Thursday, 22 March 2012

mathematics-related occupation :)

Why Choose a Mathematics-Related Profession ?

Mathematics teaches patience, discipline, and step-by-step problem-solving skills. For those with a substantial background in mathematics, an unlimited number of career opportunuities are available. According to Jobs Rated Almanac , a 1990 publication of World Almanac Books of New York, NY, careers that require a very strong background in mathematics were listed as the five "best" jobs. They were :
  • software engineer
  • actuary
  • computer systems analyst
  • computer programmer
  • mathematician
Almost all of the top fifty jobs in this "best" jobs list involved mathematical reasoning and knowledge. This list was the result of the comparison of two hundred fifty jobs classified according to :
  • income
  • future outlook
  • physical demands
  • job security
  • stress
  • work environment

A List of Professions

The following list briefly describes work associated with some mathematics-related professions :
  • actuary-- assemble and analyze statistics to calculate probabilities of death, sickness, injury, disability, unemployment, retirement, and property loss; design insurance and pension plans and ensure that they are maintained on a sound financial basis
  • mathematics teacher-- introduce students to the power and beauty of mathematics in elementary, junior high, or high school mathematics courses
  • operations research analyst-- assist organizations (manufacturers, airlines, military) in developing the most efficient, cost-effective solutions to organizational operations and problems; this includes strategy, forecasting, resource allocation, facilities layout, inventory control, personnel schedules, and distribution systems
  • statistician-- collect, analyze, and present numerical data resulting from surveys and experiments
  • physician-- diagnose patient illnesses, prescribe medication, teach classes, mentor interns, and do clinical research; students with a good mathematics background will find themselves being admitted to the best medical schools and discover that mathematics has prepared them well for the discipline, analysis, and problem- solving required in the field of medicine
  • research scientist-- model atmospheric conditions to gain insight into the effect of changing emissions from cars, trucks, power plants, and factories; apply these models in the development of alternative fuels
  • computer scientist-- interface the technology of computers with the underlying mathematical principles of such diverse applications as medical diagnoses, graphics animation, interior design, cryptogrraphy, and parallel computers
  • inventory strategist-- analyze historical sales data, model forecast uncertainty to design contingency plans, and analyze catalog displays to make them more successful; analyze consumer responses
  • staff systems air traffic control analyst-- apply probability, statistics, and logistsics to air traffic control operations; use simulated aircraft flight to monitor air traffic control computer systems
  • cryptologist-- design and analyze schemes used to transmit secret information
  • attorney-- research, comprehend, and apply local, state, and federal laws; a good background in mathematics will help a student get admitted to law school and assist in the understanding of complicated theoretical legal concepts
  • economist-- interpret and analyze the interrelationships among factors which drive the economics of a particular organization, industry, or country
  • mathematics professor-- teach mathematics classes, do theoretical research, and advise undergraduate and graduate students at colleges and universities
  • environmental mathematician-- work as member of interdisciplinary team of scientists and professionals studying problems at specific Superfund sites; communicate effectively across many academic discilplines and be able to summarize work in writing
  • robotics engineer-- combine mathematics, engineering, and computer science in the study and design of robots
  • geophysical mathematician -- develop the mathematical basis for seismic imaging tools used in the exploration and production of oil and gas reservoirs
  • design -- use computer graphics and mathematical modeling in the design and construction of physical prototypes; integrate geometric design with cost-effective manufacturing of resulting products
  • ecologist -- study the interrelationships of organisms and their environments and the underlying mathematical dynamics
  • geodesist -- study applied science involving the precise measurement of the size and shape of the earth and its gravity field (courtesy of Bruce Hedquist)
  • photogrammetrist -- study the applied science of multi-spectral image acquisition from terrestrial, aerial and satellite camera platforms, followed up by the image processing, analysis, storage, display, and distribution in various hard-copy and digital format (courtesy of Bruce Hedquist)
  • civil engineer -- plan, design, and manage the construction of land vehicle, aircraft, water, and energy transport systems; analyze and control systems for land vehicular traffic; analyze and control environmental systems for sewage and water treatment; develop sites for industrial, commercial and residential home use; analyze and control systems for storm water drainage and storage; manage construction of foundations, structures and buildings; analyze construction materials ; and surface soils and subterranean material analysis (courtesy of Bruce Hedquist)
  • geomatics engineer -- once known as "surveying engineer", includes geodetic surveying : takes into account the size and shape of the earth, in order to determine the precise horizontal and vertical positions of geodetic reference monuments; cadastral surveying : establishes and reestablishes the reference monuments for the U.S. Public Land Survey System, i.e., township and section corners; topographic surveying : determines the detailed configuration or contour of the natural earth's surface and the position of fixed objects thereon or related thereto; hydrographic surveying : similarly determines underwater contours and features; land surveying : is the location of existing parcel and new land subdivision lines, road and utility rights-of-way and easement lines, and determination of the location of existing and new reference monuments, which mark property lines and parcel corners; land surveying : also involves the preparation of legal descriptions for officially recorded land ownership conveyance deeds and other land title documents; construction surveying : is the determination of the direction and length between and the elevations of reference points for fixed private and public works, as embraced within the definition and practice of civil engineering, and the labeling of reference markers containing critical information for the construction thereof; design, operation and management of advanced Geographic Information Systems (GIS and Land Information Systems (LIS), as well as other sophisticated computer mapping and CAD based geospatial applications (courtesy of Bruce Hedquist)

