100-651: Brooklyn Technical High School , commonly called Brooklyn Tech and administratively designated High School 430 , is a public high school in New York City that specializes in science, technology, engineering, and mathematics . It is one of the three original specialized high schools operated by the New York City Department of Education , along with Stuyvesant High School and the Bronx High School of Science . Admission to Brooklyn Tech involves taking
200-591: A set whose elements are unspecified, of operations acting on the elements of the set, and rules that these operations must follow. The scope of algebra thus grew to include the study of algebraic structures. This object of algebra was called modern algebra or abstract algebra , as established by the influence and works of Emmy Noether . Some types of algebraic structures have useful and often fundamental properties, in many areas of mathematics. Their study became autonomous parts of algebra, and include: The study of types of algebraic structures as mathematical objects
300-469: A $ 10,000 grant and brought in the Royal National Theatre of Great Britain for student workshops, but after Alcala had done so, McCaskill repeatedly denied her access to the auditorium and gave her low performance rankings. Shortly after, Alcala left for Manhattan 's Murry Bergtraum High School , where she brought in $ 1,800 in grants for Shakespeare education; meanwhile, at Brooklyn Tech, there
400-579: A different formula (PI index) used to rank students according to their ranking preference of the majors and their current averages from freshman and sophomore year. A student with a higher PI index for their second preference if they did not get into their first, will get priority over another student with a lower average on the same major preference. Bret Stephens , an opinion columnist, wrote in The New York Times that "The success of Brooklyn Tech only casts an unflattering light on every other corner of
500-614: A foundation for all mathematics). Mathematics involves the description and manipulation of abstract objects that consist of either abstractions from nature or—in modern mathematics—purely abstract entities that are stipulated to have certain properties, called axioms . Mathematics uses pure reason to prove properties of objects, a proof consisting of a succession of applications of deductive rules to already established results. These results include previously proved theorems , axioms, and—in case of abstraction from nature—some basic properties that are considered true starting points of
600-637: A fruitful interaction between mathematics and science , to the benefit of both. Mathematical discoveries continue to be made to this very day. According to Mikhail B. Sevryuk, in the January ;2006 issue of the Bulletin of the American Mathematical Society , "The number of papers and books included in the Mathematical Reviews (MR) database since 1940 (the first year of operation of MR)
700-576: A fund-raising campaign to raise $ 10 million to support their alma mater financially through facilities upgrades, the establishment of curriculum enhancements, faculty training, and a university-type endowment . The endowment fundraiser, the first of its kind for an American public school, received front-page attention in The New York Times and sparked a friendly competition amongst the specialized high schools, with both Bronx Science and Stuyvesant announcing their own $ 10 million campaigns within weeks of
800-404: A mathematical problem. In turn, the axiomatic method allows for the study of various geometries obtained either by changing the axioms or by considering properties that do not change under specific transformations of the space . Today's subareas of geometry include: Algebra is the art of manipulating equations and formulas. Diophantus (3rd century) and al-Khwarizmi (9th century) were
900-422: A mathematical statement that is taken to be true without need of proof. If a mathematical statement has yet to be proven (or disproven), it is termed a conjecture . Through a series of rigorous arguments employing deductive reasoning , a statement that is proven to be true becomes a theorem. A specialized theorem that is mainly used to prove another theorem is called a lemma . A proven instance that forms part of
1000-402: A more general finding is termed a corollary . Numerous technical terms used in mathematics are neologisms , such as polynomial and homeomorphism . Other technical terms are words of the common language that are used in an accurate meaning that may differ slightly from their common meaning. For example, in mathematics, " or " means "one, the other or both", while, in common language, it
1100-545: A new position as an NYC Education Department senior advisor to help reduce the Absent Teacher Reserve . Throughout Asher's tenure, the school's reputation was sullied by several allegations of sexual harassment and assault of students by faculty members, resulting in the termination of Sean Shaynak (an aerospace engineering teacher hired by Asher) and the reassignment of English teacher and school newspaper advisor David Lo. Music teacher Marisa Cazanave abruptly resigned in
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#17328549200731200-535: A population mean with a given level of confidence. Because of its use of optimization , the mathematical theory of statistics overlaps with other decision sciences , such as operations research , control theory , and mathematical economics . Computational mathematics is the study of mathematical problems that are typically too large for human, numerical capacity. Numerical analysis studies methods for problems in analysis using functional analysis and approximation theory ; numerical analysis broadly includes
