Mathematics as science

Carl Friedrich Gauss, himself known as the "prince of mathematicians", referred to mathematics as "the Queen of the Sciences".

Carl Friedrich Gauss referred to mathematics as "the Queen of the Sciences". In the original Latin Regina Scientiarum, as well as in German Königin der Wissenschaften, the word corresponding to science means a "field of knowledge", and this was the original meaning of "science" in English, also. Of course, mathematics is in this sense a field of knowledge. The specialization restricting the meaning of "science" to Natural science follows the rise of Baconian science, which contrasted "natural science" to scholasticism, the Aristotelean method of inquiring from first principles. Of course, the role of empirical experimentation and observation is negligible in mathematics, compared to natural sciences such as psychology, biology, or physics. Albert Einstein stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."

Many philosophers believe that mathematics is not experimentally falsifiable, and thus not a science according to the definition of Karl Popper. However, in the 1930s Gödel's incompleteness theorems convinced many mathematicians that mathematics cannot be reduced to logic alone, and Karl Popper concluded that "most mathematical theories are, like those of physics and biology, hypothetico-deductive: pure mathematics therefore turns out to be much closer to the natural sciences whose hypotheses are conjectures, than it seemed even recently." Other thinkers, notably Imre Lakatos, have applied a version of falsificationism to mathematics itself.

An alternative view is that certain scientific fields (such as theoretical physics) are mathematics with axioms that are intended to correspond to reality. In fact, the theoretical physicist, J. M. Ziman, proposed that science is public knowledge and thus includes mathematics. In any case, mathematics shares much in common with many fields in the physical sciences, notably the exploration of the logical consequences of assumptions. Intuition and experimentation also play a role in the formulation of conjectures in both mathematics and the (other) sciences. Experimental mathematics continues to grow in importance within mathematics, and computation and simulation are playing an increasing role in both the sciences and mathematics, weakening the objection that mathematics does not use the scientific method

The opinions of mathematicians on this matter are varied. Many mathematicians feel that to call their area a science is to downplay the importance of its aesthetic side, and its history in the traditional seven liberal arts; others feel that to ignore its connection to the sciences is to turn a blind eye to the fact that the interface between mathematics and its applications in science and engineering has driven much development in mathematics. One way this difference of viewpoint plays out is in the philosophical debate as to whether mathematics is created (as in art) or discovered (as in science). It is common to see universities divided into sections that include a division of Science and Mathematics, indicating that the fields are seen as being allied but that they do not coincide. In practice, mathematicians are typically grouped with scientists at the gross level but separated at finer levels. This is one of many issues considered in the philosophy of mathematics.

by Nadhirah

Mathematics as a career

Those who qualify in mathematics are in the fortunate position of having a wide range of career choices. The abilities

• to use logical thought,
• to formulate a problem in a way which allows for computation and decision,
• to make deductions from assumption,
• to use advanced concepts,

are all enhanced by a mathematics degree course. It is for this reason that mathematician are increasingly in demand. With a mathematics degree, you should be able to turn your hand to finance, statistics, engineering, computers, teaching or accountancy with a success not possible to other graduates. This flexibility is even more important nowadays, with the considerable uncertainty as to which areas will be the best for employment in future years.

[The most recent surveys show graduates in mathematicians and computer science at the top of the earning lists six years after graduation.]

Computer science has a considerable mathematical component, which is becoming more important as the designers of software are required to prove that the software meets its specification. This kind of rigour is one of the basic techniques of mathematics, and can be learned only through a mathematics course.

By Nur Shahirah Hider(shiro)

Roman Numerals :)

Roman numerals are expressed by letters of the alphabet:

I=1

V=5

X=10

L=50

C=100

D=500

M=1000

There are four basic principles for reading and writing Roman numerals:

• 1. A letter repeats its value that many times (XXX = 30, CC = 200, etc.). A letter can only be repeated three times.
• 2. If one or more letters are placed after another letter of greater value, add that amount.

  VI = 6 (5 + 1 = 6)

  LXX = 70 (50 + 10 + 10 = 70)

  MCC = 1200 (1000 + 100 + 100 = 1200)

3. If a letter is placed before another letter of greater value, subtract that amount.

IV = 4 (5 – 1 = 4)

XC = 90 (100 – 10 = 90)

CM = 900 (1000 – 100 = 900)

Several rules apply for subtracting amounts from Roman numerals:
• a. Only subtract powers of ten (I, X, or C, but not V or L)

  For 95, do NOT write VC (100 – 5).
  DO write XCV (XC + V or 90 + 5)

• b. Only subtract one number from another.

