A secret witch most of the **Indians** doesn’t know - By kishan Aryabhatta a **great** **mathematician** invented the number 0.He looked at the shape of planets and made a number 0. before people were using only /symbols. Later Egyptians also used this but in the form which we use now 1/10=0.1……………and so on. **Indian** way of decimals The "Kerala school," a little-known group of scholars and **mathematicians** in fourteenth century India, identified the "infinite series" — one of the basic components of calculus — around 1350. /

women could leave Life in Gupta India The Gupta period was a golden age of cultural and scientific achievements. Many **great** works created during Gupta period One of greatest writers, Kalidasa –Poet, playwright –Wrote plays for royal court –Sakuntala,/ today Gupta scholars most advanced **mathematicians** of their day Developed modern math system First to use concept, symbol of zero Hindu-Arabic numerals; created by **Indians**, brought to Europe by Arabs Mathematics Ancient **Indians** quite advanced Made medicines from/

Indias First Empire By: Sydney MAIN IDEA#1 #1 The Mauryan dynasty built Indias first **great** empire. Chandragupta Maurya was and **Indian** prince who conquered a large area in the Ganges River valley. Maurya found the Mauryan dynasty in/ stone. Images of with many hands were created to show that the deities had many abilities. Main Idea#3 **Indian** math made important contributions. Aryabhata was the leading **mathematician** of the Gupta empire. He was one of the first scientists known to have used algebra. Main Idea#3/

and Medicine Ocean trade leads to advances in astronomy **Indian** astronomers in Gupta Empire prove that world is round **Mathematicians** develop idea of zero and decimal system Doctors write medical guides and make advances in surgery **Indian** Trade Grows India’s Valuable Resources India has spices,/to keep people happy Liu Bang dies in 195 B.C. ; wife Lü seizes control of empire Liu Bang’s **great**-grandson Wudi rules from 141 to 87 B.C. “Martial Emperor” Wudi defeats Xiongnu (nomads) and mountain tribes Colonizes /

**Great** Civilization 1500 B.C.E. - 500 C.E. Origins of Hindu India ● The Aryans: o During the 1500s B.C.E., an Indo-European group of people known as the Aryans invaded the **Indian** subcontinent and conquered the civilizations of the Indus River Valley. To invade the **Indian**/ **Indian** folk tales that provided moral lessons to **Indian** children. The Gupta Empire ● Gupta Achievements: o Mathematics: During the reign of the Gupta Empire, major achievements were made in the area of mathematics. Gupta **mathematicians** /

**Indians**? Native Americans Native Americans developed different cultures and ways of life because of geographical diversity Despite being so different Native Americans did hold common beliefs: Kinship Respected and honored the spirit world Land wasn’t something that could be owned Native American Life **Mathematicians**/ once one mega-continent Continental plate movement created the Appalachian and Rocky Mountains The **Great** Ice Age thrust down over North America and scoured the present day American Midwest /

name for one and many. Some languages still have this shortcoming. The Siriono **Indians** of Bolivia and the Brazilian Yanoama people do not have words for anything /entire philosophy that the brotherhood struggled to build. For revealing that secret, the **great** Pythagoras himself sentenced Hippasus to death by drowning. The Greek Mathematical Cult The/ of many buildings, musical works, and works of art. Some historians and **mathematicians** argue that the Parthenon, the Athenian temple, was built so that the golden/

education – Churches & self-help organizations formed African American Intellectuals Benjamin Banneker – born free in MD most accomplished **mathematician** & Astronomer of his time Jupiter Hammon – NY Slave, took up contemporary issues in poems and issues “Address to/ Policy of extermination of all **Indians**. – **greatly** swayed public opinion resulting in the election of many more officials that hated **Indians**. Land A New York editor, Brackenridge rather than whites acknowledging **Indian** title to any land he /