lots of mathematics related jobs, just for you ;)

Tuesday, 20 March 2012

Number Basses

Working with Number Bases

We now have a generalization for expressing numbers of any base r in terms of a 
power series. Using this generalization, we can convert from any base to decimal (or any other if you can readily add and take exponents in that base).

Power Series Expansions

We are accustomed to using a decimal system for most of our mathematical computations. This is a base ten system, in which each digit of a number represents a power of 10. For example, the number 987.65, can be expressed as:
[9·10^2] + [8·10^1] + [7·10^0] + [6·10^-1] + [5·10^-2]
This format can be rewritten more generally by assigning the digits 9, 8, 7, 6, 5 to the expressions D(2), D(1), D(0), D(-1), D(-2), respectively. (The numbers in parentheses are the same as the exponents of the powers of ten they correspond to.) We can also express the base, in this case, 10, as r. These substitutions give us the following expression:
[D(2)·r^2] + [D(1)·r^1] + [D(0)·r^0] + [D(-1)·r^-1] + [D(-2)·r^-2]
For example, we can find the decimal value of 212.01(3) as follows:
  [2·3^2] + [1·3^1] + [2·3^0] + [0·3^-1] + [1·3^-2]
= 2·9 + 1·3 + 2·1 + 0·1/3 + 1·1/9
= 18 + 3 + 2 + 1/9 = 23.1111...

Binary, Octal, and Hexadecimal Numbers

The binary number system is a base 2 number system, using only the digits 0 and 1. It is commonly used when dealing with computers because it is well suited to represent logical expressions, which have only 2 values, TRUE(1) and FALSE(0). Single binary digits are often referred to as bits.
Octal Numbers are base 8 numbers, using only the digits 0 through 7. Hexadecimal numbers(often referred to as hex) are base 16 numbers, using the digits 0 through 9, and the letters A through F (A representing 10(10), B representing 11(10), and so on). Since 8 and 16 are both powers of 2, each of their digits can be represented as a group of bits, the number of bits being the same as the power of 2 that the base is. In other words, since 16 = 2^4, a base 16 digit can be represented as 4 bits, and since 8 = 2^3, a base 8 digit can be represented as 3 bits, as in the following examples:
237.44(8) = 010|011|111|.|100|100(2)
A443.4CB(16) = 1010|0100|0100|0011|.|0100|1100|1011(2)
7372.01(8) = 111|011|111|010|.|000|001(2)
1AA.03(16) = 0001|1010|1010|.|0000|0011(2)
Notice that each group of bits on the right corresponds to a digit in the higher based number on the left. It is also easy to convert the other way, from binary to hex or octal. You simply start at the decimal point and count out groups of threes or fours, depending on the base to which you are converting, and add leading and following zeros to fill the outer groups. This ease of conversion makes octal and hex good shorthand for binary numbers.

