with gas Leeuwenhoek –1632-1723 –Dutch naturalist –Perfected microscope –**Studied** “invisible” world **of** bacteria, protozoa, and animal and plant cells Blaise Pascal 1623-1662 French **mathematician** and scientist Pascal’s Wager –"God is, or He is not/**John** Locke In 1689 after James II removed, returned to England In 1690 published philosophical justification **of** Glorious Revolution in his Two Treatises **of** Government Locke ’ s State **of** Natural Man People in original state **of** nature –Happy –Natural rights to **life**/

included geometric solutions to quadratic equations and early methods **of** integration. He **studied** the classic problem **of** squaring the circle showing how to square a /A more extensive description **of** Grassmanns **life** and work is given in the interesting book : A History **of** Vector Analysis. was an amateur **mathematician** (a lawyer by profession/System **of** Axioms for Geometry" (1903) as his doctoral thesis. Continuing work in the foundations **of** geometry led to axiom systems **of** projective geometry, and with **John** Young /

his results first. As a result **of** this squabble, British **mathematicians** ignored the fruitful developments in mathematics on the continent and stagnated/the philosophes believed in the ideal **of** progress. They wished to apply sciences emphasis on reason to the **study** **of** peoples moral and social **life**. The philosophes believed that knowledge could/group. **John** Wesley **John** Wesley (1703-1791) **John** Wesley was a clergyman **of** the Church **of** England, was a founder **of** Methodism. He was the foremost leader in England **of** the /

**Mathematicians** –Analysis & Correlation **of**/**Johns** Hopkins University Expression Technologies There are currently four commonly used approaches to high throughput, comprehensive analysis **of** relative transcript expression levels. The enumeration **of** expressed sequence tags (ESTs), Serial Analysis **of** Gene Expression (SAGE), Differential Display Approaches, Array-based hybridization The enumeration **of**/ specializing in gene **studies** from a multitude **of** disciplines, including human/ Nanogen NEN **Life** Science Pro /

**of** continuing to short-shift his other customers. How could Poincare possibly know that he was always given the largest loaf? Poincare had used his weights from the year to draw a bell shaped curve with max at 950 grams, but truncated on the left side. The **mathematician** **John**/**of** the day and insisted that his son **study** readings in ancient languages. When Pascal, at age nine, asked about geometry, he was simply told it was the **study** **of**/ the **mathematician** must do the same thing. As for myself, all my **life** I have/

fill **of** ambrosia, food **of** the gods. (**studying** the star sure makes me happy) Quoted in C B Boyer, A History **of** Mathematics (New York 1968) Ptolemy Ptolemy’s full Latin name was Claudius Ptolemaeus (fl. AD 87-150, Alexandria), He was an ancient astronomer, geographer, and **mathematician** who considered the Earth the center **of** the universe (the "Ptolemaic system"). Virtually nothing is known about his **life**/

**of** the whole work by **John** Colson (1680–1760), the Lucasian professor **of** mathematics at Cambridge, "inspected" by **John** Hellins, was published in 1801 at the expense **of** Baron Maseres. Picture **of** Maria Gaetana Agnesil Her later **life** In 1750, on the illness **of**/**study** **of** theology, and especially **of** the Fathers and devoted herself to the poor, homeless, and sick. After holding for some years the office **of** director **of**/ was one **of** the most important **mathematicians** **of** the 20th century picture Carl’s **life** Siegel was /

a girl. The whole world looks different when he sees her. Her voice reminds him **of** something he has been trying to remember all his **life**, and ten minutes casual chat with her is more precious than all the favours that/ made. **John** Lennox, Oxford Professor, **Mathematician**, Christian Apolgist You can **study** a letter from two approaches. The one approach is that you can analyze the composition **of** the ink and paper **of** a letter. **John** Lennox, Oxford Professor, **Mathematician**, Christian Apolgist You can **study** a letter/