1300-411: A separate branch of mathematics until the seventeenth century. At the end of the 19th century, the foundational crisis in mathematics and the resulting systematization of the axiomatic method led to an explosion of new areas of mathematics. The 2020 Mathematics Subject Classification contains no less than sixty-three first-level areas. Some of these areas correspond to the older division, as
1400-424: A single unknown , which were called algebraic equations (a term still in use, although it may be ambiguous). During the 19th century, mathematicians began to use variables to represent things other than numbers (such as matrices , modular integers , and geometric transformations ), on which generalizations of arithmetic operations are often valid. The concept of algebraic structure addresses this, consisting of
1500-418: A statistical action, such as using a procedure in, for example, parameter estimation , hypothesis testing , and selecting the best . In these traditional areas of mathematical statistics , a statistical-decision problem is formulated by minimizing an objective function , like expected loss or cost , under specific constraints. For example, designing a survey often involves minimizing the cost of estimating
1600-429: A student level. Tech has a variety of community service clubs, such as Key Club , Red Cross Club, and BETA. Tech students put on a play each fall, and a musical each spring. There are two step teams, Lady Dragons and Organized C.H.A.O.S. The school has several Coordinators of Student Activities (COSA). A list of notable alumni of Brooklyn Technical High School is listed below. Brooklyn Technical High School also has
1700-689: A technical career in industry. By 1922, Dr. Colston's concept was approved by the Board of Education, and Brooklyn Technical High School opened in a converted warehouse at 49 Flatbush Avenue Extension, with 2,400 students. This location, in the shadow of the Manhattan Bridge , is the reason the school seal bears that bridge's image, rather than the more obvious symbol for the borough, the Brooklyn Bridge . Brooklyn Tech would occupy one more location before settling into its site at 29 Fort Greene Place, for which
1800-518: A unique Hall of Fame, which lists alumni who have contributed significantly to STEM . Such alumni are noted below. The Brooklyn Tech Cheerleading Squad appeared in the 1988 Spike Lee film School Daze , and a video for the movie, entitled " Da Butt ", was shot at Brooklyn Tech. Lee also used the first floor gymnasium as a shooting location for Jesus Shuttlesworth's, played by Ray Allen , Sportscenter preview in He Got Game .. School interiors for
1900-477: A wide expansion of mathematical logic, with subareas such as model theory (modeling some logical theories inside other theories), proof theory , type theory , computability theory and computational complexity theory . Although these aspects of mathematical logic were introduced before the rise of computers , their use in compiler design, formal verification , program analysis , proof assistants and other aspects of computer science , contributed in turn to
2000-703: Is Fermat's Last Theorem . This conjecture was stated in 1637 by Pierre de Fermat, but it was proved only in 1994 by Andrew Wiles , who used tools including scheme theory from algebraic geometry , category theory , and homological algebra . Another example is Goldbach's conjecture , which asserts that every even integer greater than 2 is the sum of two prime numbers . Stated in 1742 by Christian Goldbach , it remains unproven despite considerable effort. Number theory includes several subareas, including analytic number theory , algebraic number theory , geometry of numbers (method oriented), diophantine equations , and transcendence theory (problem oriented). Geometry
2100-471: Is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), analysis (the study of continuous changes), and set theory (presently used as
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#17328549200732200-602: Is based exclusively on the Specialized High Schools Admissions Test (SHSAT), open to all eighth-grade and first-time ninth-grade New York City students. The test has math (word problems and computation) and verbal (reading comprehension and grammar) sections. Of the approximately 30,000 students taking the SHSAT for September 2011 admission, with 23,085 students listing Brooklyn Tech as a choice on their application, about 1,951 offers were made (the most of any of
2300-471: Is based on the following criteria, which is cumulative: Brooklyn Tech has been considered a prestigious high school in the United States. Together with Stuyvesant High School and Bronx High School of Science , it is one of the three original Specialized High Schools of New York City , operated by the New York City Department of Education , all three of which The Washington Post cited in 2006 as among
2400-403: Is commonly used for advanced parts. Analysis is further subdivided into real analysis , where variables represent real numbers , and complex analysis , where variables represent complex numbers . Analysis includes many subareas shared by other areas of mathematics which include: Discrete mathematics, broadly speaking, is the study of individual, countable mathematical objects. An example
2500-509: Is defined by the set of all similar objects and the properties that these objects must have. For example, in Peano arithmetic , the natural numbers are defined by "zero is a number", "each number has a unique successor", "each number but zero has a unique predecessor", and some rules of reasoning. This mathematical abstraction from reality is embodied in the modern philosophy of formalism , as founded by David Hilbert around 1910. The "nature" of
