Mathematics includes the study of such topics as quantity, structure and change. Mathematicians use patterns to formulate new conjectures; when mathematical structures are good models of real phenomena mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back; the research required to solve mathematical problems can take years or centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano, David Hilbert, others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.
Mathematics is essential in many fields, including natural science, medicine and the social sciences. Applied mathematics has led to new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics without having any application in mind, but practical applications for what began as pure mathematics are discovered later; the history of mathematics can be seen as an ever-increasing series of abstractions. The first abstraction, shared by many animals, was that of numbers: the realization that a collection of two apples and a collection of two oranges have something in common, namely quantity of their members; as evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have recognized how to count abstract quantities, like time – days, years. Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic and geometry for taxation and other financial calculations, for building and construction, for astronomy.
The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry, it is in Babylonian mathematics that elementary arithmetic first appear in the archaeological record. The Babylonians possessed a place-value system, used a sexagesimal numeral system, still in use today for measuring angles and time. Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom and proof, his textbook Elements is considered the most successful and influential textbook of all time. The greatest mathematician of antiquity is held to be Archimedes 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, trigonometry (Hipparchus of Nicaea, the beginnings of algebra. 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 of sine and cosine, an early form of infinite series. During the Golden Age of Islam 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 notable achievements of the Islamic period are 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-Khwarismi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe.
The development of calculus by Newton and Leibniz in the 17th century revolutionized mathematics. Leonhard Euler was the most notable mathematician of the 18th century, contributing numerous theorems and discoveries; the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, differential geometry, matrix theory, number theory, statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show that any axiomatic system, consistent will contain unprovable propositions. Mathematics has since been extended, there has been a fruitful interaction between mathematics and science, to
Electrical engineering is a professional engineering discipline that deals with the study and application of electricity and electromagnetism. This field first became an identifiable occupation in the half of the 19th century after commercialization of the electric telegraph, the telephone, electric power distribution and use. Subsequently and recording media made electronics part of daily life; the invention of the transistor, the integrated circuit, brought down the cost of electronics to the point they can be used in any household object. Electrical engineering has now divided into a wide range of fields including electronics, digital computers, computer engineering, power engineering, telecommunications, control systems, radio-frequency engineering, signal processing and microelectronics. Many of these disciplines overlap with other engineering branches, spanning a huge number of specializations such as hardware engineering, power electronics and waves, microwave engineering, electrochemistry, renewable energies, electrical materials science, much more.
See glossary of electrical and electronics engineering. Electrical engineers hold a degree in electrical engineering or electronic engineering. Practising engineers may be members of a professional body; such bodies include the Institute of Electrical and Electronics Engineers and the Institution of Engineering and Technology. Electrical engineers work in a wide range of industries and the skills required are variable; these range from basic circuit theory to the management skills required of a project manager. The tools and equipment that an individual engineer may need are variable, ranging from a simple voltmeter to a top end analyzer to sophisticated design and manufacturing software. Electricity has been a subject of scientific interest since at least the early 17th century. William Gilbert was a prominent early electrical scientist, was the first to draw a clear distinction between magnetism and static electricity, he is credited with establishing the term "electricity". He designed the versorium: a device that detects the presence of statically charged objects.
In 1762 Swedish professor Johan Carl Wilcke invented a device named electrophorus that produced a static electric charge. By 1800 Alessandro Volta had developed the voltaic pile, a forerunner of the electric battery In the 19th century, research into the subject started to intensify. Notable developments in this century include the work of Hans Christian Ørsted who discovered in 1820 that an electric current produces a magnetic field that will deflect a compass needle, of William Sturgeon who, in 1825 invented the electromagnet, of Joseph Henry and Edward Davy who invented the electrical relay in 1835, of Georg Ohm, who in 1827 quantified the relationship between the electric current and potential difference in a conductor, of Michael Faraday, of James Clerk Maxwell, who in 1873 published a unified theory of electricity and magnetism in his treatise Electricity and Magnetism. In 1782 Georges-Louis Le Sage developed and presented in Berlin the world's first form of electric telegraphy, using 24 different wires, one for each letter of the alphabet.
