Thursday, November 28, 2019

Hotel Management System free essay sample

From Wikipedia, the free encyclopedia Hotel reservations systems, commonly known as a  central reservation system  (CRS) is a computerized system that stores and distributes information of a hotel, resort, or other lodging facilities. A Central Reservation System is a tool to reach the  Global Distribution Systems  as well as Internet Distribution Systems from one single system, namely a central reservation system. A CRS is mainly an assistance for hoteliers to manage all of their  online marketing  and sales, where they can upload their rates amp; availabilities to be seen by all sales channels that are using a CRS. Sales Channels may include conventional travel agencies as well as online travel agencies. A hotelier using a central reservation system easing his/her tasks for online distribution, because a CRS does everything to distribute hotel information to the sales channels instead of the hotelier. ABSTRACT The chapter 1 discusses the introduction and system overviewof  the  study. We will write a custom essay sample on Hotel Management System or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page This  section  deals  with  the  following  statement  of  theproblem according to the study, objective, scope and delimitation of thestudy. The chapter 2 deals with the feasibility studies discuss whichincludes  technical  feasibility  and  operational  feasibility. Economicfeasibility deals with the hardware and software depreciation cost. Thecost will implement in the market analysis. System Analysis implements diagrams that discuss the flow of  the  proposed  system. It  helps  the  proponents  to  take  action  for  theproposed system. Computer programmers develop things like computer system thatthe rest of us could use. The computer programmers tell the users what todo. They make programs that users can easily used or understand. The advent of new technology gave rise to easy and hassle freeinteraction between and among humans. Whether it is in business, scienceor what ever task a person takes on the quality and speed of carrying it outare enhanced with automation at the core of this efficient  Today,  many systems have  used an  automation process like usingcomputer system, due to the efficient and accuracy. Hotel ReservationSystem† is a transaction processing system. In this system there are moreadvantages rather than a manual Hotel Reservation. Background of the Study The proponents want to know the reasons of hotel in using manualreservation. The proponents conduct a study towards the topic becausethey notice some of the hotel still use manual reservation. The study will emphasize the effects of using manual reservationand how a computerized reservation will be substituted. Therefore, theproponents purported to find out how to increase the number of customerusing computerized reservation. Interaction and individual stimulation have always been linked tothe technological availability of the time and place. With the transition toan information-based society, computers and transactions have evolvedfrom manual transaction. One of the solutions or alternatives to the problems that a hotel isfacing, a system was being developed which can edit, delete, filter,monitor and store and secured the records of the customers. Hotel Reservation system is a transaction processing system thatsolves the problem encountered during the manual Hotel Reservation. The computerized Hotel Reservation System aims to simplify the manualHotel Reservation fastest and accurate. Database is shared thru LocalArea  Network  (LAN). The  proponents  make  use  of  some  tools  andtechniques to build the project. The system uses Graphical User Interface(GUI) to help the user give instruction to the computer. The system once 6 implemented it will solve the most common problems that the HotelReservation encounter. Statement of the Problem Based on the research conducted, the proponents found out theproblem of this study is:How will this system help the management and the staff to have anaccurate  service  at  the  same  time  to  monitor  the  records  of  thecustomers? General Problem:The main problem of this study is the inaccurate reservation of thecustomer. Specific problem:1. Low in security2. Time monitoring3. Less data integrity4. Difficulty in searching and retrieving files5. Possible loss of records and retrieving files6. Difficulty in finding the availability of  rooms Objective of the Study This study intends to develop an Hotel Reservation System. The proponents developed an automated system suitable for thehotel; the system could save time, effort in filling and monitoring Hotel Management Thesis Sample Hotel Service Quality Control Summary December last year, I came to work in our unit internship Garden Hotel Suzhou, famous Yang began officially become my life work. After entering the hotel, we first continuous learning training started. discontinuity in learning, I deeply understand that the hotel service quality for a hotels overall image of the shape is very important. hotels belong to the service behavior. The hotel offers a main product is service . hotel service quality is the life of the hotel, service quality control is the core of the hotel management. Currently, the global hotel market in general is oversupply, different fierce competition among hotels, guests who are able to provide comprehensive quality services, who will be able to provide comprehensive quality services to the guests, who will be able to gain a competitive edge in the market, good economic returns. Service Quality Management is currently one of the hot enterprise management, enterprise competitive advantage to win long-term guarantee. So , to improve hotel service quality, we must establish the correct concept of service quality management. master effective quality of service control. while in the hotel service quality management, must be emphasized that the concept of total quality management to improve the overall customer feeling of hotel service quality, comprehensive and accurate grasp of the requirements of customers, providing services to meet customer requirements, and to customer satisfaction. This is the hotel can be based on the market, and the basic conditions for the development, management of hotel service quality is a basic principle. So , the hotel should understand current and future customer needs, satisfaction with customer requirements and strive to exceed customer expectations, while providing personalized service, is to shop for different individual needs of the guests are provided with targeted services, which create a hotel customer loyalty, pursuit of their long-term interests has an important influence, therefore, the hotel business as a service behavior in the course of activities, services, core accounting components, this paper, the control of hotel service quality are discussed. Key words: quality service hotel service quality personalized service   Abstract In twelve month of last year, I have arrived in our practice place of work Suzhou Oasis Hotel, have started me treading the life entering working position formally. In entering a hotel, we have begun to train discontinuous studying first. In molding studying disconnection, my deep acquaintance to the hotel service quality overall image to a hotel be what important. The hotel is belonged to serve a sexual behaviour. That the hotel is that the product that the guest provides is main is service. Hotel service quality is the hotel life, serving the mass under the control of is hotel management controlcore content. At present, the whole world hotel marketplace is excessive supply as a whole, hotel room competition is different fierce, who is able to provide guest with all-round high grade service, who is therefore likely to provide guest with all-round high grade service, who is therefore likely to get a competitive edge on the marketplace, gain the fine economic effect. Serving quality control is one of the hot spot that current business administration studies, guarantee being that enterprise wins the long competitive edge. Therefore, need to improve hotel service quality, must set up correct service quality control idea. Have the effective service mass under the control of in hand. In serving quality control at the same time in the hotel, must emphasize overall quality control concept, improve hotel overall service quality in customer feeling, various grasping a customer all round accurately requires that providing the service satisfying the customer request, makes a customer satisfied and. This is that the hotel can keep a foothold in the marketplace, joins the main conditions further developing, and is also that the hotel serves fundamental one quality control middle principle. Therefore, the hotel should understand current and future need of customer, demand the satisfied customer and strive for to exceed the customer expectation, but provide to individuation service, pertinency provided by individuality need had by guest of store serves coming being to satisfy diversity, this builds the faithful customer of hotel face to face, run after enterprise long-term interests having important effect, therefore, the hotel is hit by as serving a sexual behaviour in enterprise business operations process, serve a component holding core position, the main body of a book is discussed specifically for hotel service quality controlling has been in progress. Keywords: First class of service Hotel service quality Individuation service   directory.

Sunday, November 24, 2019

Evans Surname Meaning and Family History

Evans Surname Meaning and Family History Evans is a patronymic surname meaning son of Evan. The given name Evan derives from the Welsh name Ifan, a cognate of John, meaning gracious gift of Jehovah. Within the United Kingdom, Evans is the 8th most common surname, being most common in the city of Swansea, Wales. It is ranked as the 48th most common surname in the United States. Surname Origin:  Welsh Alternate Surname Spellings:  EVINS, EVENS, EVAN, EVIAN Famous People with the Evans Surname Walker Evans -  American photographerArthur Evans  - English archaeologist and curatorLee Evans  -  African-American track-and-field greatEdith Evans  -  English stage and screen actressMichael Evans - British stage and screen actor Where is the Evans Surname Most Common? The Evans surname is the 656th most common surname in the United States, according to surname distribution data from Forebears.  The name  is especially numerous in North and South Wales and in the adjacent English counties of Shropshire and Monmouth.  Evans ranks as the 5th most common surname in Wales, the 10th in England, the 20th in Australia and the 47th in the United States. Surname distribution maps from  WorldNames PublicProfiler  also demonstrate the popularity of the Evans surname in Wales and England, followed by Australia, New Zealand, Canada and the United States (especially Georgia, Mississippi, and Utah). Genealogy Resources for the Surname Evans 100 Most Common U.S. Surnames Their MeaningsSmith, Johnson, Williams, Jones, Brown... Are you one of the millions of Americans sporting one of these top 100 common last names from the 2000 census? Evans Family Crest - Its Not What You ThinkContrary to what you may hear, there is no such thing as an Evans family crest or coat of arms for the Evans surname.  Coats of arms are granted to individuals, not families, and may rightfully be used only by the uninterrupted male-line descendants of the person to whom the coat of arms was originally granted. Evans DNA ProjectMore than 570 members have joined this project for the Evans surname (and variants) to  work together to find their common heritage through DNA testing and sharing of information. Evans Family Genealogy ForumThis free message board is focused on descendants of Evans ancestors around the world. Search the forum for posts about your Evans ancestors, or join the forum and post your own queries.   FamilySearchExplore over 9.7 million  results from digitized  historical records and lineage-linked family trees related to the Evans surname on this free website hosted by the Church of Jesus Christ of Latter-day Saints. GeneaNet - Evans  RecordsGeneaNet includes archival records, family trees, and other resources for individuals with the Evans surname, with a concentration on records and families from France and other European countries. The Evans Genealogy and Family Tree PageBrowse genealogy records and links to genealogical and historical records for individuals with the Evans surname from the website of Genealogy Today. Sources Cottle, Basil.  Penguin Dictionary of Surnames. Baltimore, MD: Penguin Books, 1967. Dorward, David.  Scottish Surnames. Collins Celtic (Pocket edition), 1998. Fucilla, Joseph.  Our Italian Surnames. Genealogical Publishing Company, 2003. Hanks, Patrick and Flavia Hodges.  A Dictionary of Surnames. Oxford University Press, 1989. Hanks, Patrick.  Dictionary of American Family Names. Oxford University Press, 2003. Reaney, P.H.  A Dictionary of English Surnames. Oxford University Press, 1997. Smith, Elsdon C.  American Surnames. Genealogical Publishing Company, 1997. Glossary of Surname Meanings Origins