2600-407: Is either ambiguous or means "one or the other but not both" (in mathematics, the latter is called " exclusive or "). Finally, many mathematical terms are common words that are used with a completely different meaning. This may lead to sentences that are correct and true mathematical assertions, but appear to be nonsense to people who do not have the required background. For example, "every free module
2700-487: Is in Babylonian mathematics that elementary arithmetic ( addition , subtraction , multiplication , and division ) first appear in the archaeological record. The Babylonians also possessed a place-value system and used a sexagesimal numeral system which is still in use today for measuring angles and time. In the 6th century BC, Greek mathematics began to emerge as a distinct discipline and some Ancient Greeks such as
2800-586: Is mostly used for numerical calculations . Number theory dates back to ancient Babylon and probably China . Two prominent early number theorists were Euclid of ancient Greece and Diophantus of Alexandria. The modern study of number theory in its abstract form is largely attributed to Pierre de Fermat and Leonhard Euler . The field came to full fruition with the contributions of Adrien-Marie Legendre and Carl Friedrich Gauss . Many easily stated number problems have solutions that require sophisticated methods, often from across mathematics. A prominent example
2900-404: Is not sufficient to verify by measurement that, say, two lengths are equal; their equality must be proven via reasoning from previously accepted results ( theorems ) and a few basic statements. The basic statements are not subject to proof because they are self-evident ( postulates ), or are part of the definition of the subject of study ( axioms ). This principle, foundational for all mathematics,
3000-1192: Is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The overwhelming majority of works in this ocean contain new mathematical theorems and their proofs." Mathematical notation is widely used in science and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way. This notation consists of symbols used for representing operations , unspecified numbers, relations and any other mathematical objects, and then assembling them into expressions and formulas. More precisely, numbers and other mathematical objects are represented by symbols called variables, which are generally Latin or Greek letters, and often include subscripts . Operation and relations are generally represented by specific symbols or glyphs , such as + ( plus ), × ( multiplication ), ∫ {\textstyle \int } ( integral ), = ( equal ), and < ( less than ). All these symbols are generally grouped according to specific rules to form expressions and formulas. Normally, expressions and formulas do not appear alone, but are included in sentences of
3100-547: Is often held to be Archimedes ( c. 287 – c. 212 BC ) of Syracuse . He developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series , in a manner not too dissimilar from modern calculus. Other notable achievements of Greek mathematics are conic sections ( Apollonius of Perga , 3rd century BC), trigonometry ( Hipparchus of Nicaea , 2nd century BC), and
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3200-433: Is one of the oldest branches of mathematics. It started with empirical recipes concerning shapes, such as lines , angles and circles , which were developed mainly for the needs of surveying and architecture , but has since blossomed out into many other subfields. A fundamental innovation was the ancient Greeks' introduction of the concept of proofs , which require that every assertion must be proved . For example, it
3300-554: Is sometimes mistranslated as a condemnation of mathematicians. The apparent plural form in English goes back to the Latin neuter plural mathematica ( Cicero ), based on the Greek plural ta mathēmatiká ( τὰ μαθηματικά ) and means roughly "all things mathematical", although it is plausible that English borrowed only the adjective mathematic(al) and formed the noun mathematics anew, after
3400-448: Is the list of majors at Brooklyn Tech. Students are placed into a major during the second semester of their sophomore year after ranking all the majors in order of preference. These majors include courses, typically Advanced Placement or Project Lead the Way (PLTW) courses, that concentrate in that specific area of interest given to students during their last two years at Tech. Each major has
3500-418: Is the purpose of universal algebra and category theory . The latter applies to every mathematical structure (not only algebraic ones). At its origin, it was introduced, together with homological algebra for allowing the algebraic study of non-algebraic objects such as topological spaces ; this particular area of application is called algebraic topology . Calculus, formerly called infinitesimal calculus,
3600-405: Is the set of all integers. Because the objects of study here are discrete, the methods of calculus and mathematical analysis do not directly apply. Algorithms —especially their implementation and computational complexity —play a major role in discrete mathematics. The four color theorem and optimal sphere packing were two major problems of discrete mathematics solved in the second half of
3700-508: Is true regarding number theory (the modern name for higher arithmetic ) and geometry. Several other first-level areas have "geometry" in their names or are otherwise commonly considered part of geometry. Algebra and calculus do not appear as first-level areas but are respectively split into several first-level areas. Other first-level areas emerged during the 20th century or had not previously been considered as mathematics, such as mathematical logic and foundations . Number theory began with