’s modality first Modes **of** Learning I **John** 1:1 Modes **of** Learning I **John** 1:1 Visual Visual /**of** reasoning and to recognize patterns and order in the world. The ability to handle long chains **of** reasoning and to recognize patterns and order in the world. Scientist, **Mathematician** Scientist, **Mathematician**/objects Open-ended questions Prefers open-ended **studies**/work Participatory authority structures Free with feelings/ in the Lamb’s book **of** **Life**….all the assessments **of** one’s **life** are recorded as processes, not/

Michael Faraday (1791-1867) Electro-magnetism **John** Ambrose Fleming (1849-1945) Galileo Galilei /**of** Scientists 1998 Larson found that: "among the top natural scientists, disbelief is greater than ever; almost total". **Mathematicians** had the highest rate **of** belief - 14.3% Biologists had the lowest rate **of**/**life** – human beings Universe is young Secular Big Bang origin **of** the universe **Life** formed via natural processes Universe 12 – 15 billion years old What do you need to do to be prepared? – you must **study**/

**mathematician** Urbain Jean Joseph Le Verrier first proposed its existence The Expanding Earth Our modern understanding **of** the interior and behaviors **of** the Earth is strongly based around plate tectonics and the concept **of**/ nondenominational World Christian Database, a project **of** the Center for the **Study** **of** Global Christianity at Gordon-Conwell Theological Seminary/**of** how Allah loves II.**John** 14 – (way, truth, and **life**) – speaking for Allah on the true path as revealed by all **of** the prophets III.Downplays **John**/

with abstract ideas which exist independently **of** us, our practice, or our world (Plato) Physics: the **study** **of** the most fundamental properties **of** the real world, especially motion and change (Aristotle) **Mathematicians** prove theorems and value rigorous proofs/algebraic geometry (1950s). Israel Gelfand (1913-2009) was a famous Soviet **mathematician** and Maxims mentor. Somewhat atypically for pure **mathematicians** **of** his era, Gelfand maintained a **life**-long interest in physics. (In fact, this was less atypical in /

] 38 What is a mathematical entity? **Mathematicians** themselves have not produced a definition **of** the idea. We can try to generalize from the kinds **of** things **mathematicians** **study**: –numbers, sets, functions, predicates. /an available space **of** states. They might also involve transformation or reconfiguration. Objects might have a limited **life** span (get created /a synthesis **of** the two kinds **of** entities, giving rise to new abstractions **of** physical entities! 65 Thanks Peter O’Hearn, Bob Tennent, **John** Reynolds./

**mathematician** and writer, author **of** Alice In Wonderland, as well as photographer, 1832-1898), 1863], William Holman Hunt (1827-1910), **John** /**of** painting grew out **of** his **studies** with Henry Holiday, a designer **of** stained glass. La Belle Dame Sans Merci,1902, Oil on canvas. City **of** Bristol Art Gallery, Bristol, England. Romeo and Juliet, Southampton City Art Gallery. He passionately championed the Victorian ideals **of** High Art and publicly condemned the artistic trends that emerged towards the end **of** his **life**/

**of** arithmetic situations that are encountered in real **life**.” Madell, AT, (October 1987) Jack drew a sketch **of** /**mathematicians** for work together. Dr. Richard Schaar, Texas Instruments, calls Peace Commission. Park City Mathematics Institute hosts NCTM and **mathematicians**/**of** Teachers **of** Mathematics. Curriculum and Evaluation Standards for School Mathematics. Reston, VA: NCTM, 1989. Newton, **John** E. “From Pattern-blocks Play to Logo Programming,” Arithmetic Teacher 35 (May 1988): 6-9. School Mathematics **Study**/

10 **John** Wallis 1693 4XX + 3X = 10 Types **of** Algebra Algebra is divided into two types: Classical algebra – equation solving Abstract/Modern algebra – **study** **of** groups Classical algebra has been developed over a period **of** 4,/**study** **of** algebraic structures such as: Groups Rings Fields Modules Vector spaces The permutations **of** Rubik’s Cube have a group structure; the group is a fundamental concept within abstract algebra. 19th century Galois (French, 1811-1832) Cayley (British, 1821-1895) British **mathematicians**/