Thursday, November 21, 2019

Hazardous Material Management and Hazard Communication Essay - 9

Hazardous Material Management and Hazard Communication - Essay Example In order to add a new chemical to HazCom program chemical inventory, one has to follow a well outlined guideline. Since it is done online, the employer needs to access the website then log in. after entering the name of the new chemical into the site, he should proceed to search for CAD then click on ‘Add chemical’ then generate for it a CAS number if it does not have one already. Thereafter, upload all the information regarding the new chemical’s regulatory information, NFPA ratings and physical properties. Finally, save and submit the details and wait for a review (Aldrich, 2009). HazCom program chemical inventory is stored online because having a computer data base is good. It is efficient and can be easily up dated and retrieved for use. Therefore, all employers who have harzadious chemicals should ensure that their information is captured in the HazCom program chemical inventory. It is recommended for optimal safety of the employees operating

Wednesday, November 20, 2019

The Benefits of QuickBooks Online Essay Example | Topics and Well Written Essays - 250 words

The Benefits of QuickBooks Online - Essay Example The template forms developed for data entry on the quick book platform is imperative for the consistency the approach offers in data entry (Keep it Simple Accounting, 2013). Moreover, functional entities including the state abbreviations, phone numbers and dates have consistent formats. I acknowledge these findings owing to the simplicity it offers to the analysis of data and report generation. The highly built relational table structure allows propagation of changes throughout the system in case a single entry is altered. The inbuilt functions can be tuned to suit a given scenario. For instance when implementing a new tax policy, changing the tax rate in one entity amounts to a propagated change across the system’s sale records. I guarantee the platform offers more benefits in line with query endeavors. Searching for information is an ease yet quick. It has capabilities to sort, filter and display the specific information as needed and queried by the user. In that respect, multiple reports based on different templates and formats can be viewed or printed (Keep it Simple Accounting, 2013). The platform offers the capacity to track bounced checks, report in instant clicks and customizable content generated for clients. The functions support the advantages offered by quick books that I regard to be true. The utility that enables import of bank activity into quick book online makes it even better in the accounting process. Within the record is the contact information for vendors, manufacturers, clients, and employee (Keep it Simple Accounting, 2013). With such information at the user’s disposal quick books becomes a key tool in the financial division of an institution. The user interfaces developed are better set with the user in mind. They offer in a friendly way and an icon approach to functions. The profile of a company can easily be developed with quick books online making it a superior tool. I specifically adore the interview approach to customization of

Monday, November 18, 2019

War and displacement Essay Example | Topics and Well Written Essays - 750 words

War and displacement - Essay Example World War II or the â€Å"good war† was also not morally a clean war. It resulted in the deaths of 50 million people, maiming millions more. The war was a cover for genocide, systematic destruction of cities and populations, crippling of a very strong economy, development and use of nuclear weapons and above all the trauma that every civilian and soldier had to go through in the post war life. One might think that all the past experience would have caused people to think rationally and avoid wars in the future but that has not been the case and war is prevalent even today, be it the Iran Iraq war or the earlier Russian Cold War. While claiming for justice, often the war farers overlook the centric point of war- consequentalism. (Wittner, 2003). War has never been a good path to demand justice and in the long run has brought only death and destruction. The immediate impact of war is first on the people of the war faring countries. Then comes the society, the economy and the env ironment. War takes its toll only emotionally and mentally but also affects indirectly with destruction of property, economy and well being of a society. Population Displacement Displaced population is referred to people driven away from their homes and countries. They are forcibly displaced from their roots leaving behind their property, trade and extended families. The five main causes to population displacement have been clustered as: 1. Displacement due to war and political turmoil, 2. Displacement due to natural disasters like floods, famine, earthquakes and so on 3. Displacement due to religious, ethnic or racial persecution 4. Displacement due to new infrastructures and new developments and, 5. Displacement due to disintegration of state structures or borders. Whatever be the reason for population displacement, it has dire consequences. There is massive loss of life and property, destruction of assets and economy (Christensen, 2003).That in turn causes depreciation in the sta ndard of living, unemployment and alienation of masses. Those people who get displaced also face cultural and identity crisis as the new place where they set up their home may not always welcome them. The population displacement causes increase in population in the host country that permits the refugees to come in, thereby increases hostility, unemployment and competition for both the refugees and the inhabitants. Apart from these, there is tremendous mental, emotional and psychological trauma for the population that got uprooted. Men, women and children, the aged and the elderly, the sick and the handicapped all bear the brunt of such movement. The after effects of war have been portrayed in a unique manner through a documentary by a musician Michael Frantis – I know I am not alone. (Frantis, 2005) The documentary is filmed in war torn Baghdad where the musician meets people from all walks of life like taxi drivers, craftsmen, nurses, musicians, writers who all share the sam e grief and feeling of torment. It shows Iraq today, with no water, no security and safety, entire city is run on generators as there is no electricity. The loss of lives has been tremendous but sadly that has not been highlighted in any of the news channels or political forums. The city has been shredded to bits, with people made refugees, economy in tatters and no hope of rebuilding the country. The film involves real people and shows how war has affected