3800-574: The Babylonians and Egyptians began using arithmetic, algebra, and geometry for taxation and other financial calculations, for building and construction, and for astronomy. The oldest mathematical texts from Mesopotamia and Egypt are from 2000 to 1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical concept after basic arithmetic and geometry. It
3900-753: The Golden Age of Islam , especially during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics. The most notable achievement of Islamic mathematics was the development of algebra . Other achievements of the Islamic period include advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarizmi , Omar Khayyam and Sharaf al-Dīn al-Ṭūsī . The Greek and Arabic mathematical texts were in turn translated to Latin during
4000-456: The High School for Math, Science and Engineering (HSMSE), as interim acting principal. Asher had previously served as Brooklyn Tech's assistant principal in mathematics from 2000 to 2002 before leaving to become founding principal of HSMSE. During his time as principal, the total student enrollment increased from 4,200 to 5,700. In the beginning of January 2017, Asher abruptly left Tech to take on
4100-514: The Long Island Rail Road . Additionally, New York City Bus 's B25 , B26 , B38 and B52 routes stop near Brooklyn Tech. Students residing a certain distance from the school are provided full-fare or half-fare student MetroCards for public transportation on their first day of school at BTHS, as well as the first day of each school term onward. Brooklyn Tech uses a college-style system of majors, unusual for an American high school. Below
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4200-588: The Materials Science department, and closed the seventh-floor foundry. In the mid-1980s, a violent street gang known as the Decepticons were founded at Brooklyn Tech. As well, in 2000, the city issued a special report concerning the lack of notification to law enforcement during a string of robberies within the high school, including armed robbery with knives and stun guns. In March 1998, an alumni group led by Leonard Riggio , class of 1958, announced plans for
4300-639: The New York City Department of Education launched an investigation of McCaskill on February 2, 2006, concerning unpaid enrollment of New Jersey resident McCaskill's daughter in a New York City public school, which is illegal for non-residents of the city. Dr. McCaskill produced a lease claiming that he rented an apartment in Brooklyn, but the copyright date on the lease was after the signatures were dated. On February 6, McCaskill announced his resignation from Brooklyn Tech and agreed to pay $ 19,441 in restitution. A week later special commissioner Richard J. Condon rebuked
4400-505: The Pythagoreans appeared to have considered it a subject in its own right. Around 300 BC, Euclid organized mathematical knowledge by way of postulates and first principles, which evolved into the axiomatic method that is used in mathematics today, consisting of definition, axiom, theorem, and proof. His book, Elements , is widely considered the most successful and influential textbook of all time. The greatest mathematician of antiquity
4500-524: The Renaissance , mathematics was divided into two main areas: arithmetic , regarding the manipulation of numbers, and geometry , regarding the study of shapes. Some types of pseudoscience , such as numerology and astrology , were not then clearly distinguished from mathematics. During the Renaissance, two more areas appeared. Mathematical notation led to algebra which, roughly speaking, consists of
4600-594: The Specialized High Schools Admissions Test and scoring the cutoff for Brooklyn Tech. Each November, about 30,000 eighth and ninth graders take the 3-hour test for admittance to eight of the nine specialized high schools. About 1,400 to 1,500 students are admitted each year. Brooklyn Tech counts top scientists, inventors, innovators, Fortune 500 company CEOs and founders, high-ranking diplomats, academic scholars, literary and media figures, professional athletes, National Medal recipients, Nobel laureates , and Olympic medalists among its alumni. Admission to Brooklyn Tech
4700-446: The controversy over Cantor's set theory . In the same period, various areas of mathematics concluded the former intuitive definitions of the basic mathematical objects were insufficient for ensuring mathematical rigour . This became the foundational crisis of mathematics. It was eventually solved in mainstream mathematics by systematizing the axiomatic method inside a formalized set theory . Roughly speaking, each mathematical object
4800-400: The 17th century, when René Descartes introduced what is now called Cartesian coordinates . This constituted a major change of paradigm : Instead of defining real numbers as lengths of line segments (see number line ), it allowed the representation of points using their coordinates , which are numbers. Algebra (and later, calculus) can thus be used to solve geometrical problems. Geometry
4900-405: The 19th century, mathematicians discovered non-Euclidean geometries , which do not follow the parallel postulate . By questioning that postulate's truth, this discovery has been viewed as joining Russell's paradox in revealing the foundational crisis of mathematics . This aspect of the crisis was solved by systematizing the axiomatic method, and adopting that the truth of the chosen axioms is not
5000-406: The 2021 U.S. News & World Report "Best High Schools" list, making it the highest ranked Specialized High School. In 2008, Newsweek listed it among five public high schools that were not in the magazine's 13 "Public Elite" ranking, explaining, " Newsweek ' s Challenge Index is designed to recognize schools that challenge average students, and not magnet or charter schools that draw only