The Buddha’s “real” name. $500 Answer from Religion Sidhartha Gautama $100 Question from **Indian** Achievements This Mauryan ruler was a **great** military leader, until he converted to Buddhism and vowed to pursue a life of peace. He/ $200 Answer from **Indian** Achievements plastic surgery $300 Question from **Indian** Achievements These step by step solutions to problems were developed by **Indian** **mathematicians**. $300 Answer from **Indian** Achievements algorithms $400 Question from **Indian** Achievements This beautiful 17/

who enroll get a monthly check from the government 3. Population is decreasing rapidly 4. Have been on continent nearly 5,000 years 5. Were **great** **mathematicians** & architects What do you know (cont)? 6. U.S. always accorded **Indian** nations the rights of independent nations 7. Tribal system was run by warrior- chiefs 8. Basic worldview: all things in natural world are connected/

many small kingdoms. The Greeks, under Alexander the **Great**, entered India but turned back when his homesick troops threatened to rebel. India’s First Empire After Alexander left India, an **Indian** military officer named Chandra Gupta Maurya built a strong/known to have used algebra. The **Indians**’ invention of zero affected the study of mathematics and science. Gupta **mathematicians** developed symbols for the numbers 1 to 9 that we use today. Advances in Science **Indian** astronomers mapped the movements of planets /

part of life in this land. The Winter Monsoons are hot and dry and the Summer Monsoons consist of a lot of rain. However, **great** civilizations developed and flourished amidst the rivers, mountains, plains and deserts of the subcontinent. Many rivers also flowed through ancient India making the land fertile/ contributed to a growth of arts and learning. Gupta artists were best known for their sculptures and paintings in temples. **Indian** **mathematicians** began the concept of zero and developed the decimal system.

Muslim University (1920) University of Delhi (1922). 1841 - 1950 : 12 **Indians** were elected Fellow of the Royal Society of London. A. Cursetjee, Engineer & Shipbuilder S. Ramanujan, **Mathematician** Sir J. C. Bose, Bio-physicist Sir C. V. Raman, Physicist / has become a standard description of protein structure **Great** Discovery in Biological Science IISc has become epitome of **Indian** excellence in Scientific Research **Indian** Institutes of Technology The first **Indian** Institute of Technology (IIT) was established at/

**Indian** languages, Mysore LTT-IT: VALEDICTORY ADDRESS Two faces of language Language is a human construct, undoubtedly – which is why the saying Language is species specific and species general is so apt. Lets turn the question around: To what extent is man a construct of language? To a **great**/important ways. Problems facing our endangered languages Compare this scenario with a recent prediction by a bio- **mathematician** called Pagel that, out of 6,000 odd distinct human languages spoken all over the world, only/

4.9%, Northern Irish 2.9%) 92.1%, black 2%, **Indian** 1.8%, Pakistani 1.3%, mixed 1.2%, other 1.6% (2001 census) Chart Time: **Great** Britain’s Ethnics 1. English 83.6% 2. Scottish 8.6% 3. **Indian** 1.8% 4. Welsh 4.9% 5. Black 2%/literature. He wrote dozens of plays which continue to dominate world theater 400 years later. Sir Isaac Newton -Isaac Newton was a **mathematician** and scientist who invented differential calculus and formulated the theory of universal gravitation, a theory about the nature of light, and three/

Gupta empire encouraged peace, prosperity, and trade. The Gupta empire is considered a golden age of Hindu culture. A golden age is known as a time of peace, prosperity, and **great** achievements. **Indian** **mathematicians** discovered the concept of zero and the decimal system **Indian** artists created beautiful works of art and **great** works of literature were produced during the golden age Video – Maurya Empire

