New Mathematics – Mathematics in the 21st century Since the beginning of the new century mathematics has become an increasingly complex subject area. This is due to more and more conjunctive and innovative ways of carrying out mathematics. Mathematics still provides us with models to describe natural phenomena. If there is such a thing as … Read more
New Mathematics The foundation of mathematics is a logical proof based on pure thought, but at the same time, proven statements are generally accepted truths. A conflict exists in mathematics over whether it is a tool for science or an end in itself. While there have been strong movements to reduce mathematical objects to their … Read more
Pure and applied Mathematics – Applied Mathematics Although the fields of pure and applied mathematics overlap, the latter can be said to be most occupied with the solutions to problems and application of methods, in concert with other sciences such as physics or economics. Due to its analytical properties mathematics can be used as a … Read more
Pure and Applied Mathematics During the 20th century, mathematics became a very abstract discipline that lost its connection to concrete mathematical problems somewhat. Despite a high level of abstract thinking, it often results in newly developed theories that are surprisingly useful for practical applications, for example, in the financial industries. Mathematics – Pure Mathematics The … Read more
Probability – Probability Theory Probability theory, the mathematical study of the estimated consequences of future events, is useful for predicting costs and planning complex processes when not all variables are available. If the consequences of a future event have to be estimated, probability theory is used to help make an informed decision. For example, a … Read more
Mathematics – Probability As numbers themselves cannot lie, any harm or misunderstanding caused by numbers is the fault of the presenter or interpreter of the numbers. Probability theory and statistics help to describe events with numbers, allowing predictions and forecasts regarding the probability that certain events will occur to be made with a degree of … Read more
Infinitesimal Calculus – Integral Calculus Originally, integral calculus was developed to calculate the surface area underneath the curve of a function. In general, integral calculus is a method to calculate the sum of infinite elements of a function within a continuous space. Using integral calculus, an infinitely large number of infinitely small areas are added … Read more
Mathematics – Differential Calculus Differential calculus, founded in part by Sir Isaac Newton and Gottfried Wilhelm Leibniz, describes the behavior of a function in infinitely small parts. The information available about, for instance, a hike up a mountain to a certain height above sea level is usually of interest to a hiker, but perhaps how … Read more
Analytic Geometry – Vectors Vectors are used to describe movements in planes and space and are represented in a coordinate system by their components in x, y, and sometimes z directions. A vector is often drawn as an arrow rep-resenting the movement of a point in space. The length (magnitude) of an arrow and its … Read more
Mathematics – Analytic Geometry All geometry problems are solved graphically. Using algebra and geometry together, the same problems can be solved with calculations using variables. Vectors are mathematical objects with length and direction. They can be represented by arrows placed on a coordinate system and denoted by letters set in boldface or with tiny arrows … Read more
