Publications

  • Elementary General Topology

    . Englewood Cliffs, N.J., 1964, 174p.

    1. Mathematical Monthly had this review in its October 1965 issue, page 923:The author of this carefully written text states in his preface that he has kept in mind especially the undergraduate students who have not yet had advanced calculus. Thus, one of his aims is to develop mathematical maturity. He has been remarkably successful in his part of the task—the rest is up to the teacher and student. The author repeatedly urges the student to try giving his own proof for each theorem before reading the one in the text. Problem sets appear sprinkled through the text, rather than at the ends of chapters. The problem material includes some development of theory; hints and partial solutions to selected problems are given after the problem sets, with an exhortation to the reader not to look at the hints unless it is absolutely necessary. An intelligent, diligent student who complies with the author’s suggestions should really develop mathematical maturity.Explanations and proofs are given in careful detail. Some material on motivation, and the origin of various concepts is included. The author starts with a general topological space (metric spaces appear in Chapter 6) because he feels it is easier for the student to give the first proofs in the general case rather than in a special case where there is much irrelevant information available. Interpretation of results for the case of the real numbers is emphasized throughout. The last three chapters discuss function spaces, nets and convergence, and Peano spaces. The text is suitable for a one-term course or a year course. The reviewer feels that this is a very good text for a first course in topology, and that this course might be at the junior level in one institution and at the graduate level in another.B. H. Arnold, Oregon State University
    2. Mathematical Reviews had this review in its April 1965 issue, # 4018, page 768:An undergraduate text with unusual precision, efficiency, and very good problems. The usual material is covered, and two fine chapters on nets and Peano spaces, respectively, are added. All concepts are well-motivated and studied to the extent practicable on this level.J. Mayer (Albuquerque, New Mexico)
  • Complex Analysis

    . Series in Pure Mathematics-Volume 9. By Moore, Theral O. and Hadlock, Edwin H.Teaneck, N.J., World Scientific, 1991, 391p.

    1. Review by K. Chandrasekhara Rao (Zbl 728:30001):This book is a self-contained, comprehensive up-to-date text for an introductory course in complex functions, covering complex numbers, complex functions, complex integration, Laurent series, poles and residues, residue calculus, Rouche’s theorem, the open mapping theorem, harmonic functions, conformal mapping, and the Riemann mapping theorem. The system of real numbers and countable sets appear in the appendix. Proofs of the Cauchy-Goursat theorem, Liouville’s theorem, the Mittag-Leffler theorem, Morera’s theorem and Weierstrass’ M-test are given with clarity and rigour. There are examples and exercises. Some of the exercises are presented below:
      • Find the radius of convergence of
        $$\sum_{n=1}^{\infty} n!z^n\ \ \ \ {\rm page\ 107}$$
      • Find the Laurent series for
        $$e^{1/x}\ \ {\rm for }\ \ |z|>\theta\ \ \ \ {\rm page\ 154}$$
      • Verify
        $$\int_0^{\infty} \sin \alpha x \frac{dx}{x(x^2 + a^2)}= \frac{\pi}{2a^{2}} (1 – e^a \alpha)\ \ \ \ {\rm page\ 193}$$
      • Prove that $$\pi \tan \pi z = \sum_{n=0}^\infty\ \frac{2z}{(n + 1/2)^2 – z^2}\ \ \ \ {\rm page\ 216}$$
      • State why there is no analytic mapping of
        $$R^2 \ {\rm onto\ the\ unit\ disc.\ page\ 372}$$

      On the whole, this textbook may be used by both undergraduate and graduate students in engineering, physics and mathematics. The printing and layout are additional attractions to the material presented in the book. Many proofs and concepts are explained using figures, especially in the chapter on conformal mapping. Compared with existing books [e.g., L. V. Ahlfors, Complex analysis, third edition, McGraw-Hill, New York, 1978; MR 80c:30001; J. B. Conway, Functions of one complex variable, Springer, New York, 1973; MR 56 #5843], the book under review contains more detail. The authors and publishers deserve our congratulations.

    2. Another review of this Book:As explained in the preface the text was written to serve both undergraduate and graduate students in engineering, physics, and mathematics. The style of Definition – Theorem – Proof is used and proofs are carefully presented in details. The content of the book is more or less standard and includes also approx. 100 pages on conformal mapping and Riemann Mapping Theorem. Harmonic functions are treated in about 40 pages. The style is clear, the authors try to choose the most economical path to arrive at results, providing readers with all details which must be omitted when the allocated time for the course is not sufficient. A lot of examples are solved in the text; a good number of exercises presented in the text will help students to apply the material explained……It is a good multipurpose book on complex analysis to have in the library.!

Journal Publications

    • (with E. H. Hadlock), “A new definition of a reduced form,” Proceedings of the American Mathematical Society, Vol. 25, No. 1, (May 1970), 105–113.
A review from Mathemical Reviews:
The authors show that every integral ternary quadratic form (positive or indefinite) with determinant d (not equal 0) is equivalent to a unique reduced form $latex f=ax^2 + by^2 + cz^2 + 2ryz + 2sxz + 2txy$ with the coefficients satisfying the following conditions. a (or -a) is the minimum nonzero integer represented by \[ |f|; t|(a,d)\ {\rm and}\ s = 0,\ {\rm or }\ t = 0\ {\rm and}\ s|(a,d); |b|, \ {\rm then}\ |c|,\ {\rm then}\ |t|\ {\rm or}\ |s|,\] are minimal subject to the prior restrictions. Conventions remove sign ambiguities, and determine whether s or t is to be zero when both possibilities occur. Three examples are given illustrating the reduction to the reduced form. D. G. James (Gottingen)
  • (with E. H. Hadlock), “A New Definition of a Reduced Binary Quadratic Form,” Journal of Natural Science and Math., Pakistan, Vol. XI, No. 2, (October 1971).
  • (with E. H. Hadlock), “Lattice points of a parabola,” Journal of Natural Science and Math., Pakistan, Vol. XVIII, No. 1, (April 1978).