**Great** Awakening, proposed Albany Plan— vision of colonial union to deal with common problems Pearson Education, Inc., publishing as Longman © 2008 THE ENLIGHTENMENT IN AMERICA Founders of colonies had been contemporaries of Galileo Galilei (1564-1642): astronomer René Descartes (1596-1650): philosopher- **mathematician**/ a Philadelphia Quaker, gathered and classified plants from Florida to the **Great** Lakes. He also studied **Indians**. Benjamin Franklin 1752 kite experiment Invented lightening rod, Franklin stove, /

city. Aryan invaders overran the region. Chapter 3, Section Video Clip of Ancient **Indian** Civilizations Chapter 3, Section The Geography of China China was the most isolated of /recorded Aztec knowledge and ran schools for sons of nobles. Some priests were astronomers or **mathematicians**. Priests were a special class. The sun god was the chief Aztec god. / their own language and religion on the people. They created one of the **great** road systems in history, allowing armies and news to travel rapidly around the /

a powerful leader and be known to history as Alexander the **Great**. Alexander the **Great** Although Alexander was only 20 years old when be became king/ new culture emerged. Greek culture blended with the conquered Egyptian, Persian, and **Indian** influences. This blending became known as Hellenistic culture. During the Hellenistic period,/a geometry text compiled by Euclid. Euclid was a highly regarded Alexandrian Greek **mathematician** who created the Elements, a book of 465 carefully presented geometric positions and/

chiefs called Rajahs. Brahmins (priests) Kshatriyas (warriors) Vaisyas (farmers, artisans) Sudras (slaves) Government Social Structure **Indian** people were divided into social classes in what was called the Caste System. A person could not change their place/ **great** cultural achievement. The Gupta Golden Age Trade and farming flourished under the Gupta Empire, which contributed to a growth of arts and learning. Gupta artists were best known for their sculptures and paintings in temples. **Indian** **mathematicians** /

– Invaders – Persians, Greeks, Macedonians **Indian** people unify = Strong empires – Mauryan, Kushan, Gupta Mauryan Empire Chandragupta Maurya -founder – drove out foreign invaders – Harsh, but effective – Secret police, large army- feared – Assassination Asoka – **Great** ruler – Converted to Buddhism – Rejected /goods for what? Woolen and linen clothes, glass, and precious stones Who was the famous **Indian** **mathematician**? Aryabhata By the late fifth century A.D., invasions by nomadic Huns did what? Reduced/

without religion is blind.” Albert Einstein Vedic Mathematics “We owe a lot to the **Indians**, who taught us how to count, without which no worthwhile scientific discovery could have/ ignore its true merit. But its very … Vedic Mathematics... simplicity, the **great** ease which it has lent to all computations, puts our arithmetic in the/of the greatest men produced by antiquity.“ -- Pierre Simon de Laplace, (French **mathematician**, philosopher, and astronomer), “India has a well-developed academic community with a /

the first scientists known to have used algebra. Aryabhata was one of the first scientists known to have used algebra. Math **Indian** **mathematicians** also introduced the concept of zero and used a symbol (0) for it. This system was adopted by Arab scholars and /monetary system and ordering the building of a system of roads. Qin Shihuangdi also was instrumental in starting the building the **Great** Wall. The founder of the Han dynasty was Liu Bang, a man of peasant origin. He discarded Legalism and /

a rise in Hinduism. Early years of the Gupta dynasty is called the “golden age” of **Indian** civilization **great** achievements in the arts extreme prosperity for the people. Economy Most people were extremely poor Very few people/ Math Understood abstract & negative numbers Had a concept of zero & infinity Aryabhata – famous **mathematician** – first known user of algebra & quadratic equations. Medicine **Indian** doctors were very advanced. Understood the importance of the spinal cord. Had surgical procedures to mend/

of Athens in 529 AD Greek mathematics of the period following Alexander the **Great** is sometimes called Hellenistic mathematics. The Greeks used logic to derive conclusions from/ Archimedes (c.287–212 BC) of Syracuse, widely considered the greatest **mathematician** of antiquity, used the method of exhaustion to calculate the area under the arc/a long history, and with the proof of the existence of irrational numbers **Indian** mathematics The oldest extant mathematical records from India are the Sulba Sutras,/

