Further Mathematics
From Wikipedia, the free encyclopedia
Further Mathematics is the title given to a number of advanced secondary mathematics courses. Higher and Further Mathematics may also refer to any of several advanced mathematics courses at many institutions.
In the United Kingdom Further Mathematics describes a course studied in addition to the standard mathematics AS-Level and A-Level courses. In Victoria, Australia it describes a course delivered as part of the Victorian Certificate of Education. See the section on Victoria for a more detailed explanation. Globally, it describes a course delivered as part of the International Baccalaureate Diploma.
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[edit] UK
[edit] Background
A qualification in Further Mathematics involves studying both pure and applied modules. Whilst the pure modules - formerly known as Pure 4-6 (or Core 4-6), now known as Further Pure 1-3 (4 exists for the AQA board [1]) - are of a higher standard than those in the standard course, the applied modules need not be. The topics covered by Further Mathematics are more sophisticated and conceptually advanced compared to the single A-level Mathematics.
Some schools and colleges in places such as Hong Kong and India take examinations set by British boards and consequently the subject is offered internationally.
Because smaller schools and colleges may not be able to offer Further Mathematics (as it is a very low-intake course requiring well-trained teachers), universities do not require the course, and may offer "catch-up" classes covering the additional content. An exception is the University of Cambridge, where you must have Further Mathematics to at least AS level to study for a degree in mathematics at all colleges except Emmanuel, which accepts physics as an alternative[2].
Further Maths is currently the fastest-growing subject at A level, with the number of students increasing by 23% in 2006, and a network has been set up to offer the subject to pupils at schools which cannot provide it. [3]
[edit] List of the areas of study on the syllabus
- Inequalities
- Series
- Complex numbers
- Numerical solutions to equations
- First and second order differential equations
- Hyperbolic functions
- Further calculus
- Coordinate systems, including polar coordinates and intrinsic coordinates.
- Maclaurin series and Taylor series
- Matrix algebra
- Vectors
- Numerical methods
- Proof
[edit] Australia (Victoria)
The section below this paragraph is copied from a course description and is not very readable. That said, here is a more practical summation of what Further Mathematics is in Victoria, Australia. In contrast with what Further is in most countries, Further is the 'lowest' maths offered in the VCE, including little to no algebra. The next level up is Mathematical Methods, and the highest is Specialist Mathematics. Specialist is generally not required for most courses (even engineering), but in some cases must be substituted with a high level of achievement in Methods. Some students undertake both Methods and Further, as Further is considered relatively easy for someone whose strong point is mathematics, so a high score can be easier to get. Students who do only do Further in VCE however, close off any option of doing tertiary studies in any of the fields of Science, Engineering, Commerce and Economics, Mathematics, and some Information Technology degrees (without doing a 'bridging' short course in between). Further Mathematics consists of 6 modules. 3 of these are core modules of statistics, which all students undertake: Univariate Data; Bivariate Data; and Time Series. The other 3 are chosen by the student, or often by the school, out of a selection of: Number Patterns; Geometry and Trigonometry; Graphs and Relations; Business-Related Mathematics; Networks and Decision Mathematics; or Matrices.
[edit] International Baccalaureate
Further Mathematics, as studied within the International Baccalaureate Diploma is a Standard Level course that can only be taken in conjunction with Higher Level (HL) Mathematics. It assumes knowledge of the core syllabus of the HL course, and consists of studying all four of the options studied at Higher Level, plus an extra geometry unit.
The syllabus consists of:
- Topic 1 - Geometry
- Topic 2 - Statistics and Probability
- Topic 3 - Sets, Relations, and Groups
- Topic 4 - Series and Differential Equations
- Topic 5 - Discrete Mathematics
