Math Trivia – Page 3 – Trivia Mastermind

The subject of math is immensely varied, making it great for trivia. Below you will find over 251 advanced Math trivia questions and answers covering many fields and areas of math. These trivia questions provide quite the range in difficulty and only true math lovers will be able to handle these questions. With many areas of focus and a high degree of difficulty, these 251 Advanced Math trivia questions and answers cover topics only a deep lover of math will appreciate. Use these trivia questions to challenge yourself and others, especially anyone that says, "they know everything about math." Contents 251 Advanced Math Topics Trivia Questions & Answers1.1 Play 251 Advanced Math Topics Trivia Questions Quiz1.2 Read 251 Advanced Math Topics Trivia Questions & AnswersAdvanced Math Topics Trivia Questions & Answers by Category1.3 Algebra Math Trivia Questions & Answers1.4 Arithmetic & Miscellaneous Math Trivia Questions & Answers1.5 The Branches of Math Trivia Questions & Answers1.6 Calculus Math Trivia Questions & Answers1.7 Geometry Math Trivia Questions & Answers1.8 Important Mathematicians in History Trivia Questions & Answers1.9 Math Fun Facts Trivia Questions & Answers2.0 Math Symbols Trivia Questions & Answers2.1 Theorems of Math Trivia Questions & AnswersRelated Content2.2 Play Science Trivia2.3 Play Computer & Technology Trivia2.4 Play Video Game Trivia2.5 Play American History Trivia2.6 Play Random Trivia Play 251 Advanced Math Topics Trivia Questions Quiz Click Play Now to Launch Advanced Math Topics Trivia Play NowPage 1 of 252 What is the process of extracting the underlying structures, patterns or properties of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena called? Extraction Abstraction Diffraction Benefaction Page 2 of 252 What is the " ∇ " symbol called in calculus? Vector Integral Epsilon Nabla Page 3 of 252 What is the name for a symmetrical plane curve that forms when a cone intersects with a plane parallel to its side, with an example being, a u-shaped graph of a quadratic function? The Parabola The Vertex The Chord The Ray Page 4 of 252 In mathematics, what is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables called? A Derangement A Sinusoid A Conjecture A Polynomial Page 5 of 252 Which theorem describes the algebraic expansion of powers of a binomial where, it is possible to expand the polynomial (x + y)n into a sum involving terms of the form axbyc, where the exponents b and c are non-negative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending on n and b? Dirichlet’s Theorem The Abel–Ruffini Theorem The Binomial Theroem The Pólya Enumeration Theorem Page 6 of 252 What does the blackboard bold " ℤ " symbol denote a set of? Integers Primorials Rational Numbers Factorial Operations Page 7 of 252 What is the mathematical term for the number that sits above the line in a fraction? An Axiom A Fractal A Denominator A Numerator Page 8 of 252 Which theorem states that every non-zero, single-variable, degree n polynomial with complex coefficients has, counted with multiplicity, exactly n complex roots? Ptolemy's Theorem The Fundamental Theorem of Algebra The Four Color Theorem The Pólya Enumeration Theorem Page 9 of 252 What is a non-self-evident statement that has been proven to be true, either on the basis of generally accepted statements such as axioms, or on the basis of previously established statements in mathematics called? A Primorial A Ratio A Mathematical Proof A Theorem Page 10 of 252 What kind of equation is an equation that equates a quartic polynomial to zero, of the general form ax⁴ + bx³ + cx² + dx + e = 0 where a ≠ 0 ? Pell's Equation The Pythagorean Equation A Cubic Equation A Quartic Equation Page 11 of 252 What does the " ≤ " symbol mean in mathematics? Greater Than or Equal To Less Than or Equal To Greater Than Less Than Page 12 of 252 What German mathematician and physicist, who made significant contributions to a number fields in mathematics and science said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics"? Carl Friedrich Gauss Omar Khayyam Giuseppe Peano Leonhard Euler Page 13 of 252 Which theorem states that, if ƒ (x, y) is an analytic germ in two variables, then the solutions y = φ (x) of the equation ƒ = 0 can be expanded as Puiseux series that are convergent in a neighborhood of the origin? The Prime Number Theorem Minkowski's Theorem The Newton-Puiseux Theorem Wilson's Theorem Page 14 of 252 What does the ø symbol denote in set theory? A False Set An Empty Set A Primorial The Set Difference Page 15 of 252 What kind of function is represented by " ⌊x⌉ " ? A Nearest Integer Function A Floor Function A Polynomial Function A Ceiling Function Page 16 of 252 In arithmetic, what is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces a quotient and a remainder smaller than the divisor? Euclidean Division Quotient Division Field Division Short Division Page 17 of 252 What is the smallest perfect number? 24 28 6 8 Page 18 of 252 What is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion, which may use previously established statements, but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference? A Composition Operator An Exponentiation A Conjecture A Mathematical Proof Page 19 of 252 Which theorem of probability establishes that in many situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed? The Central Limit Theorem The Cayley–Hamilton Theorem Ptolemy's Theorem The Four Color Theorem Page 20 of 252 In ring theory, what is the name of a ring that is a special subset of its elements, generalizes certain subsets of the integers, such as the even numbers or the multiples of 3, addition and subtraction of even numbers preserves evenness, and multiplying an even number by any other integer results in another even number? A Morita An Ideal A Nilpotent A Polynomial Page 21 of 252 What are the next three numbers in the golden ration? 1.61_ _ _ 803 308 038 830 Page 22 of 252 What does the blackboard bold " ℕ " symbol denote a set of? Complex Numbers Real Numbers Rational Numbers Natural Numbers Page 23 of 252 Which theorem states that, given any separation of a plane into contiguous regions when producing a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color? The Fundamental Theorem of Arithmetic The Four Color Theorem The Fundamental Theorem of Calculus The Lebesgue Differentiation Theorem Page 24 of 252 Which ancient language is the term "math" derived from? Latin Aramaic Hebrew Greek Page 25 of 252 What is the study of mathematical concepts independently of any application outside of mathematics, where the appeal is attributed to the intellectual challenge and aesthetic beauty of working out the logical consequences of basic principles called? Pure Mathematics Algebra Geometry Calculus Page 26 of 252 What does the " Φ " symbol represent? The Spectral Radius The Plane Angle The Golden Ratio The Chromatic Number Page 27 of 252 Which theorem describes the asymptotic distribution of the prime numbers among the positive integers, that formalizes the idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs? The Prime Number Theorem The Intermediate Value Theorem The Factor Theorem Lagrange's Four-square Theorem Page 28 of 252 What branch of mathematical logic studies sets, which informally, are collections of objects? Statistics Number Theory Game Theory Set Theory Page 29 of 252 What does the " ≠ " symbol mean? Not Equal Greater Than Equal Less Than or Equal To Page 30 of 252 What is the fundamental relation in Euclidean geometry among the three sides of a right triangle which states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides called? The Fundamental Theorem of Arithmetic Wilson's Theorem The Pythagorean Theorem The Factor Theorem Page 31 of 252 What does the logical predicate " ⊤ " symbol denote? Always False Sometimes False Never True Always True Page 32 of 252 Who posed the 18th century question about knowing the probability that a dropped needle on a parallel strip wood floor will lie across a line between two strips? Leonhard Euler Augustin-Louis Cauchy Georges-Louis Leclerc Abraham de Moivre Page 33 of 252 Who was the German-Austrian logician and mathematician, who published two incompleteness theorems in 1931, that demonstrated the inherent limitations of every formal axiomatic system capable of modeling basic arithmetic? David Hilbert Kurt Gödel Carl Friedrich Gauss Leonhard Euler Page 34 of 252 Which theorem states that there are infinitely many prime numbers contained in the collection of all numbers of the form na + b, in which the constants a and b are integers that have no common divisors except the number 1 and the variable n is any natural number? The Remainder Theorem Ptolemy's Theorem Minkowski's Theorem Dirichlet’s Theorem Page 35 of 252 What is this " ∫ " symbol called? The Integral Symbol The Composition Operator The Set Theoretic Union The Factorial Operation Page 36 of 252 What is the numeral system with sixty as its base, that originated with the ancient Sumerians in the 3rd millennium BC and was passed down to the ancient Babylonians, still used in a modified form for measuring time, angles, and geographic coordinates today? Octagesimal Sexagesimal Decagesimal Pentagesimal Page 37 of 252 In set theory, the what is the " ℶ " symbol called? An Aleph An Omega A Beth A Alpha Page 38 of 252 If changing the order of operands in a binary operation, does not change the result, what is the property of this binary operation? Closure Commutative Associative Distributive Page 39 of 252 Which theorem states that if f is a continuous function whose domain contains the interval [a, b], then it takes on any given value between f(a) and f(b) at some point within the interval? The Pólya Enumeration Theorem The Remainder Theorem Bertrand's Postulate The Intermediate Value Theorem Page 40 of 252 What is the branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions? Number Theory Algebra Arithmetic Combinatorics Page 41 of 252 What does the " > " symbol in mathematics mean? Less Than Greater Than or Equal To Greater Than Less Than or Equal To Page 42 of 252 What is the quantity that expresses the extent of a two-dimensional region, shape, or planar lamina, in the plane called? The Radius The Circumference The Diameter The Area Page 43 of 252 Who was the Persian polymath and mathematician whose most notable work was on the classification and solution of cubic equations, where he provided geometric solutions by the intersection of conics and contributed to the understanding of the parallel axiom? Sharaf al-Din al-Tusi Muḥammad ibn Mūsā al-Khwārizmī Omar Khayyam Abū ʿAlī al-Ḥusayn ibn ʿAbd Allāh ibn Sīnā Page 44 of 252 What is the " ∘ " symbol called in algebraic operations? The Composition Operator The Root Operator The Power Operator The Division Operator Page 45 of 252 What does the acronym MSC, which is an alphanumeric classification scheme collaboratively produced from two major mathematical reviewing databases, stand for? Mathematics Supplemental Classification Mathematics Subject Classification Mathematics Sector Classification Mathematics Sphere Classification Page 46 of 252 In mathematics, what is the name of the periodic function composed of harmonically related sinusoids, combined by a weighted summation, and with appropriate weights, one cycle of the summation can be made to approximate an arbitrary function in that interval? A Fourier Series A Finite Geometric Series A Fibonacci Series A Harmonic Series Page 47 of 252 Which theorem is the statement that every convex set in ℝⁿ which is symmetric with respect to the origin and which has volume greater than 2ⁿ contains a non-zero integer point? Morley's Trisector Theorem Desargues's Theorem Minkowski's Theorem The Cayley–Hamilton Theorem Page 48 of 252 In combinatorial mathematics, what is a permutation of the elements of a set, such that no element appears in its original position and is a permutation that has no fixed points called? A Derangement An Arrangement A Dispostion An Array Page 49 of 252 What does the " ≥ " symbol mean? Greater Than Less Than or Equal To Equal To Greater Than or Equal To Page 50 of 252 What is the subfield of mathematics that explores the formal applications