ICE AGES & GLACIATIONS “Every **great** scientific truth goes through three/ latitudes in the northern hemisphere. The Antarctic continent was situated over the South Pole, the **Indian** sub-continent was impinging upon Asia, and ocean basin configurations were changing, as the Tethyan Seaway/ that changes in the Earth’s orbital parameters were the ultimate cause of glaciation. The Serbian **mathematician**, Milutin Milankovitch formalized the theory relating changes in the Earth’s orbital parameters to climate change./

been fully recognized by posterity. Sir George Howard Darwin (1845 – 1912) A **mathematician** and astronomer; the most distinguished of Darwin’s children Known for his work on/Middlesex village noted for what was reputedly the finest private school in England – **Great** Ealing School. **Great** Ealing School had many famous pupils, including William S. Gilbert (of Gilbert /the west coast of Africa, around the Cape of Good Hope, and across the **Indian** Ocean to Tasmania (June 24, 1847). The HMS Rattlesnake (1822) Life on /

the **Great** 4. Legacy a. Now what? i. Empire broken into 3 main territories ii. Would last for centuries Hellenism b. Hellenism i. Hellenistic Culture: blending of Egyptian, Persian, Greek and **Indian** influences ii/not for personal gain, but to perform virtuous acts for the good of all. true happiness is found in **great** achievements. Hellenism: The Arts & Sciences Scientists / **Mathematicians**: Aristarchus heliocentric theory. Euclid geometry Archimedes pulley Hellenistic Art: More realistic; /

geocentric theory) Hellenistic Period 300 Points Ptolemy **Mathematician** credited with estimating Pi and developing the /**Great** 200 Points Alexander the **Great** 300 Points Northern African country conquered by Alexander Alexander the **Great** 300 Points Egypt The 4 different cultures that blended together to create Hellenistic culture. Alexander the **Great** 400 Points Greek, Persian, **Indian**, Egyptian Hellenistic Period 400 Points Alexander’s Greek tutor Alexander the **Great** 500 Points Aristotle Alexander the **Great**/

wanted qualified physicians treating them. The faithful throughout the empire relied on **mathematicians** and astronomers to calculate times for prayer and the direction of Mecca. /called the Comprehensive Book that drew on knowledge from Greek, Syrian, Arabic, and **Indian** sources as well as his own. Medicine (cont.) Al-Razi was highly influential /features, such as baths using Roman heating system. In Cordoba, Spain, the **Great** Mosque there (see right) incorporated a multi-lobed interwoven arch never seen before/

important contributions of Greek culture to Western civilization? How did the empire of Alexander the **Great** establish a basis for the spread of Hellinistic culture? Results of the Persian Wars Greece wins/culture with Egyptian, Persian, and **Indian** influences Hellenistic Trade Hellenistic culture spread through trade Hellenistic Trade Routes Hellenistic Achievements Advances continued in Greek art, architecture, philosophy, mathematics and science Greek **Mathematicians** Pythagoras and Euclid “Pythagoras and/

was Alexander of Macedonia Alexander the **Great**. Hellenistic Culture As a result of Alexander’s conquering, a brand new culture emerged. –The Hellenistic culture A blend of Egyptian, Persian, and **Indian** influences –Language: A dialect of Greek/, their calculations were pretty impressive due to the lack of ancient technology. Mathematics & Physics Hellenistic astronomers and **mathematicians** used a geometry text created by a Alexandrian teacher Euclid. Euclid wrote a book called Elements. –Contained 465/

Macedonia, Greek city-states –Egypt –Old Persia (India) Hellenistic Culture: Greek, Persian, Egyptian, and **Indian** The Empire of Alexander the **Great** 5 In ten years, Alexander of Macedonia created the largest empire in the world up to that / than Earth –Proposes planets revolve around sun Mathematics and Physics –Pythagoras: creates the Pythagorean theorem –Archimedes—scientist and **mathematician** He accurately estimated the value of pi ( ). Securing a legacy Alexander made Babylonia the capital of his Empire/