5100-532: The 20th century. The P versus NP problem , which remains open to this day, is also important for discrete mathematics, since its solution would potentially impact a large number of computationally difficult problems. Discrete mathematics includes: The two subjects of mathematical logic and set theory have belonged to mathematics since the end of the 19th century. Before this period, sets were not considered to be mathematical objects, and logic , although used for mathematical proofs, belonged to philosophy and
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#17328549200735200-1049: The Brooklyn Tech announcement. In November 2005, the Brooklyn Tech Alumni Association announced the completion of the fundraising phase of what they had termed the Campaign for Brooklyn Tech. In April 2008, the Brooklyn Tech Alumni Foundation launched a second endowment campaign. Sixteen alumni died in the September 11 attacks in 2001. They are Dennis Cross '59, Ronald F. Orsini '60, Joel Miller '63, Sheldon R. Kanter '66, Stephen Johnson '75, Danny Libretti '76, Dominick E. Calia '79, Dipti Patel '81, Andre Fletcher '82, Courtney W. Walcott '82, Gerard Jean Baptiste '83, Wai C. Chung '84, Paul Innella '85, Michael McDonnell '85, Thomas Tong '87, and Paul Ortiz '98. Since 2001, Brooklyn Tech has undergone refurbishing such as
5300-511: The Department of Education for allowing McCaskill to retire, still collecting $ 125,282 in accrued vacation time, just days before the OSI completed its investigation. Condon also recommended that Cathy Furman McCaskill, the principal's wife, be dismissed from her position as a teacher at Boys and Girls High School in Brooklyn for her part in submitting fake leases and other fraudulent documents to indicate
5400-620: The Middle Ages and made available in Europe. During the early modern period , mathematics began to develop at an accelerating pace in Western Europe , with innovations that revolutionized mathematics, such as the introduction of variables and symbolic notation by François Viète (1540–1603), the introduction of logarithms by John Napier in 1614, which greatly simplified numerical calculations, especially for astronomy and marine navigation ,
5500-542: The New York State Legislature as specialized high schools of New York City. The act called for a uniform exam to be administered for admission to Brooklyn Tech, Bronx Science, and Stuyvesant. The exam would become known as the Specialized High Schools Admissions Test (SHSAT) and tested students in Math and English. With its statewide recognition, the school had to become co-educational . Previous to this, Brooklyn Tech
5600-574: The beginnings of algebra (Diophantus, 3rd century AD). The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics . Other notable developments of Indian mathematics include the modern definition and approximation of sine and cosine , and an early form of infinite series . During
5700-551: The best students in their areas. These [...] were excluded from the list of top high schools because [...] their sky-high SAT and ACT scores indicate they have few or no average students". In 1918, Dr. Albert L. Colston, chair of the Math Department at Manual Training High School, recommended establishing a technical high school for Brooklyn boys. His plan envisioned a heavy concentration of math , science, and drafting courses with parallel paths leading either to college or to
5800-511: The class of 2010, each student must meet the following requirements by the end of their senior year to receive a Brooklyn Tech diploma: I. A minimum of 50 hours of community service outside of the school or through specified club activities. II. A minimum of 32 club credits earned through participation in Tech clubs, teams, and/or participation in designated school related events. The maximum amount of credits that can be earned per club, team, or event
5900-399: The classrooms for the first time, thanks to the 420-foot WNYE-TV tower atop Brooklyn Tech. For the school year beginning in the last half of 1970, young women began attending; all three NYC specialized and test-required science high schools were now coeducational. In 1972, Brooklyn Tech, Bronx Science , Stuyvesant High School , and High School for Performing Arts become incorporated by
6000-503: The concept of a proof and its associated mathematical rigour first appeared in Greek mathematics , most notably in Euclid 's Elements . Since its beginning, mathematics was primarily divided into geometry and arithmetic (the manipulation of natural numbers and fractions ), until the 16th and 17th centuries, when algebra and infinitesimal calculus were introduced as new fields. Since then,
6100-595: The country's best magnet schools (a category the school is often placed in, though its founding predates the concept of a "magnet school", whose intended purpose was not the same). Admission is by competitive examination . As a public school, BTHS has no tuition fee , but only students who reside in New York City are allowed to attend, as per the Hecht-Calandra Act. Brooklyn Tech ranked 2nd in New York State on
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#17328549200736200-399: The current language, where expressions play the role of noun phrases and formulas play the role of clauses . Mathematics has developed a rich terminology covering a broad range of fields that study the properties of various abstract, idealized objects and how they interact. It is based on rigorous definitions that provide a standard foundation for communication. An axiom or postulate is
6300-553: The derived expression mathēmatikḗ tékhnē ( μαθηματικὴ τέχνη ), meaning ' mathematical science ' . It entered the English language during the Late Middle English period through French and Latin. Similarly, one of the two main schools of thought in Pythagoreanism was known as the mathēmatikoi (μαθηματικοί)—which at the time meant "learners" rather than "mathematicians" in the modern sense. The Pythagoreans were likely