of logic to mathematics? Number Theory Mathematical Logic Set Theory Numerical Analysis Page 51 of 252 Which theorem of linear algebra states that every square matrix over a commutative ring satisfies its own characteristic equation? The Factor Theorem The Remainder Theorem The Cayley–Hamilton Theorem The Pólya Enumeration Theorem Page 52 of 252 What does the abbreviation " ∋ " mean? "Under the Condition that" "Because" "Therefore" "Logically Implies That'' Page 53 of 252 Which branch of mathematics is concerned with properties of space that are related with distance, shape, size, and relative position of figures? Trigonometry Geometry Optimization Probability Page 54 of 252 What is the name of the widely read expository mathematical journal founded by Benjamin Finkel in 1894, published ten times each year by Taylor & Francis ,for the Mathematical Association of America? The Monthly American Mathematic Journal The Journal of American Math The Weekly Mathematic The American Mathematical Monthly Page 55 of 252 What does the " ¬ " symbol read as in basic logic? "If and Only If" "Not" "Or" "For All" Page 56 of 252 In combinatorics, what problem is this the answer to? (p − q) ⁄ (p + q) Bertrand's Ballot Problem The Basel Problem The Seven Bridges of Königsberg The Birthday Paradox Page 57 of 252 What is the study of mathematical models of strategic interaction among rational decision-makers, and has applications in all fields of social science, as well as in logic, systems science and computer science called? Ring Theory Arithmetic Model Theory Game Theory Page 58 of 252 In x^y, what would the " ^ " symbol denote? Always False Exponentiation A Primorial The Set Difference Page 59 of 252 What does the " ∥ " symbol denote in elementary geometry? A Factorial Operation A Set Theoretic Intersection Rational Numbers Parallelism Page 60 of 252 Which two mathematicians independently developed calculus in the late 17th century? Isaac Newton and Gottfried Wilhelm Leibniz Johann Bernoulli and Gottfried Wilhelm Leibniz Isaac Newton and Giuseppe Peano Albert Girard and Isaac Newton Page 61 of 252 Which theorem states that every integer >1 has a prime factorization and that prime factorization is unique? The Fundamental Theorem of Arithmetic Wilson's Theorem The Remainder Theorem The Pólya Enumeration Theorem Page 62 of 252 What kind of number is the square root of 2? A Prime Number An Irrational Number A Composite Number A Rational Number Page 63 of 252 What does " Ω " symbol mean in math? Both Plus and Minus Grads Angle Unit The Unit for Resistance An Unknown Value Page 64 of 252 What kind of numbers do number theorists study? Double Factorials Destiny Numbers Bhargavan Numbers Prime Numbers Page 65 of 252 Who solved the Basel problem, first posed by Pietro Mengoli in 1650? Leonhard Euler G. H. Hardy David Hilbert Peter Ludwig Sylow Page 66 of 252 What does the set A ⊃ B mean? A is Union of Set B A is a Strict Subset of B A is a Universal Set A is a Strict Superset of B Page 67 of 252 Which theorem states that there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients? Ptolemy's Theorem The Abel–Ruffini Theorem Mean Value Theorem Lagrange's Four-square Theorem Page 68 of 252 What does the logical predicate "⊥" symbol denote? Always False Sometimes False Always True Sometimes True Page 69 of 252 What is the name of the mathematical curve that describes a smooth periodic oscillation in a continuous wave and occurs often in both pure and applied mathematics? Square Wave Triangle Wave Sine Wave Sawtooth Wave Page 70 of 252 In mathematics, what indicates how many times one number contains another? A Ratio A Proportion A Magnitude A Rate Page 71 of 252 What is the value of a function that must be provided to obtain the function's result called? A Dependent Variable A Variance An Argument A Parameter Page 72 of 252 In number theory, what does the " # " symbol denote? A Rational Number Forall A Primorial Prime Page 73 of 252 Which ancient Greek philosopher are Platonic solids named after? Plato Aristotle Pythagoras Archimedes Page 74 of 252 In mathematics, what is the amount "left over" after performing some computation called? The Product The Quotient The Sum The Remainder Page 75 of 252 Who proved that the sum of the reciprocals of all prime numbers diverges? Carl Friedrich Gauss Leonhard Euler Georges-Louis Leclerc Kurt Gödel Page 76 of 252 What is the study of algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers called? Ring Theory Linear Equations Object Relation Theory Vector Analysis Page 77 of 252 In mathematics, what is the name of the technique for getting information on the number of positive real roots of a polynomial, which asserts that the number of positive roots is at most the number of sign changes in the sequence of polynomial's coefficients, and that the difference between these two numbers is always even? Descartes' Rule of Signs The Inclusion–Exclusion Principle Mathematical Induction Differential Geometry Page 78 of 252 What does the " ∖ " symbol denote in set theory? The Difference of a Set The Set Difference The Intersection of a Set The Union of Set Page 79 of 252 In number theory, what is the name of a positive integer that is equal to the sum of its positive divisors, excluding the number itself? The Rational Number The Golden Number The Irrational Number The Perfect Number Page 80 of 252 In mathematics, what is a conclusion or a proposition which is suspected to be true due to preliminary supporting evidence, but for which no proof or disproof has yet been found called? A Conjecture A Theorem A Postulate An Axiom Page 81 of 252 Who was the Persian mathematician who has been credited with proposing the idea of a function and also developed a novel method for determining the conditions under which certain types of cubic equations would have two, one, or no solutions? Omar Khayyam Muḥammad ibn Mūsā al-Khwārizmī Sharaf al-Din al-Tusi Abu al-Wafa' Buzjani Page 82 of 252 What is the application of probability theory, specifically to mathematical techniques, which is used for mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory called? Foundations Arithmetic Number Theory Mathematical Statistics Page 83 of 252 What is the name of the equation, which is any Diophantine equation of the form x² − ny² = 1 where n is a given positive non-square integer and integer solutions are sought for x and y? Pell's Equation The Pythagorean Equation A Cubic Equation A Quartic Equation Page 84 of 252 What does the blackboard bold " ℚ " symbol denote a set of? Real Numbers Rational Numbers Complex Numbers Integers Page 85 of 252 Who was the Dutch mathematician and philosopher that established himself as the founder of modern topology, with his fixed-point theorem and the topological invariance of dimension? L. E. J. Brouwer Carl Friedrich Gauss Kurt Gödel Gottfried Wilhelm Leibniz Page 86 of 252 In Euclidean geometry, which theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral, which is a quadrilateral whose vertices lie on a common circle? Ptolemy's Theorem The Factor Theorem Fundamental Theorem of Calculus Lagrange's Four-square Theorem Page 87 of 252 What kind number is a number that can be expressed as the ratio of two integers? An Irrational Number A Prime Number A Rational Number A Liouville Number Page 88 of 252 Who first presented the form of the theorem, which later became Green's theorem? Leonhard Euler Augustin-Louis Cauchy Albert Girard Erdős-Szekeres Page 89 of 252 What is the method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape called? The Euclidean Method The Method of Exhaustion A Series Expansion The Axiomatic Method Page 90 of 252 Which theorem states that a natural number n > 1 is a prime number if and only if the product of all the positive integers less than n is one less than a multiple of n? Wilson's Theorem Mean Value Theorem Fermat's Little Theorem Desargues's Theorem Page 91 of 252 Who is de Moivre's formula named after? William de Moivre Jonah de Moivre Roger de Moivre Abraham de Moivre Page 92 of 252 What does the " ∨ " symbol read as in basic logic? "Or" "And" "If" "Either" Page 93 of 252 What is the algebraic structure that is a set equipped with two binary operations satisfying properties analogous to those of addition and multiplication of integers? A Curve A Ring An Angle A Line Page 94 of 252 Which theorem was the first major theorem to be proved using a computer? The Optional Stopping Theorem The Binomial Theroem The Four Color Theorem The Central Limit Theorem Page 95 of 252 Who proved the polyhedron formula? Muḥammad ibn Mūsā al-Khwārizmī Leonard Euler G. H. Hardy Peter Ludwig Sylow Page 96 of 252 What are the next three numbers of pi? 3.14_ _ _ 915 519 159 195 Page 97 of 252 In logic, what is the procedure by which an entire system is generated in accordance with specified rules by logical deduction from certain basic propositions, which in turn are constructed from a few terms taken as primitive called? Euclidean Method A Theorem Inclusion–Exclusion Method Axiomatic Method Page 98 of 252 Who was the Italian mathematician and glottologist that authored over 200 books and papers, and was a founder of mathematical logic and set theory? Giuseppe Peano Leonardo Pisano Gerolamo Cardano Luca Pacioli Page 99 of 252 In number theory, what is the theorem that states that for any integer n > 3, there always exists at least one prime number p with n < p < 2n - 2 ? Bertrand's Postulate Parallel Postulate Euclid's Postulate Euler's Postulate Page 100 of 252 What are two quantities in, if their ratio is the same as the ratio of their sum to the larger of the two quantities? The Brilliant Ratio The Perfect Ratio The Golden Ratio The Special Ratio Page 101 of 252 What is the perimeter of a circle called? The Radius The Diameter The Area The Circumference Page 102 of 252 What is the type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set, with two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows? Hyperbola Circle Parabola Ellipse Page 103 of 252 In combinatorics, what is the counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets called? The Rule of Sum Principle The Pigeonhole Principle The Rule of Product Principle The Inclusion–Exclusion Principle Page 104 of 252 Who was the Persian polymath who produced vastly influential works in mathematics, astronomy, and geography and wrote the treatise on algebra, The Compendious Book on Calculation by Completion and Balancing? Muḥammad ibn Mūsā al-Khwārizmī Abu Sa'id Ahmed ibn Mohammed ibn Abd al-Jalil al-Sijzi Abu Rayhan Muhammad ibn Ahmad al-Biruni Ghiyāth al-Dīn Jamshīd Masʿūd al-Kāshī Page 105 of 252 Which theorem states that a polynomial ƒ(x) has a factor (x − k) if and only if ƒ(k) = 0 ? The Triangle Inequality Theorem Lagrange's Four-square Theorem The Mean Value Theorem The Factor Theorem Page 106 of 252 Which theorem states that when a polynomial, f(x), is divided by a linear polynomial , x - a, the remainder of that division will be equivalent to f(a)? The Binomial Theroem The Newton-Puiseux Theorem The Remainder Theorem The Central Limit Theorem Page 107 of 252 What does the " ∩ " symbol denote in set theory? A Set Theoretic Union A Set Theoretic Intersection A Set Theoretic Subset A Set Theoretic Power Set Page 108 of 252 In the foundations of mathematics, what is the term that came from a famous British polymath and mathematician showing that some attempted formalizations of the naive set theory created by Georg Cantor led to a contradiction? Russell's Paradox Zeno's Dichotomy Paradox The Rich Guest Paradox Banach–Tarski Paradox Page 109 of 252 What does the " < " symbol mean in mathematics? Less Than Less Than or Equal To Greater Than Greater Than or Equal To Page 110 of 252 In number theory, what kind of numbers are "almost rational", and can thus be approximated "quite closely" by sequences of rational numbers? Irrational Numbers Complex Number Liouville Numbers Composite Number Page 111 of 252 What is the mathematic study of points of algebraic varieties with coordinates in the integers, rational numbers, and their generalizations, which are typically fields that are not algebraically closed, such as number fields, finite fields, function fields, and p-adic