This telegraph connected two rooms. It was an electrostatic telegraph. In 1795, Francisco Salva Campillo proposed an electrostatic telegraph system. Between 1803-1804, he worked on electrical telegraphy and in 1804, he presented his report at the Royal Academy of Natural Sciences and Arts of Barcelona. Salva’s electrolyte telegraph system was innovative though it was influenced by and based upon two new discoveries made in Europe in 1800 – Alessandro Volta’s electric battery for generating an electric current and William Nicholson and Anthony Carlyle’s electrolysis of water. Electrical telegraphy may be considered the first example of electrical engineering. Electrical engineering became a profession in the 19th century. Practitioners had created a global electric telegraph network and the first professional electrical engineering institutions were founded in the UK and USA to support the new discipline. Francis Ronalds created an electric telegraph system in 1816 and documented his vision of how the world could be transformed by electricity.
Over 50 years he joined the new Society of Telegraph Engineers where he was regarded by other members as the first of their cohort. By the end of the 19th century, the world had been forever changed by the rapid communication made possible by the engineering development of land-lines, submarine cables, from about 1890, wireless telegraphy. Practical applications and advances in such fields created an increasing need for standardised units of measure, they led to the international standardization of the units volt, coulomb, ohm and henry. This was achieved at an international conference in Chicago in 1893; the publication of these standards formed the basis of future advances in standardisation in various industries, in many countries, the definitions were recognized in relevant legislation. During these years, the study of electricity was considered to be a subfield of physics since the early electrical technology was considered electromechanical in nature; the Technische Universität Darmstadt founded the world's first department of electrical engineering in 1882.
The first electrical engineering degree program was started at Massachusetts Institute of Technology in the physics department
The Apple II is an 8-bit home computer, one of the first successful mass-produced microcomputer products, designed by Steve Wozniak. It was introduced in 1977 at the West Coast Computer Faire by Jobs and was the first consumer product sold by Apple Computer, Inc, it is the first model in a series of computers which were produced until Apple IIe production ceased in November 1993. The Apple II marks Apple's first launch of a personal computer aimed at a consumer market – branded towards American households rather than businessmen or computer hobbyists. Byte magazine referred to the Apple II, Commodore PET 2001 and the TRS-80 as the "1977 Trinity." The Apple II had the defining feature of being able to display color graphics, this capability was the reason why the Apple logo was redesigned to have a spectrum of colors. By 1976, Steve Jobs had convinced the product designer Jerry Manock to create the "shell" for the Apple II – a smooth case inspired by kitchen appliances that would conceal the internal mechanics.
The earliest Apple IIs were assembled in Silicon Valley, in Texas. The first computers went on sale on June 10, 1977 with a MOS Technology 6502 microprocessor running at 1.023 MHz, two game paddles, 4 KB of RAM, an audio cassette interface for loading programs and storing data, the Integer BASIC programming language built into the ROMs. The video controller displays 24 lines by 40 columns of monochrome, uppercase-only text on the screen, with NTSC composite video output suitable for display on a TV monitor, or on a regular TV set by way of a separate RF modulator; the original retail price of the computer was $1,298 and $2,638. To reflect the computer's color graphics capability, the Apple logo on the casing has rainbow stripes, which remained a part of Apple's corporate logo until early 1998. Most the Apple II was a catalyst for personal computers across many industries. In the May 1977 issue of Byte, Steve Wozniak published a detailed description of his design; this arrangement eliminated the need for a separate refresh circuit for the DRAM chips, as the video transfer accessed each row of the dynamic memory within the timeout period.