6400-428: The expansion of these logical theories. The field of statistics is a mathematical application that is employed for the collection and processing of data samples, using procedures based on mathematical methods especially probability theory . Statisticians generate data with random sampling or randomized experiments . Statistical theory studies decision problems such as minimizing the risk ( expected loss ) of
6500-554: The faculty and Principal McCaskill, "spilled into the open in October, with news reports that several teachers accused him of repeatedly sending sexually explicit e-mail messages from his school computer to staff members." While the article praised him for his addition of music and sports programs, it mostly described the principal as autocratic , controlling the school "largely through fear and intimidation," and documented acts of personal vindictiveness toward teachers; severe censorship of
6600-427: The fall of 2016 when faced with charges of having an inappropriate relationship with a male student. The school was also rocked by allegations of racism against black students and Asher faced mounting student pressure on social media to fix the situation. Following Asher's departure, former assistant principal David Newman took on the new position as acting principal of the specialized high school. In February 2020, Newman
6700-511: The family lived in the Cobble Hill section of Brooklyn. The next day, the Department of Education announced that it would fire her. After retiring from Brooklyn Tech, McCaskill became principal of Hillside High School in New Jersey, where in 2013, he resigned following accusations he spanked a female student. On February 7, 2006, the Department of Education named Randy Asher, founding principal of
6800-591: The first Tech alumnus to hold that position. The following year, Tech received the Excellence in Education award from the U.S. Department of Education . The Alumni Association was formally created during this time, and coalitions were formed with the New York City Department of Transportation. Mandery oversaw the addition of a Bio-Medical major to the curriculum. John Tobin followed as principal in 1987, abolished
6900-567: The first to constrain the use of the word to just the study of arithmetic and geometry. By the time of Aristotle (384–322 BC) this meaning was fully established. In Latin and English, until around 1700, the term mathematics more commonly meant " astrology " (or sometimes " astronomy ") rather than "mathematics"; the meaning gradually changed to its present one from about 1500 to 1800. This change has resulted in several mistranslations: For example, Saint Augustine 's warning that Christians should beware of mathematici , meaning "astrologers",
7000-412: The groundbreaking was held in 1930. Atypical for American high schools, Brooklyn Tech uses a system of college-style majors. The curriculum consists of two years of general studies with a technical and engineering emphasis, followed by two years of a student-chosen major. The curriculum remained largely unchanged until the end of Dr. Colston's 20-year term as principal in 1942. Upon his retirement, Tech
7100-491: The interaction between mathematical innovations and scientific discoveries has led to a correlated increase in the development of both. At the end of the 19th century, the foundational crisis of mathematics led to the systematization of the axiomatic method , which heralded a dramatic increase in the number of mathematical areas and their fields of application. The contemporary Mathematics Subject Classification lists more than sixty first-level areas of mathematics. Before
7200-400: The introduction of coordinates by René Descartes (1596–1650) for reducing geometry to algebra, and the development of calculus by Isaac Newton (1643–1727) and Gottfried Leibniz (1646–1716). Leonhard Euler (1707–1783), the most notable mathematician of the 18th century, unified these innovations into a single corpus with a standardized terminology, and completed them with the discovery and
7300-409: The manipulation of numbers , that is, natural numbers ( N ) , {\displaystyle (\mathbb {N} ),} and later expanded to integers ( Z ) {\displaystyle (\mathbb {Z} )} and rational numbers ( Q ) . {\displaystyle (\mathbb {Q} ).} Number theory was once called arithmetic, but nowadays this term
7400-400: The natural numbers, there are theorems that are true (that is provable in a stronger system), but not provable inside the system. This approach to the foundations of mathematics was challenged during the first half of the 20th century by mathematicians led by Brouwer , who promoted intuitionistic logic , which explicitly lacks the law of excluded middle . These problems and debates led to
7500-536: The objects defined this way is a philosophical problem that mathematicians leave to philosophers, even if many mathematicians have opinions on this nature, and use their opinion—sometimes called "intuition"—to guide their study and proofs. The approach allows considering "logics" (that is, sets of allowed deducing rules), theorems, proofs, etc. as mathematical objects, and to prove theorems about them. For example, Gödel's incompleteness theorems assert, roughly speaking that, in every consistent formal system that contains
7600-413: The official school newspaper. Tech has a literary art journal, Horizons, for those who want to express themselves through art, poetry, photography, and prose. The Model United Nations provides students with a venue for discussing foreign affairs and also hosts a conference each year called TechMUN. Other clubs cater to a wide range of topics such as public transportation (notably Tech Transit Association ,