Converting from Decimal to Other Bases

We have seen how to convert to decimal from other bases using a power series. You can use the same principle to convert from decimal to other bases.
In this case, you make a power series in the base you want to change to, with coefficients of 1. Then find the first number larger than your decimal number. Divide the decimal number by the next smallest number in the power series, and take an integer result. Then repeat the process with the remainder. The number in the new base is the results of the divides, lined up in order of exponent from left to right, making sure to remember to put zeros in places where the divide result was zero.
For example, let us find the value of 174(10) in base 3:
First we take a power series of 3:
3^0=1     3^1=3     3^2=9     3^3=27     3^4=81     3^5=243
Since 81 is the next smallest number, we start by dividing 175 by 81, and continue through the power series as follows:
175 / 81 = 2   Remainder 13
 13 / 27 = 0   Remainder 13
 13 /  9 = 1   Remainder  4
 4  /  3 = 1   Remainder  1
 1  /  1 = 1   Remainder  0
Thus, the result is 20111(3)
This method can be simplified by MODing the dicimal number by the new base, and repeating the process with the integer result of dividing the decimal number by the new base until the division result is 0. The result is then the results of the MODs taken from bottom to top.
For example, let us repeat the example from above:
175 MOD 3 = 1     175 / 3 = 58
 58 MOD 3 = 1      58 / 3 = 19
 19 MOD 3 = 1      19 / 3 =  6
  6 MOD 3 = 0       6 / 3 =  2
  2 MOD 3 = 2       2 / 3 =  0
Thus, the result is 20111(3)

Fractions in Different Bases

Base conversions are handled similarly for fractional parts of numbers. You can take a power series for the base you are converting to and subtract, or use a method similar to the one we just looked at, multiplying by the new base instead of taking MODs, and taking off the integer parts of the results from top to bottom to obtain the number in the new base.
Let's use both methods to convert from .59342(10) into binary:
Power Series method:
First, we'll take a power series of 8, with increasing negative exponents:
2^-1=0.5     2^-2=0.25     2^-3=0.125     2^-4=0.0625     2^-5=0.03125     2^-6=0.015625
We will stop at 6 decimal places. Unlike base conversions between integers, fractional parts of numbers are not limited to a set number of digits, and in some cases they can even go on infinitely. For example, the number 1/3, expressed as .1 in base three, is infinitely long in base 10. Thus it is often necessary to decide on a set precision to expand the number to.
Next we will subtract:
0.59376 = 1·0.5 + 0.09376 0.09342 = 0·0.25 + 0.09376 0.09342 = 0·0.125 + 0.09376 0.09342 = 1·0.0625 + 0.03126 0.03126 = 1·0.03125 + 0.00001 0.00001 = 0·0.016525 + 0.00001
Thus our result is 0.10011(2)
Multiplication Method:
0.59376·2 = 1 + 0.18752 0.18752·2 = 0 + 0.37504 0.37504·2 = 0 + 0.75008 0.75008·2 = 1 + 0.50016 0.50016·2 = 1 + 0.00032 0.00032·2 = 0 + 0.00064
Again, we get the result 0.10011(2)

by:  Nurul Adlina Syazwani binti Mohamad Arif

Saturday, 17 March 2012

Math's Video's :)

Abascus Video

Maths Tric of Calculation

Maths Tricks

Fast Maths

Real Life Maths

Maths Song :)

By Soniadeep Kaur & Dorothy Irene Petrus
    Mathematics is one of the deepest and most powerful expressions of pure human reason, and, at the same time, the most fundamental resource for description and analysis of the experiential world.
    - Hyman Bass

Maths Teaser

1. If you take three apples from five apples, how many do you have?

Answer: You have three apples. 

