The Book of Psalms referred to as Psalms, the Psalter or "the Psalms", is the first book of the Ketuvim, the third section of the Hebrew Bible, thus a book of the Christian Old Testament. The title is derived from the Greek translation, ψαλμοί, meaning "instrumental music" and, by extension, "the words accompanying the music"; the book is an anthology of individual psalms, with 150 in the Jewish and Western Christian tradition and more in the Eastern Christian churches. Many are linked to the name of David; the Book of Psalms is divided into five sections, each closing with a doxology —these divisions were introduced by the final editors to imitate the five-fold division of the Torah: Book 1 Book 2 Book 3 Book 4 Book 5 Many psalms have individual superscriptions, ranging from lengthy comments to a single word. Over a third appear to be musical directions, addressed to the "leader" or "choirmaster", including such statements as "with stringed instruments" and "according to lilies". Others appear to be references to types of musical composition, such as "A psalm" and "Song", or directions regarding the occasion for using the psalm.

Many carry the names of individuals, the most common being of David, thirteen of these relate explicitly to incidents in the king's life. Others named include Asaph, the sons of Korah, Moses, Ethan the Ezrahite, Heman the Ezrahite; the LXX, the Peshitta, the Latin Vulgate each associate several Psalms with Haggai and Zechariah. The LXX attributes several Psalms to Ezekiel and Jeremiah. Psalms are identified by a sequence number preceded by the abbreviation "Ps." Numbering of the Psalms differs -- by one, see table -- between Greek manuscripts. Protestant translations use the Hebrew numbering, but other Christian traditions vary: Roman Catholic official liturgical texts, such as the Roman Missal, use the Greek numbering Modern Roman Catholic translations use the Hebrew numbering Eastern Orthodox and Eastern Catholic translations use the Greek numbering For the remainder of this article, the Hebrew numbering is used, unless otherwise noted; the variance between Massorah and Septuagint texts in this numeration is enough due to a gradual neglect of the original poetic form of the Psalms.

It is admitted that Pss. 9 and 10 were a single acrostic poem. Pss. 42 and 43 are shown by identity of subject, of metrical structure and of refrain, to be three strophes of one and the same poem. The Hebrew text is correct in counting as one Ps. 146 and Ps. 147. Liturgical usage would seem to have split up these and several other psalms. Zenner combines into. 1, 2, 3, 4. A choral ode would seem to have been the original form of Pss. 14 and 70. The two strophes and the epode are Ps. 14. It is noteworthy that, on the breaking up of the original ode, each portion crept twice into the Psalter: Ps. 14 = 53, Ps. 70 = 40:14–18. Other such duplicated portions of psalms are Ps. 108:2–6 = Ps. 57:8–12. This loss of the original form of some of the psalms is allowed by the Biblical Commission to have been due to liturgical practices, neglect by copyists, or other causes; the Septuagint, present in Eastern Orthodox churches, includes a Psalm 151. Some versions of the Peshitta include Psalms 152–155. There are the Psalms of Solomon, which are a further 18 psalms of Jewish origin originally written in Hebrew, but surviving only in Greek and Syriac translation.

These and other indications suggest that the current Western Christian and Jewish collection of 150 psalms were selected from a wider set. Hermann Gunkel's pioneering form-critical work on the psalms sought to provide a new and meaningful context in which to interpret individual psalms—not by looking at their literary context within the Psalter, but by bringing together psalms of the same genre from throughout the Psalter. Gunkel divided the psalms into five primary types: Hymns, songs of praise for God's work in creation or history, they open with a call to praise, describe the motivation for praise, conclude with a repetition of the call. Two sub-categories are "enthronement psalms", celebrating the enthronement of Yahweh as king, Zion psalms, glorifying Mount Zion, God's dwelling-place in Jerusalem. Gunkel described a special subset of "eschatological hymns" which includes themes of future restoration or of judgment. Communal laments. Both communal and individual laments but not always include the following elements: address to God, description of suffering, cursing of t

Carl Barnett Allendoerfer was an American mathematician in the mid-twentieth century, known for his work in topology and mathematics education. Allendoerfer was born in the son of a prominent banker, he graduated from Haverford College in 1932 and attended New College, Oxford as a Rhodes Scholar, 1932-1934. He received his Ph. D. in mathematics from Princeton University in 1937. Allendoerfer taught at Haverford College in the mid-1940s where he became known for work with André Weil on the Gauss–Bonnet theorem, an important theorem in differential geometry, he continued his studies of differential geometry at the Institute for Advanced Study. In 1951, he became professor and chair of the Mathematics Department at the University of Washington, where he is known for establishing the Summer Mathematics Institute for High School Teachers. Allendoerfer was president of the Mathematical Association of America and editor of its monthly journal. In 1966 he won a Lester R. Ford Award. In 1972, he received the MAA's Award for Distinguished Service to Mathematics.

