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Tertiary school mathematics

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All students in STEM, especially mathematics, physics, chemistry, computer science, and engineering must take single-variable calculus unless they have Advanced Placement credits (or equivalents, such as IB Math HL). Students majoring in mathematics, the physical sciences,[1][2] and engineering[3] then take multivariable calculus,[4][5][6] linear algebra,[7][8][9] complex variables,[10][11][12] ordinary differential equations,[13][14][15] and partial differential equations.[16][17][18]

Mathematics majors may take a course offering a rigorous introduction to the concepts of modern mathematics[19][20][21] before they tackle abstract algebra,[22][23][24] number theory,[25][26][27] real analysis,[28][29][30][31] advanced calculus,[32][33][34] complex analysis,[35][36][37][38] probability theory,[39][40] statistics,[41][42] and advanced topics, such as set theory and mathematical logic,[43][44][45][46] stochastic processes,[47] integration and measure theory,[48][49][50][51] Fourier analysis,[52][53] functional analysis,[54] differential geometry,[55][56][57] and topology.[58][59] They may further choose courses in applied mathematics, such as mathematical modelling, numerical analysis,[60] game theory,[61][62][63] or mathematical optimization. The calculus of variations,[64][65][66] the history of mathematics,[67][68][69][70] and topics in theoretical or mathematical physics (such as classical mechanics,[71][65][72][73] electrodynamics,[74][75] nonlinear dynamics,[76] fluid mechanics,[77][78] quantum mechanics,[79][80][81] or general relativity[82][83][84][85]) may be taken as electives.

Computer science majors must study discrete mathematics[86][87] (such as combinatorics and graph theory), information theory,[88] the theory of computation,[89][90] and cryptography. Students in computer science and economics might have the option of taking algorithmic game theory.[91]

Those who study biomedical and social sciences have to study elementary probability[92] and statistics.[93] Students in the physical sciences and engineering need to understand error analysis for their laboratory sessions and courses.[94][95] Advanced undergraduates and beginning graduate students in physics may take a course on advanced mathematical methods for physics, which may cover contour integration, the theory of distributions (generalized functions), Fourier analysis, Green's functions, special functions (especially Euler's gamma and beta functions; Bessel functions; Legendre polynomials; Hermite polynomials; Laguerre polynomials; and the hypergeometric series), asymptotic series expansions, the calculus of variations, tensors, and group theory.[96][97][98][99][100][101] Exact requirements and available courses will depend on the institution in question.

Info box

[edit]
James Terrell
Born
Nelson James Terrell Jr.

(1923-08-15)August 15, 1923
Houston, Texas
DiedMarch 21, 2009(2009-03-21) (aged 85)
Los Alamos, New Mexico
CitizenshipAmerican
OccupationPhysicist
Known forTerrell rotation
Academic background
Alma materRice University
Academic work
DisciplinePhysics
Sub-discipline
  • Special relativity
  • Astrophysics
InstitutionsLos Alamos National Laboratory

Books by Cornelius Lanczos

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  • The Variational Principles of Mechanics (4th ed.). University of Toronto Press. 1970. ISBN 0-486-65067-7. Dedicated to Albert Einstein. This is a graduate text on mechanics.[102] He published it shortly after moving to Los Angeles.[103] In the preface of the first edition (1949) it is described as a two-semester graduate course of three hours weekly. The second edition (1962) contains a new chapter on relativistic mechanics and the third (1966) has an appendix on Noether's theorem for cyclic coordinates. In the fourth edition (1970), Lanczos discusses at length continuum mechanics and makes further use of Noether's theorem.[104]
  • Applied Analysis. Prentice Hall. 1956. Reprinted 2010 by Dover Publications. ISBN 978-0-486-65656-4. An exposition of his investigations of ideas in the boundary between classical and numerical analysis illustrated by worked examples, topics covered include large scale linear systems, harmonic analysis, data analysis, numerical quadrature and power series expansions.[105] The chapter on numerical quadrature was inspired by a number of problems posed by Schrödinger.[106]
  • Linear Differential Operators. Van Nostrand. 1961. OCLC 1213191.
  • Albert Einstein and the Cosmic World Order. Interscience Publishers. 1965. OCLC 530604. Based on six lectures delivered at the University of Michigan in the spring of 1962.
  • Discourse on Fourier Series. Edinburgh: Oliver & Boyd. 1966. OCLC 1222573.
  • Numbers without End, Edinburgh: Oliver & Boyd. 1968.
  • Judaism and Science. Leeds University Press. 1970. ISBN 978-0-853-16021-2. Lectures given in honor of Selig Brodetsky.
  • Space Through the Ages: The Evolution of Geometrical Ideas from Pythagoras to Hilbert and Einstein. Academic Press. 1970. ISBN 9780124358508. Based on a series of lectures given to mathematicians, physicists, chemists, engineers, and philosophers at North Carolina State University in 1968, Lanczos overviews the history of geometry from the time of the ancient Greeks up until the early twentieth century. He does not, however, discuss topology.[107]
  • The Einstein Decade (1905-1915). London: Elek. 1974. ISBN 978-0-236-17632-8. In this book, Lanczos made use of his fluency in the German language as his grasp of to mathematics and physics discuss in detail the scientific publications of Albert Einstein during that time.[103]
  • Davis, William R., ed. (1998). Cornelius Lanczos: Collected Published Papers with Commentaries. North Carolina State University. ISBN 0-929493-01-X.