2. It happens once in a minute, twice in a week, and once in a year. What is it?

Answer: The letter 'e'.

3. Why are diapers like 100 dollar bills?

Answer: They need to be changed.

4. What did one math book say to the other math book?

Answer: Wow, have I got problems!

5. When do giraffes have 8 feet?

Answer: When there are two of them.

6. How many eggs can you put in an empty basket?

Answer: Only one, after that the basket is not empty.

Famous Mathematician

Euclid of Megara
Euclid may have been a student of Aristotle. He founded the school of mathematics at the great university of Alexandria. He was the first to prove that there are infinitely many prime numbers; he stated and proved the unique factorization theorem; and he devised Euclid's algorithm for computing gcd. He introduced the Mersenne primes and observed that (M2+M)/2 is always perfect (in the sense of Pythagoras) if M is Mersenne. (The converse, that any even perfect number has such a corresponding Mersenne prime, was tackled by Alhazen and proven by Euler.) He proved that there are only five "Platonic solids," as well as theorems of geometry far too numerous to summarize; among many with special historical interest is the proof that rigid-compass constructions can be implemented with collapsing-compass constructions. Although notions of trigonometry were not in use, Euclid's theorems include some closely related to the Laws of Sines and Cosines. Among several books attributed to Euclid are The Division of the Scale (a mathematical discussion of music), The OpticsThe Cartoptrics (a treatise on the theory of mirrors), a book on spherical geometry, a book on logic fallacies, and his comprehensive math textbook The Elements. Several of his masterpieces have been lost, including works on conic sections and other advanced geometric topics. Apparently Desargues' Homology Theorem (a pair of triangles is coaxial if and only if it is copolar) was proved in one of these lost works; this is the fundamental theorem which initiated the study of projective geometry. Euclid ranks #14 on Michael Hart's famous list of the Most Influential Persons in History. The Elements introduced the notions of axiom and theorem; was used as a textbook for 2000 years; and in fact is still the basis for high school geometry, making Euclid the leading mathematics teacher of all time. Some think his best inspiration was recognizing that the Parallel Postulate must be an axiom rather than a theorem.

By: Khadijah Bt. Mohd Yunos

Wednesday, 14 March 2012

History of Mathematics

Every culture on earth has developed some mathematics. In some cases, this mathematics has spread from one culture to another. Now there is one predominant international mathematics, and this mathematics has quite a history. It has roots in ancient Egypt and Babylonia, then grew rapidly in ancient Greece. Mathematics written in ancient Greek was translated into Arabic. About the same time some mathematics of India was translated into Arabic. Later some of this mathematics was translated into Latin and became the mathematics of Western Europe. Over a period of several hundred years, it became the mathematics of the world.
There are other places in the world that developed significant mathematics, such as China, southern India, and Japan, and they are interesting to study, but the mathematics of the other regions have not had much influence on current international mathematics. There is, of course, much mathematics being done these and other regions, but it is not the traditional math of the regions, but international mathematics.
By far, the most significant development in mathematics was giving it firm logical foundations. This took place in ancient Greece in the centuries preceding Euclid. SeeEuclid's Elements. Logical foundations give mathematics more than just certainty-they are a tool to investigate the unknown.
By the 20th century the edge of that unknown had receded to where only a few could see. One was David Hilbert, a leading mathematician of the turn of the century. In 1900 he addressed the International Congress of Mathematicians in Paris, and described 23 important mathematical problems.
Mathematics continues to grow at a phenomenal rate. There is no end in sight, and the application of mathematics to science becomes greater all the time.

