When applied to vector spaces of functions ( which typically are infinite-dimensional ), dual spaces are employed for defining and studying concepts like measures, distributions, and Hilbert spaces.

When planning a visit from Bonn, where he was immersed in studying physics, his fellow mathematician and friend Hermann Minkowski joked he had to spend 10 days in quarantine before being able to visit Hilbert.

When studying inorganic compounds, one often encounters parts of the different classes of inorganic chemistry ( an organometallic compound is characterized by its coordination chemistry, and may show interesting solid state properties ).

When Beethoven was finished studying with Albrechtsberger he decided to get a few more tips and pointers, so to speak, from Haydn.

When working on a major specimen like an eagle, he would spend up to four 15-hour days, preparing, studying, and drawing it.

When she was not studying, she took independent courses from Ohio University and spent her free time casting bronzes in the school foundry.

When asked how he developed his mathematical abilities so rapidly, he replied " by studying the masters, not their pupils.

When studying axiomatic probability theory, many deep consequences follow from merely these three axioms.

When night came, they would deny her warm clothes and a fire for her bedroom to try to keep her from studying, but after they left she would take out candles, wrap herself in quilts and do mathematics.

When he was eleven, his parents sent him to the Protestant Academy at Sedan, where he spent four years studying Greek under Jacques du Rondel.

When the word " seashells " is used to refer only to the shells of marine mollusks then studying seashells is part of conchology.

When studying the whole molluscan animal is included as well as studying the shell, then the study is known as malacology ; a person who studies mollusks is known as a malacologist.

When this topic turned out not to be feasible, he switched to studying the question of Italian unification over a two-year period.

When the school's high school was founded in the late 1940s, he instituted a number of innovations in the curriculum, including teaching Talmud to boys and girls studying in classes together.

When studying the etiology of a disease, it is better to analyze incidence rather than prevalence since prevalence considers the duration of a condition rather than providing a measure of risk alone.

When Steinberg and Kincheloe wrote the first edition of Kinderculture: The Corporate Construction of Childhood in 1997 ( second edition, 2004 ) many people who made their living studying, teaching, or caring for children were not yet aware of the nature of the changes in childhood that they encountered daily.

When studying the anatomy of the human body, he did not believe that the living organisms could be explained mechanistically.

When Thalberg returned to school, he lacked the stamina to enroll in college which he felt would have required constant late-night studying and cramming for exams.

When he was 17, he moved to the United States with the intention of studying towards eventually entering medical school, but Wang changed his mind and ended up in the arts, studying film and television at California College of Arts and Crafts in Oakland.

When Shunryu had first come to Zoun-in, 8 other boys were studying there.

When about a year old he lost his sight through smallpox ; but this did not prevent him from acquiring a knowledge of Latin and Greek, and studying mathematics.

When Wüthrich joined the Bell Labs, he was put in charge of one of the first superconducting NMR spectrometers, and started studying the structure and dynamics of proteins.

When theories are studied in mathematics, they are usually expressed in some formal language and their statements are closed under application of certain procedures called rules of inference.

When it becomes necessary to distinguish these special vectors from vectors as defined in pure mathematics, they are sometimes referred to as geometric, spatial, or Euclidean vectors.

When Ulam returned to Los Alamos, his attention turned away from weapon design and toward the use of computers to investigate problems in physics and mathematics.

When the central schools were replaced by other educational institutions, Jacotot occupied the chairs of mathematics and of Roman law until the overthrow of the empire.

They include mountain climbers ( Heidi Howkins, class of 1989, the only woman to lead expeditions to both Everest and K-2 ), authors ( such as Harriet Stratemeyer Adams, class of 1914, pen name Carolyn Keene ), astronomers ( including Annie Jump Cannon, class of 1884, who developed the well-known Harvard Classification of stars based upon temperature ), screenwriters, ( including Nora Ephron, class of 1962, famous for such films as When Harry Met Sally and Sleepless in Seattle ), journalists ( Linda Wertheimer, class of 1965, Lynn Sherr, class of 1963, Diane Sawyer, class of 1967, and Cokie Roberts, class of 1964, being a few notable examples ), entrepreneurs ( including Robin Chase, class of 1980, the co-founder of ZipCar ), mathematicians ( Winifred Edgerton Merrill, class of 1883, was the first woman to ever receive a PhD in mathematics ), judges ( including Jane Bolin, class of 1928, the first African-American woman to become a judge, and current federal appeals judges Reena Raggi, Amalya Kearse, and Susan P. Graber ).

: " When calculators can do multidigit long division in a microsecond, graph complicated functions at the push of a button, and instantaneously calculate derivatives and integrals, serious questions arise about what is important in the mathematics curriculum and what it means to learn mathematics.

When choosing three vectors that must be at right angles to each other, there are two distinct solutions, so when expressing this idea in mathematics, one must remove the ambiguity of which solution is meant.

When, in 1537, the Portuguese University located in Lisbon returned to Coimbra, he moved to the re-founded University of Coimbra to teach mathematics, a post he held until 1562.

When applying the Riemann constant in sigma mathematics, or when using integrals, it is a common practice to apply the quadratic function when ascertaining the equation's alpha variable.

When Bronx Science celebrated its silver anniversary in June 1963, President John F. Kennedy hailed it as " a significant and pathfinding example of a special program devoted to the development of the student gifted in science and mathematics.

In mathematics, a generalized flag variety ( or simply flag variety ) is a homogeneous space whose points are flags in a finite-dimensional vector space V over a field F. When F is the real or complex numbers, a generalized flag variety is a smooth or complex manifold, called a real or complex flag manifold.

When Fenn was considering graduate school, he was advised to take additional mathematics courses by Henry Bent, then a chemistry professor at Harvard University.

When they had finished their task in 1738, at the invitation of the Viceroy of Peru, Godin accepted the professorship in mathematics in Lima, where he also established a course of astronomical lectures.

When cylindrical correction is needed, the mathematics used to denote the combination of spherical and cylindrical power in a lens can be notated two different ways to indicate the same correction.

Orderings of the 3-subset s of ( and the corresponding Binary numeral system | binary Vector ( mathematics and physics ) | vectors ) When the ( blue ) triples are in lex order the ( red ) vectors are in revlex order, and vice versa.

When such children go to primary school, teachers observe a significant improvement in reading, writing, mathematics, social skills and many other areas.

When he returned in 1883, he took an appointment as professor of mathematics and astronomy and director of the observatory at Washington University in St. Louis.

When Ken Anderson was a senior at Batavia High School in Batavia, Illinois, he was offered a basketball scholarship to Augustana College ( Illinois ) and given a grant for exceptionally gifted children in mathematics but while a senior at Batavia High School he wrote a letter to then-Augustana football coach Ralph Starenko asking if he " could try out for football ".

When Malcolm was 11, his father, who was a professor of mathematics and engineering at the University of Waterloo, allowed him to wander around the offices at his university, which stoked the boy's interest in reading and libraries.

When the 1929 Hebron massacre broke out, he joined the Haganah in Jerusalem, where he was studying philosophy and mathematics at the Hebrew University.

When a British soldier found that he was studying mathematics, he drove him home and released him, and told him to continue studying.