Texas Symposium on Relativistic Astrophysics

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The Texas Symposium on Relativistic Astrophysics is an international scientific conference currently held once every two years, intended for astronomers, astrophysicists, and other researchers interested in general relativity and its implications. These gatherings helped end the insularity of the specialists of these diverse subjects.[108][109]: 341  These Symposia originally met in Texas, United States, but was later held in many other places. A typical Symposium has hundreds of attendees from around the world, reaching a peak of around 1,000 in 1972 (New York) and nearly so in 1998 (Paris).[110] Ivor Robinson, one of the organizers of the first few Symposia, likely coined the term "relativistic astrophysics" in 1963.[110]

The First Symposium, chiefly organized by Robinson, Alfred Schild, Engelbert Schücking, and Peter Bergmann, convened in Dallas, Texas, in December 16–18, 1963, shortly after the assassination of John F. Kennedy.[110] One of the major topic of discussion of the time was the optical and radio observations of quasi-stellar objects (quasars).[111] J. Robert Oppenheimer opened the first session on what would later be named "black holes" by John Archibald Wheeler.[111] Wheeler gave an extensive lecture on the gravitational collapse of stars, and expressed his enthusiasm for the Oppenheimer–Snyder model.[109]: 240  Another notable speaker was Roy Kerr, who presented his newfound exact solution to the Einstein field equations. With the notable exception of Achilles Papapetrou, most physicists did not grasp its significance, but they later realized that the Kerr metric described rotating black holes.[109]: 341–2  The First Symposium attracted approximately 300 people from many different countries worldwide. However, against the backdrop of the Cold War, a number of physicists from the Soviet Union were not able to attend due to a ban from their own government or their inability to obtain a visa to visit the United States.[111] The gathering was sponsored by Texas Instruments, the RAND Corporation, Lockheed, Boeing, among others.[110] The U.S. Air Force and Navy provided funding for some the early conferences, but stopped doing so after Congress passed the Mansfield Amendments, forbidding the use of the defense budget on basic research. The Texas Symposia were put in this category, despite the relevance of relativistic physics for missile guidance and the functioning of the Global Positioning System (GPS).[110]

The Second Symposium convened at the University of Texas at Austin in December 15–19, 1964. Discussions of quasars continued, now with astronomical observations at various portions of the electromagnetic spectrum, including X-rays and gamma-rays. Astronomers exhibited their discoveries on highly energetic cosmic rays, such as neutrinos. Robert Dicke presented his improved Eötvös experiment, verifying the principle of equivalence to one part in 1011. The Symposium concluded with a seminar on gravitational collapse, the energy released from such an event, and the relevance of relativistic hydrodynamics in the strong-field regime.[108]

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  • MoM-z14 and part of the COSMOS field imaged by the James Webb Space Telescope
    MoM-z14 and part of the COSMOS field imaged by the James Webb Space Telescope
  • An infrared image of MoM-z14 from NASA's James Webb Space Telescope that was taken by the NIRCam
    MoM-z14 has been determined to be at a redshift of z=14.44.
  • A picture showing various filters from JWST NIRCam of the most distant galaxy MoM-z-14.
    A picture showing various filters from JWST NIRCam of the most distant galaxy MoM-z-14.
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Bluey and her father, Bandit, are modelled after real-life blue heelers or Australian cattle dogs.
Bluey's mother, Chilli, and younger sister, Bingo, are red heelers

MAIA

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See also: Cosmic Crisp, SweeTango, Zestar apple, MN55 (apple), and Arctic Apples

Midwest Apple Improvement Association (MAIA)

