MEANING OF MATHEMATICS
· “Mathematics is the Science of number and space”
· “Mathematics is Science of measurement, quantity and magnitude”.
· “Mathematics is taken as a chest filed up with so many valuable tools concerning with the operations like measuring, weighing, counting etc. and helps in proper understanding of the nature’s work and complicated problems of life by converting them into its language of signs and symbols.
Mathematics is a pivot of all civilizations. Mathematics is that subject which indisputably forms the very basis of entire world commercial system. Mathematics is fascinating because of its opportunities for creation and discovery as well as for its utility. It is basic to the understanding of every science. It enters every walk of life. Therefore, in schools much impetus is given to the study of mathematics. It is established that permanence in mathematics is attributed to the intelligence of an individual.
DEFINITION OF MATHEMATICS
ü Mathematics is a Science of number and space.
ü Mathematics has its own language – Sings, symbols, terms and operations etc.
ü Mathematics involves man’s high cognitive Powers.
ü Mathematics has own tools like intuition, logic, reasoning, analysis, construction, generality and individuality etc.
ü Mathematics helps in drawing conclusions and interpreting various ideas and themes.
ü Mathematics is the tool especially suited for dealing with abstract concepts of any kind.
ü It helps in solving the problems of our and disclosing the realm of nature.
Aristotle - The science of quantity. In Aristotle's classification of the sciences, discrete quantities were studied by arithmetic, continuous quantities by geometry.
Oxford English Dictionary –“The abstract science which investigates deductively the conclusions implicit in the elementary conceptions of spatial and numerical relations, and which includes as its main divisions geometry, arithmetic, and algebra”.
American Heritage Dictionary - “The study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols”.
Encyclopaedia Britannica- “The science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects”.
Galileo Galilee - “The universe cannot be read until we have learned the language and become familiar with the characters in which it is written”. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth.
Albert Einstein - "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."
NATURE, CHARACTERISTICS AND OF MATHEMATICS
MEANING OF MATHEMATICS
Mathematics is commonly defined as the study of patterns of structure, chance, and space; more informally, one might say it is the study of figures and numbers. In the formalist view, it is the investigation of axiomatically defined abstract structures using logic and mathematical notation; other views are described in philosophy of mathematics.
CHARACTERISTICS OF MATHEMATICS
Children may exhibit feelings in insecurity, as well as fears of failure, punishment, ridicule, or stigmatizing labels. Children with math anxiety may also have a negative attitude or negative emotional reaction to math. Teachers need to provide students with experiences that they will be successful in, in order to promote a more positive attitude. They learning bridge or strategies are good ways to help prevent the early development of math anxiety.
LOGICAL SEQUENCE IN MATHEMATICS
The problem is predicting the next term of a partially specified sequence. The user shall input the rest few terms of a mathematical sequence. The expert system will rest try you understand the pattern and using the found pattern it would predict the next term.
INTEGER SEQUENCES
Integer sequences are the most commonly seen sequences. For integer sequences, it’s the addition, subtraction and multiplication operators that play the major role in Xing up in the function f. so, in order to discover the function f, we need to perform various operations on the integers that are the first few given terms of the sequence.
For example, consider the sequence 3; 7; 11; 15; the way this sequence is understood is by taking the deference between adjacent terms of the sequences.
STRUCTURE OF MATHEMATICS
The focus of my presentation will be on such structural aspects of mathematics that are known or likely to cause problems or challenges for the process of learning mathematics, and hence for its teaching. I shall interpret the term ―the structure of mathematics‖ in a somewhat broad sense, by taking into account also the nature of mathematics and its characteristics as a discipline and not solely its architectural features as reflected in one or more possible construction(s) of edifice.
ABSTRACTION
Mathematical thinking often begins with the process of abstraction-that is, noticing a similarity between two or more objects or events. Aspects that they have in common, whether concrete or hypothetical can be represented by symbols such as numbers, letters, other marks, diagrams, geometrical constructions, or even words.
Whole numbers are abstractions that represent the size of sets of things and events or the order of things within a set. The circle as a concept is an abstraction derived from human faces, flowers, wheels, or spreading ripples; the letter a may be an abstraction for the surface area of objects of any shape, for the acceleration of all moving objects, or for all objects process of addition, whether one is adding apples or oranges, hours, or miles per hour.
SYMBOLISM OF MATHEMATICS
The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle-they are strictly limited in number, they require fresh horses, and must only be made at decisive moments. The symbolism of mathematics is in truth the outcome of the general ideas which dominate the science.