fields? Plane Geometry Diophantine Geometry Commutative Geometry Noncommutative Geometry Page 112 of 252 Which theorem states that, in a party of n persons, if every pair of persons has exactly one common friend, then there is someone in the party who is everyone else's friend? The Union Theorem The Mutual Theorem The Relationship Theorem The Friendship Theorem Page 113 of 252 In the mathematical field of topology, what is a continuous function between topological spaces that has a continuous inverse function called? An Isomorphism A Topological Conjugacy A Homeomorphism Trefoil Knot Page 114 of 252 What is this equation called? A² + B² = C² The Pythagorean Equation Newton's Universal Law of Gravitation Euler's Formula for Polyhedra The Wave Equation Page 115 of 252 In the field of algebra, what is a ring formed from the set of polynomials in one or more variables with coefficients in another ring, often a field called? A Null Ring A Commutative Ring A Polynomial Ring A Unity Ring Page 116 of 252 Which theorem in combinatorics both follows from and ultimately generalizes Burnside's lemma on the number of orbits of a group action on a set? The Pólya Enumeration Theorem Morley's Trisector Theorem Pick's Theorem Desargues's Theorem Page 117 of 252 What does the " √ " symbol denote? The Obelus The Square Root An Exponent The Cubic Root Page 118 of 252 What is the branch of number theory that uses methods from mathematical analysis to solve problems about the integers? Model Theory Set Theory Algebraic Number Theory Analytic Number Theory Page 119 of 252 In mathematics, what is a set S which is the set of all subsets of S, including the empty set and S itself called? The Power Set The Function Set The Union Set A Real Number Set Page 120 of 252 Which theorem links the concept of differentiating a function with the concept of integrating a function? Fundamental Theorem of Calculus Mean Value Theorem Lagrange's Four-square Theorem Schröder–Bernstein Theorem Page 121 of 252 What is the ratio of a circle's circumference to its diameter called? Area Length Radius Pi Page 122 of 252 What kind of function is represented by ⌈x⌉ ? An Identity Function A Ceiling Function A Quadratic Function Polynomial Function Page 123 of 252 What is the name of the professional society, founded in 1915, that focuses on mathematics accessible at the undergraduate level, with 25,000+ members, spanning university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists; statisticians; and many others in academia, government, business, and industry professionals? The Mathematical Association The Math Organization The U.S. Mathematical Union The Math Consortium Page 124 of 252 What kind of real number cannot be written as a simple fraction? A Rational Number A Composite Number An Irrational Number A Complex Number Page 125 of 252 What is the name of the theorem that is an efficient method for computing the greatest common divisor of two integers, the largest number that divides them both without a remainder, and is named after an ancient Greek mathematician, who first described it in his book Elements? The Branch and Bound Algorithms The Randomized Algorithm The Dynamic Programming Algorithm The Euclidean Algorithm Page 126 of 252 What is does this formula represent? 1 - ⅓ + ⅕ - ¹⁄₇ + ¹⁄₉ - ⋯ = π⁄₄ The Euler Formula for Polyhedra The Leibniz Formula for Pi The Fundamental Formula of Calculus The Logarithm Identities Formula Page 127 of 252 The sum of the three angles of any triangle is equal to how many degrees? 90 Degrees 180 Degrees 360 Degrees 270 Degrees Page 128 of 252 Which theorem states that if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) is equal to the function's average rate of change over [a,b] ? The Mean Value Theorem Dirichlet’s Theorem The Binomial Theorem Ptolemy's Theorem Page 129 of 252 Who was the Swiss mathematician that made important and influential discoveries in many branches of mathematics, such as calculus, graph theory, and analytic number theory, while also introducing much of the modern mathematical terminology and notation? Pierre-Simon Laplace Blaise Pascal Joseph Fourier Leonhard Euler Page 130 of 252 What does this equation represent? r = aθ The Isosceles Triangle Theorem The Pascal Line The Spiral of Archimedes The Area of a Circle Page 131 of 252 Which theorem states that every natural number can be represented as the sum of four integer squares? Lagrange's Four-square Theorem Pick's Theorem Intersecting Chords Theorem Fermat's Last Theorem Page 132 of 252 What is the mathematical term for the number that sits below the line in a fraction? The Numerator The Lowest Term The Denominator The Improper Page 133 of 252 In two-dimensional geometry, which postulate states that if a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles? The Bertrand Postulate The Addition Postulate The Partition Postulate The Parallel Postulate Page 134 of 252 Which theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side? The Triangle Inequality Theorem The Intersecting Chords Theorem The Isosceles Triangle Theorem The Prime Number Theorem Page 135 of 252 What does the " ∈ " symbol mean in set theory? Is a Superset of Is a Powerset of Is an Element of Is a Complement of Page 136 of 252 Which theorem is a hypothesis about the possible sizes of infinite sets and states, there is no set whose cardinality is strictly between that of the integers and the real numbers? The Riemann Hypothesis The Continuum Hypothesis The Infinite Set Hypothesis The Spectrum Hypothesis Page 137 of 252 What is the name of the explicit formula in linear algebra, which is the explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution, and expresses the solution in terms of the determinants of the coefficient matrix and of matrices obtained from it by replacing one column by the column vector of right-hand-sides of the equations? Cramer's Rule Bernoulli's Rule Bernay's Rule Stiefel's Rule Page 138 of 252 What is the branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them such as addition, subtraction, multiplication, division, exponentiation and extraction of roots called? Algebra Arithmetic Probability Statistics Page 139 of 252 Which theorem states that if two sides of a triangle are congruent, then angles opposite to those sides are congruent? The Pythagorean Theorem Fermat's Last Theorem The Lebesgue Differentiation Theorem The Isosceles Triangle Theorem Page 140 of 252 What is a binary relation between two sets that associates to each element of the first set exactly one element of the second set called? A Function A Quartic Equation A Proof A Polynomial Page 141 of 252 In Mathematics, what is the study of the relationship between formal theories and their models, taken as interpretations that satisfy the sentences of that theory called? Braid Theory Model Theory Theory of equations Topos theory Page 142 of 252 Which theorem states that if p is a prime number, then for any integer a, the number ap − a is an integer multiple of p? Optional Stopping Theorem Bezout's Theorem Intersecting Chords Theorem Fermat's Little Theorem Page 143 of 252 What does the symbol " e " represent in math? Endpoint Number Elapsed Number Euler's Number Edge Number Page 144 of 252 What is a set endowed with some additional features on the set, such as an operation, relation, metric, or topology, where often, the additional features are attached or related to the set, so as to provide it with some additional meaning or significance called? A Mathematical Structure A Scientific Structure A Statistical Structure A Sociological Structure Page 145 of 252 What is the name of the mathematics formula that is an approximation for factorials, which is a good approximation, leading to accurate results even for small values of n? The Pythagorean Formula Stirling's Formula Newton's Formula Euler's Formula Page 146 of 252 What is the name of the historically notable problem in mathematics, where the problem was to devise a walk through of a Russian city, where the walker would only cross each of two bridges between two islands once? Hilbert's Problem Thurston's Question Smale's Problem The Seven Bridges of Königsberg Page 147 of 252 In mathematics, what is a method for calculating a function that cannot be expressed by just elementary operators such as addition, subtraction, multiplication and division, with examples that include a Taylor series, a Maclaurin series, a Laurent series, a Dirichlet series, a Fourier series, and more? A Set Union A Series Expansion A Sequence Induction A String Extension Page 148 of 252 In which ancient cultures did elementary arithmetic such as addition, subtraction, multiplication and division first appear, according to archaeological record? Babylon and Egypt China and Indus Babylon and China Egypt and Indus Page 149 of 252 Which theorem of plane geometry states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle? Fermat's Last Theorem The Newton-Puiseux Theorem Morley's Trisector Theorem The Prime Number Theorem Page 150 of 252 In group theory, what is the order of a group and the number of elements in its set called? Membership Cardinality Membership Equivalent Page 151 of 252 What is the name of the association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs, which goes by the acronym AMS? Achieving Mathematical Societies Achieving Math Scholars American Math Scholars American Mathematical Society Page 152 of 252 What does the " ∪ " symbol denote in set theory? A Set Theoretic Intersection A Subset A Set Theoretic Union Not a Subset Page 153 of 252 Which theorem of set theory states that, if there exist injective functions f : A → B and g : B → A between the sets A and B, then there exists a bijective function h : A → B? Schröder–Bernstein Theorem Feuerbach's Theorem The Optional Stopping Theorem Dirichlet’s Theorem Page 154 of 252 What is the branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations? Elementary Number Theory Analytic Number Theory Algebraic Number Theory Geometric Number Theory Page 155 of 252 Who was the English mathematician, known for his achievements in number theory, mathematical analysis, the Hardy–Weinberg principle in biology, and his 1940 essay, A Mathematician's Apology? Georges-Louis Leclerc G. H. Hardy Omar Khayyam Sharaf al-Din al-Tusi Page 156 of 252 Which theorem represented by this formula? A = i + ᵇ⁄₂ − 1 Gödel's Incompleteness Theorems Euclid's Theorem Intersecting Chords Theorem Pick's Theorem Page 157 of 252 What does the " ≡ " symbol mean in math? Identical To Division Equal To Square Root Page 158 of 252 Which ancient language is the term "algebra" derived from? Arabic Latin Greek Arabic Page 159 of 252 In the hexagrammum mysticum theorem, if six arbitrary points are chosen on a conic and joined by line segments in any order to form a hexagon, then the three pairs of opposite sides of the hexagon meet at three points which lie on a straight line; what is the name of the line where the hexagon points meet? The Ray Line The Pascal Line The Diametric Line The Internal Segment Line Page 160 of 252 In mathematics, what is a value of a continuous quantity that can represent a distance along a line or alternatively, a quantity that can be represented as an infinite decimal expansion called? An Irrational Number A Composite Number A Real Number A Prime Number Page 161 of 252 In set theory, what is the " ℵ " symbol called? An Aleph An Epsilon A Delta A Modulo Page 162 of 252 In algebra, what is a structure-preserving map between two algebraic structures of the same type such as two groups, two rings, or two vector spaces called? A Homeomorphism A Trefoil Knot A Homomorphism An Isomorphism Page 163 of 252 Which is the mathematical study of continuous change called? Trigonometry Number Theory Probability Calculus Page 164 of 252 What operation does the " ! " symbol denote? A Primorial Operation A Factorial Operation A Non-divisibility Operation An Exclusive Operator Page 165 of 252 In arithmetic, what is the term for a quantity produced by the division of two numbers? A Quotient A Product A Sum A Multiplier Page 166 of 252 What is the theorem of real analysis, which states that for almost every point, the value of an integrable function is the limit of infinitesimal