Across
- 5. algebra or logic: a type of algebra which can be applied to the solution of logical problems and mathematical functions, in which the variables are logical rather than numerical, and in which the only operators are AND, OR and NOT
- 7. the part of mathematics that studies quantity, especially as the result of combining numbers (as opposed to variables) using the traditional operations of addition, subtraction, multiplication and division (the more advanced manipulation of numbers is usually known as number theory)
- 8. (infinitesimal calculus): a branch of mathematics involving derivatives and integrals, used to study motion and changing values
- 9. a step by step procedure by which an operation can be carried out
- 10. a branch of mathematics that uses symbols or letters to represent variables, values or numbers, which can then be used to express operations and relationships and to solve equations
- 13. a one-to-one comparison or correspondence of the members of two sets, so that there are no unmapped elements in either set, which are therefore of the same size and cardinality
- 14. (mathematical analysis): grounded in the rigorous formulation of calculus, analysis is the branch of pure mathematics concerned with the notion of a limit (whether of a sequence or of a function)
- 16. algebra: the area of modern mathematics that considers algebraic structures to be sets with operations defined on them, and extends algebraic concepts usually associated with the real number system to other more general systems, such as groups, rings, fields, modules and vector spaces
- 17. coefficients: the coefficients of the polynomial expansion of a binomial power of the form (x + y) n, which can be arranged geometrically according to the binomioal theorem as a symmetrical triangle of numbers known as Pascal’s Triangle, e.g. (x + y)4 = x4 + 4x3y + 6x2y2 + 4xy3 + y4 the coefficients are 1, 4, 6, 4, 1
- 18. n: the number of unique digits (including zero) that a positional numeral system uses to represent numbers, e.g. base 10 (decimal) uses 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 in each place value position; base 2 (binary) uses just 0 and 1; base 60 (sexagesimal, as used in ancient Mesopotamia) uses all the numbers from 0 to 59; etc
Down
- 1. property: property (which applies both to multiplication and addition) by which numbers can be added or multiplied in any order and still yield the same value, e.g. (a + b) + c = a + (b + c) or (ab)c = a(bc)
- 2. a proposition that is not actually proved or demonstrated, but is considered to be self-evident and universally accepted as a starting point for deducing and inferring other truths and theorems, without any need of proof
- 3. to Top
- 4. numbers: numbers used to measure the cardinality or size (but not the order) of sets - the cardinality of
- 5. probability: a popular interpretation of probability which evaluates the probability of a hypothesis by specifying some prior probability, and then updating in the light of new relevant data
- 6. equation: a combination of numbers and letters equivalent to a sentence in language, e.g. y = x2 + 3x - 4
- 7. a line that the curve of a function tends towards as the independent variable of the curve approaches some limit (usually infinity) i.e. the distance between the curve and the line approaches zero
- 11. numbers: pairs of numbers for which the sum of the divisors of one number equals the other number, e.g. 220 and 284, 1184 and 1210
- 12. a polynomial algebraic expression or equation with just two terms, e.g. 2x3 - 3y = 7; x2 + 4x; etc
- 15. (Cartesian) geometry: the study of geometry using a coordinate system and the principles of algebra and analysis, thus defining geometrical shapes in a numerical way and extracting numerical information from that representation
- 17. curve: the shape of the graph that indicates a normal distribution in probability and statistics