Tragic figure alive in British consciences Led to block by Sir **John** Brydges (Lieutenant **of** Tower) Pure historical nonsense –Executed in open air –More /**studies** it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, **life** would not be worth living. - Jules Henri Poincaré (1854 - 1912) 28 SOME FAMOUS NUMBERS **Mathematicians** –Ancient Greece: Pythagoras and Euclid –Medieval Italian: Leonardo **of**/

blank slate upon which experience inscribes knowledge “natural rights”: all individuals possess the rights **of** **life**, liberty & property (it is the responsibility **of** the government to protect those rights) “natural rights”: all individuals possess the rights **of** **life**, liberty & property (it is the responsibility **of** the government to protect those rights) **John** Locke **John** Locke’s Beliefs all people are born equal all people are born equal education/

in Pater. The celebrated alliance between the New York Schools **of** painting and **of** poetry, with the best poets serving as art critics, has brought little clarification to the **study** **of** the poetry **of** **John** Ashbery, whatever it may have done to the reception **of** the Abstract Expressioninists." He also notes that "Compared to the darker complexities **of** interpoetic and intervisiual reference, languages and visual imagerys allusions to/

parasites, leaves, fruit Peter and Rosemary Grant **Studying** Darwin’s finches since 1973 14 finch / reproduce Brodie: 2 Bullfrogs-----50,000 eggs/**life** (frog =.5 lb; egg mass=25 /**mathematician**, pioneer in multivariate approaches to evolution. Developed shifting balance theory **of** maintenance **of** variation R. A. Fisher: Competing **mathematician** and father **of** linear statistics (Regression); "The Genetical Theory **of**/**of** 1925 **John** Scopes taught evolution to his students despite a Tennessee law preventing the teaching **of**/

to form mathematical theory from measurements **of** planets Published result **of** measurements **of** orbit **of** Mars after Brahe’s death Kepler, German **Mathematician** Brahe and Kepler Johannes Kepler (1571-1630) Student **of** mathematics and astronomy **studied** with Tycho Brahe tested hypothesis after/form Using the experiments **of** **John** Priestly, Lavoisier showed that air is made **of** two parts; However, he tried to take the credit –One part was oxygen and the other he called azote (Greek for no **life**) Lavoisier Cont. /

**of** arcana--‘hidden knowledge’, 2 The medieval alchemical tradition had dual aspects – Alchemy was regarded as a form **of** personal knowledge, a “divine science, …a way **of** **life** **of** **life**/ c. onwards, especially among **mathematicians** -- reputational competition gives rise to increasingly frequent priority disputes towards the end **of** 16 th century ● A / properties **of** large and complex natural systems, and their implications and interpretation often remain contextually determined and problematic. As **John** Wilbanks/

Galileo –1564-1642 –Italian astronomer/physicist –**Studied** in Florence –Demonstrated law **of** gravity –Improved telescope, confirming Copernicus Kepler –1571-1630 –German astronomer and **mathematician** –Found that planets follow elliptical, not circular/**John** Locke In 1689 after James II removed, returned to England In 1690 published philosophical justification **of** Glorious Revolution in his Two Treatises **of** Government Locke ’ s State **of** Natural Man People in original state **of** nature –Happy –Natural rights to **life**/

that CA, which reflect, simplified physical model **of** the real world, is solution **of** his search In early 1950s CA was also **studied** as possible model for biological systems At present CA are numbered among wide and fashionable domains like artificial intelligence The best-known example and implementation **of** CA is “The Game **of** **Life**” - devised by British **mathematician** **John** Horton Conway in 1970 Stanisław Ulam, 1909/

theory Disproved Ptolemy’s theory Achievements cont. Kepler – German astronomer & **mathematician** Kepler – German astronomer & **mathematician** Laws **of** planetary motion Laws **of** planetary motion However, planets follow an elliptical (oval) not circular orbit /**John** Locke – every person is born a tabula rasa (blank slate); knowledge from environment, not heredity Two Treatises **of** Government Two Treatises **of** Government 1. People possess natural rights **of** **life**, liberty & property 2. Governments exist by the consent **of**/

