Reference material


Rationale: The Internet has been likened to a massive encyclopaedia, and can be used as a means of looking up various kinds of mathematical things for various purposes. A few different examples of this species of web use are shown below. These might be used by students from home, especially as few homes will have a mathematical reference source such as a dictionary or encyclopaedia. They might also be used in school, by both individual students and teachers or by a whole class, seeking clarification or information of a reference kind. As well as mathematical reference materials, statistical reference materials are also available. Some sites allow users to undertake calculations, another kind of reference.


Here are some examples:



Interactive Mathematics Dictionary


The Intermath site has been produced and developed by the University of Georgia and provides a great deal more than paper-based dictionaries are able to provide. Pitched at middle-school or lower secondary school level, it allows students to browse maths terms or to search by entering a maths term, and then to explore many aspects of the meaning of the concepts involved: a description, related terms, everyday examples, interactive checkpoints, more web-based information and a link to challenging investigation starting points related to the term. There is also a Constructionary, providing detailed information about geometric constructions





This website provides a reference of a different kind: it allows for automated execution of many routine mathematical procedures over the Internet, using the powerful software Mathematica as the engine that drives it all. It is essentially an online calculator, but allows for symbolic calculations (such as symbolic manipulation, equation solving, matrix operations and calculus) not merely numerical calculations. A limited online grapher is also provided. A reminder of what is routine and what requires thinking, and a resource for students at home trying to answer mathematical questions. A donation is requested, but not required.



History of Mathematics


The MacTutor History of Mathematics Archive at the University of St Andrews has deservedly won many awards, and offers opportunities for students to see that mathematics has involved the work of people throughout recorded history and continues into the present day. The archive can be efficiently searched through the indexes on the opening page. These in turn lead to other indexes (eg start with Mathematicians of the Day and search on posters and quotations). Searches may also be undertaken in other ways via the Search Index on the home page: by topic, by person, by date, by geography, etc. The site has an excellent and comprehensive glossary, which goes far beyond the needs of secondary school Few students have good access to materials that allow them to see the place of mathematics and mathematicians throughout history.



Mathematical Quotations server


As its name suggests, this site comprises quotations from mathematicians and from others about mathematics. Located at Furman University in South Carolina, the collection may be browsed by author or searched to find quotations that include particular keywords, which may be mathematical terms or people. It also includes a random quotation generator, for those who are less systematically inclined. The entire collection may be downloaded, although it is just as easy to search it on the web. The quotations collectively give a rich idea of what mathematicians and others have thought and felt about mathematics over the years, at least as far as their words have been recorded.


Maths Dictionary for Kids


Jenny Eather’s dictionary is presented in lively colours, and (unlike most such objcets) is Australian in origin. As well as providing definitions, many of the dictionary entries provide interactive elements. Although there are a few errors, this seems like a useful resource for children.

Multimedia Math Glossary


This interactive glossary, produced by Harcourt, has some nice features, including the classification of mathematical terms into grade levels. As users become more sophisticated, so too do the definitions offered. There are spoken definitions available (with North American accents). Some definitions use North American spellings and meanings.



Wikipedia is a very large online encyclopedia which can be edited by anybody who accesses it. The Mathematics parts of Wikipedia are quite extensive and provide a lot of useful information, as well as a good sense of the scope of mathematics. Of course, some care must be exercised in regarding such a resource as completely authoritative.



This is the definitive mathematical encyclopedia on the web, sponsored by Wolfram, makers of the Mathematica software and carefully constructed over many years by Eric Weisstein. Mathematica is used as the engine behind the entries, many of which are interactive in some sense. Most of the resource extends well beyond the needs of school, however, although it provides a window into the amazing and rich world of modern mathematics. The site is huge and readily searched, although probably of most use to professionals and senior students




This website can be used as a kind of reference for prime factorisations. Andrew Hodges’ Java applet allows for an integer to be entered, and it will then generate a sequence of factorisations. The website is mostly self-explanatory: after starting the applet, enter an integer to find its factors, if any. Enter a number larger than 1 in the right box to generate a sequence of integers, with their factors.

Cool Math 4 kids


This website is clearly designed to appeal visually to kids, young and old, but serves also to be a rather good reference source for many aspects of school mathematics, while also presenting a positive view of modern mathematics. Although it contains an assortment of advertising, the basic messages and ‘feel’ for mathematics that are provided would seem more likely to attract than repel students looking for information. The site contains a dictionary as well as a large geometry reference area, amongst other features.

Math Open Reference


Described as a prototype, this free web-based secondary school geometry textbook developed by John Page incorporates student learning with interactive tools and Java and Flash animations. Many of the tools and animations refer to specific concepts or single-purpose mathematics tasks, such as constructions, and could be used for a range of purposes, including demonstrations in class or on an interactive whiteboard. Use the index link to find specific topics. Recently, the materials have been expanded to include coordinate geometry and some graphing applets.

Measure 4 Measure


This site provides links to a large number of websites that contain measurements of some sort, with a wide variety of contexts, some of them unexpected sources of measurement. Most of the sites linked to are interactive, in the sense that they will generate results on the web, generally using JavaScript. As well as providing measurements, many of the sites provide information about the underlying mathematical relationships as well.

Gallup Worldview


The Gallup organisation is well-known as a major market research company, using statistical procedures to get good samples of data on questions of interest. The term ‘Gallup Poll’ derives from the organiser’s founder, George Gallup, who developed the techniques, which rely on mathematics and random sampling to obtain credible data. This website contains limited (free) access to various kinds of statistical information from around the world, and allows a close look at data from individual countries (such as Australia). [Access the limited version of Gallup WorldView for free. Complete access to the full Gallup Worldview application requires a paid subscription.]



This website may well be the ultimate mathematical reference. WolframAlpha was launched early in 2009 and attracted a lot of attention since then. The website, built on a Mathematica platform in part, makes the modest claim: “Wolfram|Alpha's long-term goal is to make all systematic knowledge immediately computable and accessible to everyone. We aim to collect and curate all objective data; implement every known model, method, and algorithm; and make it possible to compute whatever can be computed about anything.” There are many examples on the site to get you started. Enetr a computation or anything else and watch what happens! Extraordinary.



This website of the Real Time Statistics Project provides very many world statistics, updated in real time. Statistics include those related to population, environment, health, economics, energy use, Internet use, among others. Data are carefully obtained, and details of their sources and the methods of updating them are available on the site. The same project maintains the Stop The Hunger website, concerned with describing world poverty.

Keisan online calculator


Although mathematics is commonly confused with calculation, calculation is also useful. This site, hosted by CASIO, allows users to calculate almost anything, with calculations divided into various categories of interest: Life, Education (Mathematics and Science) and Professional. Users enter data and the website calculates with it. Comments made by users are also of interest, and users can add their own comments.



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Last updated: 20 May 2015