BROWSE
ALPHABETICALLY
LEVEL:
Elementary
Advanced
Both
INCLUDE TOPICS:
Basic Math
Algebra
Analysis
Biography
Calculus
Comp Sci
Discrete
Economics
Geometry
Graph Thry
History
Foundations
Number Thry
Phys Sci
Statistics
Topology
Trigonometry
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INSTRUCTIONS
The PRIME encyclopedia is designed to be browsed alphabetically. To begin, type up to six characters in the box at left and click “GO.” For example, to find the listing for “vector space” you would type “vector” in the box and then click the button. Use the “back/forth” buttons to move back and forth from your current location in the encyclopedia.
If a listing includes an ARTICLE tag, clicking the tag will take you to an extended article for that listing.
To reduce the number of listings displayed, deselect one or more boxes under “INCLUDE TOPICS.” By default, every box is preselected.
Almost every listing will contain links to other listings, and these will appear in blue. Clicking an internal link will move you to the corresponding listing in the encyclopedia. If the linked listing falls under a currently deselected topic, that topic will become selected when subsequent pages are displayed.
The level designations “elementary” and “advanced” are broad designations whose meaning varies from topic to topic. Entries relevant to precollegiate mathematics are always “elementary.” However, for many topics, including algebra, analysis, and topology, “elementary” also includes terms, concepts, and theorems encountered in beginning graduate-level mathematics. Advanced graduate and research-level topics will always be displayed if “advanced” is selected. School-age students will probably wish to select “elementary” and “basic math” only. Students from senior high school through beginning graduate study are encouraged to accept the defaults (all topics and levels selected). Researchers may wish to limit their enquiries to “advanced” entries. (If you do so and do not find what you are looking for, consider becoming a contributor!)
“Basic Math” includes all encyclopedia entries relevant to topics one would be expect to encounter before beginning a course in college algebra (or advanced high school/O-level algebra).
Many listings relate to more than one topic. For example, the listing for “closed set” will appear if any of the topics “Analysis,” “Foundations,” or “Topology” is currently selected.
The topics checkboxes are only a rough guide, and their purpose is primarily negative; they are meant to help reduce the number of listings displayed so as to make topical browsing somewhat easier. Most – but not all – fields of mathematics fall naturally under one or more of these broad categories.
- Algebra: College algebra topics such as linear algebra, abstract algebra from group theory to Galois theory, and algebra as used in other fields such as algebraic topology, etc.
- Analysis: Advanced calculus, real analysis, complex analysis, functional analysis, measure theory, integration theory, harmonic analysis and wave theory, etc.
- Biography: Biographical listings only.
- Calculus: All topics related to single and multi-variable calculus, including vector calculus and analytic geometry.
- Computer Science: All topics peculiar to computer science.
- Discrete: Basic topics one might encounter in a freshman course in discrete math, including basic set theory, graph theory, probability, networks, and beginning logic and proofs.
- Economics: All topics peculiar to business, finance, and economics.
- Geometry: College-level topics, including non-Euclidean geometry.
- Graph Theory: College-level topics in the theory of graphs.
- History: any entries except biography that are related in some way to the history of mathematics, including notation, methods and devices, and important events.
- Foundations: Set theory, logic, category theory, recursion theory, etc. Also includes listings for philosophy of mathematics.
- Number Theory: All related topics, including algebraic and analytic number theory, and advanced topics such as modular forms, etc.
- Physical Science: All topics peculiar to the physical and natural sciences.
- Statistics: All related topics.
- Topology: All related topics.
- Trigonometry: All related topics.
When looking for a topic that does not naturally fit into any of the above, the best strategy is to leave them all selected.
The PRIME is far from complete. While new listings are being prepared on an ongoing basis, we always welcome suggestions for entries and articles, as well as comments and constructive criticisms. Please address all correspondence to editor@mathacademy.com.
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