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93-608: Krames was born on September 5, 1964, and raised in New York City. He attended the Bronx High School of Science before going on to college in upstate New York at age 16. He graduated magna cum laude from State University of New York at Albany . He is a direct descendant of German and Polish Holocaust survivors. He joined publisher Prentice-Hall as a sales representative in the midwest region. After being promoted to marketing manager in 1984, Krames relocated to

186-408: A 63-foot (19 m), Venetian glass mosaic mural overhead, depicting major figures from the history of science such as Marie Curie and Charles Darwin under the protective hands of a God-like figure representing knowledge, with this quote from John Dewey : "Every great advance in science has issued from a new audacity of imagination." The mural, Humanities Protecting Biology, Physics, Chemistry ,

279-591: 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

372-515: A biological lab science at Bronx Science, a requirement that can be satisfied either by freshman biology or, if students took biology in middle school, one of the many advanced electives offered, including AP Biology , AP Environmental Science , AP Psychology ; non-AP advanced courses include animal behavior , cell biology , epidemiology , forensic science , microbiology , neuroscience , and nutritional science . Post-AP level classes in evolution , genetics , and psychology are also offered. In

465-866: A class in the research program, a three-year long program that culminates in an independent research project and final research paper that is submitted to Regeneron and other prestigious competitions in senior year. The research program is divided into biology, math, physical science/engineering, and social science research. The mathematics department offers standard AP courses in AB/BC calculus , statistics , and computer science . Students can take precalculus alongside honors algebra 2 and trigonometry in their sophomore year, allowing them to take AP Calculus in their junior year. Post-AP courses in mathematics include multivariable calculus , linear algebra and differential equations , ordinary differential equations , video game development , app development , game theory , and

558-479: A college preparatory curriculum that includes four years of science, English, and social studies; three (usually four) years of math; two or three years of foreign language; and a year of fine arts, with required courses and a wide selection of electives, including honors and advanced placement (AP) classes, which allow students to place out of introductory college science courses. Over 100 unique courses are offered. All New York State Regents classes are offered, with

651-470: A contingent from Stuyvesant High School . Meister put his imprint on the school from its formation, for example selecting as school colors "green to represent chlorophyll and gold the sun, both of which are essential to the chain of life." From the beginning, the Parents Association and Principal Morris Meister campaigned for a new building. The number of students exceeded the capacity of

744-614: 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

837-669: 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)

930-499: A list of the best 1,000 high schools in the country on The Daily Beast 's "America's Best High Schools" list. In 2014 it was ranked second highest on Cities Journal ' s list of the "15 Best High Schools in New York", along with Stuyvesant (ranked third) and Brooklyn Tech (ranked eighth). The average SAT score at Bronx Science was 2100 out of 2400. Almost all Bronx Science graduates continue on to four-year colleges, and it

1023-404: 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

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1116-422: 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

1209-402: 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

1302-522: A newly introduced course in financial and actuarial math. Students are required to take four years of English. AP English Language and AP English Literature are offered, along with journalism workshop and yearbook design. In junior year, students have the option to take the unique AP American Studies course, an interdisciplinary course that correlates the AP English Language and AP United States History courses, while in senior year,

1395-535: 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

1488-411: 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

1581-424: 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

1674-418: 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

1767-477: 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

1860-468: A year of language prior to high school. Bronx Science offers French, Spanish, Latin, Italian, Chinese, and Japanese. At one time Hebrew, Russian, Korean, and German were also offered. Students must also obtain credits from two terms of a class in the fine arts or the equivalent. The fine arts requirement is usually satisfied during Bronx Science's Summer Program which offers Drama, Music, and Art. Students usually "double up" on two of these courses to satisfy

1953-703: 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

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2046-602: Is Bronx Science's prize-winning yearbook. The yearbook office has a custom-built web server to manage its production, powered by MediaWiki and Coppermine software. Vox Discipulorum is a student-led monthly publication sponsored by the World Language Department, providing students with a platform to creatively express their language and cultural experiences. Through essays, poems, and artwork, students showcase their linguistic skills and explore diverse cultures. Other department-produced publications include

2139-756: Is a public specialized high school in The Bronx in New York City . It is operated by the New York City Department of Education . Admission to Bronx Science involves passing the Specialized High Schools Admissions Test . Founded in 1938 in the Bronx , New York City, Bronx Science is located in what is now Kingsbridge Heights , also known as Jerome Park, a neighborhood in the northwest portion of

2232-474: Is a "feeder school", with many graduates going on to Ivy League schools and other institutions of higher learning each year. Bronx Science has counted 132 finalists in the Regeneron (formerly Intel) Science Talent Search , the largest number of any high school. Nine graduates have won Nobel Prizes —more than any other secondary education institution in the world —and nine have won Pulitzer Prizes . Of

2325-467: Is an original work by Frank J. Reilly . Legions of students over the years, bemoaning the lack of swimming facilities, have sarcastically referred to the mural as "the Science swimming pool", perpetuating the thesis that a choice was made to fund a mural rather than a pool in the new building. In the first spring of the move, rumors swept the school that various Bronx youth street gangs were coming to