Conquered Greece Father of Alexander the **Great** Alexander the **Great** Son of Phillip II Adopted Greek /**Great** Hellenistic Age The years of Greek influence following Alexander’s death and ending with the Roman conquest. Blending of Greek (Hellenic) culture with Egyptian, Persian, and **Indian** influences Hellenistic Trade Hellenistic culture spread through trade Hellenistic Trade Routes Alexander’s Legacy: The Hellenistic Age Advances art, architecture, philosophy, mathematics and science Greek **Mathematicians**/

so that things done by men not lose their color in time, nor deeds **great** and marvelous, some bought forth by Greeks and some by foreigners, lose their /**Great** Hellenistic Age Years of Greek influence following Alexander’s death and ending with the Roman conquest. Hellenism Blending of Greek (Hellenic) culture with Egyptian, Persian, and **Indian** influences Hellenism Hellenistic culture spread through trade Advances continued in Greek art, architecture, philosophy, mathematics and science Greek **Mathematicians**/

History “This is ….presented so that things done by men not lose their color in time, nor deeds **great** and marvelous, some bought forth by Greeks and some by foreigners, lose their renown” Thucydides Greek historian “/Blending of Greek (Hellenic) culture with Egyptian, Persian, and **Indian** influences Hellenistic culture spread through trade Advances continued in Greek art, architecture, philosophy, mathematics and science Greek **Mathematicians** Pythagoras and Euclid “Pythagoras and Euclid thought math was not /

formed Macedonians into formidable army, attacked and defeated Greece 2.Alexander the **Great**—336 B.C., after his father’s death, Alexander proclaimed himself/own unique culture. II. Hellenistic Culture: Greek culture mixed with Egyptian, Persian and **Indian** influences 1. Alexandria—the city located at the western side of the Nile delta / astronomers could study the planets and stars 2. Math and Physics: A. Euclid—**mathematician** who opened a school in Alexandria and whose works are still the basis for courses/

Computer Science 15-251 **Great** Theoretical Ideas in Computer / 1 1 3 200000 311000 343 2110 2 22 10 12111110 11111111 1 1 “Dad, it’s **INDIAN**-PENDANT like you said.” Isaac Rudich 3 200000 311000 343 2110 2 22 10 12111110 11111111 ??1??1?? Think of Yourself as /to have every line commented (using a special syntax) as to why you wrote that line ProverVerifier A successful **mathematician** plays both roles in their head when writing a proof Gratuitous Induction Proof = k(k+1)/2 + (/

has two distinct NLZB representations, which contradicts the induction hypothesis. So n must have a unique representation Inductive definition is **great** for showing UNIQUE representation: f(Xb) = 2f(X) + b Let n be the smallest number reprinted by two/ digit can be 0, 1, or 2 How could this be Egyptian? Historically, negative numbers first appear in the writings of the **Indian** **mathematician** Brahmagupta (628 AD) One weight for each power of 3 Left = “negative”. Right = “positive” Study Bee Unary and Binary /

Olmec The first **great** Mesoamerican culture was the Olmec, who lived on the Gulf of Mexico. They developed the beginnings of a calendar and writing. Used slash and burn farming Unsure why civilization declined The Maya Maya **mathematicians** devised a number system/ dwellings in the Southwest. They abandoned their communities in about 1300. The Anasazi are the ancestors of the Pueblo **Indians** The Hohokam lived approximately from ad 200 to 1400 in present-day central and southern Arizona, largely along the Gila/

the two component motions together thereby finding the tangent to the curve.Greek mathematicianArchimedes The **Indian** **mathematician**-astronomer Aryabhata in 499 used a notion of infinitesimals and expressed an astronomical problem in / GaussClausiusDirichletRiemannvon Neumann HeineKroneckerLipschitzChristoffelKirchhoffBeltrami Other applications It is impossible in this place to enter into the **great** variety of other applications of analysis to physical problems. Among them are the investigations of/

the Gupta Empire 13. Most famous **mathematician** of the Gupta Empire First scientist to have used algebra First scientist to have used algebra Some of the earliest examples of **Indian** architecture stem from the time of Asoka when Buddhism became the religion of the state. The desire to spread the ideas of Gautama Buddha inspired the **great** architecture of the Mauryan dynasty and/

