• Dr. Melvin Henriksen, “Multiplicative Summability Methods and the Stone-Cech Compactification,” August 24, 1964.
• Dr. Thomas Ferguson, “Game Theory and Statistical Decisions Theory,”December 7, 1964.
• Dr. R. Khazanie, “Markov Processes,” December 12, 1964.
• Dr. Donald Stevens, “Probability,” January 8, 1965.
• Dr. John McCloskey, “The Computer Simulation of a Model for the Distribution of Individuals by Species in an Environment,” January 11, 1965.
• Dr. Galen Seever, “Non-negative Projections on c₀(X),” February 11, 1965.
• Dr. Charlotte Froese, “The Numerical Solution of Certain Two Point Boundary Condition Differential Equations,” February 19, 1965.
• Dr. A. A. Baylor, “Mathematical Models for Economics,” February 20, 1965.
• Dr. Donald Owen, “Tolerance Limits and Sampling Plans,” February 25, 1965.
• Dr. Edgar Rutter, “Ring Theory,” March 5, 1965.
• Dr. Howard Egan, "The Frattini-Subgroup and its Relation to Generalizations of Nilpotent Groups,” March 9, 1965.
• Dr. Louis Solomon, “Recent Results on Classical Groups,” March 11, 1965.
• Mr. Dalton Tarwater, “Galois' Theory of Abelian Groups,” March 15, 1965.
• Dr. Alston Householder, “The Kantorovitch and Related Inequalities,” March 16, 1965.
• Dr. M. L. Juncosa, “Monte Carlo Methods and Random Number Generation,” March 23, 1965.
• Dr. F. D. Williams, “A Hopf Construction for Homotopy-Commutative H-Spaces,” March 24, 1965.
• Dr. H. W. Davis, “The Mean Value of Almost Periodic Functions,” March 26, 1965.
• Dr. R. J. Griego, “Some Aspects of Potential Theory,” April 29, 1965.
• Dr. Ray Mines, “On a Conjecture of Harrison,” May 6, 1965.
• Pi Mu Epsilon speakers: Dr. Robert Wisner, Dr. Fred Richman, Dr. John Thomas, Jimmie Johnson, Dr. Arthur Kruse, Dr. Dorothy Daybell, and Dennis Bertholf.
• Drs. E. A. Walker, Richman, Irwin and C. Walker conducted an Algebra Seminar for faculty and students.
• The annual Holiday Symposium in Mathematics was held during the week of December 28, 1964 through January 1, 1965. Ten lectures by Mark Kac on "Probability Theory and Differential Equations" were well received by our staff and about 30 mathematicians from the Southwest.

• Dr. Mark Kac, Rockefeller Institute, New York.
• Dr. William Rosen, National Science Foundation.
• Dr. Milton Rose, Mathematics Research Division, NSF.
• Dr. Melvin Henriksen, Department Chairman, Case Institute of Technology.
• Dr. Alston Householder, Head of Mathematics Panel, Oak Ridge Institute of Nuclear Studies.

A revised sequence of courses for science majors was started this year with the cooperation of the engineering college. Some minor changes will be made next year but on the whole the new sequence seems to represent a definite improvement. A revision of this se­quence on the junior level was made and the new courses will be offered next year.
 

Several new courses were introduced to meet the needs of students and staff interests. They are: 476 - Automatic Computer Programming, 477 - Numerical Analysis, 505 - Mathematical Machine Theory, and 689 - Algebraic Number Theory. Plans for expanding the offerings in statistics and computer sciences have been discussed with a view to implementation next year. Consideration of the graduate level applied mathematics curriculum has continued but final plans await staff additions in this area.
 

The mathematics library is excellent. Over 140 current journals are subscribed to and back issues of most of these are relatively complete. A considerable expansion in journal subscriptions in statistics and computer sciences was made this year to anticipate an expansion of our program in these areas.

There is still a need for more graduate books. It will be necessary to purchase multiple copies of many of these in the future.

