# Cornell Mathematics Doctorates, 1960-1969.

The sixties are a period of extraordinary growth at Cornell and in US higher education in general. It is also the period of the Vietnam War protests on Campuses and of the racial tensions that led to the occupation of Willard Straight in 1969.

Before 1960, 161 Ph.D.s were awarded in mathematics at Cornell. Between 1940 and 1959, the average number of doctorates was a very steady 3 per year.

Seventy three Mathematics Ph.D.s were awarded at Cornell in the sixties, twenty one during the first half of the decade and fifty two during the second half. Eight Ph.D.s were earned by women. The year 1965 is the first in which more than 10 doctorates wee awarded. Twenty two faculty supervised at least one Ph.D. during this period. The most active were Anil Nerode (11), Peter Hilton and Alex F.T.W. Rosenberg (6), Jack Kiefer (5) Israel Berstein, Wolfgang Fuchs and Gerald Sacks (4). Remarkably, Sacks is also one of the students who received their Ph.D. during this period.

### 1960 (3 doctorates)

### Martin Arkowitz

Title: The Generalized Whitehead Product. Advisor: Peter Hilton and Paul Olum. Career: Dartmouth College.

### Alan Gustave Konheim

Title: Some Properties of a Class of Finite Trigonometric Sums. Advisor: Mark Kac. Career: IBM; Computer Sciences at University of California Santa Barbara.

### Samuel Kotz

Title: Exponential Bounds for the Probability of Error in Discrete Memoryless Channels. Advisor: Jacob Wolfowitz. Career: University of Toronto; Temple University; University of Maryland; Operations Research Department at George Washington University. Fellow of the Institute of Mathematical Statistics and of the Royal Statistical Society.

### 1961 (3 doctorates)

### Roger David Joseph

Title: Contribution to Perceptron Theory. Advisor: Mark Kac. Career: unknown.

### Shing-Meng Lee

Title: On a Two-Parameter Family of Summation Methods. Advisor: Ralph Agnew. Career: Taiwan, National Tsing Hua University.

### Gerald Enoch Sacks

Title: On Suborderings of Degrees of Recursive Insolvability. Advisor: John Barkley Rosser. Career: Cornell, Massachusetts Institute of Technology; Harvard University. Supervised over 30 Ph.D.s and has over 500 mathematical descendants. Speaker at the 1970 International Congress in Nice. The Sacks Prize is awarded annually by the Association for Symbolic Logic for the most outstanding doctoral dissertation in mathematical logic.

### No doctorate awarded in 1962.

### 1963 (6 doctorates)

### Charles Arnold Berger

Title: Normal Dilations. Advisor: Morris Schreiber. Career: Lehman College, City University of New York.

### Gordon Elliott Brown

Title: On Commutators in Certain Lie Algebras. Advisor: Israel N. Herstein. Career: University of Colorado, Boulder.

### Frans Martin Djorup

Title: On the Operator Equation AX=XB. Advisor: Morris Schreiber. Career: University of Illinois, Urbana Champaign; Institute of Defense Analyses.

### David Stanley Newman

Title: On the Exact Calculation of the Partition Function of one dimensional Systems. Advisor: Mark Kac. Career: Boeing Company, Aerospace Group.

### David Freeman

Title: Tabulation of Transcendental Functions by the Continued Fraction of Gauss. Advisor: John Barkley Rosser. Career: Computer Industry.

### Gerald Joseph Porter

Title: Higher Order Whitehead Products. Advisor: William Browder Career: University of Pennsylvania.

### 1964 (9 doctorates)

### Bruce Alan Barnes

Title: Modular Annihilator Algebras. Advisor: Robert A. Bonic. Career: University of Oregon.

### Lawrence David Brown

Title: On the Admissibility of Invariant Estimators of Location Parameters.

Advisor: Jack Kiefer. Career: University of California Berkeley; Cornell; Rutgers University; Wharton School, University of Pennsylvania; President of the Institute for Mathematical Statistics; Fellow of the American Academy of Arts and Sciences; member of the National Academy of Sciences. Speaker at the 2002 International Congress of Mathematicians in Beijing.

### Ross Hunter Cornell

Title: Commutator Product in Function Spaces. Advisor: Israel Berstein. Career: Wellesley College.

### Paul Stephen Green

Title: KSC*(X), An Extraordinary Cohomology Theory. Advisor: Israel Berstein and William Browder. Career: University of Maryland.

### Chia-Hui Shih

Title: On Secondary Operations in Homotopy and Homology. Advisor: Peter Hilton. Career: National Taiwan University.

### Jerrold Norman Siegel

Title: Generalized Homology with Continuous Coefficients. Advisor: Israel Berstein. Career: University of Missouri, St. Louis.