2418-403: 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

2511-513: 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

2604-407: 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

2697-493: 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

2790-586: 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

2883-404: 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,

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2976-1192: 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

3069-547: 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

3162-433: 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

3255-567: 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

3348-418: 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,

3441-405: 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

3534-508: 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

3627-586: 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

3720-768: 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

3813-542: The New York City Department of Education . The New York City Subway 's Bedford Park Boulevard ( B and ​ D trains) and Bedford Park Boulevard–Lehman College ( 4 train) stations are located nearby. Additionally, New York City Bus 's Bx10 , Bx22 , Bx26 and Bx28 routes stop near Bronx Science. Many people who attended the Bronx High School of Science have achieved distinction in their respective fields, including winning

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3906-629: The New York City Panel for Educational Policy , with Morris Meister as the first principal of the school. They were given use of an antiquated Gothic-gargoyled edifice located at Creston Avenue and 184th Street, in the Fordham Road - Grand Concourse area of the Bronx. The building, built in 1918 for Evander Childs High School, had been successively occupied by Walton High School (1930) and by an annex of DeWitt Clinton High School (1935). The initial faculty were composed in part by

3999-511: 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

4092-536: 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

4185-446: 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

4278-400: 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

4371-405: 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

4464-532: 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

4557-715: The 4E's of Leadership, publishing magazine Kirkus said it was "destined to become a leadership classic." His latest book is Inside Drucker's Brain , published by Portfolio in October 2008. Aside from his book publications, he also has written for a variety of newspapers including The Wall Street Journal , The New York Times , The Los Angeles Times , The Chicago Tribune , and has been quoted in Time Magazine , Newsweek , The New York Times , The Chicago Tribune , Publishers Weekly , etc. Bronx High School of Science The Bronx High School of Science

4650-583: The 4th best STEM school in the nation. In 2014, the school ranked 34th out of all high schools nationwide and 1st in New York ; nationwide, Bronx Science ranked 33rd in 2008 and 58th in 2009. It attracts an intellectually gifted blend of culturally, ethnically, and economically diverse students from New York City. As of 2012 , Bronx Science is ranked as one of the "22 top-performing schools" in America on The Washington Post as well as number 50 out of

4743-1068: The AP English Literature course is divided into courses in creative writing and traditional literature. Four years of social studies or history classes are required. AP European History and AP World History are both offered in sophomore year in preparation for the Global History Regents, while juniors can take AP United States History to satisfy the U.S. history requirement. Senior social studies classes consist of several combinations of AP classes in U.S. Government and Politics , Comparative Government and Politics , Microeconomics , and Macroeconomics . Additional classes in social studies, which must be taken along with these ones, include AP Human Geography , race and gender, and unique classes in Holocaust leadership and speech and debate leadership. A minimum of 2 years of languages are required, if students had previously taken

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4836-483: The Bronx. Although originally known for its focus on mathematics and science, Bronx Science also emphasizes the humanities and social sciences . Bronx Science has produced the most Nobel laureates in science of any secondary school in the world. Bronx Science alumni have also won three Turing Awards , sometimes unofficially referred to as the Nobel Prize in computer science; six National Medals of Science ,

4929-702: The Health requirement may also be fulfilled during the Bronx Science Summer Program in addition to the two fine arts courses. Bronx Science offers all of the AP courses, except for AP German Language and Culture , AP Precalculus , and the AP Capstone program. The courses include: The Science Survey is Bronx Science's entirely student-run newspaper. Students manage everything: reporting, layout, design, editing, and final production, under

5022-734: The McGraw-Hill Companies acquired all of Richard D. Irwin, which included the trade business book imprint Irwin Professional Publishing (the company had been sold to Times Mirror and had changed its name). At McGraw-Hill Mr. Krames served in a variety of positions, including Publisher of Investing & Finance before being promoted to Publisher of the Business Book division of the Professional Book Group. In 2006 he left McGraw-Hill to join

5115-637: 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 ,

5208-534: The New York area before being promoted to acquisitions editor in 1985. In that position he spearheaded the absorption of the Reston business book line into the Prentice-Hall publishing program. After two additional promotions, Krames left Prentice-Hall, which had now been acquired by Simon & Schuster to join publisher Dow Jones-Irwin in 1988, which at the time was still owned by Dow Jones & Co. In 1996

5301-713: The Nobel and Pulitzer Prizes, the Academy, Emmy and Turing Awards, the U.S. National Medal of Science, political office and numerous professional society honors. Bronx Science was the primary rival of Millard Fillmore High School in Head of the Class , a television series that aired from 1986 to 1991. The main character of Northern Exposure , Joel Fleischman, reveals he went to Bronx Science in Season 2, Episode 4. Bronx Science formed

5394-601: The Penguin Group as Editorial Director of its Portfolio book imprint, where he continues to this day. As former Vice President and Publisher of McGraw-Hill's trade business books division, Jeffrey Krames has personally edited and published more than 1,000 business books, including many award-winning, best-selling titles on business luminaries that include Jack Welch , Michael Ovitz , Ross Perot , William Paley , Michael Dell , Bill Gates , Herb Kelleher , and Lou Gerstner among others. Recently, Krames published seven of