MATHEMATICS AS SCIENCE OF MEASUREMENT
Mathematics and science education, including the metric system of measurement, will be strengthened throughout the system, especially in the early grades.
STRATEGIES
1. Implement the Missouri academic performance standards and frameworks for math and science.
2. Develop and implement state wide assessments aligned to the state’s content, performance, and skills standards.
3. Expand active learning opportunities through the use of technology.
4. Evaluate and disseminate effective math and science programmers.
OBJECTIVE
The number of teachers with a substantive background in mathematics and science, including the metric system of measurement, will increase by 50 per cent.
STRATEGIES
1. Ensure authentic assessment training for all teachers.
2. Increase the availability of math and science professional development activities aligned with the state’s knowledge, performance, and skill standards.
3. Institute competency-based teacher certification
MATHEMATICS AND ITS RELATIONSHIP
MATHEMATICS WITH SCIENCE
The knowledge and skills students engage within the various dimensions of mathematics support students in their studies of all aspects of science. In science students use measurement and number concepts particularly in data collection estimation of error analysis and modes of reporting. The mathematics domain supports students in developing number handling skills.
To collect the records interpret and display data appropriately, looking for patterns, drawing conclusions and making generalizations. Predictions for further investigations, extrapolations and interpolations may be made from their own experimental results or from reliable second and data.
MATHEMATICS WITH ARTS
The arts and mathematics involve students understanding of relationships between time and space, rhythm and line through the experience of these abstract concepts in various arts forms and mathematical ideas. Mathematically related aesthetic considerations, such as the golden ratio, are used across visual, performing and multi-modal arts forms.
MATHEMATICS WITH CIVICS AND CITIZENSHIP
The concepts developed in the study of mathematics are applicable to a range of civic and citizenship understandings. Mathematical structure and working play essential roles in key aspects of our society as well as key civics concepts. Particular aspects of civics and citizenship require mathematical understanding, including concepts of majority rule, absolute majority, one vote one value representation and proportional voting systems.
MATHEMATICS WITH COMMUNICATION
Mathematics structure and working mathematically play essential roles in understanding natural and human worlds. Developments of the languages of mathematics are crucial to its practical application. Students learn to use the language and concepts of mathematics both within the discipline itself and also its applications to modelling and problem solving across the other domains. In this process they employee a range of communication tools for illustrating relationships and displaying results such as Venn diagrams and tree diagrams.
MATHEMATICS AND PHYSICS
All the physical laws, laws of motion, laws of lever and pulleys, laws of refraction and reflection, laws of magnetization, laws of electric current movement of the earth and planets and law of quantum energy can only by understood and applied with the help of the understanding of Mathematics.
The lenses and other equipment’s used in microscope, telescope, photographic camera movie can only be made useful and workable with the help of intensity, power and arrangement decided by the basic principles of Mathematics.
MATHEMATICS AND CHEMISTRY
The Study of compounds, mixtures, laws of chemical combination and the study of molecular or atomic structures, chemical names of formula and chemical equations all are based on the laws of Mathematics. In the preparation of different gases and chemical products like bleaching powder, salts, acids, medicines and other day to use products, we need exact measurements in terms of weight, ratios and other calculations.
In this way it is no exaggeration in saying that Mathematics is used in the study of chemistry right from a petty chemical reaction to the preparation of chemical fuels of modern rockets and bombs.
MATHEMATICS AND BOTANY – ZOOLOGY
The cellular construction of animals and vegetables, heredity, process of reproduction, balanced diet and similar other topics need the knowledge of Mathematics. In any organism if we try to study the anatomical structure and pattern of definite growth and development, we have to take the help of the subject Mathematics. The graphs and statistical concepts used in these branches can also reveal the need of Mathematics or Geometry.
MATHEMATICS AND MEDICAL SCIENCE
In preparation of the doses of medicines one has to take it to account the mechanism of measurement which is not possible without Mathematics.
MATHEMATICS AND ENGINEERING
Mathematics is the base of all the Engineering, Surveying and measurements which help the Science of Engineering. To construct large bridges, plan the network of canals and dams, extend railway lines across the wide forests and lofty mountains, control the floods and establish the heavy industry.
Actually the relationship between Mathematics and Science is just like the relationship between the body and its soul. Body (science) has no meaning without its soul (Mathematics).