### Walter William Whitman

Title: Some Strong Laws for Random Walks and Brownian Motion. Advisor: Frank Spitzer. Career: unknown.

### Carol Euwema Wolf

Title: Partial Recursive Operators on Recursively Closed Sets. Advisor: Anil Nerode. Career: Computer Science at Pace University.

### Yuen-Fat Wong

Title: Pi-Manifolds and Homotopy Type of Manifolds. Advisor: William Browder. Career: DePaul University.

### 1965 (12 doctorates)

### Clark Tabor Benson

Title: Generalized Quadrangles and (B,N) Pairs. Advisor: Walter Feit. Career: University of Arizona, National Security Agency.

### Graham Cameron Driscoll

Title: Contributions to Metarecursion Theory. Advisor: Gerald Sacks. Career: IBM.

### Louise Schmir Hay

Title: Topics in Recursion Theory: 1. The Co-simple Isols 2. Creative Sets. Advisor: Anil Nerode. Career: Mount Holyoke; University of Illinois at Chicago. Founding member of the Association for Women in Mathematics. The AWM has established the Louise Hay Award for Contributions to Mathematics Education.

### Marcel Herzog

Title: On Finite Groups with a Subgroup Containing the Normalizer of Each of Its Nonunit Elements. Advisor: Walter Feit. Career: Tel Aviv University.

### Sol Kaufman

Title: Asymptotic Efficiency of the Maximum Likelihood Estimator. Advisor: Jacob Wolfowitz. Career: Cornell Aeronautical Laboratory.

### Alfred Berry Manaster

Title: Higher Order Indecomposable Isols. Advisor: Anil Nerode. Career: University of California, San Diego.

### Alan McConnell

Title: On Amitsur Cohomology. Advisor: Alex F.T.W. Rosenberg. Career: Howard University.

### John Crawford Mineka

Title: The Existence and Uniqueness of Positive Solutions to the Wiener-Hopf Equation with Positive Kernel. Advisor: Frank Spitzer. Career: Lehman College of the the City University of New York.

### Irwin Samuel Pressman

Title: A Comparison of Two Functors in Homological Algebra. Advisor: Peter Hilton. Career: Carleton University.

### David Edward Schroer

Title: Church-Rosser Theorem. Advisor: Anil Nerode and John Barkley Rosser. Career: Adelphi University.

### Alan Schumitzky

Title: Wiman-Valiron Theory for Entire Functions of Several Variables. Advisor: Wolfgang Fuchs. Career: University of Southern California.

### Kenneth Gordon Whyburn

Title: Operational Calculus and Related Topics. Advisor: Gilbert Hunt. Career: University of Washington; Lawyer specializing in Tax law in San Francisco.

### 1966 (12 doctorates)

### Lindsay Nathan Childs

Title: A Galois Theory for Separable Algebras. Advisor: Alex F.T.W. Rosenberg. Career: State University of New York at Albany.

### David Drasin

Title: An Integral Tauberian Theorem and Other Topics. Advisor: Wolfgang Fuchs. Career: Purdue University.

### Serge Dubuc

Title: Topological Convex Spaces. Advisor: James Eells. Career: Université de Montréal.

### Michael Fisher

Title: Singular Integrals on Hilbert Space. Advisor: Leonard Gross. Career: University of Montana.

### Gary Allen Lorden

Title: Integrated Risk of Asymptotically Bayes Sequential Tests and Some Essentially Complete Class Results. Advisor: Jack Kiefer. Career: California Institute of technology.

### James Claggett Owings

Title: Topics in Metarecursion Theory. Advisor: Gerald Sacks. Career: University of Maryland.

### Robert William Robinson

Title: The Inclusion Lattice and Degrees of Unsolvability of the Recursively Enumerable Sets. Advisor: Gerald Sacks. Career: Computer Science, University of Georgia.

### Joseph Geoffrey Rosenstein

Title: Recursive Functions of Arguments of Finite Type. Advisor: Anil Nerode. Career: Rutgers Univeristy.

### Richard Edward Schwartz

Title: Properties of Invariant Multivariate Tests. Advisor: Jack Kiefer. Career: Defense Research and Engineering.

### Linda Ruth Sons

Title: The Distribution of Values of Functions Defined by Gap Power Series. Advisor: Wolfgang Fuchs. Career: Northern Illinois University.

### Steven Karl Thomason

Title: Investigations in the Structure of the Upper Semi-lattice of Hyperdegrees. Advisor: Gerald Sacks. Career: Simon Fraser University.

### John Shu-Ping Wang

Title: On the Groups of the Homotopy Classes of the Stable Maps Between Z2-Moore spaces. Advisor: Peter Hilton. Career: Purdue University.

