Mathematics and its Relationship with other Subjects B.Ed Notes

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 form

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 civies 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 in Geography

Geography is nothing but a scientific and mathematical description of our earth in its universe. The dimension and magnitude of earth, its situation and position in the universe the formation of days and nights, lunar and solar eclipses, latitude and longitude, maximum and minimum rainfall, etc are some of the numerous learning areas of geography which need the application of mathematics. The surveying instruments in geography have to be mathematically accurate. There are changes in the fertility of the soil, changes in the distribution of forests, changes in ecology etc., which have to be mathematically determined, in order to exercise desirable control over them.

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 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 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.

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 in Biological Sciences

Biomathematics is a rich fertile field with open, challenging and fascination problems in the areas of mathematical genetics, mathematical ecology, mathematical neuron- physiology, development of computer software for special biological and medical problems. mathematical theory of epidemics, use of mathematical programming and reliability theory in biosciences and mathematical problems in biomechanics, bioengineering and bioelectronics.

Mathematical and computational methods have been able to complement experimental structural biology by adding the motion to molecular structure. These techniques have been able to bring molecules to life in a most realistic manner, reproducing experimental data of a wide range of structural, energetic and kinetic properties. Mathematical models have played, and will continue to play, an important role in cellular biology. A major goal of cell biology is to understand the cascade of events that controls the response of cells to external legends. (hormones, transport proteins, antigens, etc.). Mathematical modeling has also made an enormous impact on neuroscience. Three-dimensional topology and two-dimensional differential geometry are two additional areas of mathematics when it interacts with biology. Its application is also very important to cellular and molecular biology in the area of structural biology. This area is at the interface of three disciplines: biology, mathematics and physics. In Population Dynamics, we study deterministic and stochastic models for growth of population of micro-organisms and animals, subject to given laws of birth, death, immigration and emigration. The models are in terms of differential equations, difference equations, differential difference equations and integral equations.

In Internal physiological Fluid Dynamics, we study flows of blood and other fluids in the complicated network of cardiovascular and other systems. We also study the flow of oxygen through lung airways and arteries to individual cells of the human or animal body and the flow of synovial fluid in human joints. In External Physiological Fluid Dynamics we study the swimming of micro organisms and fish in water and the flight of birds in air.

In Mathematical Ecology, we study the prey predator models and models where species in geographical space are considered. Epidemic models for controlling epidemics in plants and animals are considered and the various mathematical models pest control is critically examined. In Mathematical Genetics, we study the inheritance of genetic characteristics from generation to generation and the method for genetically improving plant and animal species. Decoding of the genetic code and research in genetic engineering involve considerable mathematical modelling. Mathematical theory of the Spread of Epidemics determines the number of susceptible, infected and immune persons at any time by solving systems of differential equations. The control of epidemics subject to cost constraints involves the use of control theory and dynamic programming. We have also to take account of the incubation period, the number of carriers and stochastic phenomena. The probability generating function for the stochastic case satisfies partial differential equations which cannot be solved in the absence of sufficient boundary and initial conditions.

In Drug kinetics, we study the spread of drugs in the various compartments of the human. body. In mathematical models for cancer and other diseases, we develop mathematical models for the study of the comparative effects of various treatments. Solid Biomechanics deals with the stress and strain in muscles and bones, with fractures and injuries in skulls etc. and is very complex because of non symmetrical shapes and the composite structures of these substances. This involves solution of partial differential equations. In Pollution Control Models, we study how to obtain maximum reduction in pollution levels in air, water or noise with a given expenditure or how to obtain a given reduction in pollution with minimum cost. Interesting non-conventional mathematical programming problems arise here.

Mathematics in Chemistry

Math is extremely important in physical chemistry especially advanced topics such as quantum or statistical mechanics. Quantum relies heavily on group theory and linear algebra and requires knowledge of mathematical/physical topics such as Hilbert spaces and

Hamiltonian operators. Statistical mechanics relies heavily on probability theory. Other fields of chemistry also use a significant amount of math. For example, most modern IR (Infra Red) and NMR (Nuclear magnetic resonance) spectroscopy machines use the Fourier transform to obtain spectra. Even biochemistry has important topics which rely heavily on math, such as binding theory and kinetics. Even Pharmaceutical companies require teams of mathematicians to work on clinical data about the effectiveness or dangers of new drugs. Pure scientific research in chemistry and biology also needs mathematicians, particularly those with higher degrees in computer science, to help develop models of complicated processes.

All chemical combinations and their equations are governed by certain mathematical laws. Formation of chemical compounds is governed by mathematical calculations. For instance, water is a compound; its formation is possible when exactly two atoms of hydrogen combines with one atom of oxygen. Without this strict observance of the mathematical fact, the preparation is improbable. In the manufacture of any chemical, there is some mathematical ratio in which different elements have to be mixed. For estimation of elements in organic compounds, the use of percentage and ratio has to be made. Molecular weights of organic compounds are calculated mathematically.

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