In addition, it did not require separate RAM chips for the video RAM, while the PET and TRS-80 had SRAMs for the video. Rather than use a complex analog-to-digital circuit to read the outputs of the game controller, Wozniak used a simple timer circuit whose period is proportional to the resistance of the game controller, used a software loop to measure the timer. A single 14.31818 MHz master oscillator was divided by various ratios to produce all other required frequencies, including the microprocessor clock signals, the video transfer counters, the color-burst samples. The text and graphics screens have a complex arrangement. For instance, the scanlines were not stored in sequential areas of memory; this complexity was due to Wozniak's realization that the method would allow for the refresh of the dynamic RAM as a side effect. This method had no cost overhead to have software calculate or look up the address of the required scanline and avoided the need for significant extra hardware. In the high-resolution graphics mode, color is determined by pixel position and thus can be implemented in software, saving Wozniak the chips needed to convert bit patterns to colors.
This allowed for subpixel font rendering, since orange and blue pixels appear half a pixel-width farther to the right on the screen than green and purple pixels. The Apple II at first used data cassette storage like most other microcomputers of the time. In 1978, the company introduced an external 5 1⁄4-inch floppy disk drive, the Disk II, attached via a controller card that plugs into one of the computer's expansion slots; the Disk II interface, created by Wozniak, is regarded as an engineering masterpiece for its economy of electronic components. The approach taken in the Disk II controller is typical of Wozniak's designs. With a few small-scale logic chips and a cheap PROM, he created a functional floppy disk interface at a fraction of the component cost of standard circuit configurations. Steve Jobs extensively pushed to give the Apple II a case that looked visually appealing and sellable to people outside of electronics hobbyists, rather than the generic wood and metal boxes typical of early microcomputers.
The result was a futuristic-looking molded white plastic case. Jobs paid close attention to the keyboard design and decided to use dark brown keycaps as it contrasted well with the case; the first production Apple IIs had hand-molded cases. In addition, the initial case design ha
Robert M. Frankston is the co-creator with Dan Bricklin of the VisiCalc spreadsheet program and the co-founder of Software Arts, the company that developed it. Frankston graduated in 1966 from Stuyvesant High School in New York City and in 1970 from M. I. T. Frankston has received numerous honors and awards for his work: Fellow of the Association for Computing Machinery "for the invention of VisiCalc, a new metaphor for data manipulation that galvanized the personal computing industry" MIT William L. Stewart Award for co-founding the M. I. T. Student Information Processing Board; the Association for Computing Machinery Software System Award The MIT LCS Industrial Achievement Award The Washington Award from the Western Society of Engineers In 2004, he was made a Fellow of the Computer History Museum "for advancing the utility of personal computers by developing the VisiCalc electronic spreadsheet."In recent years, Frankston has been an outspoken advocate for reducing the role of telecommunications companies in the evolution of the Internet with respect to broadband and mobile communications.
He coined the term "Regulatorium" to describe what he considers collusion between telecommunication companies and their regulators that prevents change. Bob Frankston's site/blog Biographical article from Smart Computing Bob Frankston interviewed on the TV show Triangulation on the TWiT.tv network
IPad is a line of tablet computers designed and marketed by Apple Inc. which run the iOS mobile operating system. The first iPad was released on April 3, 2010; as of May 2017, Apple has sold more than 360 million iPads, though sales peaked in 2013. It is the most popular tablet computer by sales as of the second quarter of 2018; the user interface is built around the device's multi-touch screen, including a virtual keyboard. All iPads can connect via Wi-Fi. IPads can shoot video, take photos, play music, perform Internet functions such as web-browsing and emailing. Other functions – games, reference, GPS navigation, social networking, etc. – can be enabled by downloading and installing apps. As of March 2016, the App Store has more than million apps for the iPad by third parties. There have been eight versions of the iPad; the first generation established design precedents. The 2nd-generation iPad introduced a new thinner design, a dual-core Apple A5 processor, VGA front-facing and 720p rear-facing cameras designed for FaceTime video calling.
