Mathematics has been described as the Queen of Science – occupying the highest position among all science subjects. But one wonders why Math is considered a science? We are familiar with traditional science subjects like Biology, Chemistry,Physics and Psychology but why Math? One explanation is that Math is a rigorous intellectual subject replete with theorems, theories and laws as in the aforementioned common science subjects, and that its study represents a pure cognition in logic and reasoning – and this is central to all scientific enquiries. Another reason why Mathematic is regarded as science is that the results of many modern Math research have found applications in many fields of engineering, biology and other physical and biological fields.
There are so many different fields of Mathematics, from early number theory to the modern research areas of game theory, fractals, probability theories, spherical and spatial geometry etc.
Mathematics may broadly be divided into the following fields:
Algebra is a branch of Math most people who have gone through High School would have studied at some stage: it introduces symbols (your familiar x, y , z etc) and a series of mathematical operations like factorization, expansions, etc. It can be studied from a very elementary level ( like addition and simplifications of algebraic fractions, solving simple simultaneous linear equations involving 2 unknowns ) up to college and university levels and beyond where one studies complex linear systems, determinants, matrices, eigenvalues, vectors spaces, fractals, etc.
This is the branch of Math studying angles; in fact, it generally forms part of what used to be called Plane Geometry. In trigonometry the angles are associated with certain defined ratios and thus are born the trigonometric concepts of sine, cosine, tangent, secant, cosecant and cotangent associated with an angle of any magnitude. One studies the various trigonometric ratios and trigonometric identities and various operations involving these.
In Geometry, various theorems and lemmas regarding plane figures ( straight lines, triangles, quadrilaterals, trapeziums, circles, ellipses etc ) are studies in detail. Geometry theorems are often associated with angles( see Trigonometry above ) . You probably have studied graphing, with horizontal axis (the x-axis ) and the vertical axis (y-axis ) with straight lines and methods of determining the slope of the straight line. This subdivision of Geometry is Cartesian Geometry or Co-ordinate Geometry, attributed to Rene Descartes . Again, the study of Geometry can progress from the very simple but can become highly complex as in Vector and Spherical Geometry, Topology etc.
This is probably one of the most important branches of Mathematics, not least because it has many applications in other fields of knowledge – social science, physical sciences, biological sciences and all divisions of engineering. It introduces various important concepts ( e.g the derivative or differential coefficient of one variable with respect to another, the anti-derivative ) and provides powerful mathematical tools that allow mathematicians to determine accurately and efficiently quantities like rates of flow of water from a tunnel, rate of decay of a radioactive chemical, etc.
This subject, usually studied together with Probability Theory ( which some regard as a branch of Algebra, or Boolean Algebra ) is the Math subject that examines the methods of collecting, representing, collating, comparing, analysing and interpreting data. In probability theory, the concept of a probability of an event is defined, followed by discussions of various probability theorems and probability distributions like the Normal Distribution, Binomial Distribution etc. It introduces terms like mean or average, median, mode, and discusses various ways of representing data – in ogives, histograms, etc . There are also statistical tests (chi-squared tests, the t-tests ) that are being used to co-relate sets of data to determine if there is some significant relationship between them.
I have not here provided a comprehensive and exhaustive list of all the divisions of Mathematics but I believe the above 5 broad fields may be a rough guide as to how Mathematics has traditionally been compartmentalized. There are also other ways of classifying the various mathematical fields: some academics choose to divide them into two main parts – Pure and Applied Mathematics. Pure Mathematics refers to divisions which are “pure” or the more abstract fields of algebra, functional analysis, linear systems, logic etc whereas Applied Mathematics groups those which have direct applications like Statistics etc but I think such a differentiation is not necessary: after all, Mathematic is a pure science.