After his death, the MAA established the Carl B. Allendoerfer Award, given each year for "expository excellence published in Mathematics Magazine." Allendoerfer is known as a proponent of the New Math movement in the 1950s and 1960s, which sought to improve American primary and secondary mathematics education by teaching abstract concepts like set theory early in the curriculum. Allendoerfer was a member of Commission on Mathematics of the College Entrance Examination Board whose 1959 report Program for College Preparatory Mathematics outlined many concepts of the New Math; the commission and report were criticized by some for emphasizing pure mathematics in place of more traditional and practical considerations like arithmetic. Allendoerfer was the author, with Cletus Oakley, of several prominent mathematics textbooks used in the 1950s and 1960s, he was author of a series of math films. Allendoerfer, Carl B. & Oakley, Cletus O.. Principles of Mathematics. McGraw-Hill. Allendoerfer, Carl B. & Oakley, Cletus O..

Fundamentals of Freshman Mathematics. McGraw-Hill. Allendoerfer, Carl B.. Mathematics for Parents. MacMillan. Allendoerfer, Carl B. & Oakely, Cletus O.. Fundamentals of College Algebra. McGraw-Hill. Allendoerfer, Carl B.. Principles of Arithmetic and Geometry for Elementary School Teachers. MacMillan. Allendoerfer, Carl B.. Calculus of Several Variables and Differentiable Manifolds. Macmillan. Allendoerfer, Carl B. Oakley, Cletus O. & Kerr, Donald R.. Elementary Functions. McGraw-Hill. Allendoerfer produced the following films for Ward's Natural Science in Rochester, New York: Cycloidal Curves or Tales from Wanklenberg Woods; the Gauss-Bonnet Theorem Geometric Concepts or How to Get Somewhere with Rigid Motion and Uniform Stretches Area and Pi or How to Measure What There Is Geometric Transformations Equivalent Sets Mathematics Association of America Carl B. Allendoerfer Award

The 2019 Batanes earthquake was a magnitude 5.9 magnitude earthquake which struck Batanes, Philippines on July 27, 2019. It was preceded by a 5.4 magnitude foreshock. Nine people were killed by the combined effects of the earthquakes; the main shock of the 2019 Batanes earthquake was the 5.9 magnitude earthquake which had a depth of focus of 43 kilometers. The Philippine Institute of Volcanology and Seismology earlier recorded the tectonic earthquake as a magnitude 6.4 but revised their records. The earthquake occurred at 7:38 a.m. on July 2019 near Itbayat, Batanes. A noted foreshock of the earthquake was the magnitude 5.4 earthquake which struck the same town at 4:16 a.m.. It had a depth of focus of 12 kilometers One of the stronger aftershocks was a magnitude 5.8 earthquake which occurred at 9:24 a.m.. According to the PHIVOLCS Earthquake Intensity Scale, the earthquake was most felt in the town of Itbayat, Batanes at Intensity VII while the other towns of the same province reported a lesser intensity.

According to the United States Geological Survey, the earthquake had a maximum intensity of VI or has caused "Strong" shaking according to the Modified Mercalli intensity scale. No tsunami warning was raised following the main earthquake. At least 9 people were killed and 60 injured due to the earthquakes; the historic, Santa Maria de Mayan Church in Itbayat, built in 1888, sustained heavy damage from the earthquake with its bell tower falling off. Several stone houses, two schools, two health centers were damaged. According to the National Disaster Risk Reduction and Management Council, 911 families or 2,963 individuals were affected by the Batanes earthquakes; the Department of Public Works and Highways on their part made an estimate that the damage caused by the earthquake costed at least ₱292 million. President Rodrigo Duterte made a visit to Batanes on July 28, 2019 to check the situation in the province, he made a pledge for the government to release ₱40 million for the construction of a new clinic with Duterte citing the uncertainty regarding the integrity of the still functional Itbayat District Hospital which sustained minimal cracks.

Vice President Leni Robredo visited the island province. The NDRRMC provided tents and other relief goods to people displaced due to earthquake via C-130. Other provinces and private organizations provided aid to Batanes; the agency shipped construction materials for new houses meant for the victims of the earthquake. By August 1, 2019, the whole province of Batanes has been placed under a state of calamity. China through its embassy in Manila donated ₱10 million as aid following the earthquake. 2019 Luzon earthquake 2019 Visayas earthquake Manila Trench Philippine Trench The International Seismological Centre has a bibliography and/or authoritative data for this event