Friday, November 15, 2019

Gordon Allport An American Psychologist Psychology Essay

Gordon Allport An American Psychologist Psychology Essay Psychology  of  the lack  of interest  and  limited  methods, in general,  fails  to  disclose  or study  of the  integrity  and consistency of  the characters  that  actually  exist.  The greatest drawback  of a psychologist  at the present  time   is  his  inability to  prove the truth  of  what he  knows. Gordon Allport is an outstanding figure in the world of psychology, and now there is hardly a book on psychology of personality without a special chapter on his theory, or at least references to it.  Having experienced the impact of different schools, Allport did not actually belong to any of them, and created his own.  He believed that the comprehensive theory of personality can be created by combining the achievements of different scientific fields, and thus, of course, has earned numerous accusations of eclecticism.  Today, such accusations can be viewed more as praise, for the future of scientific psychology more clearly seen in a balanced position rather than in an opposition of antagonists.  In approving such a position Allport played a very important role, and now has a decent place of honor in the gallery of masters of psychology.  His influence  on  the psychology of  the world  can not be overestimated.   Allport  refers to a rare  type of  systematizers, he  was  perhaps  the smartest  person  of those  who  engaged in the psychology of  personality,  a man  with imagination,  but the  most striking  feature of Allport  was  logical thinking.  Allport introduced  into  the psychology a lot  of new ideas, he smoothed out  the extremes  and  overcome the contradictions of  the science,  that is why he  can rightly be  called one  of the  dialectically-minded  psychologists. He was often  called   eclectic,  and he agreed  with  it,  specifying  that eclecticism  in this  sense  was  not a vice,  but a very  productive  method  of research. (Evans, 1971, p.19) Perhaps  few people  can be  compared  with him  on the number of  ideas  that are included  in textbooks  on  theories  of personality,  and  in  the main  body  of knowledge  of personality psychology.  Allport  was behind the  theory of  traits,  humanistic   psychology,  wrote the first textbook  on  the synthesis  of personality psychology,  has legalized  the introduction  to the academic  science  of qualitative  methods,  research problems  such as  personal  maturity, vision, self-actualization, religiosity.   He  did not make  discoveries or breakthroughs,  has not created a  school or any new paradigm,  but  in many respects  he  is credited with  creating  the psychology of personality  as a  particular subject  area  Ã‚  it  is no exaggeration to  call him the  architect of  personality psychology. During his lifetime Allport managed to get all kinds of honors: he was elected as the president of the American Psychological Association (1939), president of Society of the Study of Social Problems, received the award for outstanding contribution to science (1964), etc. But in his autobiography he admitted that among the  numerous scientific distinctions the most valuable to him was the prize given to him in 1963, a two-volume collection of works of 55 of his former graduate students with the inscription from the students with gratitude for the respect for their individuality. The list of Allports publications includes his reviews and prefaces to other peoples books, as he was engaged in the educational activity: he enriched the American science with ideas of personology of W. Stern, Psychology of the spirit of E. Spranger and Gestalt K. Koffka, W. Kohler and M. Wertheimer.  He was able to assess the significance for psychology of the ideas of existentialism, and supported the establishment of the Association of Humanistic Psychology.     Another distinctive feature of scientific style of Allport is to be always on the cutting edge of social issues of the time, because he wanted to study what was more important for people.  In many specific areas he has created articles and books: the Psychology of expressive movements, psychology radio, rumors psychology, psychology of war, the psychology of religion, and his 600-page work devoted to the nature of prejudice for almost 50 years remains the main source of the problem, and its relevance only increases. Gordon Allport Biography Gordon Willard Allport was born on November 11, 1897 in Montezuma, Indiana.  He was the youngest of four sons of John and Nellie Allport.  His father was a modest and not very successful doctor, his private clinic was situated within the walls of his own house.  Allports mother was a schoolteacher, and, most importantly, a devout and pious woman, and she thought the children of reasonable, orderly and virtuous life skills.  And the character of Gordon was formed largely under the influence of a strict, but humane maternal morality.   Gordon in 1915 went to Harvard, and from then began a half-century of his collaboration with Harvard University.  At Harvard, the intellectual abilities of Gordon turned in full force and gained focus.  In parallel with the psychology he dealt with social ethics from an early age his interest was divided between psychology and the broader social context, and not by accident in the 30 years he created at Harvard the Department of Social Relations, an interdisciplinary by its very nature, with synthetic approaches of psychology, sociology and anthropology.   A distinctive feature of the scientific outlook of Allport was a pretty big influence on him of European psychology, especially of William Stern, Eduard Spranger, and Gestalt psychology (in many respects this was caused by staying of young scientist in Europe in the early 1920s).  Influenced by these ideas, Allport, having been engaged in a 1920 in study of the issues of personality psychology, especially of personality traits and expressive movements, he quickly realized the need to consider the whole personality, rather than its parts. After returning  to  Harvard,  Allport  at the age of 24  wrote his doctorate  in psychology, but the key  ideas of  his work  were  presented  to them  a year earlier  in  the article  Personality  traits:  their classification and  measurement,  written jointly  with  his brother  Floyd, and  published  in the  Journal of Abnormal and Social Psychology. In the next two years Allport went to the internship in Europe first in Germany, where he worked with M. Wertheimer, V. Kohler, W. Stern, C. Stumpf, and then for a short time in England, at Cambridge.  Drawing on personal experience with work with masters of German psychology, he later at home has long been a leading expert in this area and the interpreter of their ideas. In 1924 he returned to Harvard, where he began to read a completely new course of personality psychology.  It is important to note that until then, many psychologists considered problems in the theory of personality not as psychological.  The final breakthrough in this area has occurred in 1937, after publication of the Allports major monograph Personality: a psychological study.  In it the author (by the way, long before the groundbreaking theory of Maslow) was first to study a healthy personality and described its essential features. Allports collection of works Personality in Psychology presents a wide range of his interests: health issues, religion and superstition, social prejudices, as well as the main methodological problems of psychology.  In his work, which was reflected in 12 books and more than two hundred articles, he tried to capture the complexity of human existence in the contemporary social context and resolutely refused to follow the fashionable tenets of his profession, demonstrating commitment to the imaginative and systematic eclecticism. During his career, Allport was awarded with almost all the regalia of a psychologist: he was elected president of the American Psychological Association (1939), President of the psychological study of social problems, in 1963 he was awarded the Gold Medal of the American Psychological Foundation, in 1964, APA received an award for outstanding contribution  in science.   Allports approach to personality Allport was the first in the world of psychology to build a holistic theoretical knowledge of the scientific psychology of personality.  His book Personality: a psychological interpretation, which was published in 1937, marked the beginning of the academic personality psychology.  Personality, by Allport, is a dynamic organization of psycho-physical systems of the individual, which defines a unique adaptation of the individual to his environment. (Allport, 1937) G. Allport theory of personality is a combination of humanistic and individual approaches to the study of human behavior.  Humanistic approach lies in an attempt to identify all aspects of human beings, and individual approach is reflected in an effort of G. Allport to understand and predict the development of the real, specific person.  One of the main postulates of the theory of G. Allport is that personality is open and self-developing.  People first and foremost are a social beings and therefore can not develop without contacts with other people and society.  Here comes the Allport rejection of psychoanalysis on the antagonistic, hostile relations between the individual and society.  In this case, G. Allport argued that the communication of personality and society is not striving for balance with the medium, but for networking and interaction.  Thus, he strongly objected to the generally accepted postulate that development is an adaptation, an adaptation of man to the outside world, arguing that human nature just need to blow up the balance and reach more and more new peaks.   Explaining human behavior, G. Allport introduced the concept of traits.  He defined the trait as à ¢Ã¢â€š ¬Ã‚ ¦the neuropsychological structure capable of converting a set of functionally equivalent stimuli, and to encourage and guide equivalent forms of adaptive and expressive behavior.  Simply it is propensity to behave in a similar manner in a wide range of situations.  G. Allport theory states that human behavior is relatively stable over time and in diverse situations.  In the G. Allport system personality is characterized by traits, or defining characteristics. He proposed eight basic criteria for determining personality traits:   personality traits are real: they exist in humans, and are not theoretical abstractions;   personality trait is a more generalized notion than a habit; personality traits is the driving, or at least, a defining element of behavior, it motivates the individual;   the existence of personality traits can be established empirically;   personality traits is only relatively independent, as people tend to react to events and phenomena according to a generalized manner;   personality traits can not be associated with this individual moral or social assessment; the fact that actions and habits are inconsistent with the personality traits is not evidence of lack of that traits.   Allports Theory of Individual Trait and Common Trait Each person is an idiom unto himself, an apparent violation of the syntax of the species.   ( Allport G. Becoming: Basic Considerations for a Psychology of Personality,1955, p.19).   G. Allport pointed general and individual traits.  The first include any characteristics peculiar to some number of people within a particular culture.  Individual traits represent characteristics of the individual, which does not allow comparison with other people, that are those neuropsychiatric elements that direct, manage and motivate a certain type of behavior.  This category of traits more fully reflects the personality structure of each individual.   Later G. Allport called individual personality traits as dispositions, and identified three types of them: Radical disposition.  Almost all human actions can be explained by the influence of inborn traits.   Central dispositions.  They do not dominate, but are the foundation of human individuality.   Secondary dispositions.  These traits are less visible, less generalized, less stable and therefore less suitable for the characteristics of personality.  For example, eating habits and clothing, etc.   G. Allport believed that personality is determined by the unity and integration of individual traits that give him originality.   The Proprium In 1950 Allport, however, introduced a new concept to replace the traditional I concept the notion of proprium.  A  Proprium by Allport is similar to what William James once explained as an area of I.  The main thing that has developed Allport in connection with the concept of the proprium and proprium structures of personality is periodization of personal development, based on seven aspects of proprium.   G. Allport identified seven stages of development of proprium from childhood to adulthood:    During the first three years child demonstrate three aspects: the sense of a body, a sense of continuous self-identity and self-esteem or pride. At the age of four to six years, there are two other aspects: self-identification and self-image. Between six and twelve years a child develops self-awareness, so that he can cope with problems on the basis of rational thought. In adolescence, there are intentions, plans and long-term goals, they called their own aspirations. So,  in  an adult  individual we can see  a person  whose  determinants  of behavior  is  a system  of organized  and  congruent  traits, these  traits  resulted from many different motivations of a  newborn.  Normal  individuals  usually know  what  they are  doing and why.  This  behavior is consistent with  congruent  pattern,  and  at the core  of this pattern  lie traits that  G.  Allport  called  proprium.  Complete  understanding of  the adult  is not possible without  considering his  goals  and  aspirations. Motive and Functional Autonomy According to Allport, the core of the personality are the motives of activity.  In order to explain the nature of motivation, he introduced the concept of functional autonomy, which means that the motivation of the adult is not functionally connected with his childhood experiences.  Motives of human activity do not depend on the initial circumstances of their occurrence.   Thus, adults are responsible for their deeds and actions, and do not depend on the vicissitudes of childhood. Motives  of adults  can not, according to  Allport,  result  from their  childrens  intentions and perceptions,  and  these goals  are determined by  the current  situation  and  current intentions.   Thus, functional  autonomy,  in the view of  Allport,  are motives of adults  which do not depend  on  their  childrens   experiences. Criticism of Allport Despite his  influence in  psychology,  theory of  Allport  has not received  sufficient experimental  confirmation.  What is the empirical validity of the theoretical concept of personality in Allport?  Analysis of relevant literature shows that the Allports theory does not rise any study to confirm its validity.  With his views and concepts agreed only few well-known authors in the field Personology (Maddi, 1972).   Allports position,  emphasizing the  uniqueness of the human  personality, as well as  the importance  of understanding   personal  goals  and expectations,  had a  significant  impact on  the views of  Abraham  Maslow,  Carl  Rogers  and  other members of  humanistic psychology.  Allport  work  on  personality theory  have played  a significant  role  in the renewed interest  of researchers in  this  subject.  His  idea of  produce  a very  strong impressionà ¢Ã¢â€š ¬Ã‚ ¦Ã‚  and  gives  impetus to  a number  of new theoretical and  applied  research  in contemporary  personality psychology. (Evans, 1971) Conclusion During the years of his long and highly productive career at Harvard University, Gordon Allport has done much to make research on the psychology of the individual of an academic importance.  Before his book Personality: psychological interpretation, the theory of personality problems in general was not considered as the subject of psychology.  G. Allport was one of the few psychologists who made a bridge between academic psychology with its traditions on the one hand, and rapidly evolving field of clinical psychology and personality psychology on the other.  This connection not only enriches sub-discipline discoveries, but also allows to set the intellectual continuity that is important for the future development of psychology.   Finally, the novelty of the position of G. Allport lies in the fact that he focused on the future and present, and rarely on the past.   Gordon Allport was a unique, proactive, integrated, forward-looking person, who left great theoretical material on the psychology of individual, and  influenced  many  scientists, their  views and  approaches,  as well as all   the science of psychology.

Wednesday, November 13, 2019

Islam in Italy Essay -- Islam Italy History Essays

Islam in Italy Problems with format 'Like many minority communities of varying religious and ethnic backgrounds, Muslims have struggled to define their place in societies around the world.' As immigration patterns have ebbed and flowed through the centuries, Italy is one of many European countries that plays host to a growing number of Muslim immigrants.? Muslims struggle with identity, intermarriage, gender relations, worship, education, and civil rights in the context of their new country.? These issues are particularly poignant for Muslims entering and living within Italy during this religiously momentous time.? During the past twenty years, Italy has seen a resurgence of immigrants who hold to the Islamic tradition.? For the largely Catholic Italy, the impact of this is immeasurable and has catapulted society and government toward decisions that will forever alter the country (Israely). A Brief Look at an Ancient History Historically, the Italian peninsula has been exposed to Islamic influence since the beginning of the Muslim age in the seventh century A.D. (Matthews).? As Islam spread north and west, the Byzantine Empire effectively remained a blockade until the fall of Constantinople in 1453.? But another road into Europe was open for Islam by traveling across North Africa, over the sea, and up to the island of Sicily and the Italian mainland.? After years of skirmishes, Sicily was taken in 902.? The Roman Empire quelled much of the Muslim activity in mainland Italy, and there are still remnants of Saracen towers, positions to watch for Muslim invaders approaching by sea.? Though the Muslims never gained a strong foothold in mainland Italy, the island of Sicily was securely theirs for two centuries.? Du... ....fieri.it/leggi_e_provv/liberta_religiosa/statuto_giur_islam_en.htm>. Holzner, Claudio. ?Re-Birth of Islam In Italy: Between Indifference and Intolerance.? The Journal of the International Institute. Vol. 3, Issue 2, (1996): 4pp. Israely, Jeff. ?In Catholic Italy, Islam makes inroads.? The Boston Globe. 14 May. 2000. ?< http://www.boston.com/dailyglobe2/135/nation/In_Catholic_Italy_Islam_makes_?inroadsP.shtml>. Kern, Gunther. ?Italy?s Muslims in Uphill Battle for Recognition.? IslamOnline. 2003. < http://www.islam-online.net/English/News/2000-11/26/article4.shtml>. Matthews, Jeff. ?Early Islam in Italy.? 2001.< http://faculty.ed.umuc.edu/~jmatthew/naples/earlyislam.html>. Roggero, Maria Adele. ?Muslims in Italy? Muslims in the West, From Sojourners to Citizens. ed.Yvonne Y. Haddad. New York, NY: Oxford University Press, Inc., 2002. 131-143.