  For 13, do NOT write IIXV (15 – 1 - 1).
  DO write XIII (X + I + I + I or 10 + 3)

• c. Do not subtract a number from one that is more than 10 times greater (that is, you can subtract 1 from 10 [IX] but not 1 from 20—there is no such number as IXX.)

  For 99, do NOT write IC (C – I or 100 - 1).
  DO write XCIX (XC + IX or 90 + 9)

• 4. A bar placed on top of a letter or string of letters increases the numeral's value by 1,000 times.

  XV = 15, = 15,000

One	I	Eleven	XI	Thirty	XXX
Two	II	Twelve	XII	Forty	XL
Three	III	Thirteen	XIII	Fifty	L
Four	IV	Fourteen	XIV	Sixty	LX
Five	V	Fifteen	XV	Seventy	LXX
Six	VI	Sixteen	XVI	Eighty	LXXX
Seven	VII	Seventeen	XVII	Ninety	XC
Eight	VIII	Eighteen	XVIII	One hundred	C
Nine	IX	Nineteen	XIX	Five hundred	D
Ten	X	Twenty	XX	One thousand	M

By Husnina

The Beauty of Mathematics

The Beauty of Mathematics 

1 x 8 + 1 = 9 
12 x 8 + 2 = 98 
123 x 8 + 3 = 987 
1234 x 8 + 4 = 9876 
12345 x 8 + 5 = 98765 
123456 x 8 + 6 = 987654 
1234567 x 8 + 7 = 9876543 
12345678 x 8 + 8 = 98765432 
123456789 x 8 + 9 = 987654321 

1 x 9 + 2 = 11 
12 x 9 + 3 = 111 
123 x 9 + 4 = 1111 
1234 x 9 + 5 = 11111 
12345 x 9 + 6 = 111111 
123456 x 9 + 7 = 1111111 
1234567 x 9 + 8 = 11111111 
12345678 x 9 + 9 = 111111111 
123456789 x 9 +10= 1111111111 

9 x 9 + 7 = 88 
98 x 9 + 6 = 888 
987 x 9 + 5 = 8888 
9876 x 9 + 4 = 88888 
98765 x 9 + 3 = 888888 
987654 x 9 + 2 = 8888888 
9876543 x 9 + 1 = 88888888 
98765432 x 9 + 0 = 888888888 

Brilliant, isn't it? 

And look at this symmetry: 

1 x 1 = 1 
11 x 11 = 121 
111 x 111 = 12321 
1111 x 1111 = 1234321 
11111 x 11111 = 123454321 
111111 x 111111 = 12345654321 
1111111 x 1111111 = 1234567654321 
11111111 x 11111111 = 123456787654321 
111111111 x 111111111 = 12345678987654321

Mind Boggling...    
Now, take a look at this... 

100% 

From a strictly mathematical viewpoint: 

What Equals 100%? 

What does it mean to give MORE than 100%?

What equals 100% in life? 
Here's a little mathematical formula that might help
answer these questions: 
If:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 
Is represented as: 
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26. 

Then: 

H-A-R-D-W-O- R- K 

8+1+18+4+23+ 15+18+11 = 98% 
And: 

K-N-O-W-L-E- D-G-E 

11+14+15+23+ 12+5+4+7+ 5 = 96% 
But: 

A-T-T-I-T-U- D-E 
1+20+20+9+20+ 21+4+5 = 100% 

Therefore, one can conclude with mathematical certainty that:
While Hard Work and Knowledge will get you close, and Attitude will get you there


By Sook Lynn

Math Anxiety

Math Anxiety is a phenomenon that is often considered when examining students’ problems in mathematics.

         Mark H. Ashcraft, Ph.D. defines math anxiety as “a feeling of tension, apprehension, or fear that interferes with math performance” (2002, p. 1). The first math anxiety measurement scale was developed by Richardson and Suinn in 1972. Since this development, several researchers have examined math anxiety in empirical studies. Hembree (1990) conducted a thorough meta-analysis of 151 studies concerning math anxiety. It determined that math anxiety is related to poor math performance on math achievement tests and that math anxiety is related to negative attitudes concerning math. Hembree also suggests that math anxiety is directly connected with math avoidance.

         
       Ashcraft (2002) suggests that highly anxious math students will avoid situations in which they have to perform mathematical equations. Unfortunately, math avoidance results in less competency, exposure and math practice, leaving students more anxious and mathematically unprepared to achieve. In college and university, anxious math students take fewer math courses and tend to feel negatively towards math. In fact, Ashcraft found that the correlation between math anxiety and variables such as confidence and motivation are strongly negative.