not yet monopolized by university system, and was **studied** informally – so women’s exclusion from university/**of** his **life** Catholic Inquisition places Copernicus’s On the Revolution **of** the Heavenly Spheres on Index **of** Prohibited Books, 1616 Roman Catholic Church formally admits errors **of** biblical interpretation in Galileo’s case, 1992 Copyright © 2010 Pearson Education, Inc., Upper Saddle River, NJ 07458. All rights reserved. Attempts to Reconcile Reason and Faith Blaise Pascal (1623–1662), French **mathematician**/

control theory... Minor role in more famous lives—Wiener. Percy **John** Daniell (1889-1946) Born 9th **of** January 1889 in Valparaiso Chile. First child **of** William and Florence. Family returned to Birmingham in 1895. /**of** a happy family **life**. Stewart 1947 I have very fond memories **of** him. He was charming, delightful, low key, modest. Arthur Porter phone conversation 20th October 2006 Pure and applied mathematics Stewart: “Daniell was highly accomplished as a pure **mathematician** as well as an applied **mathematician**/

challenge **of** conventional mores led to his trial and execution. Greek **mathematicians** Archimedes (287-212 B.C.) – Greek **mathematician**, engineer/**of** the Spanish renaissance He was born in Crete, He **studied** in Venice and Rome where he enriched his style with elements **of**/**of** a great cosmopolitan Mediterranean port. OUNESCO sites in Greece city **of** Rhodes The Order **of** St **John** **of**/**of** water or ice and is the perfect accompaniment for appetizers. Ouzo drinking is an art. Or maybe its a way **of** **life**, the Greek way **of** **life**/

. They emphasized **study** **of** the humanities, such as grammar, rhetoric, poetry, and history. Humanists **studied** the works **of** Greece and Rome/**of** **John** Calvin. Terms and People indulgences – in the Roman Catholic Church, pardons for sins committed during a person’s **life**/**of** Aristotle; stressed experimentation and observation René Descartes – French philosopher and **mathematician** who proposed the need to search for provable knowledge scientific method – a step-by-step process **of** discovery requiring the collection **of**/

tomorrow Method Wrote to 35 **of** the “best and brightest” involved in CAS work for at least the past 15 years. Four Questions about CAS 19 generous responses **Mathematicians** Lynn Steen Tom Dick Jeanette Palmiter Bert Waits Teachers **John** Mahoney Lin McMullin Natalie Jakucyn/ that we have gotten to the point yet where we know enough about the use **of** CAS and its affect on student learning.” Fey: “We really have not **studied** this carefully enough.” Ronau mentions the current “learning curve for CAS being a true /

eparchies; - the existence **of** Romanian illuminated manuscripts (the 15 th – 16 th centuries) proves that some schools functioned; “Saint **John** the Baptist” Monastery, Cenad/**of** „Mathematical Organs” (instruments for geodesy and practical application **of** Mathematics); Petrache Poenaru, 1799-1875, **studied** in Paris, Vienna and in England and was a **mathematician**, physicist, inventor, teacher and organiser **of**/“**Life** Quality”, no. XIV, 2003, no. 3. Urechia, V.A., Istoria şcoalelor de la 1800-1864 (The History **of** /

subtle insistence on the rhythm.. it tended ever towards what seemed like indian singing’ (**John** Masefield). Ellmann – curiously rhythmical manner **of** speaking that others found hard to reproduce. Ellmann – curiously rhythmical manner **of** speaking that others found hard to reproduce. Yeats **studied** in manner and speech unremittingly poetic (A. Cronin). Yeats **studied** in manner and speech unremittingly poetic (A. Cronin). William Butler Yeats Reading: Could/

planets travel in oval paths. He also explained why planets travel in oval paths. He **studied** light and was the first to explain why objects have color. He **studied** light and was the first to explain why objects have color. Newton used science to show/British. He was a great writer, but many **of** his ideas came from **John** Locke. He was a great writer, but many **of** his ideas came from **John** Locke. These included: people have “ the right to **life**, liberty, and the pursuit **of** happiness ” and if a government fails it ’ /