averages taken about the point? Erdős-Szekeres Theorem Feuerbach's Theorem Lebesgue Differentiation Theorem Cantor's Theorem Page 167 of 252 What does this formula represent? r=πr² The Area of a Rectangle The Area of a Triangle The Area of a Square The Area of a Circle Page 168 of 252 What does the blackboard bold " ℝ " symbol denote a set of? Integers Real Numbers Natural Numbers Rational Numbers Page 169 of 252 What is the branch of mathematics, that classically studies zeros of multivariate polynomials? Algebraic Geometry Vector Spaces Matrix Decomposition Relations and Computations Page 170 of 252 What is this equation a general mathematical representation of? ax³ + bx² + cx + d = 0 A Radical Equation A Cubic Equation A Cubic Function A Square Root Equation Page 171 of 252 What is the name of the operator used often in vector calculus as a vector differential operator, that when applied to a function defined on a one-dimensional domain, denotes the standard derivative of the function as defined in calculus? Derivative Epsilon Del Integral Page 172 of 252 Who introduced the axiomatic method, still used today? Edward Nelson Carl Friedrich Gauss David Hilbert Giuseppe Peano Page 173 of 252 Which Swiss mathematician initially introduced a theorem to Guillaume de l'Hôpital in 1694, that would later go on to become the L'Hôpital's rule? Erdős-Szekeres Johann Bernoulli Paul Bernays Eduard Stiefel Page 174 of 252 In additive number theory, who first made the observation on the theorem on sums of two squares, published in 1625? Augustin-Louis Cauchy Gottfried Wilhelm Leibniz Albert Girard William Rowan Hamilton Page 175 of 252 What does the " ∤ symbol denote? Roughly Equal Perpendicular To Parallel Sum Operator Non-divisibility Page 176 of 252 Which theorem is a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords within a circle and states that the products of the lengths of the line segments on each chord are equal? Intersecting Chords Theorem The Optional Stopping Theorem Frederick Douglas John Adams Page 177 of 252 What is the name of the major international reviewing service that provides reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe? ALEKS Assigns Math Mathematical Reviews Zentralblatt MATH Page 178 of 252 What does the ∧ symbol read as in basic logic? "Not" "And" "Or" "Either" Page 179 of 252 Which ancient language is the term "equal" derived from? Greek Arabic Latin Hebrew Page 180 of 252 Who was the influential German mathematician that discovered and developed a broad range of fundamental ideas including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics, particularly in proof theory? Carl Friedrich Gauss David Hilbert Georges-Louis Leclerc Kurt Gödel Page 181 of 252 Which theorem of projective geometry states that two triangles are in perspective axially if and only if they are in perspective centrally? Dirichlet’s Theorem Brouwer Fixed-point Theorem Gödel's Incompleteness Theorems Desargues's Theorem Page 182 of 252 What is the plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant, and generalizes a circle? A Deltoid An Ellipse A Quadrangle A Parallelogram Page 183 of 252 What does the " ∏ " symbol denote of a finite number of terms, in linear and multilinear algebra? The Set The Sum The Product The Superscript Page 184 of 252 Which theorem states, given r, s, any sequence of distinct real numbers with length at least (r − 1)(s − 1) + 1 contains a monotonically increasing subsequence of length r or a monotonically decreasing subsequence of length s? Euclid's Theorem Erdős-Szekeres Theorem Bezout's Theorem Cantor's Theorem Page 185 of 252 In Mathematics, what assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data? A Factor A Series An Integral A Coefficient Page 186 of 252 What does the blackboard bold " ℂ " symbol represent a set of? Complex Numbers Integers Natural Numbers Rational Numbers Page 187 of 252 In probability theory, what is the name of the paradox which shows that in a set of n randomly chosen people, some pair of them will have the same birthday? Russell's Paradox The Rich Guest Paradox The Birthday Paradox Zeno's Dichotomy Paradox Page 188 of 252 Who are the finite group theory Sylow theorems named after? Julius Plücker Sylow Camille Jordan Sylow Niels Henrik Sylow Peter Ludwig Sylow Page 189 of 252 What is the name of this broad area of mathematics, which is the study of mathematical symbols and the rules for manipulating these symbols and functions is a unifying thread of almost all of mathematics, including everything from elementary equation solving to the study of abstractions such as groups, rings, and fields? Algebra Geometry Combinatorics Arithmetic Page 190 of 252 Which theorem states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2? The Binomial Theorem Cantor's Theorem Fermat's Last Theorem The Newton-Puiseux Theorem Page 191 of 252 What are the next three numbers of Euler's number? 2.718_ _ _ 128 281 821 218 Page 192 of 252 What does this formula find the sum of, where n is the number of terms, a1 is the first term and r is the common ratio? Sn=a1(1−rn)1−r,r≠1Sn=a1(1−rn)1−r,r≠1 , A Finite Geometric Series An Infinite Algebraic Series An Infinite Geometric Series A Finite Algebraic Series Page 193 of 252 What does the " ⊻ " symbol denote in basic logic? The Material Implication The Exclusive Or The Material Equivalence The Negation Page 194 of 252 What is the Delian problem more commonly known as? Tripling the Cube The Square Root of a Cube Doubling the Cube The Treble Cube Problem Page 195 of 252 What is the study of algebraic structures, which includes groups, rings, fields, modules, vector spaces, lattices, and algebras called? Linear Algebra Commutative Algebra Abstract Algebra Advanced Algebra Page 196 of 252 Which proposition states that the nine-point circle of any triangle is tangent internally to the incircle and tangent externally to the three excircles? The Optional Stopping Theorem Feuerbach's Theorem The Brouwer Fixed-point Theorem The Binomial Theorem Page 197 of 252 Which theorem proves there are infinitely many primes? Euclid's Theorem Bezout's Theorem Taylor's Theorem The Optional Stopping Theorem Page 198 of 252 What is the name of the identities, that are a set of three identities in vector calculus relating the bulk with the boundary of a region on which differential operators act? Euler's Identities Descartes' Identities Green's Identities Russell's Identities Page 199 of 252 What was complex analysis traditionally known as? The Theory of Manipulation of a Compound Variable The Theory of Complex Manipulation Analysis The Theory of Derivative Compound Analysis The Theory of Functions of a Complex Variable Page 200 of 252 In mathematics, what is a multiplicative factor in some term of a polynomial, a series, or any expression, which is usually a number, but may be any expression, including variables such as a, b and c? A Matrix An Abstraction A Coefficient A Combinatoric Page 201 of 252 What does the " ∉ " symbol mean in set theory? Not In Intersection Union Not Subset Page 202 of 252 Which theorem states that in general, the number of common zeros equals the product of the degrees of the polynomials? Brouwer's Fixed-point Theorem The Central Limit Theorem Bezout's Theorem The Optional Stopping Theorem Page 203 of 252 Which ancient Greek mathematician is considered to be one of the greatest of all time, with achievements that include deriving an accurate approximation of pi; defining and investigating the spiral that now bears his name; and creating a system using exponentiation for expressing very large numbers? Geminus Theudius Euclid Archimedes Page 204 of 252 What is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns called in mathematics? A Set A Vector A Matrix A Determinant Page 205 of 252 What are the two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system capable of modeling basic arithmetic? Gödel's Incompleteness Theorems The Binomial Theorem The Fundamental Theorem of Algebra The Prime Number Theorem Page 206 of 252 Which branch of mathematics deals with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions, and these theories are usually studied in the context of real and complex numbers and functions? Probability Analysis Number Theory Optimization Page 207 of 252 What is the name of the type of triangle where the three points of intersection of the adjacent angle trisectors form an equilateral triangle? An Isosceles Triangle A Scalene Triangle An Obtuse Triangle A Morley Triangle Page 208 of 252 When a triangle's sides are a Pythagorean Triple, what kind of triangle is it? An Obtuse Triangle A Right Angled Triangle An Equiangular Triangle An Acute Triangle Page 209 of 252 In mathematics, what is the term for the fundamental algebraic structure where addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do? An Identity An Operation A Field A Set Page 210 of 252 Which area of mathematics is primarily concerned with counting, both as a means and an end in obtaining results, certain properties of finite structures, and finding the best structure or solution among several possibilities? Combinatorics Probability Statistics Calculus Page 211 of 252 Which mathematical proof is a technique that is used to prove that a statement P(n) holds for every natural number n = 0, 1, 2, 3, ... meaning that the overall statement is a sequence of infinitely many cases? Mathematical Deduction Mathematical Abstraction Mathematical Induction Mathematical Abatement Page 212 of 252 What does the set A ⊂ B mean? A is a Subset of B A is a Strict Subset of B The Union of A and B A set A is a subset of a set B if every element in A is also in B Page 213 of 252 What is the major branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques? Proof Theory Model Theory Recursion Theory Set Theory Page 214 of 252 Which theorem of set theory states that the cardinality of a set is strictly less than the cardinality of its power set, or collection of subsets? Dirichlet’s Theorem The Four Color Theorem The Fundamental Theorem of Algebra Cantor's Theorem Page 215 of 252 What term denotes the mathematics developed or practiced by the people of Mesopotamia? Sumerian Mathematics Egyptian Mathematics Babylonian Mathematics Mayan Mathematics Page 216 of 252 In probability theory, what is a sequence of random variables for which, at a particular time, the conditional expectation of the next value in the sequence is equal to the present value, regardless of all prior values called? Sumerian Mathematics A Martingale Babylonian Mathematics Mayan Mathematics Page 217 of 252 Who developed internal set theory, the mathematical theory of sets that provides an axiomatic basis for a portion of the nonstandard analysis introduced by Abraham Robinson? Georges-Louis Leclerc Edward Nelson Omar Khayyam L. E. J. Brouwer Page 218 of 252 Which theorem states that if a₁, …, an are algebraic numbers that are linearly independent over the rational numbers ℚ, then eª₁, …, eªn are algebraically independent over ℚ? The Law of Quadratic Reciprocity Lindemann–Weierstrass Theorem The Brouwer Fixed-point Theorem Taylor's Theorem Page 219 of 252 What kind of number in mathematics, is a number that is not algebraic, i.e. not the root of a non-zero polynomial with rational coefficients? Transcendental Number Liouville number Dudeney Number Automorphic Number Page 220 of 252 What is the " ∆ " symbol called in calculus? Vector Nabla Complex Conjugate Laplacian Page 221 of 252 What is the colloquial term for a number that can be written without a fractional component? A Figure An Integer A Numeral A Character Page 222 of 252 Which theory of probability theorem describes the result of performing the same experiment a large number of times and according to the law, the average of the results obtained from a large number of trials should be close to the expected value and will tend to become closer to the expected value as more trials are performed? The Law of Quadratic Reciprocity The Normal Distribution Law The Wave Equation The Law of Large Numbers Page 223 of 252 What does the " : " symbol denote of two quantities? Exponentiation The Square Root The Ratio The Opposite Page 224 of 252 In number theory, what is the theorem that is about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers? The Fundamental Theorem of Algebra The Newton-Puiseux Theorem The Law of Quadratic Reciprocity The Central Limit Theorem Page 225 of 252 Which ancient language is the term "geometry" derived from? Greek Latin Hebrew Arabic Page 226 of 252 Taylor's theorem is named after which 18th century mathematician? Leonhard Taylor Brook Taylor Carl Taylor Jonathan Taylor Page 227 of 252 What is the only even prime number? 