Mathematics reference data
Core mathematical concepts, theorems, and notation.
Topic guide
What Mathematics covers
Mathematics reference data collects the facts that are looked up rather than derived: counting rules, constants, geometric formulas, set notation, descriptive statistics, trigonometric identities and the primes. These are exact by definition, which makes them the cleanest kind of reference data for an agent: a lookup either matches a known value or it does not. The usual trouble is not accuracy but context, such as which formula applies to which shape, what a symbol means in a given convention, and how many digits of a constant are meaningful.
Key ideas
- Exact vs approximate
- Constants such as pi and e are irrational: any decimal value is a rounded approximation. Keep symbolic form where exactness matters.
- Permutation vs combination
- A permutation counts ordered selections, a combination unordered ones. Choosing seats is a permutation; choosing a committee is a combination.
- Set operation
- Union, intersection, difference and complement combine sets by membership. De Morgan's laws relate them.
- Descriptive statistic
- A number that summarizes a dataset, such as the mean, median or standard deviation. Different summaries respond differently to outliers.
- Identity
- An equation true for every value of its variables, such as sin squared plus cos squared equals 1, as opposed to an equation true only for some values.
- Prime number
- An integer greater than 1 whose only positive divisors are 1 and itself. The prime factorization of any integer is unique.
- Radian
- The angle measure in which a full turn is 2 pi, used by calculus and most programming-language trig functions.
Common pitfalls
- Using degrees where a library expects radians, or the reverse.
- Quoting a decimal expansion of an irrational constant as exact; floating-point arithmetic keeps only about 15 to 17 significant digits.
- Mixing population and sample formulas for variance and standard deviation (dividing by n versus n minus 1).
- Reading 1 as prime. By the usual definition it is not, which keeps unique factorization true.
Using it from an agent
- Show the formula and the meaning of each variable before substituting numbers, so the user can check the setup.
- For computed results, state the unit and whether angles are in degrees or radians.
- Prefer a tool or code execution for arithmetic with many steps instead of mental arithmetic, and use these datasets for definitions and constants.
Start with: Common Mathematical Constants · Statistics Basics
Datasets in Mathematics
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Combinatorics Fundamentals
Core counting principles and combinatorial formulas.
16 entries -
Common Mathematical Constants
Widely used mathematical constants and their approximate values.
17 entries -
Experimental Design and Inference Pitfalls
Common threats to experiment validity, with a practical design adjustment and reporting consequence.
10 entries -
Geometric Formulas
Common formulas for area, perimeter, surface area, and volume.
20 entries -
Prime Numbers List
The first 100 prime numbers with their position in the sequence.
100 entries -
Probability Distribution Selection Reference
Common probability distributions with support, mean, and practical modeling boundaries.
10 entries -
Set Theory Basics
Fundamental set operations and relations.
14 entries -
Statistics Basics
Fundamental statistical measures and concepts.
15 entries -
Trigonometric Identities
Fundamental identities used in trigonometry.
17 entries
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