The third generation added a Retina Display, the new Apple A5X processor with a quad-core graphics processor, a 5-megapixel camera, HD 1080p video recording, voice dictation, 4G. The fourth generation added the Apple A6X processor and replaced the 30-pin connector with an all-digital Lightning connector; the iPad Air added the Apple A7 processor and the Apple M7 motion coprocessor, reduced the thickness for the first time since the iPad 2. The iPad Air 2 added the Apple A8X processor, the Apple M8 motion coprocessor, an 8-megapixel camera, the Touch ID fingerprint sensor; the iPad introduced in 2017 added the Apple A9 processor, while sacrificing some of the improvements the iPad Air 2 introduced in exchange for a lower launch price. There have been five versions of the iPad Mini; the first generation has similar internal specifications to the iPad 2 but uses the Lightning connector instead. The iPad Mini 2 added the Retina Display, the Apple A7 processor, the Apple M7 motion coprocessor matching the internal specifications of the iPad Air.
The iPad Mini 3 added the Touch ID fingerprint sensor. The iPad Mini 4 features the Apple M8 motion coprocessor; the 5th generation features the Apple A12 SoC. There have been three generations of the iPad Pro; the first generation came with 9.7" and 12.9" screen sizes, while the second came with 10.5" and 12.9" sizes, the third with 11" and 12.9" sizes. The iPad Pros have unique features such as the Smart Connector, which are exclusive to this series of iPads. Apple co-founder Steve Jobs said in a 1983 speech that the company's strategy was simple: "What we want to do is we want to put an great computer in a book that you can carry around with you and learn how to use in 20 minutes... and we want to do it with a radio link in it so you don't have to hook up to anything and you're in communication with all of these larger databases and other computers." Apple's first tablet computer was the Newton MessagePad 100, introduced in 1993, powered by an ARM6 processor core developed by ARM, a 1990 spinout of Acorn Computers in which Apple invested.
Apple developed a prototype PowerBook Duo based tablet, the PenLite, but decided not to sell it in order to avoid hurting MessagePad sales. Apple released several more Newton-based PDAs. Apple re-entered the mobile-computing markets in 2007 with the iPhone. Smaller than the iPad, but featuring a camera and mobile phone, it pioneered the multi-touch finger-sensitive touchscreen interface of Apple's iOS mobile operating system. By late 2009, the iPad's release had been rumored for several years; such speculation talked about "Apple's tablet". The iPad was announced on January 27, 2010, by Steve Jobs at an Apple press conference at the Yerba Buena Center for the Arts in San Francisco. Jobs said that Apple had begun developing the iPad before the iPhone. Jonathan Ive in 1991 had created an industrial design for a stylus-based tablet, the Macintosh Folio, as his first project for Apple. Ive stated that after seeking to produce the tablet first, he came to agree with Jobs that the phone was more important, as the tablet's innovations would work as well in it.
The iPad's internal codename was K48, revealed in the court case surrounding leaking of iPad information before launch. Apple began taking pre-orders for the first-generation iPad on March 12, 2010; the only major change to the device between its announcement and being available to pre-order was the change of the behavior of the side switch to perform either sound muting or screen rotation locking. The Wi-Fi version of the iPad went on sale in the United States on April 3, 2010; the Wi-Fi + 3G version was released on April 30. 3G service in the United States is provided by AT&T and was sold with two prepaid contract-free data plan options: one for unlimited data and the other for 250 MB per month at half the price. On June 2, 2010, AT&T announced that effective June 7 the unlimited plan would be replaced for new
Boston Computer Society
The Boston Computer Society was an organization of personal computer users, based in Boston, Massachusetts, U. S. that ran from 1977 to 1996. At one point, it was the largest such group in the world, with regular user group meetings, many publications, permanent offices in Boston, hosting major product announcements, including the East Coast release of the Apple Macintosh in 1984; the organization was co-founded by thirteen-year-old Jonathan Rotenberg in 1977, grew to become the largest such organization in the world, with over 30,000 members in all 50 U. S. states and 40 other countries. The other co-founder was Richard Gardner. Among the early members were many well-known names in the computer industry, including Stewart Alsop II, Daniel S. Bricklin, Philip D. Estridge, Dan Fylstra, William H. Gates, Wayne Green, Mitchell Kapor, Cary Lu, Mike Markkula, Seymour Papert, Jon Shirley, Clive Sinclair, Benjamin M. Rosen, Nigel Searle. At its peak in the early 1990s, BCS supported more than 75 different user and special interest groups and held more than 150 monthly meetings.