Sunday, November 10, 2019

Compilation of Mathematicians and Their Contributions

I. Greek Mathematicians Thales of Miletus Birthdate: 624 B. C. Died: 547-546 B. C. Nationality: Greek Title: Regarded as â€Å"Father of Science† Contributions: * He is credited with the first use of deductive reasoning applied to geometry. * Discovery that a circle is  bisected  by its diameter, that the base angles of an isosceles triangle are equal and that  vertical angles  are equal. * Accredited with foundation of the Ionian school of Mathematics that was a centre of learning and research. * Thales theorems used in Geometry: . The pairs of opposite angles formed by two intersecting lines are equal. 2. The base angles of an isosceles triangle are equal. 3. The sum of the angles in a triangle is 180 °. 4. An angle inscribed in a semicircle is a right angle. Pythagoras Birthdate: 569 B. C. Died: 475 B. C. Nationality: Greek Contributions: * Pythagorean Theorem. In a right angled triangle the square of the hypotenuse is equal to the sum of the squares on the other two sides. Note: A right triangle is a triangle that contains one right (90 °) angle.The longest side of a right triangle, called the hypotenuse, is the side opposite the right angle. The Pythagorean Theorem is important in mathematics, physics, and astronomy and has practical applications in surveying. * Developed a sophisticated numerology in which odd numbers denoted male and even female: 1 is the generator of numbers and is the number of reason 2 is the number of opinion 3 is the number of harmony 4 is the number of justice and retribution (opinion squared) 5 is the number of marriage (union of the ? rst male and the ? st female numbers) 6 is the number of creation 10 is the holiest of all, and was the number of the universe, because 1+2+3+4 = 10. * Discovery of incommensurate ratios, what we would call today irrational numbers. * Made the ? rst inroads into the branch of mathematics which would today be called Number Theory. * Setting up a secret mystical society, known as th e Pythagoreans that taught Mathematics and Physics. Anaxagoras Birthdate: 500 B. C. Died: 428 B. C. Nationality: Greek Contributions: * He was the first to explain that the moon shines due to reflected light from the sun. Theory of minute constituents of things and his emphasis on mechanical processes in the formation of order that paved the way for the atomic theory. * Advocated that matter is composed of infinite elements. * Introduced the notion of nous (Greek, â€Å"mind† or â€Å"reason†) into the philosophy of origins. The concept of nous (â€Å"mind†), an infinite and unchanging substance that enters into and controls every living object. He regarded material substance as an infinite multitude of imperishable primary elements, referring all generation and disappearance to mixture and separation, respectively.Euclid Birthdate: c. 335 B. C. E. Died: c. 270 B. C. E. Nationality: Greek Title: â€Å"Father of Geometry† Contributions: * Published a book called the â€Å"Elements† serving as the main textbook for teaching  mathematics  (especially  geometry) from the time of its publication until the late 19th or early 20th century. The Elements. One of the oldest surviving fragments of Euclid's  Elements, found at  Oxyrhynchus and dated to circa AD 100. * Wrote works on perspective,  conic sections,  spherical geometry,  number theory  and  rigor. In addition to the  Elements, at least five works of Euclid have survived to the present day. They follow the same logical structure as  Elements, with definitions and proved propositions. Those are the following: 1. Data  deals with the nature and implications of â€Å"given† information in geometrical problems; the subject matter is closely related to the first four books of the  Elements. 2. On Divisions of Figures, which survives only partially in  Arabic  translation, concerns the division of geometrical figures into two or more equal par ts or into parts in given  ratios.It is similar to a third century AD work by  Heron of Alexandria. 3. Catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. The attribution is held to be anachronistic however by J J O'Connor and E F Robertson who name  Theon of Alexandria  as a more likely author. 4. Phaenomena, a treatise on  spherical astronomy, survives in Greek; it is quite similar to  On the Moving Sphere  by  Autolycus of Pitane, who flourished around 310 BC. * Famous five postulates of Euclid as mentioned in his book Elements . Point is that which has no part. 2. Line is a breadthless length. 3. The extremities of lines are points. 4. A straight line lies equally with respect to the points on itself. 5. One can draw a straight line from any point to any point. * The  Elements  also include the following five â€Å"common notions†: 1. Things that are equal to the same thi ng are also equal to one another (Transitive property of equality). 2. If equals are added to equals, then the wholes are equal. 3. If equals are subtracted from equals, then the remainders are equal. 4.Things that coincide with one another equal one another (Reflexive Property). 5. The whole is greater than the part. Plato Birthdate: 424/423 B. C. Died: 348/347 B. C. Nationality: Greek Contributions: * He helped to distinguish between  pure  and  applied mathematics  by widening the gap between â€Å"arithmetic†, now called  number theory  and â€Å"logistic†, now called  arithmetic. * Founder of the  Academy  in  Athens, the first institution of higher learning in the  Western world. It provided a comprehensive curriculum, including such subjects as astronomy, biology, mathematics, political theory, and philosophy. Helped to lay the foundations of  Western philosophy  and  science. * Platonic solids Platonic solid is a regular, convex poly hedron. The faces are congruent, regular polygons, with the same number of faces meeting at each vertex. There are exactly five solids which meet those criteria; each is named according to its number of faces. * Polyhedron Vertices Edges FacesVertex configuration 1. tetrahedron4643. 3. 3 2. cube / hexahedron81264. 4. 4 3. octahedron61283. 3. 3. 3 4. dodecahedron2030125. 5. 5 5. icosahedron1230203. 3. 3. 3. 3 AristotleBirthdate: 384 B. C. Died: 322 BC (aged 61 or 62) Nationality: Greek Contributions: * Founded the Lyceum * His biggest contribution to the field of mathematics was his development of the study of logic, which he termed â€Å"analytics†, as the basis for mathematical study. He wrote extensively on this concept in his work Prior Analytics, which was published from Lyceum lecture notes several hundreds of years after his death. * Aristotle's Physics, which contains a discussion of the infinite that he believed existed in theory only, sparked much debate in later cen turies.It is believed that Aristotle may have been the first philosopher to draw the distinction between actual and potential infinity. When considering both actual and potential infinity, Aristotle states this:  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   1. A body is defined as that which is bounded by a surface, therefore there cannot be an infinite body. 2. A Number, Numbers, by definition, is countable, so there is no number called ‘infinity’. 3. Perceptible bodies exist somewhere, they have a place, so there cannot be an infinite body. But Aristotle says that we cannot say that the infinite does not exist for these reasons: 1.If no infinite, magnitudes will not be divisible into magnitudes, but magnitudes can be divisible into magnitudes (potentially infinitely), therefore an infinite in some sense exists. 2. If no infinite, number would not be infinite, but number is infinite (potentially), therefore infinity does exist in some sense. * He was the founder of  formal logic, pioneere d the study of  zoology, and left every future scientist and philosopher in his debt through his contributions to the scientific method. Erasthosthenes Birthdate: 276 B. C. Died: 194 B. C. Nationality: Greek Contributions: * Sieve of Eratosthenes Worked on  prime numbers.He is remembered for his prime number sieve, the ‘Sieve of Eratosthenes' which, in modified form, is still an important tool in  number theory  research. Sieve of Eratosthenes- It does so by iteratively marking as composite (i. e. not prime) the multiples of each prime, starting with the multiples of 2. The multiples of a given prime are generated starting from that prime, as a sequence of numbers with the same difference, equal to that prime, between consecutive numbers. This is the Sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime. Made a surprisingly accurate measurement of the circumference of the Earth * He was the first per son to use the word â€Å"geography† in Greek and he invented the discipline of geography as we understand it. * He invented a system of  latitude  and  longitude. * He was the first to calculate the  tilt of the Earth's axis  (also with remarkable accuracy). * He may also have accurately calculated the  distance from the earth to the sun  and invented the  leap day. * He also created the first  map of the world  incorporating parallels and meridians within his cartographic depictions based on the available geographical knowledge of the era. Founder of scientific  chronology. Favourite Mathematician Euclid paves the way for what we known today as â€Å"Euclidian Geometry† that is considered as an indispensable for everyone and should be studied not only by students but by everyone because of its vast applications and relevance to everyone’s daily life. It is Euclid who is gifted with knowledge and therefore became the pillar of todayâ€℠¢s success in the field of geometry and mathematics as a whole. There were great mathematicians as there were numerous great mathematical knowledge that God wants us to know.In consideration however, there were several sagacious Greek mathematicians that had imparted their great contributions and therefore they deserve to be appreciated. But since my task is to declare my favourite mathematician, Euclid deserves most of my kudos for laying down the foundation of geometry. II. Mathematicians in the Medieval Ages Leonardo of Pisa Birthdate: 1170 Died: 1250 Nationality: Italian Contributions: * Best known to the modern world for the spreading of the Hindu–Arabic numeral system in Europe, primarily through the publication in 1202 of his Liber Abaci (Book of Calculation). Fibonacci introduces the so-called Modus Indorum (method of the Indians), today known as Arabic numerals. The book advocated numeration with the digits 0–9 and place value. The book showed the practical im portance of the new numeral system, using lattice multiplication and Egyptian fractions, by applying it to commercial bookkeeping, conversion of weights and measures, the calculation of interest, money-changing, and other applications. * He introduced us to the bar we use in fractions, previous to this, the numerator has quotations around it. * The square root notation is also a Fibonacci method. He wrote following books that deals Mathematics teachings: 1. Liber Abbaci (The Book of Calculation), 1202 (1228) 2. Practica Geometriae (The Practice of Geometry), 1220 3. Liber Quadratorum (The Book of Square Numbers), 1225 * Fibonacci sequence of numbers in which each number is the sum of the previous two numbers, starting with 0 and 1. This sequence begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987†¦ The higher up in the sequence, the closer two consecutive â€Å"Fibonacci numbers† of the sequence divided by each other will approach the golden ratio (ap proximately 1: 1. 18 or 0. 