Let's Get Mathematical!

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Across
  1. 5. a way of writing rational numbers (numbers that are not whole numbers), also used to represent ratios or division, in the form of a numerator over a denominator, e.g. 3⁄5 (a unit fraction is a fraction whose numerator is 1)
  2. 7. a mathematical statement or hypothesis which has been proved on the basis of previously established theorems and previously accepted axioms, effectively the proof of the truth of a statement or expression
  3. 10. a physical quantity having magnitude and direction, represented by a directed arrow indicating its orientation in space
  4. 11. 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
  5. 12. the inverse operation to exponentiation, the exponent of a power to which a base (usually 10 or e for natural logarithms) must be raised to produce a given number, e.g. because 1,000 = 103, the log10 100 = 3
  6. 14. an equality that remains true regardless of the values of any variables that appear within it, e.g. for multiplication, the identity is one; for addition, the identity is zero
  7. 16. the part of mathematics concerned with the size, shape and relative position of figures, or the study of lines, angles, shapes and their properties
  8. 17. a relation or correspondence between two sets in which one element of the second (codomain or range) set ƒ(x) is assigned to each element of the first (domain) set x, e.g. ƒ(x) = x2 or y = x2 assigns a value to ƒ(x) or y based on the square of each value of x
  9. 20. the ratio of a circumference of a circle to its diameter, an irrational (and transcendental) number approximately equal to 3.141593...
  10. 23. a measure of relationship between two variables or sets of data, a positive correlation coefficient indicating that one variable tends to increase or decrease as the other does, and a negative correlation coefficient indicating that one variable tends to increase as the other decreases and vice versa
  11. 25. the field of mathematics concerned with spatial properties that are preserved under continuous deformations of objects (such as stretching, bending and morphing, but not tearing or gluing)
  12. 27. the operation in calculus (inverse to the operation of differentiation) of finding the integral of a function or equation
  13. 30. the theory that mathematics is just an extension of logic, and that therefore some or all mathematics is reducible to logic
  14. 31. a mathematical structure consisting of a set together with an operation that combines any two of its elements to form a third element, e.g. the set of integers and the addition operation form a group
  15. 33. the mathematical operation where a number (the base) is multiplied by itself a specified number of times (the exponent), usually written as a superscript an, where a is the base and n is the exponent, e.g. 43 = 4 x 4 x 4
  16. 34. a number that will divide into another number exactly, e.g. the factors of 10 are 1, 2 and 5
  17. 38. in an algebraic expression or equation, either a single number or variable, or the product of several numbers and variables separated from another term by a + or - sign, e.g. in the expression 3 + 4x + 5yzw, the 3, the 4x and the 5yzw are all separate terms
  18. 39. the ordered pair that gives the location or position of a point on a coordinate plane, determined by the point’s distance from the x and y axes, e.g. (2, 3.7) or (-5, 4)
  19. 41. the product of all the consecutive integers up to a given number (used to give the number of permutations of a set of objects), denoted by n!, e.g. 5! = 1 x 2 x 3 x 4 x 5 = 120
  20. 46. a step by step procedure by which an operation can be carried out
  21. 47. a statement that appears to contradict itself, suggesting a solution which is actually impossible
  22. 48. an ordered set whose elements are usually determined based on some function of the counting numbers, e.g. a geometric sequence is a set where each element is a multiple of the previous element; an arithmetic sequence is a set where each element is the previous element plus or minus a number
  23. 49. the area bounded by a graph or curve of a function and the x axis, between two given values of x (definite integral), found by the operation of integration
  24. 50. a rectangular array of numbers, which can be added, subtracted and multiplied, and used to represent linear transformations and vectors, solve equations, etc
Down
  1. 1. a type of conic section curve, any point of which is equally distant from a fixed focus point and a fixed straight line
  2. 2. the steepness or incline of a line, determined by reference to two points on the line, e.g. the slope of the line y = mx + b is m, and represents the rate at which y is changing per unit of change in x
  3. 3. whole numbers, both positive (natural numbers) and negative, including zero
  4. 4. a member of, or an object in, a set
  5. 6. a collection of distinct objects or numbers, without regard to their order, considered as an object in its own right
  6. 8. an algebraic expression consisting of a single term (although that term could be an exponent), e.g. y = 7x, y = 2x3
  7. 9. a flat two-dimensional surface (physical or theoretical) with infinite width and length, zero thickness and zero curvature
  8. 13. a smooth symmetrical curve with two branches produced by the section of a conical surface
  9. 15. the operation in calculus (inverse to the operation of integration) of finding the derivative of a function or equation
  10. 18. quantities or objects so small that there is no way to see them or to measure them, so that for all practical purposes they approach zero as a limit (an idea used in the developement of infinitesimal calculus)
  11. 19. in geometry, a one-dimensional figure following a continuous straight path joining two or more points, whether infinite in both directions or just a line segment bounded by two distinct end points
  12. 21. the branch of mathematics that studies the relationships between the sides and the angles of right triangles, and deals with and with the trigonometric functions (sine, cosine, tangent and their reciprocals)
  13. 22. a polynomial algebraic expression or equation with just two terms, e.g. 2x3 - 3y = 7; x2 + 4x; etc
  14. 24. the factors of the terms (i.e. the numbers in front of the letters) in a mathematical expression or equation, e.g. in the expression 4x + 5y2 + 3z, the coefficients for x, y2 and z are 4, 5 and 3 respectively
  15. 26. the study of the formal laws of reasoning (mathematical logic the application of the techniques of formal logic to mathematics and mathematical reasoning, and vice versa)
  16. 28. a number which, when multiplied by x yields the multiplicative identity 1, and can therefore be thought of as the inverse of multiplication, e.g. the reciprocal of x is 1⁄x, the reciprocal of 3⁄5 is 5⁄3
  17. 29. two geometrical figures are congruent to one another if they have the same size and shape, and so one can be transformed into the other by a combination of translation, rotation and reflection
  18. 32. a particular ordering of a set of objects, e.g. given the set {1, 2, 3}, there are six permutations: {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, and {3, 2, 1}
  19. 35. an algebraic equation with 3 terms, e.g. 3x + 5y + 8z; 3x3 + 2x2 + x; etc
  20. 36. an algebraic expression or equation with more than one term, constructed from variables and constants using only the operations of addition, subtraction, multiplication and non-negative whole-number exponents, e.g. 5x2 - 4x + 4y + 7
  21. 37. a subsidiary collection of objects that all belong to, or is contained in, an original given set, e.g. subsets of {a, b} could include: {a}, {b}, {a, b} and {}
  22. 40. 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)
  23. 42. a quantity or set of numbers without bound, limit or end, whether countably infinite like the set of integers, or uncountably infinite like the set of real numbers (represented by the symbol ∞)
  24. 43. a self-similar geometric shape (one that appears similar at all levels of magnification) produced by an equation that undergoes repeated iterative steps or recursion
  25. 44. a rule or equation describing the relationship of two or more variables or quantities, e.g. A = πr2
  26. 45. a number by which two given numbers can be divided by integer division, and produce the same remainder, e.g. 38 ÷ 12 = 3 remainder 2, and 26 ÷ 12 = 2 remainder 2, therefore 38 and 26 are congruent modulo 12, or (38 ≡ 26) mod 12
  27. 46. 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