7700-514: The pattern of physics and metaphysics , inherited from Greek. In English, the noun mathematics takes a singular verb. It is often shortened to maths or, in North America, math . In addition to recognizing how to count physical objects, prehistoric peoples may have also known how to count abstract quantities, like time—days, seasons, or years. Evidence for more complex mathematics does not appear until around 3000 BC , when
7800-700: The pilot episode of the 2013 series The Tomorrow People were filmed in Brooklyn Tech. (Subsequent episodes were filmed in Vancouver rather than New York City.) Brooklyn Tech was also used to film the FOX series Gotham . The Netflix series Grand Army is also loosely based on Brooklyn Tech. High school (North America) High schools in North America are schools for secondary education , which may also involve intermediate education . Highschooling in North America may refer to: Math Mathematics
7900-654: The proof of numerous theorems. Perhaps the foremost mathematician of the 19th century was the German mathematician Carl Gauss , who made numerous contributions to fields such as algebra, analysis, differential geometry , matrix theory , number theory, and statistics . In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems , which show in part that any consistent axiomatic system—if powerful enough to describe arithmetic—will contain true propositions that cannot be proved. Mathematics has since been greatly extended, and there has been
8000-746: The public school bureaucracy." Brooklyn Tech fields 30 junior-varsity and varsity teams in the Public School Athletic League (PSAL). The school's historic team name has been the Engineers. The school colors are navy blue and white. The school's more than 100 organizations include the Brooklyn Tech Amateur Radio Club (club station call sign W2CXN), Civil Air Patrol Brooklyn Tech Cadet Squadron, chess , debate , football , wrestling, forensics (speech), hockey, mock trial , robotics, and rowing teams and clubs, and The Survey, [2]
8100-426: The renovation of the school's William L. Mack Library entrance, located on the fifth-floor center section. As well, two computer labs were added. The school also reinstated a class devoted to the study of Shakespeare, which students can elect to take in their senior year. Dr. Lee D. McCaskill , the appointed principal in 1992, served for 14 years, during which Tech saw the installation of more computer classrooms and
8200-552: The school's first of such clubs since 1964), anime , the Stock Market, Dance Dance Revolution , ultimate Frisbee , politics , quilting , fashion , debate (which offers Public Forum, Congress and Policy), table tennis and animal rights . The cheerleading squad is named the Enginettes. In 2012, Tech students created a Junior State of America Chapter at their school. Brooklyn Tech has its own student union, to address issues on
8300-487: The specialized high schools, partly due to the school's size). Per the New York State graduation requirements, students can earn a local diploma, a Regents diploma, or an advanced Regents diploma. To earn a Brooklyn Tech diploma, students must meet "service credit" requirements (which can be dated to at least the 1950s and likely earlier) in addition to the Advanced Regents Diploma requirements. Beginning with
8400-522: The student newspaper and of assigned English texts, including the refusal to let the Pulitzer Prize -finalist novel Continental Drift by Russell Banks be used for a class; and of bureaucratic mismanagement. A follow-up column in 2004 found that there was increased teacher exodus, specifically documenting Principal McCaskill's campaign against Alice Alcala, who described as one of the city's leading Shakespeare teachers. Alcala had won Brooklyn Tech
8500-657: The study and the manipulation of formulas . Calculus , consisting of the two subfields differential calculus and integral calculus , is the study of continuous functions , which model the typically nonlinear relationships between varying quantities, as represented by variables . This division into four main areas—arithmetic, geometry, algebra, and calculus —endured until the end of the 19th century. Areas such as celestial mechanics and solid mechanics were then studied by mathematicians, but now are considered as belonging to physics. The subject of combinatorics has been studied for much of recorded history, yet did not become
8600-561: The study of approximation and discretization with special focus on rounding errors . Numerical analysis and, more broadly, scientific computing also study non-analytic topics of mathematical science, especially algorithmic- matrix -and- graph theory . Other areas of computational mathematics include computer algebra and symbolic computation . The word mathematics comes from the Ancient Greek word máthēma ( μάθημα ), meaning ' something learned, knowledge, mathematics ' , and
8700-429: The swimming pool at Brooklyn Tech while swimming with his day-camp group. The next year, more than 30 graduating Seniors in the school (including many student leaders) complained that Tech's curriculum was old and outdated. Their primary complaint was that the curriculum was geared toward the small minority of students who were not planning on attending college. In 1967, the schools of New York City got to view television in
8800-600: The switch from the traditional mechanical drawing by hand to teaching the use of computer-aided design programs. In 2000, the Special Commissioner of Investigation for the NYC School District wrote a report condemning Brooklyn Technical High School administrators for failing to report several armed robberies that took place in the bathrooms and stairwells. In 2003, The New York Times published an investigative article that noted "longstanding tensions" between