618: 1). Roger Bacon Birthdate: 1214 Died: 1294 Nationality: English Contributions: * Opus Majus contains treatments of mathematics and optics, alchemy, and the positions and sizes of the celestial bodies. * Advocated the experimental method as the true foundation of scientific knowledge and who also did some work in astronomy, chemistry, optics, and machine design. Nicole Oresme Birthdate: 1323 Died: July 11, 1382 Nationality: French Contributions: * He also developed a language of ratios, to relate speed to force and resistance, and applied it to physical and cosmological questions. He made a careful study of musicology and used his findings to develop the use of irrational exponents. * First to theorise that sound and light are a transfer of energy that does not displace matter. * His most important contributions to mathematics are contained in Tractatus de configuratione qualitatum et motuum. * Developed the first use of powers with fractional exponent s, calculation with irrational proportions. * He proved the divergence of the harmonic series, using the standard method still taught in calculus classes today. Omar Khayyam Birhtdate: 18 May 1048Died: 4 December 1131 Nationality: Arabian Contibutions: * He derived solutions to cubic equations using the intersection of conic sections with circles. * He is the author of one of the most important treatises on algebra written before modern times, the Treatise on Demonstration of Problems of Algebra, which includes a geometric method for solving cubic equations by intersecting a hyperbola with a circle. * He contributed to a calendar reform. * Created important works on geometry, specifically on the theory of proportions. Omar Khayyam's geometric solution to cubic equations. Binomial theorem and extraction of roots. * He may have been first to develop Pascal's Triangle, along with the essential Binomial Theorem which is sometimes called Al-Khayyam's Formula: (x+y)n = n! ? xkyn-k / k! (n -k)!. * Wrote a book entitled â€Å"Explanations of the difficulties in the postulates in Euclid's Elements† The treatise of Khayyam can be considered as the first treatment of parallels axiom which is not based on petitio principii but on more intuitive postulate. Khayyam refutes the previous attempts by other Greek and Persian mathematicians to prove the proposition.In a sense he made the first attempt at formulating a non-Euclidean postulate as an alternative to the parallel postulate. Favorite Mathematician As far as medieval times is concerned, people in this era were challenged with chaos, social turmoil, economic issues, and many other disputes. Part of this era is tinted with so called â€Å"Dark Ages† that marked the history with unfavourable events. Therefore, mathematicians during this era-after they undergone the untold toils-were deserving individuals for gratitude and praises for they had supplemented the following generations with mathematical ideas that is very useful and applicable.Leonardo Pisano or Leonardo Fibonacci caught my attention therefore he is my favourite mathematician in the medieval times. His desire to spread out the Hindu-Arabic numerals in other countries thus signifies that he is a person of generosity, with his noble will, he deserves to be†¦ III. Mathematicians in the Renaissance Period Johann Muller Regiomontanus Birthdate: 6 June 1436 Died: 6 July 1476 Nationality: German Contributions: * He completed De Triangulis omnimodus. De Triangulis (On Triangles) was one of the first textbooks presenting the current state of trigonometry. His work on arithmetic and algebra, Algorithmus Demonstratus, was among the first containing symbolic algebra. * De triangulis is in five books, the first of which gives the basic definitions: quantity, ratio, equality, circles, arcs, chords, and the sine function. * The crater Regiomontanus on the Moon is named after him. Scipione del Ferro Birthdate: 6 February 1465 Died: 5 N ovember 1526 Nationality: Italian Contributions: * Was the first to solve the cubic equation. * Contributions to the rationalization of fractions with denominators containing sums of cube roots. Investigated geometry problems with a compass set at a fixed angle. Niccolo Fontana Tartaglia Birthdate: 1499/1500 Died: 13 December 1557 Nationality: Italian Contributions: †¢He published many books, including the first Italian translations of Archimedes and Euclid, and an acclaimed compilation of mathematics. †¢Tartaglia was the first to apply mathematics to the investigation of the paths of cannonballs; his work was later validated by Galileo's studies on falling bodies. †¢He also published a treatise on retrieving sunken ships. †¢Ã¢â‚¬ Cardano-Tartaglia Formula†. †¢He makes solutions to cubic equations. Formula for solving all types of cubic equations, involving first real use of complex numbers (combinations of real and imaginary numbers). †¢Tartagli a’s Triangle (earlier version of Pascal’s Triangle) A triangular pattern of numbers in which each number is equal to the sum of the two numbers immediately above it. †¢He gives an expression for the volume of a tetrahedron: Girolamo Cardano Birthdate: 24 September 1501 Died: 21 September 1576 Nationality: Italian Contributions: * He wrote more than 200 works on medicine, mathematics, physics, philosophy, religion, and music. Was the first mathematician to make systematic use of numbers less than zero. * He published the solutions to the cubic and quartic equations in his 1545 book Ars Magna. * Opus novum de proportionibus he introduced the binomial coefficients and the binomial theorem. * His book about games of chance, Liber de ludo aleae (â€Å"Book on Games of Chance†), written in 1526, but not published until 1663, contains the first systematic treatment of probability. * He studied hypocycloids, published in de proportionibus 1570. The generating circl es of these hypocycloids were later named Cardano circles or cardanic ircles and were used for the construction of the first high-speed printing presses. * His book, Liber de ludo aleae (â€Å"Book on Games of Chance†), contains the first systematic treatment of probability. * Cardano's Ring Puzzle also known as Chinese Rings, still manufactured today and related to the Tower of Hanoi puzzle. * He introduced binomial coefficients and the binomial theorem, and introduced and solved the geometric hypocyloid problem, as well as other geometric theorems (e. g. the theorem underlying the 2:1 spur wheel which converts circular to reciprocal rectilinear motion).Binomial theorem-formula for multiplying two-part expression: a mathematical formula used to calculate the value of a two-part mathematical expression that is squared, cubed, or raised to another power or exponent, e. g. (x+y)n, without explicitly multiplying the parts themselves. Lodovico Ferrari Birthdate: February 2, 1522 Died: October 5, 1565 Nationality: Italian Contributions: * Was mainly responsible for the solution of quartic equations. * Ferrari aided Cardano on his solutions for quadratic equations and cubic equations, and was mainly responsible for the solution of quartic equations that Cardano published.As a result, mathematicians for the next several centuries tried to find a formula for the roots of equations of degree five and higher. Favorite Mathematician Indeed, this period is supplemented with great mathematician as it moved on from the Dark Ages and undergone a rebirth. Enumerated mathematician were all astounding with their performances and contributions. But for me, Niccolo Fontana Tartaglia is my favourite mathematician not only because of his undisputed contributions but on the way he keep himself calm despite of conflicts between him and other mathematicians in this period. IV. Mathematicians in the 16th CenturyFrancois Viete Birthdate: 1540 Died: 23 February 1603 Nationality: F rench Contributions: * He developed the first infinite-product formula for ?. * Vieta is most famous for his systematic use of decimal notation and variable letters, for which he is sometimes called the Father of Modern Algebra. (Used A,E,I,O,U for unknowns and consonants for parameters. ) * Worked on geometry and trigonometry, and in number theory. * Introduced the polar triangle into spherical trigonometry, and stated the multiple-angle formulas for sin (nq) and cos (nq) in terms of the powers of sin(q) and cos(q). * Published Francisci Viet? universalium inspectionum ad canonem mathematicum liber singularis; a book of trigonometry, in abbreviated Canonen mathematicum, where there are many formulas on the sine and cosine. It is unusual in using decimal numbers. * In 1600, numbers potestatum ad exegesim resolutioner, a work that provided the means for extracting roots and solutions of equations of degree at most 6. John Napier Birthdate: 1550 Birthplace: Merchiston Tower, Edinburgh Death: 4 April 1617 Contributions: * Responsible for advancing the notion of the decimal fraction by introducing the use of the decimal point. His suggestion that a simple point could be used to eparate whole number and fractional parts of a number soon became accepted practice throughout Great Britain. * Invention of the Napier’s Bone, a crude hand calculator which could be used for division and root extraction, as well as multiplication. * Written Works: 1. A Plain Discovery of the Whole Revelation of St. John. (1593) 2. A Description of the Wonderful Canon of Logarithms. (1614) Johannes Kepler Born: December 27, 1571 Died: November 15, 1630 (aged 58) Nationality: German Title: â€Å"Founder of Modern Optics† Contributions: * He generalized Alhazen's Billiard Problem, developing the notion of curvature. He was first to notice that the set of Platonic regular solids was incomplete if concave solids are admitted, and first to prove that there were only 13 â€Å"Archi medean solids. † * He proved theorems of solid geometry later discovered on the famous palimpsest of Archimedes. * He rediscovered the Fibonacci series, applied it to botany, and noted that the ratio of Fibonacci numbers converges to the Golden Mean. * He was a key early pioneer in calculus, and embraced the concept of continuity (which others avoided due to Zeno's paradoxes); his work was a direct inspiration for Cavalieri and others. He developed mensuration methods and anticipated Fermat's theorem (df(x)/dx = 0 at function extrema). * Kepler's Wine Barrel Problem, he used his rudimentary calculus to deduce which barrel shape would be the best bargain. * Kepler’s Conjecture- is a mathematical conjecture about sphere packing in three-dimensional Euclidean space. It says that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic close packing (face-centered cubic) and hexagonal close packing arrangements.Marin Mersenn e Birthdate: 8 September 1588 Died: 1 September 1648 Nationality: French Contributions: * Mersenne primes. * Introduced several innovating concepts that can be considered as the basis of modern reflecting telescopes: 1. Instead of using an eyepiece, Mersenne introduced the revolutionary idea of a second mirror that would reflect the light coming from the first mirror. This allows one to focus the image behind the primary mirror in which a hole is drilled at the centre to unblock the rays. 2.Mersenne invented the afocal telescope and the beam compressor that is useful in many multiple-mirrors telescope designs. 3. Mersenne recognized also that he could correct the spherical aberration of the telescope by using nonspherical mirrors and that in the particular case of the afocal arrangement he could do this correction by using two parabolic mirrors. * He also performed extensive experiments to determine the acceleration of falling objects by comparing them with the swing of pendulums, r eported in his Cogitata Physico-Mathematica in 1644.He was the first to measure the length of the seconds pendulum, that is a pendulum whose swing takes one second, and the first to observe that a pendulum's swings are not isochronous as Galileo thought, but that large swings take longer than small swings. Gerard Desargues Birthdate: February 21, 1591 Died: September 1661 Nationality: French Contributions: * Founder of the theory of conic sections. Desargues offered a unified approach to the several types of conics through projection and section. * Perspective Theorem – that when two triangles are in perspective the meets of corresponding sides are collinear. * Founder of projective geometry. Desargues’s theorem The theorem states that if two triangles ABC and A? B? C? , situated in three-dimensional space, are related to each other in such a way that they can be seen perspectively from one point (i. e. , the lines AA? , BB? , and CC? all intersect in one point), then the points of intersection of corresponding sides all lie on one line provided that no two corresponding sides are†¦ * Desargues introduced the notions of the opposite ends of a straight line being regarded as coincident, parallel lines meeting at a point of infinity and regarding a straight line as circle whose center is at infinity. Desargues’ most important work Brouillon projet d’une atteinte aux evenemens des rencontres d? une cone avec un plan (Proposed Draft for an essay on the results of taking plane sections of a cone) was printed in 1639. In it Desargues presented innovations in projective geometry applied to the theory of conic sections. Favorite Mathematician Mathematicians in this period has its own distinct, and unique knowledge in the field of