5487-583: The annual Math Bulletin , consisting of student term papers, original student mathematics research, and topics in mathematics; Exposition , an annual production of the Social Studies Department; and Reactions , written by physical science students. Bronx Science has received international recognition. In 2020, Newsweek's rankings of the top 5,000 STEM High Schools in the United States (public and private), listed Bronx Science as

5580-859: The basis for the Midtown School of Science and Technology in Spider-Man: Homecoming , part of the Marvel Cinematic Universe . Mathematics Mathematics 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

5673-583: 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

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5766-527: The building on 184th Street, so the top floor of Public School 85 on Marion Avenue and 187th Street was used as the "Annex". After twenty years, plans were finally completed for a new $ 8 million building, which was designed by the architectural firm of Emery Roth and Sons . The new building was on 205th Street near Bedford Park Boulevard, in a predominantly institutional area, between DeWitt Clinton High School and its large football field on one side, and Harris Field and Hunter College (now Lehman College ) on

5859-511: 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,

5952-399: 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

6045-569: 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

6138-544: The exception of earth science. In the biological sciences, Bronx Science offers a special honors biology course, in addition to the Regents-level course, which includes additional laboratory exposure and intensive content. If students have already taken the Living Environment regents in 8th grade, they may take Regents-level or honors chemistry in freshman year. All students must take at least one year of

6231-428: 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

6324-635: The female students exercised indoors for the remainder of that year. 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." Kennedy had recently selected a 1943 Bronx High School of Science graduate, Harold Brown , as Director of Defense Research and Engineering; Brown would later serve as United States Secretary of Defense under President Jimmy Carter . Bronx Science students take

6417-474: The fine arts requirement for once and all during the time period of one summer. Students are expected to satisfy the arts requirement by the end of sophomore year. Students can also take art or music electives during the school year to satisfy the fine arts requirement by taking a music elective such as jazz band or an arts elective such as AP Art History or AP Studio Art during the regular school year. Health and physical education courses are also required, and

6510-567: 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",

6603-491: 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

6696-400: 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

6789-409: 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

6882-462: The nation's highest scientific honor; and nine Pulitzer Prizes . The Bronx High School of Science is often called Bronx Science , Bronx Sci , BX Sci , and sometimes just Science . It was formerly called Science High and its founder, Morris Meister , is said to have frequently called the school "The High School of Science". Bronx High School of Science was founded in 1938 as a specialized science and math high school for boys, by resolution of

6975-400: 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

7068-581: The nine Nobel Prizes earned by graduates, seven of them are in physics, which earned Bronx Science a designation by the American Physical Society as a "Historic Physics Site" in 2010. Bronx Science is a member of the National Consortium of Secondary STEM Schools (NCSSS). Together with Stuyvesant High School and Brooklyn Technical High School , it is one of the three original specialized science high schools operated by

7161-536: 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

7254-471: The other. On March 3, 1959, students and faculty occupied the new building for the first time, solving the problem of how to move the books from the old library to the new in typical Bronx Science manner: on Friday afternoon each student took home five library books from the old building, and on Monday returned them to the new one. They entered a school equipped with more modern classrooms, laboratories, and technical studio areas. The main lobby entrance featured

7347-521: 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

7440-705: The physical science department, AP Chemistry and AP Physics are both offered, and both may be taken alongside introductory Regents-level courses in those respective classes. Electives offered include astronomy and astrophysics , electrical engineering , green design , organic chemistry , and post-AP Physics. In 2022, the school prepared to accept an astronomical observatory. Freshmen at Bronx Science are required to take one-semester courses in research literacy and engineering, while sophomores take one-semester courses consisting of coding and rhetoric. Collectively, these are referred to as Foundational courses. Sophomore students may satisfy this requirement by instead taking

7533-658: 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

7626-470: The school, and that the Fordham Baldies would shave the hair of Science students. This never happened. Another incident did happen that spring: The first time Science girls appeared on the outdoor physical education field in gym clothes, some students from the neighboring, all-male DeWitt Clinton High School charged the separation fence between their field and the Science field. The fence held, but

7719-657: 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

7812-568: 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

7905-621: The supervision of the journalism advisor. The paper is printed using funds from its advertisers, with no fiscal school support. The paper is distributed on average five times per year at no charge. The Science Survey has been the name of the Bronx Science student newspaper since the founding of the school in 1938. Dynamo is the literary magazine sponsored by the English Department, consisting of original poems and stories submitted by students from all grades. The Observatory

7998-672: 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,

8091-487: 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

8184-449: The top 35 best business books of the year as determined by Library Journal . Krames has written nine books with three of them focusing on former General Electric CEO, Jack Welch . Krames writes extensively on leadership and CEOs , and has written an account of Secretary of Defense Donald Rumsfeld 's leadership style entitled, The Rumsfeld Way: The Leadership Wisdom of a Battle-Hardened Maverick. Of his latest book, Jack Welch and

8277-508: 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

8370-462: 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

8463-414: 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"

8556-437: 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

8649-571: 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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