The second decade in the life of the Department began with an explosion in the number of Master's and doctoral students, and with a corresponding expansion of the faculty. Thus in 1972 there were 15 professors and 26 Master's and doctoral students, of whom seven were Latin American students in a scholarship program of the OEA for outstanding Latin American youth for graduate studies in centers of academic excellence in Latin America. Unfortunately the program was later canceled.
The áreas of mathematics covered were:
- General topology (Adalberto García-Máynez and John Hunt)
- Algebraic and differential topology (José Ádem, J. Alexander, Samuel Peder and Samuel Gitler)
- Ordinary differential equations (Carlos Ímaz)
- Partial differential equations and mathematical physics (A. Plis)
- Probability (Luis Gorostiza)
- Complex analysis (Enrique Ramírez de Arellano)
- Manifolds (Eugenio Filloy and Juan José Rivaud)
- Dinamical systems (A. Verjovsky)
- Differential geometry (H. Hernández)
- Combinatorics (O. García)
The Master's program had great success, as it placed special emphasis on a general and solid preparation of its graduates, many of whom joined the faculties of universities around the country, continuing other doctoral studies.
In 1972 the Department Chairman was Samuel Gitler. As of then, the Department was completely consolidated, having earned an unparalleled reputation as a center for research and advanced studies, fully honoring the name of the institution.
Between 1972 and 1973, 14 students obtained their Master's degree. For the purpose of attracting the international scene, during one or two years, the Solomon Lefschetz position was created in 1974 for recent doctoral graduates who showed notable qualities for developing research, in honor of the activities of a famous researcher in the development of mathematics in Mexico. Thus one or two young researchers in diverse branches of mathematics began to take part each year. When the salaries were adequate, it was possible to hire brilliant youth, some of whom remained in the Department for many years.
During the period 1970-1976, at the request of the Ministry of Public Education, the Department took charge of writing free mathematics textbooks for elementary education. This was a great challenge as none of the professors of the department had experience in elementary education other than with their own children. The textbooks which appeared from this effort were excellent, requiring working on and improving over a long period. However, the governmental custom of changing textbooks every six years did not allow the books to be used for many years.
Based on this experience, several professors of the Department, especially Ímaz and Filloy, decided to devote themselves entirely to so-called "mathematics for education"; after several years they succeeded in creating the Section and later the Department of Mathematics for Education.
Between 1976 and 1977 there joined the Department Saul Hahn Goldberg in partial differential equations, Horacio Tapia in algebraic geometry, and, on sabbatical Sevín Recillas, also in algebraic geometry. The researchers who held the Solomon Lefschetz Chair were Saul Jekel in topology and Walter Schachermayer in analysis; Schachermayer recently won one of the most distinguished and best paying awards in Austria. In this period, the number of graduates increased to 67.
In 1977 a summer Master's program was started, offering intensive courses to professors and students in outlying regions who could not attend the regular Mastser's courses. The summer studies were complemented during the year with studies directed by the professors of the Department in short visits. This program was developed with four students from Jalapa, Veracruz.
Around 1977-1978, Enrique Antoniano in algebraic topology, Shirley Bromberg in análisis and José A. Vargas in algebra joined as associate professors; the two former were graduates of the Department. As one-year visiting professors there were Francisco González Acuña (UNAM) in knot theory and W. Szymanski (Poland) in functional analysis. Alfonso Castro (Colombia) in nonlinear differential equations occupied the Lefschetz Chair. At that time 27 courses and seminars were offered.
In 1978 the Solomon Lefschetz Conferences began, yearly events to which the most eminent contemporary mathematicians were invited to give a series of three talks, with the aim of keeping the researchers of the Cinvestav up-to-date on the most recent work in their specialty. Among the participating speakers there were five mathematicians who received the Fields Medal, awarded by the International Mathematical Union every four years since 1932 to persons under 40. This is as prestigious as, or even more so, than the Nobel Prizes, which do not include mathematics. The Fields medalists who visited the Cinvestav are: Michael Atiyah, John Milnor, Enrico Bombieri, David Mumford, and René Thom.
From 1979, the Department organized the Mathematics Colloquia every two years, lasting three weeks, during which courses were offered at different levels. The professors responsible for the courses were asked to write the notes beforehand, which gave rise to a good collection of course notes which in some cases became books. Also, general conferences about mathematics were given daily. Another important activity was the Research Workshops in several specialties, in which top-line mathematics professors were joined up with Bachelor's, Master's and doctoral students from around the country. These Colloquia gave the Department an excellent opportunity to establish contact with students and professors in outlying regions.
Collaborating as a teacher in these Colloquia meant a great effort, which the participants made with pleasure. Unfortunately, the holding of the Colloquia was affected by the lack of financial support from Conacyt and the Cinvestav. Also, when the system of "academic output bonuses" was established, this effort was not counted in the point system. For these reasons, the members of the Department lost interest in the Colloquia bit by bit and only nine of them could be held.
In the academic year 1979-1980 Luis Astey joined the faculty in algebraic topology and Onésimo Hernández-Lerma in stochastic processes; in recent decades Hernández-Lerma received the National Science and Art Award for the work he did in the Department. The Lefschetz Chair was held by R. M. Porter in complex variables.There were 15 visiting professors for more or less short periods. In 1980-1981, R. M. Porter became an Associate Professor and D. Gallo (U.S.) in complex variables and X. Benveniste (France) in algebraic geometry came as visitors in the Lefschetz Chair.
In summary, in this period 50 students obtained their Master's degree and five their doctorate. The scientific production of the researchers kept increasing to over 120 articles in the best journals of the field. A yearly exchange with the London Royal Society was established, making possible joint research with Liverpool, Cambridge, Oxford, Manchester y Edinburgh Universities.
Likewise, the yearly exchange with the Polish Academy of Science continued, thanks to which professors from Warsaw and Krakow Universities visited the Department. The first of several yearly visits of Tomasz Bojdecki was in 1976-1977. In Mexico he wrote the book "Teoría General de Procesos e Integración Estocástica" (General Theory of Stochastic and Integration Processes), published by the Mexican Mathematical Society. An exchange was started with the National Fishing Council of Brazil and with the following institutions: Institute of Pure and Applied de Mathematics (IMPA), Catholic Pontifical University of Rio (PUC), University of Sao Paulo, and Campiñas University. Likewise, an agreement with the Centre National de la Recherche Scientifique (CNRS) of France allowed exchanges with the Universities of París and Grenoble and with the Laboratoire d'Analyse Numérique. A fruitful exchange was held with the United States through visits by researchers to the Cinvestav and visits by members of the Department to the universities Princeton, Berkeley, Los Angeles, Massachusetts Institute of Technology (MIT), Harvard, Chicago, and Northwestern, among others.
Although the situation seemed to be going well, economic conditions in the country began to become problems which the Cinvestav as well as the Department would have to face.