Arguably one of the most important branches of science is mathematics, which seeks to understand how the universe and nature operate. The most common branches of math are algebra, trigonometry, calculus, and geometry. A more esoteric branch of math is called “astronomy” and it studies the relationship between the heavenly bodies and earthly objects. Astronomy includes a number of sub branches, including astronomy used by space exploration agencies and astronomy used by terrestrial exploration agencies.
The branches of science, or commonly referred to as sciences, are typically broken down into three general categories: Formal branches: those that require a proper a priori justification; Directed collections: those that infer their results based on observations; Foundations of mathematics: those that are based on certain formal theories. The branches of science are further sub-divided into sets of theory. For example, natural sciences deal with physical laws, physics, and chemistry; classical and modern mathematics are branches of mathematics that deal exclusively with numbers, counting, and measurement; and computer science is a field that uses computers to solve problems. In general, all branches of science are categorized into at least two main branches: formal and applied.
Formal branches of math include those that are based on a prior a priori justification, which usually involves argument and proof. The most common of these is logic, with its mostly logical premises. An important formalism in math is calculus, with its underlying assumption that theorems are geometrical relationships between numbers, which can be thought of as equivalent real numbers. Theorems in this theory are used to derive complex mathematical structures, like theorems for linear equations, polyhedra, elliptical planes, and smooth curves.
While the branches of math are generally separated into distinct theories, the relationships among them are frequently complex and intricate. Thus, it is necessary for students to develop a working knowledge of each discipline, in order to be prepared to enter the higher level courses in math and other natural sciences. Students in math need to understand the conceptual structure of math by first learning how different concepts relate to each other, and then how they are used in solving problems. A good way to learn this is through linear algebra, an easier version of which can be learned in high school. Algebraic equations are necessary for understanding algebraic concepts in higher mathematics. It is also important to grasp concepts such as properties of quantities, functions, and graphs in order to grasp the concepts of algebraic equations.
Science education curriculum emphasizes the interdependence of math and science. One way to do this is to provide examples of real life applications of math, and show how these math concepts can be used to solve real-life problems. A good math education curriculum should have a strong emphasis on hands-on science activities, such as working with physical science equipment or collecting and sorting real life samples of scientific data, for teaching concepts such as physical science, in addition to math. The topics taught in both science classes and math classes should be closely related to the topics taught in mathematics.
The programs offered by colleges and universities offer two main types of educational curriculum: the more traditional formal sciences, such as biology, chemistry, and physics; and the newer non-formal sciences, including ecology, evolution, geology, hydrology, and wildlife biology. In recent years, many schools have added a third branch to the formal sciences curriculum: art and design. Art and design departments often focus on visual arts, literature, and theater. These programs are excellent preparation for college level mathematics and advanced math classes. Some colleges and universities also offer programs that focus on the integration of math and the visual arts. Curriculum may include math elements for design, theater, photography, and music.
Math teachers generally have an outline of their class assignments, class time, and lesson plan before they begin teaching. This outline should include the basic math units, such as addition, subtraction, multiplication, division, and analysis. Other units such as computation, optimization, differential forms, real solutions, and visual objects are sometimes added to the outline. Teachers should also provide students with a review of the topics covered in class, and a summary of what they learned in each unit. Homework should not be handed out until all assignments are completed.
The classes discussed above fall into a number of different mathematical fields and subdisciplines. Students who struggle with math in high school may wish to consider whether they might need to take additional math courses to help them pass their high school math courses. Further, students who demonstrate potential in other areas of academic disciplines, such as computer science, engineering, and business administration, may be able to transfer their grades to the math department at their college or university and receive a better education in math.