, where he has been since 1966. He is the principal investigator **of** the University **of** Texas Human Factors Research Project. This group **studies** individual and team performance, human error, and the influence **of** culture on behavior in aviation and medicine. Helmreich received all his degrees at Yale. He is a member **of** the Space **Life** Sciences Committee for NASA’s University Space Research Association. He was/

calculating. **John** Napier (1550–April 4, 1617) was a Scottish **mathematician** and astrologer. He is most remembered as the inventor **of** natural logarithms, **of** Napiers bones/ **mathematician**, physicist, and religious philosopher. Important contributions by Pascal to the natural and applied sciences include the construction **of** mechanical calculators, the **study** **of** fluids, and clarification **of** / **of** his two most famous works, the Lettres provinciales and the Pensées. Pascal suffered from ill-health throughout his **life** /

gambling. First Option pricing model! Abraham de Moivre (1667-1754) **Mathematician** (analytic geometry), physicist Friend **of** Newton, Halley Published “Treatise on Annuities on Lives” (1725) Valuation **of** joint annuities on several lives; pricing tontines Johan de Witt 1625-1672 Lawyer, **mathematician** ( analytic geometry), politician (political leader **of** Holland 1653; settled two wars with England) “The Value **of** **Life** Annuities In Proportion to Redeemable Annuities” (1671) Derived a/

**studies** economics? Unit 2 Economics Lead-in Just as you cannot become a **mathematician** overnight, **study** economics and learn to think like an economist will take time. However who **studies** economics? Task 1 Listen to a talk “Who **studies**/**study** 3 They approach the **study** **of** the economy in much the same way as a physicist approaches the **study** **of** matter and a biologist approaches the **study** **of** **life**/to **study** economics well. Complete each **of** the following sentences with the correct answer. Listening 3 According to **John** /

**Life** Cycle Cost process Rethinking Whole **Life** Cycle Cost based decision- making Dr Richard **John** Kirkham Liverpool **John** Moores University School **of** the Built Environment, formerly **of** Cranfield University Richard J Kirkham Rethinking the Whole **Life** Cycle Cost process Oh no…not whole **life** costing again! Mention whole **life**/we need to employ a **mathematician** from NASA to do the sums? do we need to employ a **mathematician** from NASA to do the sums? Richard J Kirkham Rethinking the Whole **Life** Cycle Cost process …this /

to industry, that men ought to organize themselves as a sacred duty to improve and transform the conditions **of** **life**.” “I am fitted for nothing so well as the **study** **of** truth.” Galileo Galilei Pendulum The Simple Pendulum If a pendulum **of** mass m attached to a string **of** length L is displaced by an angle from the vertical, it experiences a net restoring force due/

**life** Did/**mathematician** Wrote a book called Mathematical Principles **of** Natural Philosophy Invented calculus Developed laws **of** nature & physics –The same force, gravity, rules all matter on earth and in space –Every object in the universe attracts every other The degree **of** attraction is determined by mass and distance Developments in Scientific Instruments Inventions: –Telescope –Microscope –Barometer –Thermometer Inventions: –Telescope –Microscope –Barometer –Thermometer Developments in Medicine **Study** **of**/

Greece. 1805 Byron enters Trinity College, Cambridge and befriends **John** Hobhouse. After a term at Trinity College, Byron indulged /**mathematician** Luigi Menabrea on the engine, which she supplemented with a set **of** notes **of** her own. English Charles Babbageanalytical engine Luigi Menabreaset **of**/ landlords wife and **Studies** Armenian at a monastery on the island **of** San Lazzaro. If Byron was spectacular,/ very turbulent and not very constant love-**life**. Towards the end **of** his short **life** he got a more realistic view and /

the Copernican model Contradicted the teachings **of** the Church & the Bible Galileo was put on trial and found guilty **of** heresy & disobedience Sir Isaac Newton English **mathematician** Three Laws **of** Planetary Motion Universal Law **of** Gravitation Every object in the / span **of** a century Rational criticism should be applied to all areas **of** **life**, including religion & politics Baron de Montesquieu Used the scientific method to find the natural laws governing society & politics Published his **study**, The Spirit **of** the /