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The Midwest Apple Improvement Association (MAIA) is an organization founded by apple-growers Mitch Lynd and Ed Fackler in the mid-1990s.[112] Although the MAIA is an independent organization, it is advised by Dr. Diane Miller at Ohio State University.[113] According to The MAIA, the organization grew out of a need for apple cultivars that were both suited to the climate and harvesting challenges of the Midwest.[112] The MAIA's membership were looking for a later and longer-harvesting-period fruit than the Honeycrisp, suitable for growing in the central and southern Midwest. Approximately 50 apple-growers in the Midwestern region pledged to commit US$100 per year for 15 years toward crossbreeding and growing new apple varieties on their independent orchards.[114] During MAIA's first breeding year, beginning in the spring of 1997, 5300 seedlings were developed and grown through crossbreeding existing apple cultivars as GoldRush, Sweet Sixteen, Crimson Crisp, HoneyCrisp, Fuji, and Golden Delicious.[114] The MAIA estimates over 50,000 seedlings have been distributed to MAIA members since the organisations inception over two decades ago.[115]

On the back of EverCrisp's success, the MAIA released two new apple varieties in early-2017, 'Crunch-A-Bunch' and 'Bakers Delight'.[116] According to Growing Produce magazine, the new cultivars formally known as MAIA-11 and MAIA-12 were designed not only for commercial growers but for apple hobbyists and "backyard growers" too.[117][116] The varieties are sold and distributed exclusively by Gurney's Seed and Nursery Company, mail delivering the new MAIA seeds to home apple-growers throughout the US, and through Early Morning and Wafler Nurseries for commercial orchardists.[118] According to Growing Produce, both varieties offer unique flavour profiles and disease, browning and pest resistance.[118]

In 2018 Bill Dodd, president of the MAIA, estimated that 70,000 to 80,000 bushels (a bushel holds approximately 125 medium apples) were to come from the 700,000 apple-trees MAIA have planted since the organisations inception.[119][120] According to OZY magazine, Dodd predicts that one million apple trees will have been planted under the MAIA by 2020.[119] "One of our goals for our breeding program is to have a full season of varieties," Dodd stated in an interview with Growing Produce magazine in late-2017.[116] According to OZY, these new trademarked apple varieties, 'Summerset', 'Rosalee', 'Sweet Zinger' and 'Ludacrisp', are set to be released by 2021.[119] In the next two to three years, the MAIA expect to have early, midseason, and late-season apple varieties available to the public through orchards, nurseries, independent groceries, and grocery-chains. As of early-2018, the MAIA had more than 450 members worldwide.[121] By 2019, MAIA reported that it had 700 members.[122]

Designer fruit

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Designer apple variety WA 38, trademarked as Cosmic Crisp. (2016)

In an article titled 'New Wave Varieties Upset the Apple Cart', OZY magazine reported in December 2018 that "EverCrisp is among a slew of new commercial [apple] varieties," that are not only "juicy, crunchy and flavourful, [but] can be stored longer and have a higher disease resistance".[123] EverCrisp is firmly within what has been referred to by Quartzy magazine as the "designer fruit era".[124] Among other successful designer apples as Cosmic Crisp and Zestar, EverCrisp is part of a new generation of apple cultivars that are "more delicious, beautiful, convenient for eaters and more productive for growers,"[124]

According to OZY, consumer demand for better quality produce and a wider variety of cultivars are the central forces driving the expanding market of designer apples in the U.S.[123] According to Vox, apple breeders are certainly listening. Organizations such as the MAIA are working hard to meet consumer demand by releasing new apples, each with their own nuances.[125] Vox reports that there's an apple for everyone; some look better than others, some are anti-browning, some are crunchier, warmer, cooler, sweeter or more tart.[125]

According to Quartzy, this wave of new designer cultivars have the potential to trump old favourites such as Red Delicious, Granny Smith, McIntosh and Honeycrisp.[124][126]OZY too is aware of this trend, reporting that if institutions such as the MAIA and Washington State University continue to release new apple varieties and the steady rate of apple consumption in the U.S. endures, older apple varieties will eventually be displaced.[123]

Beyond the apple itself, marketing has been an important factor in the success of club apples such as EverCrisp and Cosmic Crisp. According to The Packer magazine, Rena Montedoro, vice president of sales and marketing for Crunch Time Apple Growers, said, "the names of apples influence the consumer. They speak to each apple,"[127] EverCrisp is marketed as the apple whose "name says it all".[128] The EverCrisp Apple website claims that EverCrisp is a "durable apple [that] maintains sweetness and firmness like no other."[128] Although marketing campaigns for independent patented fruit varieties are a relatively new phenomenon, trademarked apple cultivars such as Cosmic Crisp are already experiencing success.[129] According to Seattle magazine, Cosmic Crisp's marketing campaign is heavily focused on consumer research.[130] Through think taste tests and focus groups, Cosmic Crisp has been able to generate significant "buzz" before it has even hit the shelf.[129] According to a Quartzy article in late-2017, Washington State has planted more than 12 million Cosmic Crisp trees in preparation for its debut.[131]

See also: Cosmic Crisp, SweeTango, Zestar apple, MN55 (apple), and Arctic Apples
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