8900-672: The theory under consideration. Mathematics is essential in the natural sciences , engineering , medicine , finance , computer science , and the social sciences . Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent of any scientific experimentation. Some areas of mathematics, such as statistics and game theory , are developed in close correlation with their applications and are often grouped under applied mathematics . Other areas are developed independently from any application (and are therefore called pure mathematics ) but often later find practical applications. Historically,
9000-487: The title of his main treatise . Algebra became an area in its own right only with François Viète (1540–1603), who introduced the use of variables for representing unknown or unspecified numbers. Variables allow mathematicians to describe the operations that have to be done on the numbers represented using mathematical formulas . Until the 19th century, algebra consisted mainly of the study of linear equations (presently linear algebra ), and polynomial equations in
9100-504: The two main precursors of algebra. Diophantus solved some equations involving unknown natural numbers by deducing new relations until he obtained the solution. Al-Khwarizmi introduced systematic methods for transforming equations, such as moving a term from one side of an equation into the other side. The term algebra is derived from the Arabic word al-jabr meaning 'the reunion of broken parts' that he used for naming one of these methods in
9200-531: Was All Boys, and had a sister school, Bay Ridge High School which was all girls. In 1973, Tech celebrated its 50th anniversary with a dinner-dance at the Waldorf Astoria . To further commemorate the anniversary, a monument was erected, with a time capsule beneath it, in the north courtyard. The monument has eight panels, each with a unique design representing each of Tech's eight majors at that point. In 1983, Matt Mandery's appointment as principal made him
9300-402: Was added later. Principal Pabst retired in 1964. A railroad club was established by the late Vincent Gorman, a social studies teacher, and students attended fan trips, tours of rail repair facilities and participated in the restoration of steam engine #103 and a historic rail passenger car at the former Empire State Railroad Museum. In August 1965, a ten-year-old boy named Carl Johnson drowned in
9400-498: Was appointed principal. The school, built on its present site in 1932 at a cost of $ 6 million, is 12 stories high, and covers over half a city block. Brooklyn Technical High School is directly across the street from Fort Greene Park. Facilities at BTHS include: The New York City Subway 's Fulton Street ( G train) and Lafayette Avenue ( C train) stations are located nearby, as well as more BMT and IRT services at DeKalb Avenue and Atlantic Terminal , which also serves
9500-457: Was first elaborated for geometry, and was systematized by Euclid around 300 BC in his book Elements . The resulting Euclidean geometry is the study of shapes and their arrangements constructed from lines, planes and circles in the Euclidean plane ( plane geometry ) and the three-dimensional Euclidean space . Euclidean geometry was developed without change of methods or scope until
9600-414: Was introduced independently and simultaneously by 17th-century mathematicians Newton and Leibniz . It is fundamentally the study of the relationship of variables that depend on each other. Calculus was expanded in the 18th century by Euler with the introduction of the concept of a function and many other results. Presently, "calculus" refers mainly to the elementary part of this theory, and "analysis"
9700-673: Was led briefly by acting principal Ralph Breiling, who was succeeded by Principal Harold Taylor in 1944. Tech's modernization would come under Principal William Pabst, who assumed stewardship in 1946 after serving as chair of the Electrical Department. Pabst created new majors and refined older ones, allowing students to select science and engineering preparatory majors including Aeronautical , Architecture , Chemical , Civil , Electrical (later including Electronics and Broadcast), Industrial Design , Mechanical , Structural , and Arts and Sciences. A general College Preparatory curriculum
9800-417: Was no longer any course solely devoted to Shakespeare, according to the column. In two newspaper articles in 2005, it was revealed that a $ 10,000 grant obtained by Dr. Sylvia Weinberger in 2001 to refurbish the obsolete radio studio remained unused. New classroom computers were covered in plastic rather than installed because the classrooms had yet to be wired for them. The Office of Special Investigations of
9900-437: Was not specifically studied by mathematicians. Before Cantor 's study of infinite sets , mathematicians were reluctant to consider actually infinite collections, and considered infinity to be the result of endless enumeration . Cantor's work offended many mathematicians not only by considering actually infinite sets but by showing that this implies different sizes of infinity, per Cantor's diagonal argument . This led to
10000-571: Was split into two new subfields: synthetic geometry , which uses purely geometrical methods, and analytic geometry , which uses coordinates systemically. Analytic geometry allows the study of curves unrelated to circles and lines. Such curves can be defined as the graph of functions , the study of which led to differential geometry . They can also be defined as implicit equations , often polynomial equations (which spawned algebraic geometry ). Analytic geometry also makes it possible to consider Euclidean spaces of higher than three dimensions. In
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