10 22 2 56 Page 228 of 252 What does the " ∥ " symbol denote in elementary geometry? Arcsecond Perpendicular Congruent Parallelism Page 229 of 252 What is the process in mathematics of extracting the underlying structures, patterns or properties of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena called? Abstraction Extraction Conjunction Function Page 230 of 252 What does the " ∀ " symbol read as in basic logic? If and Only If ‎Negation For All Therefore Sign Page 231 of 252 What is the title of the book of mathematical proofs by Martin Aigner and Günter M. Ziegler, which contains 45 sections in the sixth edition, each devoted to one theorem but often containing multiple proofs and related results? The Joy of x A Mathematician's Apology Proofs from THE BOOK Prime Obsession Page 232 of 252 What is the mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity? Big M Notation Big A Notation Big N Notation Big O Notation Page 233 of 252 What does the " ∑ " symbol denote of a finite number of terms, in linear and multilinear algebra? Imaginary Unit The Sum Eigenvalues Domain of Page 234 of 252 What is the mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry, using the theory of plane and space curves and surfaces in the three-dimensional Euclidean space? Differential Calculus Differential Algebra Differential Geometry Differential Trigonometry Page 235 of 252 In group theory, G ≀ H denotes what, of the groups G and H? The Wreath Product The Set The Relative Complement The Cardinality Page 236 of 252 What kind of function is represented by " ⌊x⌋ " ? A Constant Function An Identity Function A Floor Function A Quadratic Function Page 237 of 252 What is the name of the geometric formula that gives the area of a triangle when the length of all three sides are known, and there is no need to calculate angles or other distances in the triangle first? Euclid's Formula Heron's Formula Archimedes' Formula Pythagoras' Formula Page 238 of 252 What is the philosophy of mathematics term that asserts that it is necessary to find a mathematical object to prove that something exists? Constructivism Structuralism Interactionism Functionalism Page 239 of 252 What is the name of the journal published by the American Mathematical Society that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science? The Math Review American Journal The Mathematical Journal Mathematical Reviews Reviews in Mathematics Page 240 of 252 What does the " ≈ " symbol mean? Not Equal To Equal To Definitively Equal To Approximately Equal To Page 241 of 252 Which fundamental tool of calculus is a function of a real variable that measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value)? The Function The Derivative The Multivariable The Integral Page 242 of 252 Which numeral system and the rules for the use of its operations, are still in use almost exclusively throughout the world today? Hindu–Arabic Numeral System The Greek Numeral System The English Numeral System The Arabic Numeral System Page 243 of 252 What is the name of a sequence of numbers such that the difference between the consecutive terms is constant, for example, the sequence 5, 7, 9, 11, 13, 15? The Algebra Progression The Calculus Progression An Arithmetic Progression The Statistical Progression Page 244 of 252 Who wrote the mathematical treatise Elements, which consists of 13 books and is a collection of definitions, postulates, propositions, and mathematical proofs of the propositions? Pythagoras Euclid Aristotle Archimedes Page 245 of 252 What is the branch of mathematics that investigates the intuitive notion of order using binary relations and provides a formal framework for describing statements such as "this is less than that" or "this precedes that"? Order Theory Statistics Theory Numeric Theory Arithmetic Theory Page 246 of 252 What is the name of the mathematical model of computation that defines an abstract machine that manipulates symbols on a strip of tape according to a table of rules, and given any computer algorithm, is capable of simulating that algorithm's logic? A Computation Machine A Manipulation Machine A Symbol Machine A Turing Machine Page 247 of 252 What does the " ∃ " symbol read as in basic logic? "Does Not Exist" "There Exists" "If Then" "If and Only If" Page 248 of 252 What is the name of this formula, typically used in applications? ln n! = n ln n - n + 0(ln n) The Logarithm Formula Euler's Formula Stirling's Formula The Fundamental Formula of Calculus Page 249 of 252 In probability theory, which theorem says that, under certain conditions, the expected value of a martingale at a stopping time is equal to its initial expected value? The Optional Stopping Theorem The Fundamental Theorem of Algebra The Central Limit Theorem The Four Color Theorem Page 250 of 252 Which theorem states that for any continuous function ƒ mapping a compact convex set to itself there is a point x₀ such that ƒ( x₀ ) = x₀ ? The Newton-Puiseux Theorem The Brouwer Fixed-point Theorem The Prime Number Theorem Dirichlet’s Theorem Page 251 of 252 In algebraic geometry, what is the " ∞ " symbol called? A Bracket An Equivalence A Delta A Lemniscate Page 252 of 252 What is the π symbol called? Radical Pi Exponent n Read 251 Advanced Math Topics Trivia Questions & Answers The following 251 math trivia questions cover the more advanced topics of mathematics. These questions include theorems, math symbols, integral mathematicians of the field, calculus, and other difficult topics. Use them for highly challenging questions, especially with your math savvy friends. Algebra Math Trivia Back to table of contents... Algebra is the branch of mathematics that deals with symbols and the rules for manipulating those symbols. It uses variables to represent numbers in equations and expressions, allowing us to solve problems by finding values for the variables. Algebra is fundamental to all areas of mathematics, as well as many other fields such as physics, engineering, economics, and computer science. For algebra trivia facts, read on for algebra trivia questions and answers. Algebra Math Trivia Questions & Answers 1. What is the name of this formula, typically used in applications? ln n! = n ln n - n + 0(ln n) Stirling's Formula 2. In group theory, G ≀ H denotes what, of the groups G and H? The Wreath Product 3. In mathematics, what is the term for the fundamental algebraic structure where addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do? A Field 4. In mathematics, what is a multiplicative factor in some term of a polynomial, a series, or any expression, which is usually a number, but may be any expression, including variables such as a, b and c? A Coefficient 5. What kind of real number cannot be written as a simple fraction? An Irrational Number 6. What kind of number in mathematics, is a number that is not algebraic, i.e. not the root of a non-zero polynomial with rational coefficients? A Transcendental Number 7. In mathematics, what is a set S which is the set of all subsets of S, including the empty set and S itself called? The Power Set 8. What is the algebraic structure that is a set equipped with two binary operations satisfying properties analogous to those of addition and multiplication of integers? A Ring 9. What kind number is a number that can be expressed as the ratio of two integers? A Rational Number 10. What kind of number is the square root of 2? An Irrational Number 11. What is the name for a symmetrical plane curve that forms when a cone intersects with a plane parallel to its side, with an example being, a u-shaped graph of a quadratic function? The Parabola 12. In mathematics, what is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables called? A Polynomial 13. What kind of equation is an equation that equates a quartic polynomial to zero, of the general form ax⁴ + bx³ + cx² + dx + e = 0 where a ≠ 0 ? A Quartic Equation 14. In ring theory, what is the name of a ring that is a special subset of its elements, generalizes certain subsets of the integers, such as the even numbers or the multiples of 3, addition and subtraction of even numbers preserves evenness, and multiplying an even number by any other integer results in another even number? An Ideal 15. If changing the order of operands in a binary operation, does not change the result, what is the property of this binary operation? Commutative 16. In the field of algebra, what is a ring formed from the set of polynomials in one or more variables with coefficients in another ring, often a field called? A Polynomial Ring 17. In algebra, what is a structure-preserving map between two algebraic structures of the same type such as two groups, two rings, or two vector spaces called? A Homomorphism 18. What is this equation a general mathematical representation of? ax³ + bx² + cx + d = 0 A Cubic Equation 19. What does the set a ⊂ b mean? a is a Strict Subset of b 20. What is the process in mathematics of extracting the underlying structures, patterns or properties of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena called? Abstraction 180 Science Trivia Questions & Answers Learn science facts from every area of science. Click the play now button to begin. Play Now Arithmetic & Miscellaneous Math Trivia Back to table of contents... Arithmetic is the branch of mathematics that deals with the manipulation of numbers, including addition, subtraction, multiplication, division, and other operations. It is one of the oldest branches of mathematics, and is fundamental to understanding many areas of mathematics, including calculus and algebra. With the vast fields involved in mathematics, the below questions also include a variety of other areas that encompass many areas of math. For arithmetic and other more encompassing conceptual facts of math, continue on for arithmetic & miscellaneous math trivia questions and answers. Arithmetic & Miscellaneous Math Trivia Questions & Answers 21. What is the name of the mathematical model of computation that defines an abstract machine that manipulates symbols on a strip of tape according to a table of rules, and given any computer algorithm, is capable of simulating that algorithm's logic? A Turing Machine 22. What is the name of a sequence of numbers such that the difference between the consecutive terms is constant, for example, the sequence 5, 7, 9, 11, 13, 15? An Arithmetic Progression 23. What is the philosophy of mathematics term that asserts that it is necessary to find a mathematical object to prove that something exists? Constructivism 24. In probability theory, what is a sequence of random variables for which, at a particular time, the conditional expectation of the next value in the sequence is equal to the present value, regardless of all prior values called? A Martingale 25. What is the Delian problem more commonly known as? Doubling the Cube 26. In combinatorial mathematics, what is a permutation of the elements of a set, such that no element appears in its original position and is a permutation that has no fixed points called? A Derangement 27. In probability theory, what is the name of the paradox which shows that in a set of ? randomly chosen people, some pair of them will have the same birthday? The Birthday Problem or the Birthday Paradox 28. In arithmetic, what is the term for a quantity produced by the division of two numbers? A Quotient 29. In group theory, what is the order of a group and the number of elements in its set called? Its Cardinality 30. What is the mathematical term for the number that sits below the line in a fraction? The Denominator 31. What is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion, which may use previously established statements, but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference? A Mathematical Proof 