance
functions
1976,
by expansion
into
Interesting
treatment
270 pp.
the
theory.
A. R. ANDERSON, et al., The Logical F. B. Fitch, stressing deviant logics. C. BERG, AM) G. FORST, 1975, 197 pp. Beautifully analysis. The probabilistic
Design of D(gital Devices, Wiley,
Enterprise, Yale, 1975, 260
Potential Theory on Locally Compact
A Festschrift
pp.
for
Abeliun Groups, Springer,
written and accessible to anyone with connections are not explicitly stressed.
J. FANG, The IZZuro*y Infinite, Paideia, 1976, 351 pp. The author acute thinker. He brings to the limelight a host of problems which sophical establishment ignores in its unattainable quest for the kind only belong to mathematics.
a course
in functional
is a courageous and the academic philoof precision that can
S. K. C~PBELL. Flaws and FaIlacies in Statistical Thinking, Prentice-Hall, 1974. 200 pp. The author proposes as a curious novelty the notion that statistics is a branch of mathematics designed to gather arguments in favor of conclusions of which we are already privately convinced. He does not realize that this has always been the avowed purpose of statistics, and that it is what makes statistics really useful.
S. STENLUM), superb introduction
Combinators, A-Terms, and Proof Theory. Reidel, to combinatory
logic,
which
anyone
can read with
1972, gusto
184 pp. A like a novel.
J. DUSKIN, Simpiicial Methods and the Interpretation of “Triple” Cohomology, Amer. Math. Sot., 1975,139 pp. The theory of triples, and the purely combinatorial definition it leads to for very general classes of universal algebra, is probably one of the permanent contributions of category theory to mathematics. In this setting, even classical homology ‘-in the Hegelian sense. The author has done an admirable becomes clear and “necessary’ job. L. NX~ERG, Lectures on Partial 58 pp. In partial differential equations, At last he has graciously condescended beauties of this central subject, which
Differential
Equations, Amer. Math.
Louis N&&erg to give the is becoming
Sot., 1972, is “maestro di color the sanno.” public a glimpse of the glittering esoteric only by lack of adequate
6ZXpOSitiOn.S.
M. STBINBR, Mathematical Know&&e, Cornell, 1975, 164 pp. Urbane, scholarly, and unusually intelligent writing in a field ordinarily distinguished by a latter-day obscurantism, dedicated on the altar of a hallucinated precision which is as alien to philosophy ‘as writing proofs in Alcaic meter is to mathematics. GIAN-CARLO
Copyright All rights
0 1977 by Academic Press, Inc. of reproduction in any form reserved.
ISSN
ROTA EDITOR
Oool-8708
26, 97 (1977)
IN MATHEMATlCS
Book Reviews M. G. KARPO~, Finite Orthogonal 5’erie.s in the 1976, 250 pp. The analysis and synthesis of Boolean Walsh-Fourier series is an idea whose time has come. V. S. Huzu~e~w~, of Sir Harold Jeffreys’
Su&icient Statistics, Dekker, invariance
functions
1976,
by expansion
into
Interesting
treatment
270 pp.
the
theory.
A. R. ANDERSON, et al., The Logical F. B. Fitch, stressing deviant logics. C. BERG, AM) G. FORST, 1975, 197 pp. Beautifully analysis. The probabilistic
Design of D(gital Devices, Wiley,
Enterprise, Yale, 1975, 260
Potential Theory on Locally Compact
A Festschrift
pp.
for
Abeliun Groups, Springer,
written and accessible to anyone with connections are not explicitly stressed.
J. FANG, The IZZuro*y Infinite, Paideia, 1976, 351 pp. The author acute thinker. He brings to the limelight a host of problems which sophical establishment ignores in its unattainable quest for the kind only belong to mathematics.
a course
in functional
is a courageous and the academic philoof precision that can
S. K. C~PBELL. Flaws and FaIlacies in Statistical Thinking, Prentice-Hall, 1974. 200 pp. The author proposes as a curious novelty the notion that statistics is a branch of mathematics designed to gather arguments in favor of conclusions of which we are already privately convinced. He does not realize that this has always been the avowed purpose of statistics, and that it is what makes statistics really useful.
S. STENLUM), superb introduction
Combinators, A-Terms, and Proof Theory. Reidel, to combinatory
logic,
which
anyone
can read with
1972, gusto
184 pp. A like a novel.
J. DUSKIN, Simpiicial Methods and the Interpretation of “Triple” Cohomology, Amer. Math. Sot., 1975,139 pp. The theory of triples, and the purely combinatorial definition it leads to for very general classes of universal algebra, is probably one of the permanent contributions of category theory to mathematics. In this setting, even classical homology ‘-in the Hegelian sense. The author has done an admirable becomes clear and “necessary’ job. L. NX~ERG, Lectures on Partial 58 pp. In partial differential equations, At last he has graciously condescended beauties of this central subject, which
Differential
Equations, Amer. Math.
Louis N&&erg to give the is becoming
Sot., 1972, is “maestro di color the sanno.” public a glimpse of the glittering esoteric only by lack of adequate
6ZXpOSitiOn.S.
M. STBINBR, Mathematical Know&&e, Cornell, 1975, 164 pp. Urbane, scholarly, and unusually intelligent writing in a field ordinarily distinguished by a latter-day obscurantism, dedicated on the altar of a hallucinated precision which is as alien to philosophy ‘as writing proofs in Alcaic meter is to mathematics. GIAN-CARLO
Copyright All rights
0 1977 by Academic Press, Inc. of reproduction in any form reserved.
ISSN
ROTA EDITOR
Oool-8708