for individual/team faculty research projects External grants for individual/team faculty research projects Departments allowing a wider range **of** elective courses Departments allowing a wider range **of** elective courses MABI course designation MABI course designation Physical Chemistry for **Life** Sciences course Physical Chemistry for **Life** Sciences course Proposal for a Biochemistry and Molecular Biology major Proposal for a Biochemistry and Molecular Biology major/

as numerous visits by computer scientists and **mathematicians** from the faculty at leading universities Faculty **of** Chemistry Major **studies** and research projects New Materials Borderlands **of** Chemistry and Biochemistry **Studies** Organic chemistry Materials for Clean Technologies Catalysis / on the Steering Committee **of** the European network **of** Precision Polymer Materials. Faculty **of** Biology and Earth Sciences Major **studies** and research projects **Studies** on **Life** Strategies **of** Organisms in Various Environmental/

Calculators were a group **of** four Merton College **mathematicians** consisting **of** Thomas Bradwerdine, William Heytesbury, Richard Swineshead, and **John** Dumbleton. The Oxford Calculators differentiated kinematics from dynamics. Their **studies** emphasized kinematics, and included the investigation **of** instantaneous velocity. They were/was “converted” (as he wrote) by hearing and reading Romans 9:16, his **life** theme l “It [election] does not depend on man’s desire or effort, but on God’s /

ulcer... for the rest **of** his **life** he kept to an extremely strict ( over strict? ) diet which caused him slowly to lose weight.” Kurt enrolled in the University **of** Vienna in the fall **of** 1924, There he **studied** mathematics, physics and /Inconsistent, Complete System Figure 4 Truth or Consequences Unless you get the following use **of** the terms “true” and “false” right, you will not make the correct interpretation **of** **mathematicians**’ results. The only reference to something being “true” is to a proposition,/

Andrew Duchon, Aptima, Inc. **John** Santini, Alion, Inc. Acknowledgements This work was supported by: A seed money grant from the Office **of** the Vice President for Research, / the creative aspects **of** mathematics. Mathematics by Adults Mathematics is the most lawful and abstract **of** the sciences. Real **mathematicians** would not crudely associate/**Life** and Science **of** Richard Feynman Non-Verbal Science Among the virtuosos **of** intuitive (non-verbal) science are physicists with their “gedanken experiments.” At the age **of**/

much **of** his long, distinguished, and tortured **life** developing the subject further. History **of** Monte Carlo Method Credit for inventing the Monte Carlo method is shared by Stanislaw Ulam, **John** von Neuman and Nicholas Metropolis. Ulam, a Polish born **mathematician**, worked for **John** von/ 0.176 -0.140 -0.648 0.439 1.935 -0.271 -1.254 Von Neumann’s Rejection Method Case **Studies** (Topics Introduced) Temperature inside a 2-D plate (Random walk) Two-dimensional Ising model (Metropolis algorithm) Room assignment problem /

**of** his long, distinguished, and tortured **life** developing the subject further.Ludwig Boltzmann An Interesting History History **of** Monte Carlo Method Credit for inventing the Monte Carlo method is shared by Stanislaw Ulam, **John** von Neuman and Nicholas Metropolis. Credit for inventing the Monte Carlo method is shared by Stanislaw Ulam, **John** von Neuman and Nicholas Metropolis. Ulam, a Polish born **mathematician**, worked for **John**/(x) are 1.518 and 1.306 Case **Studies** (Topics Introduced) Temperature inside a 2-D plate/

might have to occasionally intervene to stabilise the solar system. **John** Hedly Brooke, Science and Religion , CUP 1991, p147 For, as Leibniz objected, if God had to remedy the defects **of** his creation, this was surely to demean his craftmanship And I/ made **mathematicians** stand up and take notice. Jonathan Wells: Icons **of** Evolution Jonathan Wells (PhD Yale, PhD Berkeley) Fathers [Rev. Moon] words, my **studies**, and my prayers convinced me that I should devote my **life** to destroying Darwinism, just as many **of** my /

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