India, about 30 km (19 mi) from Patna. He was the first in the line of **great** **mathematician**-astronomers from the classical age of **Indian** mathematics and **Indian** astronomy. His most famous works are the Āryabhaṭīya (499 CE, when he was 23 years old/Mishra, LPU Born in 1800s Srīnivāsa Rāmānujan (22 December 1887 – 26 April 1920) He was an **Indian** **mathematician** and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite/

Aiyangār Rāmānujan FRS, better known as Srinivasa Iyengar Ramanujan (22 December 1887 – 26 April 1920) was an **Indian** **mathematician** and autodidact who, with almost no formal training in pure mathematics, made substantial contributions to mathematical analysis, number theory, infinite/from strangers- as his friend C. P. Snow later put it, “pretended to prove the prophetic wisdom of the **Great** Pyramids, revelations of the Elders of the Zion or the cryptograms that Bacon had inserted in the plays of Shakespeare”-/

long Winter nights. He dislikes Christianity and prefers Buddhism & Hinduism. His philosophy is a mixture of Kant & **Indian** philosophy. He is free of nationalism He was the first to proclaim outwardly (on ground prepared by Rousseau &/ Philosophy Scientific philosophy of mathematics Both the infinitely large and its inverse, the infinitely small, have caused headaches. **Great** **mathematicians** of the 17th century were optimistic & anxious for quick results. That left the foundations of analytic geometry & /

the Han period in China, the Gupta period was a golden age of cultural and scientific achievements. Many **great** works created during Gupta period One of greatest writers, Kalidasa Poet, playwright Wrote plays for royal court Sakuntala,/calculated circumference with remarkable accuracy Achievements of **Indian** Culture Astronomy, Mathematics, and Medicine Ocean trade leads to advances in astronomy **Indian** astronomers in Gupta Empire prove that the world is round. **Mathematicians** develop the idea of zero and /

, a highly developed one in an advanced state of decay ~~~ Shashi Tharoor (**Indian** author. In his ‘The **Great** **Indian** Novel’) www.pratheep.com Delhi, India The **Indian** way of life provides the vision of the natural, real way of life. We/pratheep.com Ellora,Maharastra, India Vedanta is the most impressive metaphysics the human mind has conceived. ~~~ Alfred North Whitehead ( British **mathematician**) It is not only a country and something geographical, but the home and the youth of the soul, the everywhere and/

. He made a vow to live a peaceful life and follow Buddhism. Asoka did many **great** things for his people. Asoka did many **great** things for his people. He built hospitals and new roads and sent teachers throughout India to/India. **Indian** Literature and Science continued Remains of **Indian** art include mainly religious works made in stone. Remains of **Indian** art include mainly religious works made in stone. Aryabhata was a **mathematician** who lived during the Gupta dynasty. Aryabhata was a **mathematician** who lived/

diversity--about increasing the participation of historically under-represented groups G The argument: We have a **great** need for more **mathematicians** and scientists G Note, though, that ESP programs are about specific kinds of diversity--about / declared science majors after controlling for financial need and preparation (Johnson, 2007a) African American, Latino and American **Indian** students are less likely to graduate in science than similarly prepared White and Asian students (Huang, Taddese & Walter,/

Mathematics The collapse of Rome and the general chaos that followed has no **great** advancements in the mathematical community in it.. The Dark ages and then /**Indian** mathematics ceased after that point. Arabic Mathematics : Forgotten brilliance? Mathematics Education A Glimpse of the History of Mathematics (18) Medieval Mathematics (4) (320 –1660 AD) Arabic Mathematics : Forgotten brilliance? Many of the ideas which were previously thought to have been brilliant new conceptions due to European **mathematicians**/

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