### 1967 (7 doctorates)

### David Sheldon Moore

Title: Topics in Asymptotic Estimation Using Order Statistics. Advisor: Jack Kiefer. Career: Purdue University; President of the American Statistical Association (1998).

### Virginia (Anne) Noonburg

Title: A Nonlinear System of Differential-Difference Equations. Advisor: Wolfgang Fuchs. Career: University of Hartford.

### Philip Olin

Title: An Almost Everywhere Direct Product. Advisor: Anil Nerode. Career: York University.

### Morris Orzech

Title: Derived Functors, a Theorem of Harrison, and the Fundamental Group. Advisor: Stephen Chase. Career: Queen’s University.

### Margaret Ann Piech

Title: A Fundamental Solution of the Parabolic Equation on Hilbert Space. Advisor: Leonard Gross. Career: University of Buffalo.

### Robert Soare

Title: Recursion Theory on Dedekind Cuts, Advisor: Anil Nerode. Career: University of Chicago. Speaker at the International Congress of Mathematicians in Helsinki in 1978.

### Yei-Chiang Wu

Title: Some Contributions to the Study of Spectral Sequences. Advisor: Peter Hilton. Career: Oakland University, Michigan.

### 1968 (14 doctorates)

### Frank David Anger

Title: Algebraic K-Theory for Projective Modules with Quadratic Form. Advisor: Stephen Chase. Career: University of Puerto Rico; NSF.

### Corwin Lee Atwood

Title: Optimal and Efficient Design of Experiments. Advisor: Jack Kiefer. Career: University of California Davis; Statwood Consulting.

### Barry Belkin

Title: Some Results in The Theory of Recurrent Random Walk. Advisor: Harry Kesten. Career: Wagner Math Finance.

### Luc Demers

Title: Homology Theories and Duality of Functors. Advisor: Peter Hilton. Career: University of Ottawa.

### Paul Christian Eklof

Title: Resolutions of Singularities in Prime Characteristic for Almost All Primes. Advisor: James Ax. Career: University of California, Irvine.

### Sidnie Dresher Feit

Title: k-mersions of Manifolds. Advisor: Israel A. Berstein. Career: Yale University.

### Gerald Seymour Garfinkel

Title: Amitsur Cohomology and an Exact Sequence Involving Pic and the Brauer Group. Advisor: Alex F.T.W. Rosenberg. Career: Oakland University; New Mexico State University; DefTec Corporation.

### Martin Mayr Guterman

Title: On ABA-Groups of Finite Order. Advisor: Alex F.T.W. Rosenberg and Daniel Gorenstein. Career: Tufts University.

### Chin-Shui Hsu

Title: Cohomology of Pro-finite Groups with Continuous Coefficients. Advisor: Alex F.T.W. Rosenberg. Career: University of Iowa.

### Manuel Lerman

Title: Recursive Functions Modulo Co-maximal Sets. Advisor: Anil Nerode. Career: University of Connecticut.

### Kalyan Kumar Mukherjea

Title: Fredholm Manifolds and Cohomology. Advisor: James Eells. Career: University of California Los Angeles, Indian Statistical Institutes in Delhi and Calcutta; Composer, Sarod player, Hindustani classical music.

### Jacob Manuel Plotkin

Title: Generic Embeddings. Advisor: Anil Nerode. Career: Michigan State University.

### Arthur T. Jr. Ryan

Title: On Age-Dependent Branching Processes. Advisor: Harry Kesten. Career: Developer of the Statistical package Minitab.

### Barbara Falkenbach Ryan

Title: Omega-Cohesive Sets. Advisor: Anil Nerode. Career: Minitab.

### 1969 (7 doctorates)

### David Earl Dobbs

Title: Cech Cohomology and a Dimension Theory for Commutative Rings. Advisor: Alex F.T.W. Rosenberg. Career: The University of Tennessee.

### Lawrence Albert Harris

Title: Schwarz's Lemma and the Maximum Principle in Infinite Dimensional Spaces. Advisor: Clifford Earle. Career: University of Kentucky.

### Richard Andrew Holley

Title: The Motion of a Heavy Particle in an Infinite One-Dimensional Diffusions. Advisor: Frank Spitzer. Career: University of Colorado, Boulder.

### Robert Gerard Jeroslow

Title: Uses of Self-Reference in Arithmetic. Advisor: Anil Nerode. Career: Carnegie Melon University; Georgia Institute of Technology.

### Nishan Kay Krikorian

Title: Manifolds of Maps. Advisor: James Eells. Career: Northeastern University.

### Howard Allen Levine

Title: Convexity and Differential Inequalities in Hilbert Space. Advisor: Larry Payne. Career: Iowa State University.

### Harold Joseph Stolberg

Title: Group Cohomologies for Hopf Algebras and Other Categories. Advisor: Stephen Chase. Career: NSF.