32. What branch of mathematical logic studies sets, which informally, are collections of objects? Set Theory 33. In logic, what is the procedure by which an entire system is generated in accordance with specified rules by logical deduction from certain basic propositions, which in turn are constructed from a few terms taken as primitive called? Axiomatic Method 34. Which mathematical proof is a technique that is used to prove that a statement P(n) holds for every natural number n = 0, 1, 2, 3, ... meaning that the overall statement is a sequence of infinitely many cases? Mathematical Induction 35. In the mathematical field of topology, what is a continuous function between topological spaces that has a continuous inverse function called? A Homeomorphism 36. In number theory, what kind of numbers are "almost rational", and can thus be approximated "quite closely" by sequences of rational numbers? Liouville Numbers 37. In combinatorics, what is the counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets called? The Inclusion–Exclusion Principle 38. In mathematics, what is a conclusion or a proposition which is suspected to be true due to preliminary supporting evidence, but for which no proof or disproof has yet been found called? A Conjecture 39. In number theory, what is the name of a positive integer that is equal to the sum of its positive divisors, excluding the number itself? The Perfect Number 40. What is the process of extracting the underlying structures, patterns or properties of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena called? Abstraction 41. What is the mathematical term for the number that sits above the line in a fraction? A Numerator 42. What is a non-self-evident statement that has been proven to be true, either on the basis of generally accepted statements such as axioms, or on the basis of previously established statements in mathematics called? A Theorem 43. In arithmetic, what is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces a quotient and a remainder smaller than the divisor? Euclidean Division or Division with Remainder 44. In mathematics, what is the amount "left over" after performing some computation called? The Remainder 45. What is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns called in mathematics? A Matrix 231 Computer & Technology Trivia Questions & Answers Computer & Technology trivia from many areas of computer science. Click the play now button to begin. Play Now The Branches of Math Trivia Back to table of contents... Mathematics is an expansive field that can be divided into several branches. Whether it be the study of equations and their solutions, the study of change, the area under curves, shapes and angles, or functions, there are many types of math in existence. Each branch has its own specialized focus and application. For trivia on the different types of math that exist, keep reading for branches of math trivia questions and answers. The Branches of Math Trivia Questions & Answers 46. What is the branch of mathematics that investigates the intuitive notion of order using binary relations and provides a formal framework for describing statements such as "this is less than that" or "this precedes that"? Order Theory 47. What is the mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry, using the theory of plane and space curves and surfaces in the three-dimensional Euclidean space? Differential Geometry 48. What is the major branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques? Proof Theory 49. Which area of mathematics is primarily concerned with counting, both as a means and an end in obtaining results, certain properties of finite structures, and finding the best structure or solution among several possibilities? Combinatorics 50. Which branch of mathematics deals with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions, and these theories are usually studied in the context of real and complex numbers and functions? Analysis 51. What is the study of algebraic structures, which includes groups, rings, fields, modules, vector spaces, lattices, and algebras called? Abstract Algebra or Modern Algebra 52. What is the name of this broad area of mathematics, which is the study of mathematical symbols and the rules for manipulating these symbols and functions is a unifying thread of almost all of mathematics, including everything from elementary equation solving to the study of abstractions such as groups, rings, and fields? Algebra 53. What is the branch of mathematics, that classically studies zeros of multivariate polynomials? Algebraic Geometry 54. Which is the mathematical study of continuous change called? Calculus 55. What is the branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations? Algebraic Number Theory 56. In Mathematics, what is the study of the relationship between formal theories and their models, taken as interpretations that satisfy the sentences of that theory called? Model Theory 57. What is the branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them such as addition, subtraction, multiplication, division, exponentiation and extraction of roots called? Arithmetic 58. What is the branch of number theory that uses methods from mathematical analysis to solve problems about the integers? Analytic Number Theory 59. What is the branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions? Number Theory 60. Which branch of mathematics is concerned with properties of space that are related with distance, shape, size, and relative position of figures? Geometry 61. What is the subfield of mathematics that explores the formal applications of logic to mathematics? Mathematical Logic 62. What is the study of mathematical concepts independently of any application outside of mathematics, where the appeal is attributed to the intellectual challenge and aesthetic beauty of working out the logical consequences of basic principles called? Pure Mathematics 63. What is the study of mathematical models of strategic interaction among rational decision-makers, and has applications in all fields of social science, as well as in logic, systems science and computer science called? Game Theory 64. What kind of numbers do number theorists study? Prime Numbers 65. What is the study of algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers called? Ring Theory 66. What is the application of probability theory, specifically to mathematical techniques, which is used for mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory called? Mathematical Statistics 67. Which theorem states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2? Fermat's Last Theorem 125 Video Games Trivia Questions & Answers Video game trivia facts from every console ever created. Click the play now button to begin. Play Now Calculus Math Trivia Back to table of contents... Calculus is a branch of mathematics that deals with the study of change, in the form of functions, rates of change, and integrals. It includes the study of derivatives, which are the rates of change of a function, and integrals, which are the sums of infinitely small pieces of a function. Calculus is used to solve problems in many fields, such as physics, engineering, economics, and medicine. For trivia questions about calculus, continue on for calculus math trivia questions and answers. Calculus Math Trivia Questions & Answers 68. Which fundamental tool of calculus is a function of a real variable that measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value)? The Derivative 69. What kind of function is represented by " ⌊x⌋ " ? A Floor Function 70. What is the mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity? Big O Notation 71. What is the name of the identities, that are a set of three identities in vector calculus relating the bulk with the boundary of a region on which differential operators act? Green's Identities 72. What are the next three numbers of Euler's number? 2.718_ _ _ 281 73. In mathematics, what is a method for calculating a function that cannot be expressed by just elementary operators such as addition, subtraction, multiplication and division, with examples that include a Taylor series, a Maclaurin series, a Laurent series, a Dirichlet series, a Fourier series, and more? A Series Expansion 74. In mathematics, what is the name of the periodic function composed of harmonically related sinusoids, combined by a weighted summation, and with appropriate weights, one cycle of the summation can be made to approximate an arbitrary function in that interval? A Fourier Series 75. What kind of function is represented by " ⌊x⌉ " ? A Nearest Integer Function 76. What does the set A ⊃ B mean? A is a Strict Superset of B 77. What is the value of a function that must be provided to obtain the function's result called? An Argument or an Indépendant Variable 78. What kind of function is represented by ⌈x⌉ ? A Ceiling Function or Ceil 79. What is a binary relation between two sets that associates to each element of the first set exactly one element of the second set called? A Function 80. What is a set endowed with some additional features on the set, such as an operation, relation, metric, or topology, where often, the additional features are attached or related to the set, so as to provide it with some additional meaning or significance called? A Mathematical Structure 81. In mathematics, what is a value of a continuous quantity that can represent a distance along a line or alternatively, a quantity that can be represented as an infinite decimal expansion called? A Real Number 82. What is the name of the operator used often in vector calculus as a vector differential operator, that when applied to a function defined on a one-dimensional domain, denotes the standard derivative of the function as defined in calculus? Del or Nabla 83. In Mathematics, what assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data? An Integral 200+ American History Trivia Questions & Answers Fascinating American History trivia facts covering a variety of topics. Click the play now button to begin. Play Now Geometry Math Trivia Back to table of contents... Geometry is a branch of mathematics that deals with shapes, sizes, and relative positions of figures and the properties of space. It includes the study of points, lines, angles, surfaces, and solids. Geometry also deals with measurement and analysis of two- and three-dimensional shapes and figures. It has been used in many areas, including architecture, engineering, astronomy, physics, and navigation. For geometry trivia questions, read on for geometry math trivia questions and answers. Geometry Math Trivia Questions & Answers 84. What is the name of the geometric formula that gives the area of a triangle when the length of all three sides are known, and there is no need to calculate angles or other distances in the triangle first? Heron's Formula 85. What is the name of the type of triangle where the three points of intersection of the adjacent angle trisectors form an equilateral triangle? A Morley Triangle 86. When a triangle's sides are a Pythagorean Triple, what kind of triangle is it? A Right Angled Triangle 87. What is the π symbol called? Pi 88. What was complex analysis traditionally known as? The Theory of Functions of a Complex Variable 89. What does this formula find the sum of, where n is the number of terms, a1 is the first term and r is the common ratio? Sn=a1(1−rn)1−r,r≠1 Sn=a1(1−rn)1−r,r≠1 A Finite Geometric Series 90. What is the plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant, and generalizes a circle? An Ellipse 91. What does this formula represent? r=πr² The Area of a Circle 92. In the hexagrammum mysticum theorem, if six arbitrary points are chosen on a conic and joined by line segments in any order to form a hexagon, then the three pairs of opposite sides of the hexagon meet at three points which lie on a straight line; what is the name of the line where the hexagon points meet? The Pascal Line 93. In two-dimensional geometry, which postulate states that if a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles? The Parallel Postulate 94. What does this equation represent? r = aθ The Spiral of Archimedes 95. The sum of the three angles of any triangle is equal to how many degrees? 