No major items of equipment were purchased this year. The new mathematics building might be regarded as a significant piece of equipment, inasmuch as the library and his office with its desk and blackboard is the mathematician's laboratory for research. Plans for this building, supported partially by a $210,000 NSF grant, have been completed this year.

New staff members who have been hired are: Dr. Donald Stevens, Dr. J. Mack Adams, Dr. Edgar Rutter, Dr. Louis Solomon, Dr. Frank Williams and Dr. G. S. Rogers. The members who have resigned are: Dr. Don lick and Dr. Donald Ferguson. Dr. John Giever and Dr. Edward Thorp will be on a year^’s leave of absence. Drs. Rogers, Stevens and Rutter will aid us in developing our program in sta­tistics. Dr. Adams holds a joint appointment with the Computing Center. At this writing there are at least three vacancies.

A new advisor program was set up this year. Graduate and under­graduate committees now take care of the advisees. The previous practice of assigning advisees to all staff members led to a too diffuse assignment of responsibility. The present committee is expected to provide better advising and a better advisor-advisee relationship on both the undergraduate and graduate level.

Committees on both the graduate and undergraduate level handle the problem of student recruitment and recommend students for fellowships and scholarships (such as NSF traineeships, PSL Freshman Scholarships, etc.).
 

Dr. Wisner serves as an editorial consultant for McGraw-Hill and John Wiley and Sons Publishing Companies and editor for Wadsworth Publishing Company.

Dr. Edward Gaughan participated in the Visiting Scientist Program of the New Mexico Academy of Sciences.

Dr. Ralph Crouch was a Visiting Lecturer for the Mathematical Association of America.

He was invited to lecture at the National Council of Teachers of Mathematics summer meeting.

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Our major strength still remains a close-knit, dedicated, and active staff. The new staff added for next year are of very high quality and will further strengthen the group. A fairly successful effort was made to add staff with research and teaching interest in statistics, computer science and applied mathematics, and continued efforts must and will be made. It has been gratifying to see the staff respond to the need for having committees handle part of the heavy duties.
 

Although we are still holding our own insofar as starting salaries are concerned (by necessity!) more must be done in providing a broader range of intermediate and top salaries. We can be badly hurt by losing some of our top research people and top salaries in all ranks must be increased significantly
 

The major need is for additional staff. The senior staff has re­mained relatively constant for the past two years. Most of the new staff added have been replacements for staff who are leaving or retiring. Our staff has been strengthened but not enlarged. We need at least four new staff positions next year in addition to any replacements if the increased demands on the department are to be met. So far, we have met these demands by more efficient use of staff (e.g. large sections) but these devices will not suffice indefin­itely.  Note, for example, that the total student credit hours of the department increased from 13,036 to 14,064 last year, for a percentage increase of 8.4%, despite no increase in staff. With a growing enrollment, this increase will continue.
 

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• "Index Problem for Infinite Symmetric Groups,' Dr. Edward Gaughan, Proc. Amer. Math. Soc., 1964.
• “Homologically Complete Spaces," Dr, Arthur Kruse, Portugal. Math., 1964.
• "A Note on the Partition Calculus of P. Erdos and R. Rado," Dr. Arthur Kruse, 1965.
• “Generalized Quotient Rings," Dr. Fred Richman, to appear in Proc. Math. Soc.
• “General Channels in Information Theory," Dr. Nathan Scarritt, to appear in Illinois J. Math.
• "Operators Representation Theorems," Dr. Edward Thorp (with R. Whitley), to appear in Illinois J. Math.
• "A Partial Analysis of Go,” Dr. Edward Thorp, (with W. Walden), Computer Journal 7, 1964.
• "Probability," Dr. Edward Thorp, Cosmopolitan, 1964.
• "Repeated Independent Trials and a Class of Dice Problems," Dr. Edward Thorp, Am. Math. Monthly, 1964.
• "lsometrically Isomorphic Sets,' Dr. Edward Thorp, Am. Math. Monthly, 1964.
• "The Number of Beans in a Bottle," Dr. Edward Thorp, to appear inPopular Mechanics.
• "An Attempt at Strongest Vector Topology," Dr. Edward Thorp, to appear in Amer. Math. Monthly.
• "The Number of Basic Subgroups of p-Groups," Dr. E. A. Walker (with S. Khabbaz), Acta. Math. Sci. Hung., 1964.
• "Quotient Categories and Quasi-Isomophisms of Abelian Groups," Dr. E. A. Walker, Publishing House of Hungarian Acad. of Sciences, 1964.
• "On the Number of Basic Subgroups of Abelian Torsion Groups," Dr. E. A. Walker, (with S. Khabbaz), to appear in Acta. Math. Sci. Hung.
• "Primary Abelian Groups as Modules over their Endomorphism Rings," Dr. Fred Richman and Dr. E. A. Walker, to appear in Math. Zeit.
• "A Note on the Partition Calculus of P. Erdos and R. Rado," Dr. Arthur Kruse, J. London Math. Soc., 1965.
• “Grothendieck Universes and the Super-complete Models of Shepherdson," Dr. Arthur Kruse, Composito Mathematica, to appear.
• "An Application of a Family Homotopy Extension Theorem to ANR Spaces," Dr. Arthur Kruse (with P. Liebnitz), to appear in Pac. J. of Math.