MATHEMATICS WITH ENGLISH
Mathematics, including the use of conjectures and proof, has clear links to the development of structures and coherent argument in speaking writing. Mathematical structure is strongly related to semantics syntax and language and to the use of propositions and quantifiers embedded in principled argument in natural languages.
MATHEMATICS WITH HEALTH AND PHYSICAL EDUCATION
In health and physical education, mathematics provides tools and procedures which can be used to model situations and solve problems in areas such as:
1) Scoring different sporting events involving time distance, weight and number as variables.
2) Calculating percentage improvement in results from data collected through fitness testing or performance in physical activities.
MATHEMATICS WITH HUMANITIES-ECONOMICS
The economics and mathematics are related through the use of mathematics to model a broad range of economic, political and social phenomena. Examples include the use of statistical modelling and analysis in a census, sampling populations to predict election outcomes, and modelling and forecasting economic indicators such as the consumer price index and business confidence.
MATHEMATICS WITH GEOGRAPHY
The application of mathematical skills plays a key role in financial literacy, in particular the use of ratio, proportion and percentage in related calculations such as percentage increase or decrease in price of a commodity or personal income. Mathematics provides the basis of measurement, scale and spatial representation used in maps and plans. Geography also uses the concepts of direction, length, angle and bearing, gradient and contour and area.
MATHEMATICS WITH HISTORY
The study of history includes the analysis and interpretation of a range of historical information including population charts and diagrams and other statistical information. The concepts and skills developed in mathematics support student understanding and interpretation of a range of history sources and their presentation as evidence in demonstration historical understanding.
CONTRIBUTION OF INDIAN MATHEMATICIANS
ARYA BHATA
The Indian mathematician and astronomer Aryabhata (476 A.D) is well known for his work. He was born at Pataliputra near Patna in Bihar. His most famous book is known as ―Aryabhrtia. In arithmetic, Algebra and place Geometry Aryabhata suggested humorous rules. A few important rules are enlisted below-
1. Area of triangle = base*height
2. The value of Pi =3.1456
3. Area of the circle (pi) 2
4. Sum of AP =n/2[2a+(n-1)d
To sum up Aryabhata was really one of the greatest geniuses of his time in the field of mathematics and astronomy.
BRAHMAGUPTA
In the earlier Roman and Babylonian system of numeration, large number of characters was required to denote higher numerals. Thus enumeration and computation became unwieldy. For instance, as E the Roman system of numeration, the number thirty would have to be written as X; while as per the decimal system it would 30, further the number thirty three would be XXXIII as per roman system, would be 33 as per the decimal system. This also made computation easier.
BHASKARA
RAMANUJAN
Ramanujan was born in Brahmin family on December 22, 1887 at erode madras. He got his school education at kumbakonam. He won a scholarship in matriculation examination. His teachers were very much impressed by his injected and special gifted abilities in mathematics.
Hardy remarked: I had never seen anything the least like them before. A single look at them is enough to show that they could be written down by a mathematician of the highest class.
His work thrown light on divergent series. Hypermetric series continued fraction, definite integrals. Partition functions, ecliptic functions the theory of numbers, fractional differentiation and highly composite numbers.
SHAKUNTALA DEVI
1) She was born in 1939.She is an Indian calculating prodigy.
2) By age 6, she demonstrated her calculation and memorization abilities at university of Mysore. At the age of 8, she had successes at Annamalai University by doing the same.
3) On June 18, 1980, she demonstrated the multiplication of two 13‐digit numbers.
4) 7,686,369,774,870X2, 465,099.745,779 picked at random by the Computer Department of Imperial College, London. She answered the question in 28 seconds. However, the time is more likely the time for dictating the answer (a 26‐digit number) than the time for mental calculation (the time of 28 seconds was quoted on her website).Her answer was 18,947,668,177,995,426,773,730.This event is mentioned on page 26 of the 1995.Guinness Book of Records.
5) In Dallas, she competed with a computer to see who give the cube of 188138517 faster, she won. At University of USA she was asked to give the 23rd root of 91674867692003915809866092758538016248310668014430862240712651642793465704086709659327920576748080679002278301635492485238033574531693511190359657754734007568818688305620821016129132845564895780158806771.
6) she answered in 50 seconds. The answer is 546372891.It took a UNIVAC 1108 computer, full one minute (10 seconds more) to confirm that she was right after it was fed with 13000 instructions.
7) Now she is known to be Human Computer.
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