180 Degrees 96. What is does this formula represent? 1 - ⅓ + ⅕ - ¹⁄₇ + ¹⁄₉ - ⋯ = π⁄₄ The Leibniz Formula for Pi 97. What is the ratio of a circle's circumference to its diameter called? Pi 98. What is this equation called? A² + B² = C² The Pythagorean Equation 99. What is the type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set, with two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows? Hyperbola 100. What is the perimeter of a circle called? The Circumference 101. What is the quantity that expresses the extent of a two-dimensional region, shape, or planar lamina, in the plane called? The Area 102. In mathematics, what indicates how many times one number contains another? A Ratio 103. What is the method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape called? The Method of Exhaustion 104. What are the next three numbers of pi? 3.14_ _ _ 159 105. What are two quantities in, if their ratio is the same as the ratio of their sum to the larger of the two quantities? The Golden Ratio 106. What are the next three numbers in the golden ratio? 1.61_ _ _ 803 107. What is the name of the mathematical curve that describes a smooth periodic oscillation in a continuous wave and occurs often in both pure and applied mathematics? Sine Wave or Sinusoid 108. What is the mathematic study of points of algebraic varieties with coordinates in the integers, rational numbers, and their generalizations, which are typically fields that are not algebraically closed, such as number fields, finite fields, function fields, and p-adic fields? Diophantine Geometry Play Random Trivia Now! Play random trivia questions from any of our many trivia categories. Click the play now button to begin. Play Now Important Mathematicians in History Trivia Back to table of contents... There have been many great contributions by influential mathematicians throughout history. These mathematical discoveries made by these mathematicians in geometry, trigonometry, calculus, set theory, and many more, have laid the critical foundations for modern mathematics. Without these contributions, we may not have had the type of advanced learning and technology of today. For trivia on the most important mathematicians in history, keep reading for important mathematicians in history trivia questions and answers. Important Mathematicians in History Trivia Questions & Answers 109. Who wrote the mathematical treatise Elements, which consists of 13 books and is a collection of definitions, postulates, propositions, and mathematical proofs of the propositions? Euclid 110. Taylor's theorem is named after which 18th century mathematician? Brook Taylor 111. Who developed internal set theory, the mathematical theory of sets that provides an axiomatic basis for a portion of the nonstandard analysis introduced by Abraham Robinson? Edward Nelson 112. Who are the finite group theory Sylow theorems named after? Peter Ludwig Sylow 113. Who was the influential German mathematician that discovered and developed a broad range of fundamental ideas including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics, particularly in proof theory? David Hilbert 114. Who introduced the axiomatic method, still used today? Giuseppe Peano 115. Which Swiss mathematician initially introduced a theorem to Guillaume de l'Hôpital in 1694, that would later go on to become the L'Hôpital's rule? Johann Bernoulli 116. In additive number theory, who first made the observation on the theorem on sums of two squares, published in 1625? Albert Girard 117. Who was the English mathematician, known for his achievements in number theory, mathematical analysis, the Hardy–Weinberg principle in biology, and his 1940 essay, A Mathematician's Apology? G. H. Hardy 118. What is the name of the historically notable problem in mathematics, where the problem was to devise a walk through of a Russian city, where the walker would only cross each of two bridges between two islands once? The Seven Bridges of Königsberg 119. Who was the Swiss mathematician that made important and influential discoveries in many branches of mathematics, such as calculus, graph theory, and analytic number theory, while also introducing much of the modern mathematical terminology and notation? Leonhard Euler 120. In the foundations of mathematics, what is the term that came from a famous British polymath and mathematician showing that some attempted formalizations of the naive set theory created by Georg Cantor led to a contradiction? Russell's Paradox 121. Who was the Persian polymath who produced vastly influential works in mathematics, astronomy, and geography and wrote the treatise on algebra, The Compendious Book on Calculation by Completion and Balancing? Muḥammad ibn Mūsā al-Khwārizmī 122. Who was the Italian mathematician and glottologist that authored over 200 books and papers, and was a founder of mathematical logic and set theory? Giuseppe Peano 123. Who proved the polyhedron formula? Leonhard Euler 124. Who is de Moivre's formula named after? Abraham de Moivre 125. Who first presented the form of the theorem, which later became Green's theorem? Augustin-Louis Cauchy 126. Who was the Dutch mathematician and philosopher that established himself as the founder of modern topology, with his fixed-point theorem and the topological invariance of dimension? L. E. J. Brouwer 127. Who was the Persian mathematician who has been credited with proposing the idea of a function and also developed a novel method for determining the conditions under which certain types of cubic equations would have two, one, or no solutions? Sharaf al-Din al-Tusi 128. In mathematics, what is the name of the technique for getting information on the number of positive real roots of a polynomial, which asserts that the number of positive roots is at most the number of sign changes in the sequence of polynomial's coefficients, and that the difference between these two numbers is always even? Descartes' Rule of Signs 129. Which ancient Greek philosopher are Platonic solids named after? Plato 130. What German mathematician and physicist, who made significant contributions to a number fields in mathematics and science said, “Mathematics is the queen of the sciences—and number theory is the queen of mathematics”? Carl Friedrich Gauss 131. Who posed the 18th century question about knowing the probability that a dropped needle on a parallel strip wood floor will lie across a line between two strips? Georges-Louis Leclerc 132. Who was the German-Austrian logician and mathematician, who published two incompleteness theorems in 1931, that demonstrated the inherent limitations of every formal axiomatic system capable of modeling basic arithmetic? Kurt Gödel 133. Who was the Persian polymath and mathematician whose most notable work was on the classification and solution of cubic equations, where he provided geometric solutions by the intersection of conics and contributed to the understanding of the parallel axiom? Omar Khayyam 134. Which two mathematicians independently developed calculus in the late 17th century? Isaac Newton and Gottfried Wilhelm Leibniz 135. Who solved the Basel problem, first posed by Pietro Mengoli in 1650? Leonhard Euler 136. Who proved that the sum of the reciprocals of all prime numbers diverges? Leonhard Euler 137. Which ancient Greek mathematician is considered to be one of the greatest of all time, with achievements that include deriving an accurate approximation of pi; defining and investigating the spiral that now bears his name; and creating a system using exponentiation for expressing very large numbers? Archimedes Math Fun Facts Trivia Back to table of contents... Math fun facts come from educational resources such as history, applications, and other interesting tidbits. These math fun facts provide an entertaining way to engage with math and encourage learning through trivia and discovery. They were written for the true math enthusiasts in mind. If you truly enjoy math, read on for math fun facts trivia questions and answers. Math Fun Facts Trivia Questions & Answers 138. What term denotes the mathematics developed or practiced by the people of Mesopotamia? Babylonian Mathematics 139. Which numeral system and the rules for the use of its operations, are still in use almost exclusively throughout the world today? Hindu–Arabic Numeral System 140. What is the name of the journal published by the American Mathematical Society that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science? Mathematical Reviews 141. What is the title of the book of mathematical proofs by Martin Aigner and Günter M. Ziegler, which contains 45 sections in the sixth edition, each devoted to one theorem but often containing multiple proofs and related results? Proofs from THE BOOK 142. What is the only even prime number? 2 143. Which ancient language is the term "geometry" derived from? Greek 144. What is the colloquial term for a number that can be written without a fractional component? An Integer 145. Which ancient language is the term "equal" derived from? Latin 146. Which ancient language is the term "algebra" derived from? Arabic 147. In which ancient cultures did elementary arithmetic such as addition, subtraction, multiplication and division first appear, according to archaeological record? Babylon and Egypt 148. What is the name of the professional society, founded in 1915, that focuses on mathematics accessible at the undergraduate level, with 25,000+ members, spanning university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists; statisticians; and many others in academia, government, business, and industry professionals? The Mathematical Association of America or MAA 149. What is the name of the widely read expository mathematical journal founded by Benjamin Finkel in 1894, published ten times each year by Taylor & Francis ,for the Mathematical Association of America? The American Mathematical Monthly 150. What does the acronym MSC, which is an alphanumeric classification scheme collaboratively produced from two major mathematical reviewing databases, stand for? Mathematics Subject Classification 151. What is the numeral system with sixty as its base, that originated with the ancient Sumerians in the 3rd millennium BC and was passed down to the ancient Babylonians, still used in a modified form for measuring time, angles, and geographic coordinates today? Sexagesimal 152. What is the smallest perfect number? 