Apple Computer Corp. Lotus Software and IBM made major product announcements at BCS meetings. For example, Apple made the East Coast introduction of the Apple Macintosh at a BCS meeting in 1984, GO Corp. made the consumer introduction of PenPoint OS to BCS in 1991. Update, the BCS magazine, was renamed "Computer Update". There were a myriad of user groups meeting monthly with their own paper newsletters. Much of the promotional and support role played by the organization became obsolete with the increasing sophistication of computer users and the growth of the Internet as an alternate source of information. Membership shrank to 18,000, they ran out of money, BCS closed in October 1996. 1977: Founded in February by 13-year-old Jonathan Rotenberg to be a resource for anyone to feel comfortable with computer technology, exchange information with fellow users, learn from each other's successes and failures. 1978: Membership of 73. First mimeographed copy of BCS Update printed in November. First BCS telephone line installed - in Jonathan's bedroom.
First meetings held in the Commonwealth School cafeteria. 1979: First BCS user group forums - for the Commodore PET computer. First BCS book published. Membership: 300. VisiCalc introduced at BCS meeting by Dan Bricklin. 1980: The BCS is incorporated and rents a small downtown Boston office. First part-time employee hired. Membership at 1000 with nine user groups. BCS Update becomes a glossy 34-page magazine. 1980: April,1980 - The Apple/Boston user group becomes part of the Boston Computer society with Allen Sneider and Gary E. Haffer as the group's directors, its first meeting was held in a hall in downtown Boston. Apple Boston created the first conference dedicated to a single computer. Applefest became known as Macworld. Allen Sneider created the first Business User Group,and Home User Group - education and entertainment for the family. 1981: First full-time employee hired. Official non-profit status granted. Calendar launched and cursor button logo adopted. Membership is growing rapidly. 1982: Membership grows to 3,000 with 13 user and special interest groups.
Dues were $18. First electronic bulletin board started. IBM introduces its new personal computer in November with the group starting in January 1983. National media attention. 1983: Membership doubles to 6,300. Two more employees hired. 20 user and special interest groups. First regional chapter started in Rhode Island, under the auspices of the IBM Group. 1984: Office moves to larger office in same complex as membership hits 10,000. Resource Center opens. 29 user/special interest groups. First Buying Guide published; the Macintosh computer is introduced at a BCS meeting and the Mac Group starts. First Microsoft Windows group starts. 1985: Membership at 17,000 with 41 groups. Activist newsletter launched; the book Things the Manual Never Told You, co-written by many BCS activists, is published by Addison Wesley. Professional staff of seven employees. 1986: 50 user groups and 500 activists. First overseas affiliation with the Denmark Personal Computer Society. Calendar lists over 100 events each month. Membership is 23,000 with $35 annual 1987: Tenth Anniversary.
A special 132-page Computer Update published. IBM and Mac Group open offices. Search begins for new BCS Center. Membership at 26,000 representing all 50 states and 40 countries. 1988: Membership goes over 30,000. Computer Update changes back to BCS Update. NeXT introduces its computer at one of the largest meetings with 3,000 people lined up at Symphony Hall in Boston. Calendar lists about 140 events. Public service intiatives begin. 1989: The Massachusetts Special Access Technology Center (MASTAC, an organization assisting disabled children and their teachers and families get access to computer technology, comes under the BCS umbrella. Membership peaks in June at 31,100 with dues at $40 for an individual membership. Over 20 electronic bulletin boards and 700 activists. Revenues over $2 million. 1990 Rotenberg moves from president to chairman. Tracy Licklider named president. Declining membership and local economics force scaleback of BCS Center. Membership at 26,800. Dues reduced to $39. 1991: BCS office moves to One Kendall Square in Cambridge.
Membership shrinks to 24,400. IBM Group moves office to larger space with classrooms, still in Newton. Joint publications launched. Licklider resigns. 1992: Membership at 23,500. HP exec