• “Weak Perfect Compactness and Generalized Adjoints,” Dr. David Arterburn, to appear J. Fur. die Reine and Augewandte Math.
• “Prewhitening, filtering and recoloring dietized trajectory data,” Dr. Alfred Carver, PSL-NMSU, 1964.
• “The k-externally Disconnected Spaces as Projectures,” Dr. Henry Cohen, Canadian J. Math., 1964.
• “Injective Envelopes of Banach Spaces,” Dr. Henry Cohen, to appear Bull. Am. Math. Soc.
• “Conditions Under Which all Bounded linear Operators are Com­pact,” Dr. Elton Lacy (with R. Whitley), to appear Math. Ann.
• “Strictly singular operators and their Conjugates,” Dr. Robert Whitley, to appear in Trans. Am. Math. Soc.
• “Conditions Under Which all the Bounded Linear Operators are Compact,” Dr. Robert Whitley (with E. Lacey), to appear in Math. Ann.
• “Operator Representation Theorem,” Dr. Robert Whitley (with E. Thorp), to appear in Ill. J. Math.
• “Projecting m onto c₀,” Dr. Robert Whitley, to appear in Am. Math. Monthly.

• “Countable Direct Sums of Torsion Complete Groups,” Dr. Fred Richman, Western Regional Meeting of the American Mathematical Society at Stanford, Regional.
• “Teaching Mathematics: A Christian Method,” Dr. Robert Wisner, Southwest Section of the Mathematical Association of America, Regional.
• “Divisibility in Matrix Semigroups,” Dr. Robert Wisner, American Mathematical Society, New York City, Regional.

• “The Generalized Adjoint of a Compact Operator,” Dr. David Arterburn, Southwest Section of M.A.A., Regional.
• “Complete Continuity Conditions on Spaces of Type CCK,” Dr. Elton Lacy, Texas Section of M.A.A., State.
• “A Winning Bet in Nevada Baccarat,” Dr. William Walden, Annual Meeting of A. Math. Soc., National.
• “Operator Representation Theorems,” Dr. Robert Whitley, Annual Meeting of Am. Math. Soc., National.

Dr. Ralph Crouch, Infinite Symmetric Groups

• Dr. R. B. Crouch, National Science Foundation, A Program of Science Development at New Mexico State University, $5,306,900
• Dr. E. D. Gaughan and Dr. R. J. Wisner, Freshman Tutorial Program in Mathewatics, $3,445
• Dr. John Irwin and Dr. Fred Richman, On the Structure of Primary Abelian Groups, $72, 863
• Dr. R. J. Wisner, Holiday Symposium. This program will cover a three-year period with a symposium being held each year. These symposia will be attended by mathematicians from all over the United States, $15,917
• Dr. R. J. Wisner, Undergraduate Research Participation Program for three years, $31,500