6 153. Which ancient language is the term "math" derived from? Greek 154. What is the name of the association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs, which goes by the acronym AMS? American Mathematical Society 155. What is the name of the major international reviewing service that provides reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe? zbMATH or Zentralblatt MATH Math Symbols Trivia Back to table of contents... Math symbols are used to represent mathematical entities such as numbers, operations, functions, and equations. There are the more common symbols used in mathematics such as the plus sign, minus sign, multiplication sign, division sign and so forth. But the more advanced symbols are less common and not so easy to recognize. These symbols are used to denote various operations, functions, and equations in mathematical equations, formulas, and expressions. Read on for challenging math symbols trivia questions and answers. Math Symbols Trivia Questions & Answers 156. In algebraic geometry, what is the " ∞ " symbol called? A Lemniscate 157. What does the " ∃ " symbol read as in basic logic? "There Exists" 158. What does the " ∑ " symbol denote of a finite number of terms, in linear and multilinear algebra? The Sum 159. What does the " ∀ " symbol read as in basic logic? For All 160. What does the " ∥ " symbol denote in elementary geometry? Parallelism 161. What does the " : " symbol denote of two quantities? The Ratio 162. What is the " ∆ " symbol called in calculus? The Laplace Operator or a Laplacian 163. What does the " ⊻ " symbol denote in basic logic? The Exclusive Or 164. What does the " ∏ " symbol denote of a finite number of terms, in linear and multilinear algebra? The Product 165. What does the blackboard bold " ℝ " symbol denote a set of? Real Numbers 166. What operation does the " ! " symbol denote? A Factorial Operation 167. In set theory, what is the " ℵ " symbol called? An Aleph 168. What does the " ≡ " symbol mean in math? Identical To 169. What does the symbol " e " represent in math? Euler's Number 170. What does the " ∈ " symbol mean in set theory? Is an Element of 171. What does the " √ " symbol denote? The Square Root 172. What does the " < " symbol mean in mathematics? Less Than 173. What does the " ∨ " symbol read as in basic logic? "Or" 174. What does the blackboard bold " ℚ " symbol denote a set of? Rational Numbers 175. In number theory, what does the " # " symbol denote? A Primorial 176. What does the logical predicate "⊥" symbol denote? Always False 177. What does the " ≤ " symbol mean in mathematics? Less Than or Equal To 178. What does the " ≠ " symbol mean? Not Equal 179. What does the " > " symbol in mathematics mean? Greater Than 180. What does the " ≥ " symbol mean? Greater Than or Equal To 181. What is the " ∘ " symbol called in algebraic operations? The Composition Operator 182. What does the blackboard bold " ℤ " symbol denote a set of? Integers 183. What does the blackboard bold " ℕ " symbol denote a set of? Natural Numbers 184. What is the " ∇ " symbol called in calculus? A Del or Nabla 185. What does the ø symbol denote in set theory? An Empty Set 186. What does the logical predicate " ⊤ " symbol denote? Always True 187. What is this " ∫ " symbol called? The Integral Symbol 188. In set theory, the what is the " ℶ " symbol called? A Beth 189. What does the " Φ " symbol represent? The Golden Ratio 190. What does the abbreviation " ∋ " mean? "Such that" or "Under the Condition that" 191. What does the " ¬ " symbol read as in basic logic? "Not" 192. In x^y, what would the " ^ " symbol denote? Exponentiation 193. What does the " ∥ " symbol denote in elementary geometry? Parallelism 194. What does " Ω " symbol mean in math? The Unit for Resistance or Ohms 195. What does the " ∖ " symbol denote in set theory? The Set Difference 196. What does the " ∪ " symbol denote in set theory? A Set Theoretic Union 197. What does the " ∤ symbol denote? Non-divisibility 198. What does the " ∉ " symbol mean in set theory? Not In 199. What does the " ≈ " symbol mean? Approximately Equal To Theorems of Math Trivia Back to table of contents... Math theorems are statements that have been proven to be true through mathematical proofs. There are many important math theorems that have contributed to the foundations of modern day math. These advanced concepts proved to be critical to the evolution of mathematics, computations, and current technologies. For the critical theorems of math, continue reading for theorems of math trivia questions and answers. Theorems Math Trivia Questions & Answers 200. Which theorem states that for any continuous function ƒ mapping a compact convex set to itself there is a point x₀ such that ƒ( x₀ ) = x₀ ? The Brouwer Fixed-point Theorem 201. In probability theory, which theorem says that, under certain conditions, the expected value of a martingale at a stopping time is equal to its initial expected value? The Optional Stopping Theorem 202. Which theory of probability theorem describes the result of performing the same experiment a large number of times and according to the law, the average of the results obtained from a large number of trials should be close to the expected value and will tend to become closer to the expected value as more trials are performed? The Law of Large Numbers 203. Which theorem states that if a₁, …, an are algebraic numbers that are linearly independent over the rational numbers ℚ, then eª₁, …, eªn are algebraically independent over ℚ? Lindemann–Weierstrass Theorem 204. Which theorem of set theory states that the cardinality of a set is strictly less than the cardinality of its power set, or collection of subsets? Cantor's Theorem 205. What are the two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system capable of modeling basic arithmetic? Gödel's Incompleteness Theorems 206. Which theorem states that in general, the number of common zeros equals the product of the degrees of the polynomials? Bezout's Theorem 207. Which proposition states that the nine-point circle of any triangle is tangent internally to the incircle and tangent externally to the three excircles? Feuerbach's Theorem 208. Which theorem proves there are infinitely many primes? Euclid's Theorem 209. What does the blackboard bold " ℂ " symbol represent a set of? Complex Numbers 210. Which theorem states, given r, s, any sequence of distinct real numbers with length at least (r − 1)(s − 1) + 1 contains a monotonically increasing subsequence of length r or a monotonically decreasing subsequence of length s? Erdős-Szekeres Theorem 211. Which theorem of projective geometry states that two triangles are in perspective axially if and only if they are in perspective centrally? Desargues's Theorem 212. What is the theorem of real analysis, which states that for almost every point, the value of an integrable function is the limit of infinitesimal averages taken about the point? The Lebesgue Differentiation Theorem 213. Which theorem of plane geometry states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle? Morley's Trisector Theorem 214. In number theory, what is the theorem that is about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers? The Law of Quadratic Reciprocity 215. What is the name of the mathematics formula that is an approximation for factorials, which is a good approximation, leading to accurate results even for small values of n? Stirling's Formula or Stirling's Approximation 216. Which theorem states that if p is a prime number, then for any integer a, the number ap − a is an integer multiple of p? Fermat's Little Theorem 217. Which theorem states that if two sides of a triangle are congruent, then angles opposite to those sides are congruent? The Isosceles Triangle Theorem 218. Which theorem is a hypothesis about the possible sizes of infinite sets and states, there is no set whose cardinality is strictly between that of the integers and the real numbers? The Continuum Hypothesis 219. What is the name of the explicit formula in linear algebra, which is the explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution, and expresses the solution in terms of the determinants of the coefficient matrix and of matrices obtained from it by replacing one column by the column vector of right-hand-sides of the equations? Cramer's Rule 220. Which theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side? The Triangle Inequality Theorem 221. Which theorem states that every natural number can be represented as the sum of four integer squares? Lagrange's Four-square Theorem 222. Which theorem states that if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) is equal to the function's average rate of change over [a,b] ? Mean Value Theorem 223. What is the name of the theorem that is an efficient method for computing the greatest common divisor of two integers, the largest number that divides them both without a remainder, and is named after an ancient Greek mathematician, who first described it in his book Elements? The Euclidean Algorithm 224. Which theorem links the concept of differentiating a function with the concept of integrating a function? Fundamental Theorem of Calculus 225. Which theorem states that, in a party of n persons, if every pair of persons has exactly one common friend, then there is someone in the party who is everyone else's friend? The Friendship Theorem 226. What does the " ∩ " symbol denote in set theory? A Set Theoretic Intersection 227. Which theorem states that when a polynomial, f(x), is divided by a linear polynomial , x - a, the remainder of that division will be equivalent to f(a)? The Remainder Theorem 228. Which theorem states that a polynomial ƒ(x) has a factor (x − k) if and only if ƒ(k) = 0 ? The Factor Theorem 229. In combinatorics, what problem is this the answer to? (p − q) ⁄ (p + q) Bertrand's Ballot Problem 230. What is the name of the equation, which is any Diophantine equation of the form x² − ny² = 1 where n is a given positive non-square integer and integer solutions are sought for x and y? Pell's Equation 231. Which theorem states that there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients? The Abel–Ruffini Theorem 232. Which theorem describes the algebraic expansion of powers of a binomial where, it is possible to expand the polynomial (x + y)n into a sum involving terms of the form axbyc, where the exponents b and c are non-negative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending on n and b? The Binomial Theorem 233. Which theorem states that every non-zero, single-variable, degree n polynomial with complex coefficients has, counted with multiplicity, exactly n complex roots? The Fundamental Theorem of Algebra 234. Which theorem states that, if ƒ (x, y) is an analytic germ in two variables, then the solutions y = φ (x) of the equation ƒ = 0 can be expanded as Puiseux series that are convergent in a neighborhood of the origin? The Newton-Puiseux Theorem 235. Which theorem of probability establishes that in many situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed? The Central Limit Theorem 236. Which theorem states that, given any separation of a plane into contiguous regions when producing a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color? The Four Color Theorem 237. Which theorem describes the asymptotic distribution of the prime numbers among the positive integers, that formalizes the idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs? The Prime Number Theorem 238. What is the fundamental relation in Euclidean geometry among the three sides of a right triangle which states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides called? The Pythagorean Theorem 239. Which theorem states that there are infinitely many prime numbers contained in the collection of all numbers of the form na + b, in which the constants a and b are integers that have no common divisors except the number 1 and the variable n is any natural number? Dirichlet’s Theorem 240. Which theorem states that if f is a continuous function whose domain contains the interval [a, b], then it takes on any given value between f(a) and f(b) at some point within the interval? The Intermediate Value Theorem 241. Which theorem is the statement that every convex set in ℝⁿ which is symmetric with respect to the origin and which has volume greater than 2ⁿ contains a non-zero integer point? Minkowski's Theorem 242. Which theorem of linear algebra states that every square matrix over a commutative ring satisfies its own characteristic equation? The Cayley–Hamilton Theorem 243. Which theorem states that every integer >1 has a prime factorization and that prime factorization is unique? The Fundamental Theorem of Arithmetic 244. In Euclidean geometry, which theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral, which is a quadrilateral whose vertices lie on a common circle? Ptolemy's Theorem 245. Which theorem states that a natural number n > 1 is a prime number if and only if the product of all the positive integers less than n is one less than a multiple of n? Wilson's Theorem 246. Which theorem was the first major theorem to be proved using a computer? The Four Color Theorem 247. In number theory, what is the theorem that states that for any integer n > 3, there always exists at least one prime number p with n < p < 2n - 2 ? Bertrand's Postulate 248. Which theorem in combinatorics both follows from and ultimately generalizes Burnside's lemma on the number of orbits of a group action on a set? The Pólya Enumeration Theorem 249. Which theorem of set theory states that, if there exist injective functions f : A → B and g : B → A between the sets A and B, then there exists a bijective function h : A → B? Schröder–Bernstein Theorem 250. Which theorem represented by this formula? A = i + ᵇ⁄₂ − 1 Pick's Theorem 251. Which theorem is a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords within a circle and states that the products of the lengths of the line segments on each chord are equal? Intersecting Chords Theorem