The Babylonian mathematical tablet Plimpton 322, dated to 1800 BC.
Counting rod numerals
The numerals used in the Bakhshali manuscript, dated between the 2nd century BCE and the 2nd century CE.
Brahmi numerals (lower row) in India in the 1st century CE

By:Iqffa Nadia

Job Opportunities For Mathematicians


Significant Points

·         A Ph.D. in mathematics usually is the minimum educational requirement, except in the Federal Government.
·         Much faster than average employment growth is expected for mathematicians.
·         Keen competition for jobs is expected.
·         Ph.D. holders with a strong background in mathematics and a related field, such as computer science or engineering, should have better employment opportunities in related occupations.



Mathematicians held about 2,900 jobs in 2008. Many people with mathematical backgrounds also worked in other occupations. For example, there were about 54,800 jobs for postsecondary mathematical science teachers in 2008.
Many mathematicians work for the Federal Government, primarily in the U.S. Department of Defense which accounts for about 81 percent of the mathematicians employed by the Federal Government. Many of the other mathematicians employed by the Federal Government work for the National Institute of Standards and Technology (NIST) or the National Aeronautics and Space Administration (NASA).
In the private sector, major employers include scientific research and development services and management, scientific, and technical consulting services. Some mathematicians also work for insurance carriers.

Job Outlook

Employment of mathematicians is expected to grow much faster than average. However, keen competition for jobs is expected.

Employment change. 
Employment of mathematicians is expected to increase by 22 percent during the 2008–18 decade, which is much faster than average for all occupations. Advancements in technology usually lead to expanding applications of mathematics, and more workers with knowledge of mathematics will be required in the future. However, jobs in industry and government often require advanced knowledge of related scientific disciplines in addition to mathematics. The most common fields in which mathematicians study and find work are computer science and software development, physics, engineering, and operations research. Many mathematicians also are involved in financial analysis and in life sciences research.

Job prospects.
 Job competition will remain keen because employment in this occupation is relatively small and few new jobs are expected. Ph.D. holders with a strong background in mathematics and a related discipline, such as engineering or computer science, and who apply mathematical theory to real-world problems will have the best job prospects in related occupations.
In addition, mathematicians with experience in computer programming will better their job prospects in many occupations.
Holders of a master's degree in mathematics will face very strong competition for jobs in theoretical research. Because the number of Ph.D. degrees awarded in mathematics continues to exceed the number of available university positions—especially tenure-track positions—many graduates will need to find employment in industry and government.
Employment in theoretical mathematical research is sensitive to general economic fluctuations and to changes in government spending. Job prospects will be greatly influenced by changes in public and private funding .