mathematics.They tackled the more complex world of mathematics, this complex world of Mathematics had at times stirred their lives, ignited some conflicts between them, unfolded their flaws and weaknesses but at the end, they build harmonious world through the unity of their formulas and much has benefited from it, they indeed reflected the beauty of Mathematics. They were all excellent mathematicians, and no doubt in it. But I admire John Napier for giving birth to Logarithms in the world of Mathematics. V. Mathematicians in the 17th Century Rene Descartes Birthdate: 31 March 1596 Died: 11 February 1650Nationality: French Contributions: * Accredited with the invention of co-ordinate geometry, the standard x,y co-ordinate system as the Cartesian plane. He developed the coordinate system as a â€Å"device to locate points on a plane†. The coordinate system includes two perpendicular lines. These lines are called axes. The vertical axis is designated as y axis while the horizontal axis is designated as the x axis. The intersection point of the two axes is called the origin or point zero. The position of any point on the plane can be located by locating how far perpendicularly from e ach axis the point lays.The position of the point in the coordinate system is specified by its two coordinates x and y. This is written as (x,y). * He is credited as the father of analytical geometry, the bridge between algebra and geometry, crucial to the discovery of infinitesimal calculus and analysis. * Descartes was also one of the key figures in the Scientific Revolution and has been described as an example of genius. * He also â€Å"pioneered the standard notation† that uses superscripts to show the powers or exponents; for example, the 4 used in x4 to indicate squaring of squaring. He â€Å"invented the convention of representing unknowns in equations by x, y, and z, and knowns by a, b, and c†. * He was first to assign a fundamental place for algebra in our system of knowledge, and believed that algebra was a method to automate or mechanize reasoning, particularly about abstract, unknown quantities. * Rene Descartes created analytic geometry, and discovered an early form of the law of conservation of momentum (the term momentum refers to the momentum of a force). * He developed a rule for determining the number of positive and negative roots in an equation.The Rule of Descartes as it is known states â€Å"An equation can have as many true [positive] roots as it contains changes of sign, from + to – or from – to +; and as many false [negative] roots as the number of times two + signs or two – signs are found in succession. † Bonaventura Francesco Cavalieri Birthdate: 1598 Died: November 30, 1647 Nationality: Italian Contributions: * He is known for his work on the problems of optics and motion. * Work on the precursors of infinitesimal calculus. * Introduction of logarithms to Italy. First book was Lo Specchio Ustorio, overo, Trattato delle settioni coniche, or The Burning Mirror, or a Treatise on Conic Sections. In this book he developed the theory of mirrors shaped into parabolas, hyperbolas, and ellipses, and various combinations of these mirrors. * Cavalieri developed a geometrical approach to calculus and published a treatise on the topic, Geometria indivisibilibus continuorum nova quadam ratione promota (Geometry, developed by a new method through the indivisibles of the continua, 1635).In this work, an area is considered as constituted by an indefinite number of parallel segments and a volume as constituted by an indefinite number of parallel planar areas. * Cavalieri's principle, which states that the volumes of two objects are equal if the areas of their corresponding cross-sections are in all cases equal. Two cross-sections correspond if they are intersections of the body with planes equidistant from a chosen base plane. * Published tables of logarithms, emphasizing their practical use in the fields of astronomy and geography.Pierre de Fermat Birthdate: 1601 or 1607/8 Died: 1665 Jan 12 Nationality: French Contributions: * Early developments that led to infinitesimal calculus, inc luding his technique of adequality. * He is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of the differential calculus, then unknown, and his research into number theory. * He made notable contributions to analytic geometry, probability, and optics. * He is best known for Fermat's Last Theorem. Fermat was the first person known to have evaluated the integral of general power functions. Using an ingenious trick, he was able to reduce this evaluation to the sum of geometric series. * He invented a factorization method—Fermat's factorization method—as well as the proof technique of infinite descent, which he used to prove Fermat's Last Theorem for the case n = 4. * Fermat developed the two-square theorem, and the polygonal number theorem, which states that each number is a sum of three triangular numbers, four square numbers, five pentagonal numbers, and so on. With his gif t for number relations and his ability to find proofs for many of his theorems, Fermat essentially created the modern theory of numbers. Blaise Pascal Birthdate: 19 June 1623 Died: 19 August 1662 Nationality: French Contributions: * Pascal's Wager * Famous contribution of Pascal was his â€Å"Traite du triangle arithmetique† (Treatise on the Arithmetical Triangle), commonly known today as Pascal's triangle, which demonstrates many mathematical properties like binomial coefficients. Pascal’s Triangle At the age of 16, he formulated a basic theorem of projective geometry, known today as Pascal's theorem. * Pascal's law (a hydrostatics principle). * He invented the mechanical calculator. He built 20 of these machines (called Pascal’s calculator and later Pascaline) in the following ten years. * Corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science. * Pascal's theorem. It states that if a hexagon is inscribed in a circle (or conic) then the three intersection points of opposite sides lie on a line (called the Pascal line).Christiaan Huygens Birthdate: April 14, 1629 Died: July 8, 1695 Nationality: Dutch Contributions: * His work included early telescopic studies elucidating the nature of the rings of Saturn and the discovery of its moon Titan. * The invention of the pendulum clock. Spring driven pendulum clock, designed by Huygens. * Discovery of the centrifugal force, the laws for collision of bodies, for his role in the development of modern calculus and his original observations on sound perception. Wrote the first book on probability theory, De ratiociniis in ludo aleae (â€Å"On Reasoning in Games of Chance†). * He also designed more accurate clocks than were available at the time, suitable for sea navigation. * In 1673 he published his mathematical analysis of pendulums, Horologium Oscillatorium sive de motu pendulorum, his greatest work on horology. I saac Newton Birthdate: 4 Jan 1643 Died: 31 March 1727 Nationality: English Contributions: * He laid the foundations for differential and integral calculus.Calculus-branch of mathematics concerned with the study of such concepts as the rate of change of one variable quantity with respect to another, the slope of a curve at a prescribed point, the computation of the maximum and minimum values of functions, and the calculation of the area bounded by curves. Evolved from algebra, arithmetic, and geometry, it is the basis of that part of mathematics called analysis. * Produced simple analytical methods that unified many separate techniques previously developed to solve apparently unrelated problems such as finding areas, tangents, the lengths of curves and the maxima and minima of functions. Investigated the theory of light, explained gravity and hence the motion of the planets. * He is also famed for inventing `Newtonian Mechanics' and explicating his famous three laws of motion. * The first to use fractional indices and to employ coordinate geometry to derive solutions to Diophantine equations * He discovered Newton's identities, Newton's method, classified cubic plane curves (polynomials of degree three in two variables) Newton's identities, also known as the Newton–Girard formulae, give relations between two types of symmetric polynomials, namely between power sums and elementary symmetric polynomials.Evaluated at the roots of a monic polynomial P in one variable, they allow expressing the sums of the k-th powers of all roots of P (counted with their multiplicity) in terms of the coefficients of P, without actually finding those roots * Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function. Gottfried Wilhelm Von Leibniz Birthdate: July 1, 1646 Died: November 14, 1716 Nationality: GermanCont ributions: * Leibniz invented a mechanical calculating machine which would multiply as well as add, the mechanics of which were still being used as late as 1940. * Developed the infinitesimal calculus. * He became one of the most prolific inventors in the field of mechanical calculators. * He was the first to describe a pinwheel calculator in 1685[6] and invented the Leibniz wheel, used in the arithmometer, the first mass-produced mechanical calculator. * He also refined the binary number system, which is at the foundation of virtually all digital computers. Leibniz was the first, in 1692 and 1694, to employ it explicitly, to denote any of several geometric concepts derived from a curve, such as abscissa, ordinate, tangent, chord, and the perpendicular. * Leibniz was the first to see that the coefficients of a system of linear equations could be arranged into an array, now called a matrix, which can be manipulated to find the solution of the system. * He introduced several notations used to this day, for instance the integral sign ? representing an elongated S, from the Latin word summa and the d used for differentials, from the Latin word differentia.This cleverly suggestive notation for the calculus is probably his most enduring mathematical legacy. * He was the ? rst to use the notation f(x). * The notation used today in Calculus df/dx and ? f x dx are Leibniz notation. * He also did work in discrete mathematics and the foundations of logic. Favorite Mathematician Selecting favourite mathematician from these adept persons in mathematics is a hard task, but as I read the contributions of these Mathematicians, I found Sir Isaac Newton to be the greatest mathematician of this period.He invented the useful but difficult subject in mathematics- the calculus. I found him cooperative with different mathematician to derive useful formulas despite the fact that he is bright enough. Open-mindedness towards others opinion is what I discerned in him. VI. Mathematicians in the 18th Century Jacob Bernoulli Birthdate: 6 January 1655 Died: 16 August 1705 Nationality: Swiss Contributions: * Founded a school for mathematics and the sciences. * Best known for the work Ars Conjectandi (The Art of Conjecture), published eight years after his death in 1713 by his nephew Nicholas. Jacob Bernoulli's first important contributions were a pamphlet on the parallels of logic and algebra published in 1685, work on probability in 1685 and geometry in 1687. * Introduction of the theorem known as the law of large numbers. * By 1689 he had published important work on infinite series and published his law of large numbers in probability theory. * Published five treatises on infinite series between 1682 and 1704. * Bernoulli equation, y' = p(x)y + q(x)yn. * Jacob Bernoulli's paper of 1690 is important for the history of calculus, since the term integral appears for the first time with its integration meaning. Discovered a general method to determine evolutes of a curve as the envelope of its circles of curvature. He also investigated caustic curves and in particular he studied these associated curves of the parabola, the logarithmic spiral and epicycloids around 1692. * Theory of permutations and combinations; the so-called Bernoulli numbers, by which he derived the exponential series. * He was the first to think about the convergence of an infinite series and proved that the series   is convergent. * He was also the first to propose continuously compounded interest, which led him to investigate: Johan Bernoulli Birthdate: 27 July 1667Died: 1 January 1748 Nationality: Swiss Contributions: * He was a brilliant mathematician who made important discoveries in the field of calculus. * He is known for his contributions to infinitesimal calculus and educated Leonhard Euler in his youth. * Discovered fundamental