         
       According to Ashcraft, because math anxiety can cause math avoidance, an empirical dilemma arises. For instance, when a highly math-anxious student performs disappointingly on a math question, it could be due to math anxiety, or the lack of competency in math because of math avoidance. Ashcraft determined that by administering a test that becomes increasingly more mathematically challenging, he noticed that even highly math-anxious individuals do well on the first portion of the test measuring performance. However, on the latter and more difficult portion of the test, there was a stronger negative relationship between accuracy and math anxiety. 

Performance Anxiety

People's fear of math can be related to test taking and performance anxiety. Some scholars have suggested a strong relation between math anxiety and math performance. Current research in math anxiety concerns working memory. 

Anxiety Rating Scale

A rating scale for mathematics anxiety was written about in 1972 by Richardson and Suinn. Richardson and Suinn defined mathematical anxiety as "feelings of apprehension and tension concerning manipulation of numbers and completion of mathematical problems in various contexts." 

Math And Culture

While there are overarching similarities concerning the acquisition of math skills, researchers have shown that children’s mathematical abilities differ across countries. In Canada, students score substantially lower in math problem-solving and operations than students in Korea and Singapore. Researchers have conducted thorough comparisons between countries, and have determined that in countries such as Taiwan and Japan, parents place more emphasis on effort rather than one’s innate intellectual ability in school success. Moreover, parents in these countries tend to set higher expectations and standards for their children. In turn, students spend more time on homework and value homework more than American children. (Stevenson & Lee, 1990). 

Math And Gender

Another difference in mathematic abilities often explored in research concerns gender disparities. There has been research examining gender difference in performance on standardized tests across various countries. Beller and Gafni’s have shown that children at approximately nine years of age do not show consistent gender difference in relation to math skills. However, in 17 out of the 20 countries examined in this study, 13 year old boys tended to score higher than girls. Moreover, mathematics is often labeled as a masculine ability; as a result, girls often have low confidence in their math capabilities. These gender stereotypes can reinforce low confidence in girls and can cause math anxiety as research has shown that performance on standardized math tests is affected by one’s confidence. As a result, educators have been trying and should continue to try to abolish this stereotype by fostering confidence in math in all students in order to avoid math anxiety. 

Mathematics And Women

Related to this is gender and mathematics as younger female scholars are thought to develop anxiety towards mathematics and sciences when they become more interested in social relations in their teen years. It is thought that women experience more anxiety in mathematics as a group than men and this has also been suggested in regards computer programming. See for instance [Copper, Joel, & Weaver D, Kimberlee. Gender and Computers: "Understanding the Digital Divide" who explore computing and gender and especially have done experiments relating gender and anxiety. 

Common Beliefs

In the United States, many people believe that only a few "gifted" individuals have "what it takes" to learn math, and that hard work cannot compensate for this. Studies have shown "When asked to explain why some children do better in math than others, Asian children, their teachers, and their parents point to hard work, their American counterparts to ability."

Women mathematicians in the United States have almost always been a minority according to Margaret Murray. Although the exact difference fluctuates with the times as she has explored in her book [Women Becoming Mathematicians: Creating a Professional Identity in Post-World War II America]. "Since 1980, women have earned over 17 percent of the mathematics doctorates.... [In The United States]". The trends in gender are by no means clear, but perhaps parity is still a way to go. Thus parity will take more work to overcome mathematical anxiety and this is one reason for women in mathematics being role model for younger women. 

By Ching Khai Lin

Quotes about Mathematics

“Education should be started with mathematics. For it forms well

designed brains that are able to reason right. It is even admitted that

those who have studied mathematics during their childhood should be

trusted, for they have acquired solid bases for arguing which become

to them a sort of second nature”.

Ibn Khaldun, al-Muqaddima (born in 1332, Tunis), historian, sociologist, philosopher

Strongest personalities of Arabo-Muslim culture in the period of its deline.

Mathematics in everyday life

1. On a basic level you need to be able to count, multiply, substract and divide. Mathematics is around us. It is present in different forms whenever we pick up the phone, manage the money, travel to some place, play soccer, meet new friends; unintentionally in all these things mathematics is involved.

2. There are huge illustrations that testify the presence of mathematics in everything that we are doing. We hope you will enjoy the following slides that illustrate mathematics in everyday life. Enjoy!

Cooking: the idea of proportion

For a Chocolate cake: 5 eggs,3/4 cup of sugar, 1/2 cup of vegetable

oil,...

Percentage

Medicine/Pharmacy

Bank: savings and credit

With some good understanding of simple and compound interest,

you can manage the way your money grows.

Chance to win in lottery: Probalility

The mathematical concept that deals with the chance of winning

a lottery game is probability...
Area
Geometry in clothing

By Neesahantani