Opportunities for mathematicians

Between one third and one half of all jobs requiring graduates are open to students of any discipline. Of course, mathematicians are eligible for these jobs. In addition, there are careers for which a degree in mathematics is either essential or a strong advantage. These fall into a number of general areas:
1.      Scientific research, design and development
Large companies and government research establishments are actively involved in research and development. They employ mathematicians and statisticians, usually along with other scientists in interdisciplinary research teams. The problems being solved require a flexible approach and speedy solutions, the need being for ``best possible'' answers in the time available. Projects of this type require high mathematical skill, ability to analyse complex problems in order to formulate them mathematically and to use computers in their solution (a skill developed during mathematics degree courses), willingness to work to deadlines, and ability to communicate findings to others.
The range of problems on which mathematicians are engaged is wide. We give a few examples. In the aircraft industry, there is work on aerodynamical design, providing theoretical results which predict or complement those from (for example) experimental wind tunnels. In pollution control, mathematicians would develop ``models'' (mathematical equations) predicting dispersal rates of chimney effluents under different meteorological conditions. In telecommunications, mathematicians may work on improved communications links, computer-recognition of handwriting and speech patterns, and distortion in digital transmission.
2.     Management services and computing
The problems of coping with rapid changes in technology and market conditions in large and complex organisations make it essential for managers to call on specialist services. Management service specialists define and investigate problems systematically. The work is often mathematical, involving an area of mathematics known as Operational Research. It might involve designing a more efficient transportation programme for deliveries to a supermarket chain, or a stock control pattern for a car franchise holder.
Computing is a major part of the work of most management services departments. Entrants are usually appointed as trainee programmers, but the work can be very varied, especially for employees of a company of management consultants. Their role is to set up mathematical models of the situations they are required to analyse, and to use computers in the solution of the problems, rather than just to write computer programs.
Personal qualities are especially important - tact, understanding, ability to communicate - because in recommending action based on their work, mathematicians can face resistance to changing familiar methods and practices.
3.     Financial work
In recent years, up to half of all mathematics graduates have taken up a career in finance.
o    Accountancy
Firms of chartered accountants - the main employers - do not normally specify degree disciplines of entrants. They are particularly keen though to recruit mathematics graduates, because of their numeracy skills and logical thought, and because they are normally very successful in the professional examinations (on average, more so than accountancy graduates!). So to become an accountant, you do not need to take a degree in accountancy. A mathematics degree allows many openings in accountancy, should you wish to follow them after graduation, as well as all the other opportunities.
o    Actuarial work
This has long been a popular field for mathematics graduates. The work involves the application of probability and statistics to financial affairs such as life assurance, pensions and social security, so a degree involving a substantial proportion of these subjects is desirable. Traineeships occur with life assurance companies and insurance companies as well as with actuarial consultants. Career and salary prospects for those with managerial and commercial potential are excellent.
o    Other openings in finance
There are some opportunities in banking, particularly with the head offices of major banks, or with merchant banks. Mathematicians have frequently been successful candidates for the Tax Inspectorate.
4.     Statistical work
We have already discussed one aspect of work undertaken by statisticians - the work of an actuary. In addition, statistical work is carried out in many organisations - the Civil Service (economics and agriculture in particular), research establishments, large industrial firms and commercial concerns (e.g. market research agencies).
The work is varied, depending on the activities of the employer. In the Civil Service and in research establishments (government and industrial), statisticians work on design and analysis of experimental projects. In industry, the work may involve quality control, where statisticians collaborate in designing procedures for testing and in assessing the results of the tests. Statisticians employed by market research and advertising agencies will be involved in survey design and evaluating responses.
5.     Teaching
This is a career which is crucial for the future well-being of society, because of the central role which mathematics plays in many aspects of life.
Graduates take a one-year postgraduate certificate specialising in either the primary or the secondary sector. To maintain the stock of mathematics teachers in schools, about one quarter of all mathematics graduates need to enter the profession. This is approximately happening in Northern Ireland, whereas in England and Wales in recent years, less than 10% of mathematics graduates have entered the profession, and this had led to a serious shortage of (and hence many openings for) teachers of mathematics.
Openings also occur in Colleges of Further Education. Openings in higher education are at present very limited. However, the age structure of university staff is such that from the year 2000, openings will start to occur more frequently. A Ph.D. is normally a minimum qualification for such a post, perhaps with a couple of years post-doctoral experience as well. So present-day sixth-formers may find that there will be opportunities for them in the future.
6.     Postgraduate study
A sizeable proportion of graduates choose to continue for higher qualifications before entering the world of work. Taught Masters' courses may develop specialist interests based on work undertaken in a primary degree, or they may provide concentrated study in a new area of interest. Frequently, they are chosen by graduates with particular careers in mind.
The most common research course lasts three years and leads to the award of a Ph.D. A good honours degree is normally required for entry to such a course. The course provides training in the fundamental processes of research and so is particularly useful for those aiming to work in industrial research.



A degree in mathematics does not train you for a specific job. Rather it gives you a range of skills which enable you to enter any of a wide range of careers. It is therefore a versatile qualification. By taking a mathematics degree, you are able to make your career choice when you are 21 rather than when you are 18. Your aspirations may well have changed during the intervening years. Moreover, you will have a clearer understanding of the work you would be doing and you will have been able to talk with representatives of the companies who will wish to employ you. Three years at a university will broaden your horizons in many ways.
Done By
 Jannani and Rashmika 
5Science Dedali