principles of mechanics, and the laws of optics. * He discovered the Bernoulli series and made advances in theory of navigation and ship saili ng. * Johann Bernoulli proposed the brachistochrone problem, which asks what shape a wire must be for a bead to slide from one end to the other in the shortest possible time, as a challenge to other mathematicians in June 1696.For this, he is regarded as one of the founders of the calculus of variations. Daniel Bernoulli Birthdate: 8 February 1700 Died: 17 March 1782 Nationality: Swiss Contributions: * He is particularly remembered for his applications of mathematics to mechanics. * His pioneering work in probability and statistics. Nicolaus Bernoulli Birthdate: February 6, 1695 Died: July 31, 1726 Nationality: Swiss Contributions: †¢Worked mostly on curves, differential equations, and probability. †¢He also contributed to fluid dynamics. Abraham de Moivre Birthdate: 26 May 1667 Died: 27 November 1754 Nationality: French Contributions: Produced the second textbook on probability theory, The Doctrine of Chances: a method of calculating the probabilities of events in play. * Pioneered the development of analytic geometry and the theory of probability. * Gives the first statement of the formula for the normal distribution curve, the first method of finding the probability of the occurrence of an error of a given size when that error is expressed in terms of the variability of the distribution as a unit, and the first identification of the probable error calculation. Additionally, he applied these theories to gambling problems and actuarial tables. In 1733 he proposed the formula for estimating a factorial as n! = cnn+1/2e? n. * Published an article called Annuities upon Lives, in which he revealed the normal distribution of the mortality rate over a person’s age. * De Moivre’s formula: which he was able to prove for all positive integral values of n. * In 1722 he suggested it in the more well-known form of de Moivre's Formula: Colin Maclaurin Birthdate: February, 1698 Died: 14 June 1746 Nationality: Scottish Contributions: * Maclaurin used Taylor series to characterize maxima, minima, and points of inflection for infinitely differentiable functions in his Treatise of Fluxions. Made significant contributions to the gravitation attraction of ellipsoids. * Maclaurin discovered the Euler–Maclaurin formula. He used it to sum powers of arithmetic progressions, derive Stirling's formula, and to derive the Newton-Cotes numerical integration formulas which includes Simpson's rule as a special case. * Maclaurin contributed to the study of elliptic integrals, reducing many intractable integrals to problems of finding arcs for hyperbolas. * Maclaurin proved a rule for solving square linear systems in the cases of 2 and 3 unknowns, and discussed the case of 4 unknowns. Some of his important works are: Geometria Organica – 1720 * De Linearum Geometricarum Proprietatibus – 1720 * Treatise on Fluxions – 1742 (763 pages in two volumes. The first systematic exposition of Newton's methods. ) * Treatise on Al gebra – 1748 (two years after his death. ) * Account of Newton's Discoveries – Incomplete upon his death and published in 1750 or 1748 (sources disagree) * Colin Maclaurin was the name used for the new Mathematics and Actuarial Mathematics and Statistics Building at Heriot-Watt University, Edinburgh. Lenard Euler Birthdate: 15 April 1707 Died: 18 September 1783 Nationality: Swiss Contributions: He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. * He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. * He is also renowned for his work in mechanics, fluid dynamics, optics, and astronomy. * Euler introduced and popularized several notational conventions through his numerous and widely circulated textbooks. Most notably, he introduced the concept of a function [2] and was the first to write f(x) to denote the function f a pplied to the argument x. He also introduced the modern notation for the trigonometric functions, the letter e for the base of the natural logarithm (now also known as Euler's number), the Greek letter ? for summations and the letter i to denote the imaginary unit. * The use of the Greek letter ? to denote the ratio of a circle's circumference to its diameter was also popularized by Euler. * Well known in analysis for his frequent use and development of power series, the expression of functions as sums of infinitely many terms, such as * Euler introduced the use of the exponential function and logarithms in analytic proofs. He discovered ways to express various logarithmic functions using power series, and he successfully defined logarithms for negative and complex numbers, thus greatly expanding the scope of mathematical applications of logarithms. * He also defined the exponential function for complex numbers, and discovered its relation to the trigonometric functions. * Elaborate d the theory of higher transcendental functions by introducing the gamma function and introduced a new method for solving quartic equations. He also found a way to calculate integrals with complex limits, foreshadowing the development of modern complex analysis.He also invented the calculus of variations including its best-known result, the Euler–Lagrange equation. * Pioneered the use of analytic methods to solve number theory problems. * Euler created the theory of hypergeometric series, q-series, hyperbolic trigonometric functions and the analytic theory of continued fractions. For example, he proved the infinitude of primes using the divergence of the harmonic series, and he used analytic methods to gain some understanding of the way prime numbers are distributed. Euler's work in this area led to the development of the prime number theorem. He proved that the sum of the reciprocals of the primes diverges. In doing so, he discovered the connection between the Riemann zeta f unction and the prime numbers; this is known as the Euler product formula for the Riemann zeta function. * He also invented the totient function ? (n) which is the number of positive integers less than or equal to the integer n that are coprime to n. * Euler also conjectured the law of quadratic reciprocity. The concept is regarded as a fundamental theorem of number theory, and his ideas paved the way for the work of Carl Friedrich Gauss. * Discovered the formula V ?E + F = 2 relating the number of vertices, edges, and faces of a convex polyhedron. * He made great strides in improving the numerical approximation of integrals, inventing what are now known as the Euler approximations. Jean Le Rond De Alembert Birthdate: 16 November 1717 Died: 29 October 1783 Nationality: French Contributions: * D'Alembert's formula for obtaining solutions to the wave equation is named after him. * In 1743 he published his most famous work, Traite de dynamique, in which he developed his own laws of mot ion. * He created his ratio test, a test to see if a series converges. The D'Alembert operator, which first arose in D'Alembert's analysis of vibrating strings, plays an important role in modern theoretical physics. * He made several contributions to mathematics, including a suggestion for a theory of limits. * He was one of the first to appreciate the importance of functions, and defined the derivative of a function as the limit of a quotient of increments. Joseph Louise Lagrange Birthdate: 25 January 1736 Died: 10 April 1813 Nationality: Italian French Contributions: * Published the ‘Mecanique Analytique' which is considered to be his monumental work in the pure maths. His most prominent influence was his contribution to the the metric system and his addition of a decimal base. * Some refer to Lagrange as the founder of the Metric System. * He was responsible for developing the groundwork for an alternate method of writing Newton's Equations of Motion. This is referred to as ‘Lagrangian Mechanics'. * In 1772, he described the Langrangian points, the points in the plane of two objects in orbit around their common center of gravity at which the combined gravitational forces are zero, and where a third particle of negligible mass can remain at rest. He made significant contributions to all fields of analysis, number theory, and classical and celestial mechanics. * Was one of the creators of the calculus of variations, deriving the Euler–Lagrange equations for extrema of functionals. * He also extended the method to take into account possible constraints, arriving at the method of Lagrange multipliers. * Lagrange invented the method of solving differential equations known as variation of parameters, applied differential calculus to the theory of probabilities and attained notable work on the solution of equations. * He proved that every natural number is a sum of four squares. Several of his early papers also deal with questions of number theo ry. 1. Lagrange (1766–1769) was the first to prove that Pell's equation has a nontrivial solution in the integers for any non-square natural number n. [7] 2. He proved the theorem, stated by Bachet without justification, that every positive integer is the sum of four squares, 1770. 3. He proved Wilson's theorem that n is a prime if and only if (n ? 1)! + 1 is always a multiple of n, 1771. 4. His papers of 1773, 1775, and 1777 gave demonstrations of several results enunciated by Fermat, and not previously proved. 5.His Recherches d'Arithmetique of 1775 developed a general theory of binary quadratic forms to handle the general problem of when an integer is representable by the form. Gaspard Monge Birthdate: May 9, 1746 Died: July 28, 1818 Nationality: French Contributions: * Inventor of descriptive geometry, the mathematical basis on which technical drawing is based. * Published the following books in mathematics: 1. The Art of Manufacturing Cannon (1793)[3] 2. Geometrie descri ptive. Lecons donnees aux ecoles normales (Descriptive Geometry): a transcription of Monge's lectures. (1799) Pierre Simon Laplace Birthdate: 23 March 1749Died: 5 March 1827 Nationality: French Contributions: * Formulated Laplace's equation, and pioneered the Laplace transform which appears in many branches of mathematical physics. * Laplacian differential operator, widely used in mathematics, is also named after him. * He restated and developed the nebular hypothesis of the origin of the solar system * Was one of the first scientists to postulate the existence of black holes and the notion of gravitational collapse. * Laplace made the non-trivial extension of the result to three dimensions to yield a more general set of functions, the spherical harmonics or Laplace coefficients. Issued his Theorie analytique des probabilites in which he laid down many fundamental results in statistics. * Laplace’s most important work was his Celestial Mechanics published in 5 volumes between 1798-1827. In it he sought to give a complete mathematical description of the solar system. * In Inductive probability, Laplace set out a mathematical system of inductive reasoning based on probability, which we would today recognise as Bayesian. He begins the text with a series of principles of probability, the first six being: 1.Probability is the ratio of the â€Å"favored events† to the total possible events. 2. The first principle assumes equal probabilities for all events. When this is not true, we must first determine the probabilities of each event. Then, the probability is the sum of the probabilities of all possible favored events. 3. For independent events, the probability of the occurrence of all is the probability of each multiplied together. 4. For events not independent, the probability of event B following event A (or event A causing B) is the probability of A multiplied by the probability that A and B both occur. 5.The probability that A will occur, given th at B has occurred, is the probability of A and B occurring divided by the probability of B. 6. Three corollaries are given for the sixth principle, which amount to Bayesian probability. Where event Ai ? {A1, A2, †¦ An} exhausts the list of possible causes for event B, Pr(B) = Pr(A1, A2, †¦ An). Then: * Amongst the other discoveries of Laplace in pure and applied mathematics are: 1. Discussion, contemporaneously with Alexandre-Theophile Vandermonde, of the general theory of determinants, (1772); 2. Proof that every equation of an even degree must have at least one real quadratic factor; 3.Solution of the linear partial differential equation of the second order; 4. He was the first to consider the difficult problems involved in equations of mixed differences, and to prove that the solution of an equation in finite differences of the first degree and the second order might always be obtained in the form of a continued fraction; and 5. In his theory of probabilities: 6. Evalua tion of several common definite integrals; and 7. General proof of the Lagrange reversion theorem. Adrian Marie Legendere Birthdate: 18 September 1752 Died: 10 January 1833 Nationality: French Contributions: Well-known and important concepts such as the Legendre polynomials. * He developed the least squares method, which has broad application in linear regression, signal processing, statistics, and curve fitting; this was published in 1806. * He made substantial contributions to statistics, number theory, abstract algebra, and mathematical analysis. * In number theory, he conjectured the quadratic reciprocity law, subsequently proved by Gauss; in connection to this, the Legendre symbol is named after him. * He also did pioneering work on the distribution of primes, and on the application of analysis to number theory. Best known as the author of Elements de geometrie, which was published in 1794 and was the leading elementary text on the topic for around 100 years. * He introduced wh at are now known as Legendre functions, solutions to Legendre’s differential equation, used to determine, via power series, the attraction of an ellipsoid at any exterior point. * Published books: 1. Elements de geometrie, textbook 1794 2. Essai sur la Theorie des Nombres 1798 3. Nouvelles Methodes pour la Determination des Orbites des Cometes, 1806 4. Exercices de Calcul Integral, book in three volumes 1811, 1817, and 1819 5.Traite des Fonctions Elliptiques, book in three volumes 1825, 1826, and 1830 Simon Dennis Poison Birthdate: 21 June 1781 Died: 25 April 1840 Nationality: French Contributions: * He published two memoirs, one on Etienne Bezout's method of elimination, the other on the number of integrals of a finite difference equation. * Poisson's well-known correction of Laplace's second order partial differential equation for potential: today named after him Poisson's equation or the potential theory equation, was first published in the Bulletin de la societe philomati que (1813). Poisson's equation for the divergence of the gradient of a scalar field, ? in 3-dimensional space: Charles Babbage Birthdate: 26 December 1791 Death: 18 October 1871 Nationality: English Contributions: * Mechanical engineer who originated the concept of a programmable computer. * Credited with inventing the first mechanical computer that eventually led to more complex designs. * He invented the Difference Engine that could compute simple calculations, like multiplication or addition, but its most important trait was its ability create tables of the results of up to seven-degree polynomial functions. Invented the Analytical Engine, and it was the first machine ever designed with the idea of programming: a computer that could understand commands and could be programmed much like a modern-day computer. * He produced a Table of logarithms of the natural numbers from 1 to 108000 which was a standard reference from 1827 through the end of the century. Favorite Mathematician No ticeably, Leonard Euler made a mark in the field of Mathematics as he contributed several concepts and formulas that encompasses many areas of Mathematics-Geometry, Calculus, Trigonometry and etc.He deserves to be praised for doing such great things in Mathematics, indeed, his work laid foundation to make the lives of the following generation sublime, ergo, He is my favourite mathematician. VII. Mathematicians in the 19th Century Carl Friedrich Gauss Birthdate: 30 April 1777 Died: 23 February 1855 Nationality: German Contributions: * He became the first to prove the quadratic reciprocity law. * Gauss also made important contributions to number theory with his 1801 book Disquisitiones Arithmeticae (Latin, Arithmetical Investigations), which, among things, introduced the symbol ? or congruence and used it in a clean presentation of modular arithmetic, contained the first two proofs of the law of quadratic reciprocity, developed the theories of binary and ternary quadratic forms, state d the class number problem for them, and showed that a regular heptadecagon (17-sided polygon) can be constructed with straightedge and compass. * He developed a method of measuring the horizontal intensity of the magnetic field which was in use well into the second half of the 20th century, and worked out the mathematical theory for separating the inner and outer (magnetospheric) sources of Earth's magnetic field.Agustin Cauchy Birthdate: 21 August 1789 Died: 23 May 1857 Nationality: French Contributions: * His most notable research was in the theory of residues, the question of convergence, differential equations, theory of functions, the legitimate use of imaginary numbers, operations with determinants, the theory of equations, the theory of probability, and the applications of mathematics to physics. * His writings introduced new standards of rigor in calculus from which grew the modern field of analysis.In Cours d’analyse de l’Ecole Polytechnique (1821), by develo ping the concepts of limits and continuity, he provided the foundation for calculus essentially as it is today. * He introduced the â€Å"epsilon-delta definition for limits (epsilon for â€Å"error† and delta for â€Å"difference’). * He transformed the theory of complex functions by discovering integral theorems and introducing the calculus of residues. * Cauchy founded the modern theory of elasticity by applying the notion of pressure on a plane, and assuming that this pressure was no longer perpendicular to the plane upon which it acts in an elastic body.In this way, he introduced the concept of stress into the theory of elasticity. * He also examined the possible deformations of an elastic body and introduced the notion of strain. * One of the most prolific mathematicians of all time, he produced 789 mathematics papers, including 500 after the age of fifty. * He had sixteen concepts and theorems named for him, including the Cauchy integral theorem, the Cauchy-Sc hwartz inequality, Cauchy sequence and Cauchy-Riemann equations. He defined continuity in terms of infinitesimals and gave several important theorems in complex analysis and initiated the study of permutation groups in abstract algebra. * He started the project of formulating and proving the theorems of infinitesimal calculus in a rigorous manner. * He was the first to define complex numbers as pairs of real numbers. * Most famous for his single-handed development of complex function theory.The first pivotal theorem proved by Cauchy, now known as Cauchy's integral theorem, was the following: where f(z) is a complex-valued function holomorphic on and within the non-self-intersecting closed curve C (contour) lying in the complex plane. * He was the first to prove Taylor's theorem rigorously. * His greatest contributions to mathematical science are enveloped in the rigorous methods which he introduced; these are mainly embodied in his three great treatises: 1. Cours d'analyse de l'Ecol e royale polytechnique (1821) 2. Le Calcul infinitesimal (1823) 3.Lecons sur les applications de calcul infinitesimal; La geometrie (1826–1828) Nicolai Ivanovich Lobachevsky Birthdate: December 1, 1792 Died: February 24, 1856 Nationality: Russian Contributions: * Lobachevsky's great contribution to the development of modern mathematics begins with the fifth postulate (sometimes referred to as axiom XI) in Euclid's Elements. A modern version of this postulate reads: Through a point lying outside a given line only one line can be drawn parallel to the given line. * Lobachevsky's geometry found application in the theory of complex numbers, the theory of vectors, and the theory of relativity. Lobachevskii's deductions produced a geometry, which he called â€Å"imaginary,† that was internally consistent and harmonious yet different from the traditional one of Euclid. In 1826, he presented the paper â€Å"Brief Exposition of the Principles of Geometry with Vigorous Proofs o f the Theorem of Parallels. † He refined his imaginary geometry in subsequent works, dating from 1835 to 1855, the last being Pangeometry. * He was well respected in the work he developed with the theory of infinite series especially trigonometric series, integral calculus, and probability. In 1834 he found a method for approximating the roots of an algebraic equation. * Lobachevsky also gave the definition of a function as a correspondence between two sets of real numbers. Johann Peter Gustav Le Jeune Dirichlet Birthdate: 13 February 1805 Died: 5 May 1859 Nationality: German Contributions: * German mathematician with deep contributions to number theory (including creating the field of analytic number theory) and to the theory of Fourier series and other topics in mathematical analysis. * He is credited with being one of the first mathematicians to give the modern formal definition of a function. Published important contributions to the biquadratic reciprocity law. * In 1837 h e published Dirichlet's theorem on arithmetic progressions, using mathematical analysis concepts to tackle an algebraic problem and thus creating the branch of analytic number theory. * He introduced the Dirichlet characters and L-functions. * In a couple of papers in 1838 and 1839 he proved the first class number formula, for quadratic forms. * Based on his research of the structure of the unit group of quadratic fields, he proved the Dirichlet unit theorem, a fundamental result in algebraic number theory. He first used the pigeonhole principle, a basic counting argument, in the proof of a theorem in diophantine approximation, later named after him Dirichlet's approximation theorem. * In 1826, Dirichlet proved that in any arithmetic progression with first term coprime to the difference there are infinitely many primes. * Developed significant theorems in the areas of elliptic functions and applied analytic techniques to mathematical theory that resulted in the fundamental developme nt of number theory. * His lectures on the equilibrium of systems and potential theory led to what is known as the Dirichlet problem.It involves finding solutions to differential equations for a given set of values of the boundary points of the region on which the equations are defined. The problem is also known as the first boundary-value problem of potential theorem. Evariste Galois Birthdate: 25 October 1811 Death: 31 May 1832 Nationality: French Contributions: * His work laid the foundations for Galois Theory and group theory, two major branches of abstract algebra, and the subfield of Galois connections. * He was the first to use the word â€Å"group† (French: groupe) as a technical term in mathematics to represent a group of permutations. Galois published three papers, one of which laid the foundations for Galois Theory. The second one was about the numerical resolution of equations (root finding in modern terminology). The third was an important one in number theory, i n which the concept of a finite field was first articulated. * Galois' mathematical contributions were published in full in 1843 when Liouville reviewed his manuscript and declared it sound. It was finally published in the October–November 1846 issue of the Journal de Mathematiques Pures et Appliquees. 16] The most famous contribution of this manuscript was a novel proof that there is no quintic formula – that is, that fifth and higher degree equations are not generally solvable by radicals. * He also introduced the concept of a finite field (also known as a Galois field in his honor), in essentially the same form as it is understood today. * One of the founders of the branch of algebra known as group theory. He developed the concept that is today known as a normal subgroup. * Galois' most significant contribution to mathematics by far is his development of Galois Theory.He realized that the algebraic solution to a polynomial equation is related to the structure of a g roup of permutations associated with the roots of the polynomial, the Galois group of the polynomial. He found that an equation could be solved in radicals if one can find a series of subgroups of its Galois group, each one normal in its successor with abelian quotient, or its Galois group is solvable. This proved to be a fertile approach, which later mathematicians adapted to many other fields of mathematics besides the theory of equations to which Galois orig